Action potential: Biophysical and cellular context, initiation, phases and propagation

CELL BIOLOGY RESEARCH PROGRESS ACTION POTENTIAL: BIOPHYSICAL AND CELLULAR CONTEXT, INITIATION, PHASES AND PROPAGATION ...

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CELL BIOLOGY RESEARCH PROGRESS

ACTION POTENTIAL: BIOPHYSICAL AND CELLULAR CONTEXT, INITIATION, PHASES AND PROPAGATION

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CELL BIOLOGY RESEARCH PROGRESS

ACTION POTENTIAL: BIOPHYSICAL AND CELLULAR CONTEXT, INITIATION, PHASES AND PROPAGATION

MARC L. DUBOIS EDITOR

Nova Science Publishers, Inc. New York

Copyright © 2010 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA

Action potential : biophysical and cellular context, initiation, phases, and propagation / editor, Marc L. DuBois. p. ; cm. Includes bibliographical references and index. ISBN 978-1-61761-579-5 (eBook)

Published by Nova Science Publishers, Inc.

New York

CONTENTS Preface Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Index

What Do Plants Need Action Potentials for? Elżbieta Król, Halina Dziubińska and Kazimierz Trębacz

vii 1

Biophysical Properties Underlying Human Nerve Impulse Conduction Susanna B. Park and Matthew C. Kiernan

29

Physiological Implications of Action Potential in Characean Cell: Effects on pH Bands and Spatial Pattern of Photosynthesis Alexander A. Bulychev and Natalia A. Krupenina

65

Action Potential Production: An Ion Channel Dependent Process Richard Hahin

99

Afferent Output in Mammalian Taste Cells: A Role of Electrical Excitability in Mediating Transmitter Release Roman A. Romanov, Olga A. Rogachevskaja, Marina F. Bystrova and Stanislav S. Kolesnikov Methodologies to Unravel Cardiac Structure and Function Complexity at Cellular and Tissue Level Ioanna Chouvarda and Nicos Maglaveras The Elusive D-current: Shaping Action Potentials in the Dendrites? Xixi Chen and Daniel Johnston

133

159

191

199

PREFACE An action potential (or nerve impulse) is a transient alteration of the transmembrane voltage (or membrane potential) across an excitable membrane in an excitable cell (such as a neuron or myocyte) generated by the activity of voltage-gated ion channels embedded in the membrane. The best known action potentials are pulse-like waves of voltage that travel along the axons of neurons. This book reviews research on action potential including an overview of the role of specialized axonal excitability techniques in understanding the consequences of abnormal membrane excitability; the physiological implications of action potential in characean cells; and action potential production and the ion channel dependent process and others. Chapter1- For many years the physiological significance of electrical signalling in plants has been neglected, even though the very first action potentials (APs) were recorded in insectivorous plants in 1873 (1). Still many aspects of plant excitability are not sufficiently well elaborated. However, nowadays it is a common knowledge that in animals as well as in plants: (i) ion fluxes through plasma membrane provide AP biophysical bases; (ii) AP transmission is electrotonic, without a decrement and is followed by a refractory period; (iii) there is an ―all-or-nothing‖ principle fulfilled, with an exponential dependency of threshold stimulus strength on stimulus duration; (iv) APs are initiated and propagated by excitable tissues to control a plethora of responses indispensable for growth, nutrient winning, reproduction, and defence against biotic and abiotic challenges. AP can be viewed as a burst of electrical activity that is dependent on a depolarizing current. In plants the depolarization phase of AP consists of Cl-- and Ca2+-fluxes. The following phase—a repolarization—relies in turn on K+ fluxes and active H+ flows that both drive membrane potential back to more negative values. Thus, the AP mechanism is electrochemically governed by the selective properties of the plasma membrane with ion selective conduits as key players. A more detailed understanding of how these membrane proteins work hand in hand during excitation and signal transduction is eagerly awaited. The existence of ion channels was first hypothesized by Alan Hodgkin and Andrew Huxley (2-8), and next confirmed with a patch-clamp technique by Erwin Neher and Bert Sakmann (9). These experiments though conducted on neurons and muscles, respectively, prompted plant electrophysiology as well. Since then substantial evidence for APs in a wide array of plants has been emerging and consequently growing in number. Chapter 2- The molecular and structural organization of the axon has evolved to efficiently support the conduction of nerve impulses. Axonal membrane Na+ and K+ channels,

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Marc L. DuBois

in addition to other voltage-gated channels, ion pumps and exchangers play a critical role in the normal processes of saltatory conduction. The molecular and structural organization of the axon are key factors that determine membrane excitability, providing the basis for action potential generation and effective impulse transmission. A variety of research techniques have provided novel insights into human axonal structure and function at a molecular level, yielding an improved understanding of nerve function in both health and neurological disease states. An overview of the role of specialized axonal excitability techniques in understanding the consequences of abnormal membrane excitability in the clinical realm will be highlighted in this chapter. Through greater understanding of the contribution of axonal ion channel dysfunction and anomalous membrane excitability, it may be anticipated that novel diseasemodifying strategies may be developed to be incorporated into the future treatment of neurological diseases. Chapter 3- Most plants generate propagating action potentials (APs) upon injuries or other stimuli. The functional significance of APs is intriguing but still unclear, except for a few cases of insectivorous and sensitive plants. In characean algae, close relatives of higher plants, the membrane excitation exerts marked effects on spatial heterogeneity of chloroplast and plasmalemma functions. The light-dependent ―pH bands‖ in characean internodes are highly sensitive to AP generation. The spatial pattern of apoplastic pH collapses transiently after membrane excitation, indicating temporal inhibition of H+-pump activity in acid zones and of counter-directed passive H+ flows in alkaline areas. The plasmalemma conductance in the alkaline regions decreases several fold during post-excitation period in parallel with the drop of apoplastic pH, while the conductance in acid regions is barely affected. The blockade of high pH channels permeable to H+ (OH–) seems to be the key event in the AP impact on pH pattern and cell electrogenesis. Imaging of chlorophyll fluorescence in resting Chara corallina cells revealed the patterns of photosynthetic activity and non-photochemical quenching, which are finely concerted with the pH bands. Unlike temporal decline of the pH bands after AP propagation, heterogeneity of photosynthesis and fluorescence quenching was temporally enhanced in the post-excitation period. The enhancement might be related to opposite changes in cytosolic pH following the AP-induced cessation of counter-directed H+ fluxes in the alkaline and acid cell regions. Effects of AP on photosynthetic pattern differed strikingly in the absence and presence of the herbicide methyl viologen (MV). Under natural conditions, the spatial heterogeneity of photosynthesis was enhanced after AP owing to stronger inhibition in chloroplasts of alkaline cell regions with minor changes in acid regions. By contrast, the effect of a single AP on photosynthesis in the presence of MV was most pronounced in the acid regions and led to irreversible smoothing of the spatial pattern. These and other results indicate that MV cannot permeate the composite membrane barrier (plasmalemma + chloroplast envelope) under resting conditions but gains access to its interaction sites within the chloroplast during or after AP generation. The gated ion channels might provide a pathway for permeation of physiologically active amounts of MV across the plasmalemma. Chapter 4- Action potentials are produced as a consequence of opening (activation) and closing (deactivation) of ion channel proteins that are distributed in cell membranes. In human nerve and skeletal muscle cells the principal ion channels responsible for action potential (AP) production are voltage- dependent sodium (Nav) and potassium (Kv) channels; however voltage dependent calcium channels (Cav) do play essential roles in AP production in cardiac pacemaker and ventricular cells. A number of different homologous types

Preface

ix

(isoforms) of Nav , Cav, and Kv displaying altered properties are differentially found in various excitable cells to produce APs that differ in character. Nav , Cav, and Kv possess specialized structural features (voltage sensors) that enable them to sense voltage changes and respond to those changes by kinetically altering their states to allow ions to selectively flow through the membrane channel via a structural pore region. A number of agents act to bind to the channels and act to alter their properties and thus alter AP production. Nav acts as specific target for a number of animal and plant toxins. Binding of the toxins to the channels act to alter the size, shape and conduction velocity of the AP. Nonspecific binding of a wide number of other chemical agents to Nav act to cause changes in AP production and properties. APs have been mathematically modeled using several different approaches; however the most widely used method was developed by Hodgkin and Huxley (1952) and continues to be used in predicting AP behavior in simulation programs. Chapter 5- Although mammalian taste cells are epithelial by nature, cells of the type II and type III are electrically excitable and capable of firing action potentials in response to electrical and chemical stimulation. In hair cells and photoreceptors, sensory stimuli elicit gradual receptor potentials that govern directly, that is, without stimulating action potentials, release of the afferent neurotransmitter glutamate. Given this fact and that taste cells have no axons, physiological significance of the electrical excitability for taste transduction and encoding sensory information is unclear. Most likely, action potentials facilitate transmitter release, both ATP in type II cells and 5-HT in type III cells, although by different mechanisms. The ATP release is mediated by hemichannels, do not require a Ca2+ trigger, and is gated by membrane voltage. Meanwhile, 5-HT secretion is driven by intracellular Ca2+ and involves VG Ca2+ channels. This work is focused on molecular mechanisms of ATP release from type II cells and on a role of action potentials in mediating their afferent output. Electrical excitability is a fundamental property of neuronal and muscle cells and certain other cells, which generate all-or-none electrical signals, action potentials (APs), basically in response to an external stimulation of sufficient strength. AP serves to spread excitation over the entire surface of a muscle cell, thus triggering and synchronizing its contraction. In neurons, the elongated axon serves to transmit information in the form of APs over long distance in a non-decremental manner, while coming in the synaptic terminal, the AP triggers and shapes neurotransmitter release. Despite being epithelial in nature (Stone et al., 1995) and having no axons, taste cells are electrically excitable. Pioneer intracellular recordings from taste buds of the salamander Necturus (Roper, 1983) provided the first evidence for electrical excitability of taste cells. It is now well documented that in vertebrates, taste cells generate APs not only on electrical stimulation, but also in response to apically applied chemical stimuli (Behe et al., 1990; Avenet, Lindemann, 1991; Cummings et al., 1993; Varkevisser, Kinnamon, 2000; Yoshida et al., 2006). To generate APs, taste cells should possess a certain repertoire of ion channels, such as voltagegated (VG) Na+ and K+ channels, in combination with a high input resistance, the feature allowing small depolarizing ionic currents to produce large effects on the membrane potential. As demonstrated in earlier studies, the needed membrane properties are indeed characteristic of taste cells (Herness, Gilberson, 1999; Bigiani, 2002). Since the detailed analysis of ion permeability of the taste cell plasma membrane is beyond the scope of the present work, ion channels are considered here in two specific aspects: in context of taste cell identification and in relatedness to excitability of taste cells and to their afferent output.

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Note that certain sensory cells, such as vertebrate photoreceptors and hair cells in the Corty organ, which have no axons, do not produce APs, thus questioning why those are generated by taste cells. The likely possibility is that despite the absence of axons, taste cells need APs to control afferent output. As related to the further discussion, we provide below a brief overview of mechanisms mediating neurotransmitter discharge. Chapter 6- This chapter aims to elaborate on different aspects of current biomedical modeling and processing approaches, with respect to questions at a certain analysis scale of cardiac system. Three examples are discussed, referring to different problems and levels of detail at microscopic scales. Ways of modelling and extraction of characteristics of the underlying processes are presented, corresponding to medically interesting conditions. These examples are illustrated by use of experimental data and simulated experiments data. The proposed approaches offer the basis for discussion on further perspectives towards possible integrative approaches. Chapter 7- Most neurons host a complex combination of various K+ currents. These K+ currents differ from each other in voltage- and time- dependent kinetics, and contribute to different aspects of action potentials. The D-current was first discovered in adult pyramidal cells in the hippocampus. This K+ current activates quickly at subthreshold voltages and inactivates slowly, contributing to a long delay before action potential firing, hence its name. A prominent pharmacological feature of the D-current is its high sensitivity to 4-aminopyridine (4-AP). With this pharmacological tool, we studied the contribution of the D-current to the waveforms of back-propagating action potentials (bAPs) in the dendrites of hippocampal CA1 pyramidal neurons. We performed dendritic, whole-cell recordings from the dendrites of CA1 pyramidal neurons, with extracellular stimulation of the axons of these neurons in the acute slice preparation. Bath application of low concentration 4-AP (50 µM) led to a dramatic increase of the after-hyperpolarization following the bAPs. This increase can be completely eliminated by the GABAb receptor antagonist, CGP55845 (5 µM). This result indicates that D-current contributes significantly to the regulation of GABA release from interneuron axon terminals. In terms of the waveform of bAPs we did not observe any significant change in amplitude or initial dV/dt that‘s caused by 4-AP, at all the locations along the dendrites. However, at locations farther than 200 µm away from the soma, 4-AP did cause a small but significant increase in the half-amplitude duration of bAPs. A similar, 616% contribution of D-current was also observed by other groups, in terms of action potential after-depolarization and threshold for Ca2+ spikes, in both hippocampal and neocortical neurons. We would like to argue that the D-current makes a small but significant contribution to the shape of dendritic action potentials. The more prominent role played by D-current in the hippocampal circuit, however, may be the regulation of presynaptic neurotransmitter release.

In: Action Potential Editor: Marc L. DuBois, pp. 1-26

ISBN 978-1-61668-833-2 © 2010 Nova Science Publishers, Inc.

Chapter 1

WHAT DO PLANTS NEED ACTION POTENTIALS FOR? Elżbieta Król, Halina Dziubińska, and Kazimierz Trębacz Department of Biophysics, Institute of Biology, Maria Curie-Skłodowska University, Akademicka 19, 20–033 Lublin, Poland

ABSTRACT For many years the physiological significance of electrical signalling in plants has been neglected, even though the very first action potentials (APs) were recorded in insectivorous plants in 1873 (1). Still many aspects of plant excitability are not sufficiently well elaborated. However, nowadays it is common knowledge that in animals as well as in plants: (i) ion fluxes through plasma membrane provide AP biophysical bases; (ii) AP transmission is electrotonic, without a decrement and is followed by a refractory period; (iii) there is an ―all-or-nothing‖ principle fulfilled, with an exponential dependency of threshold stimulus strength on stimulus duration; (iv) APs are initiated and propagated by excitable tissues to control a plethora of responses indispensable for growth, nutrient winning, reproduction, and defence against biotic and abiotic challenges. AP can be viewed as a burst of electrical activity that is dependent on a depolarizing current. In plants the depolarization phase of AP consists of Cl-- and Ca2+-fluxes. The following phase—a repolarization—relies in turn on K+ fluxes and active H+ flows that both drive membrane potential back to more negative values. Thus, the AP mechanism is electrochemically governed by the selective properties of the plasma membrane with ion selective conduits as key players. A more detailed understanding of how these membrane proteins work hand in hand during excitation and signal transduction is eagerly awaited. The existence of ion channels was first hypothesized by Alan Hodgkin and Andrew Huxley (2-8), and next confirmed with a patch-clamp technique by Erwin Neher and Bert Sakmann (9). These experiments though conducted on neurons and muscles, respectively, prompted plant electrophysiology as well. Since then substantial evidence for APs in a wide array of plants has been emerging and consequently growing in number.

Elżbieta Król, Halina Dziubińska and Kazimierz Trębacz

2

INTRODUCTION Electrical sensitivity of living organisms originates from selective membranes that surround each cell. Thanks to active transport of ions by pumps and transporters (mainly K+, Na+, H+ and Ca2+ but also Cl-) and selective properties of the channels embedded in membranes, a transmembrane potential difference is generated (10-13). This membrane voltage (= membrane potential, transmembrane potential) is the difference between the inside and the outside (by convention set to 0) potential. The magnitude of the membrane potential directly depends on the membrane selective properties and hence on concentration of ions facing both sides of the membrane (12). There is a negative membrane resting potential (difference at rest) in most living cells. At rest, the net flow of ions through a selective membrane equals zero, which means that outflows and inflows of ions transported are counterbalanced. Any unbalanced movement of ions results in changes in the resting potential. Such imbalances can be triggered by stimuli as different as: electric current, light, pressure (mechanical or osmotic) and chemical substances of various derivation. The abovelisted stimuli are either directly or indirectly responsible for ion channel, transporter or pump activation/inhibition, which transiently changes membrane permeability for corresponding ions and thus make the resting potential change (14). Evoked membrane potential changes hold (i) various shapes, (ii) kinetics, (iii) duration, (iv) properties and (v) functions and accordingly can be classified as: i. ii. iii. iv. v.

hyperpolarization / depolarization (if it drives the potential to more negative / less negative values); graded / of constant amplitude (with an amplitude depending on / independent of stimulus strength); transient / long-lasting; propagable / non-propagable systemic / local (spreading within the whole organ or organism / appearing locally).

Among them the best studied and characterized are action potentials (APs), which are a transient membrane depolarization with all-or-nothing characteristics (14-17), propagating systemically (18-20) with a cell-specific velocity (14,21) and without a decrement (an amplitude decrease). As for the AP amplitude that is cell-specific, too, it cannot be increased by an increase in stimulus strength. The physical depiction of the latter statement is reflected in the above-specified ―all-or-nothing characteristics‖. In addition, the relation between threshold stimulus charge (strength) and stimulus duration can be represented by Weiss's experimental formula—the exponential dependence of threshold stimulus strength on its duration (22). The AP transmission along excitable membranes is achieved through electrotonic transmission. A local current flows between the just activated part and the adjacent yet unexcited part. After the passage of each single AP there is a refractory period—the period of transient unexcitability or, in other words, time needed for a cell to restore its excitability. Finally, one must keep in mind that excitability in electrophysiology nomenclature means the ability to generate and transmit APs. The cells on whose membranes the other potential changes but not APs occur are not considered excitable (23).

What Do Plants Need Action Potentials for?

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A PINCH OF HISTORY When in 1786 Luigi Galvani dissected a frog, touched its leg with a charged scalpel and saw the frog‘s leg kicking after the charge had jumped from the scalpel to the muscle tissue, he had no idea that the charge flow induced an AP and that the muscles contracted as a result of AP (excitation) spreading. However, his observation made Galvani the first investigator to appreciate the relationship between electricity and movement in living organisms. His associate and intellectual adversary Alessandro Volta went deeper into the nature of electrochemical processes (which allowed him invent the first battery—a galvanic cell). His intuition that ―animal electricity‖ has the same underpinnings as electrochemical reactions proved correct and widely contributed to our understanding of ion-pulling forces in living systems (24). Starting from 1830 till his death in 1865 another Italian scientist, the physician and neurophysiologist Carlo Matteucci pursued experiments on frog muscles, using them as a kind of electricity-detector (25). His work influenced directly the German physician Emil du Bois-Reymond, who, trying to duplicate Matteucci‘s results, ended up with the discovery of APs. At that time he termed them ―negative variations‖. The results of du Bois-Reymond‘s inquiries were being compiled systematically in his life-work Researches on Animal Electricity, the first part of which appeared in 1848, and the last in 1884. Though the story of bioelectricity began with a frog, its impact on plant biology was equally impressive. The very first APs recorded in plants were reported by the English physician-physiologist Sir John Scott Burdon-Sanderson, who—encouraged by Charles Darwin—was the first to recognize the electric phenomena in carnivorous plants (1). For his pioneering work in the field of electrophysiology and plant physiology, the Royal Society awarded Burdon-Sanderson a Royal Medal in 1872. Inspired by Burdon-Sanderson‘s work, another British scientist Walter Gardiner (a botanist) devoted himself to carnivorous spp. trying to find a link between excitation and histological changes in secretory glands (26). Next, the Austrian botanists and father of a plant cell totipotentiality theory, Gottlieb Johann Friedrich Haberlandt found noncarnivorous plants to move after electrical stimulation (27). At the same time in Bengal, Haberlandt‘s peer Sir Jagadish Chandra Bose (a polymath: physicist, biologist, archaeologist and writer) studied the correlation between plant development and environmental stimulants (wounds, chemical agents, light and temperature changes) with the help of his self-invented devices (a crescograph to measure plant growth; microamperemeter for current assessments; an electric probe for voltage recordings). On intact plants he measured electrical conduction and corresponding changes in the cell membrane potential in response to chemical and physical stimulation (28-29). Having generalized that all strong stimuli produced a transient diminution of growth rate, a negative mechanical response (cell shrinking) and an electric response of ―galvanometric negativity‖ (= AP), he was very close to discerning excitation as an endogenous form of cell signalling for stress/danger-sensing (29-30). He also worked on isolated vascular bundles to conclude that plants contain organs which are analogous to muscle and nerves in animals (30), just as Burdon-Sanderson had suspected (31). However, because of prevailing prejudices and general acceptance that plants should not be compared to animals, Bose‘s observations were not taken into serious consideration and neglected for over 70 years. Letting higher plants fall into oblivion, the first intracellular recordings (with a cellinserted microelectrode) of APs were registered in lower plants (32-34). Varied

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responsiveness of higher plants according to season, vigour, water status, temperature, age and previous history of stimulation (all of which Sir Jagadish Chandra Bose himself had struggled with) stumped the researchers effectively. Another reason to work on lower plants was the fact that higher species have just selected cells/tissues that are excitable while the entire body of a lower plant is so. Thus the advantage was taken from elongated alga internodes that were both excitable and accessible—big enough for a measuring electrode to be inserted into (35). That kind of recordings was almost simultaneously adopted for giant cells of plants (33) and animals (36). The former were soon considered more complicated than the latter, because of the existence of some structures missing from animal cells, namely a cell wall and a large central vacuole. Moreover, a tonoplast - a membrane embracing the vacuole - turned out to be excitable in some spp., so double-peaked APs were recorded, when the measuring electrode was placed into the vacuole (37). Because of this structure unique approaches developed (e.g. open vacuole method) to proceed electophysiological studies on algae (38); in spite of these structures Characean cells became a model tool for understanding membrane function (39). The giant neurons of squids were scrutinized simultaneously and independently by Howard James Curtis and Kenneth Stewart Cole at Woods Hole (U.S.A.) and by Sir Alan Lloyd Hodgkin and Sir Andrew Fielding Huxley at the laboratory of the Marine Biological Association in Plymouth (Great Britain). Among the scientists mentioned, a pioneering role in unifying plant and animal membrane responses was played by the biophysicist Kenneth Stewart Cole (40). He was the first to show that all principles of excitable membranes are equally applicable to plants (41-42) and animals (43-44). In his model of excitability Cole depicted an excitable cell as an electrical circuit with resistive and capacitive properties (45), which lent substance to the future ―sodium theory‖, which – in turn - validated depolarizing currents during nerve excitation. His demonstration of a large increase in membrane conductance during excitation with a parallel invariability of capacitance was a major landmark and fitted perfectly into the prevailing membrane theory of Bernstein (46). Julius Bernstein was a German physician (a student of Emil du Bois-Reymond) and neurophysiologist, who developed a differential rheotome—an instrument for resolving the time course of APs. Bernstein‘s membrane theory provided the first physico-chemical model of bioelectricity valid hitherto (47). Bernstein correctly assumed that the membrane of a cell is selectively permeable to K+ at rest and that the membrane permeability to some other ions increases during excitation. Accordingly, his theory gave reasons for the negative resting potential as a consequence of the tendency of positively charged potassium ions to diffuse from their high concentration inside a cell (cytoplasm) to their low concentration in the extracellular solution (apoplast) while the counter ions (anions) are held back (48). In Bernstein‘s theory two pivotal postulations were applied: (i) Walther Nerst’s equation describing electrical potentials as a result of concentration gradients separated by a biological membrane; (ii) Wilhelm Ostwald‘s calculation of the electrical potential at artificial semipermeable membranes (ion sieves). On the basis of Bernstein‘s and Cole‘s assumptions (―potassium theory‖ and ―sodium theory‖, respectively), a correct model of the ion mechanism of neuronal AP was elaborated. It can be summarized as a transient increase in Na+ permeability followed by K+ outflow. Thanks to Cole‘s devotion (awarded in 1967 with the National Medal of Science) the intracellular technique designed to directly measure APs and the membrane potential immediately came to be widely employed and applicable (49). During next years the intracellular technique became successively complemented with high-


5

gain amplifiers and voltage-clamping circuits so that current assessments could commence instead of voltage measurements. Two electrodes for current passing (to set the voltage at command value) and another two independent electrodes for voltage measurements were initially used, until a time-sharing system made single-microelectrode voltage-clamping possible (50). In a voltage-clamp mode the current necessary to set the command voltage is measured. For an isolated single cell it is also possible to apply a current-clamp mode, in which the membrane current is held at zero by the feedback circuit while measuring voltage necessary to nullify the flow of charges (51). The earliest measurements of ion currents known as voltage-clamp were conducted by the two above-mentioned Nobel Prize winners (Nobel Prize in Physiology or Medicine in 1963), Sir Alan Lloyd Hodgkin and Sir Andrew Fielding Huxley (36). Thanks to the voltageclamp technique, they published a mathematical formula - the Hodgkin-Huxley model (1952) - describing currents flowing through the hypothetical ion channels and giving rise to APs in excitable neurons of the Atlantic squid Loligo pealei (3). Their model largely stemmed from Cole‘s theory (52). 24 years later the existence of ion conduits was elegantly confirmed with a patch-clamp technique – a sophisticated version of voltage-clamping – by Erwin Neher and Bert Sakmann (9), a German physicist and physician, respectively, awarded for that with the Nobel Prize in 1991. From then on succeeding characterisation of various ion channels takes place (52). Now it is a common knowledge that APs in nervous cells involve the transient opening of Na+-channels and Na+ influx, in cardiac muscles the main depolarizing current flows through the Ca2+-channels, while in plant this is accomplished by a release of negative chloride ions. The subsequent release of positive potassium ions is common to plants and animals and is responsible for a repolarization – a return to the resting potential. In addition, more detailed studies on plants revealed that: (i) apart from chloride (14,53-59) also calcium is involved in the depolarization phase of AP (60-69); (ii) the Ca2+ ions may have external (70-73) and/or internal origin (64,74-76); their function is to activate calcium-dependent Cl-channels (56,77-79) and to inactivate plasma membrane H+-ATPase (80-81); (iii) along with potassium ions (55,59,82) H+-ATPase plays an important role in the repolarization (66,83); (iv) AP-delimited ion fluxes additionally serve signalling functions, such as turgor regulation, gene expression or Ca2+-dependent kinase activation (84-86); (v) in contrast to animals, plant AP-associated channels seem to be additionally regulated by cytoplasmic messengers (Ca2+, H+, ATP) and/or regulatory enzymes (kinases, phosphatases); (vi) many aspects of the plant AP-mechanism which include second messenger-activated channel and calcium ion liberation from internal stores still await more careful consideration (87). Let us say then that during the last 50 years enormous progress has been made in electrophysiological techniques, which brought about our better (but not complete yet) understanding of physico-chemical processes occurring on membranes at rest and during excitation. Action potentials are triggered when the stimulus causes transient opening of selective ion channels so that ions can start to flow down their electrochemical gradients. The various AP-mechanisms are electrochemically governed by the selective properties of the plasma membrane with different ion selective conduits as the key players. APs are initiated and propagated by excitable tissues to control a plethora of responses which in plants include growth synchronization, nutrient winning, reproduction (fertilization), defence against abiotic and biotic assaults together with an increase in pathogen-related gene expression. The role of the AP in plant movements, wound signalling, and turgor regulation is now well documented (87). Nevertheless, how exactly membrane excitation influences the nucleus (genes) and/or

6


other organelles is still obscure and a more detailed understanding of how membrane proteins work hand in hand during signal transduction and to what extent APs are involved in intracellular signalling is eagerly awaited. Likewise, AP involvement in invasion by pathogens, chilling injury, light, and gravity sensing needs further investigation (87). The following chapter is focused on the documented aspects of excitability in the plant kingdom.

AP SIGNIFICANCE Trap Closure and Enzyme Secretion Electrical signals are one of the fastest means of information transmission within a plant (88). For the first time recognized in the Venus flytrap Dionaea muscipula (1), next also found in its closest relative - the waterwheel plant Aldrovanda vesciculosa, they were linked with a trap closure right away. In the waterwheel plant they were shown to propagate at the rate of 80 mm/s (89), while different AP velocities (depending on the course along which they move) were noted for Dionaea. Accordingly, AP reached up to 250 mm/s in midrib direction (the highest value reported in plants hitherto), and ―only‖ 60 – 170 mm/s if running towards the trap margins. Moreover, while the first AP propagated to the sister-lobe with the average velocity of 100 mm/s, the succeeding one did it twice as fast (90). Considering the differences in propagation rates of succeeding APs in Dionaea, it is postulated that the first excitation facilitates the spread of the successive one (90). Likewise the propagation rate, also AP duration of 1s and 2 s in A. vesciculosa (91) and D. muscipula (92), respectively, are outstanding among plants. For comparison one should realize that APs in closely related Drosera rotundifolia last on average from 10 to 20 s (93), and in lower plants a single AP can even last up to dozens of minutes (94), propagation, in turn, hardly exceeds a few cm/s. The reported AP amplitudes of Dionaea muscipula and Aldrovanda vesciculosa exceed 100 mV (63,91,95-96) and are independent of a kind of the stimulus (mechanical stimulation, electrical stimulation, cold, light) (67). They depend, however, on [Ca2+]ext in such a way that the amplitude of AP follows [Ca2+]ext increases (92,97). Accordingly, Ca-ionophores or chemicals disturbing Ca-homeostasis hamper AP amplitudes (96) and slow down trap closure (98). Apart from Ca2+ also Cl- ions participate in the depolarization phase, since Cl-channel blocker A9C (anthraceno-9-carboxylic acid) lowers AP amplitude (67). K+ efflux is responsible for AP repolarization (99), which altogether perfectly matches ion mechanisms of excitation in plants (100). To make the Dionaea trap snap within 100 ms (101) at least two APs are needed, and the interval between the first and the second AP cannot exceed 10 s. The longer the breaks between succeeding APs, the more APs are necessary for a trap to snap (85,102). However, the trap is not completely closed yet. For a hermetical closure consecutive APs are needed; if not stimulated again, the trap re-opens relatively fast. The same refers to Aldrovanda vesciculosa which also needs more APs than one to keep the trap closed and to trigger corresponding turgor changes indispensible for the hermetical closure (85,103). Since all the cells of traps in both species are electrically coupled and all are equally excitable, they participate in fast AP transmission evenly (90-92,104). However, not all of them respond to


7

AP equally - effector responses differ. To close the trap completely, the loss of water takes place preferentially in the upper epidermis and adjacent mesophyll cells (85) while the lower epidermis extends (104). An answer to the question why the same AP makes only some cells shrink remains obscure. It may be speculated that the corresponding channels in the upper and lower sides of the trap are differently regulated by the same stimulus. Alternatively, a number of channels (channel density) differs in both sides, hence the discrepancy in the extent of water loss. In digestive glands, in turn, APs control the enzymatic activities (26), with successive APs sufficient to induce enzyme secretion (unpublished results). Moreover, excitation and secretion seem to be mutually linked (APs induce digestion - digestion products trigger APs), as many chemical substances is able to trigger both processes (105). It seems reasonable that excitation from one digestive gland spreads to the others to fully prepare the whole trap to digest a prey effectively. As a prey break-up boosts up a mineral uptake in the roots of carnivores (106), there is also a possibility that APs might be involved in inter-organ signalling. Whether APs play a role in trap-root communication after all, is still an open issue, because APs ―outside‖ the traps have never been reported so far (107). Since at least two succeeding APs are needed for Dionaea to take action, it is postulated that the plants may possess a kind of memory, which allows them to respond only to the second AP. Because the membrane potential goes back to the resting value right after the passage of an AP, the resting potential cannot act as an ―accumulator‖ in the process of memory. There is also no indication that the memory is associated in any way with a receptor potential – stimulus-dependent depolarization which if large enough leads to AP generation (108). Instead, for analogy to animal nerve systems, stepwise accumulation of bioactive substances during successive stimulations of the trap was suggested. Irrespective of the biochemical basis, the process of two successive APs during trap closure surely serves to protect a plant against any accidental mechanical stimulation. It can also be seen as a kind of protection against light-stimulation. Keeping in mind that light transiently depolarizes the membrane and that an excitable cell fires AP whenever membrane depolarization reaches the threshold value, it is not surprising that APs are noted after trap illumination (95). Another analogy to animals can be postulated, if one considers the AP-trigger trap closure as excitation-contraction coupling in muscles (1,109-110), especially that APs lead to a production of lysophosphatidic acid that increases membrane permeability to water and makes a cell shrink (111). A fast movement of the trapping organ under the control of an electric signal (AP) prompted Darwin to name Dionaea muscipula ―the most wonderful plant in the world‖ (112). However, other carnivorous spp. are very fast, too. Beside Dionaea and Aldrovanda also Drosera burmanni and D. glanduligera are able to execute snapping movements; they can bend a tentacle within 5 s and 0.15 s, respectively. As a matter of fact, the traps of all spp. of Drosera (sundews) and some of Pinguicula (butterworts) are mobile and ―use‖ APs to control the movement. Two layers of cells surrounding the conductive bundles constitute the excitable tissue of Drosera‘s tentacle and are responsible for a rapid electrotonic transmission of APs (93). These cells are electrically coupled by numerous plasmodesmata, which suits them for the fast propagation of APs (113). Moving down the stalk, APs travel with the velocity of 5 mm/s, while propagation upwards is twice as fast (114b). In addition to tentacle movements, most species of Drosera are also able to bend the whole leaf, which usually takes a couple of hours, and requires consecutive APs and subsequent turgor changes (85). The

8


successive APs are very probably indispensible for induction of enzyme secretion in these plants, too.

Fertilization The suggestive paper of Sinyukhin and Britikov published on Incarvillea grandiflora and Incarvillea delavayi (gloxinia) has reported that: (i) an AP is triggered when a pollen sets on the stigma of the pistil; the AP appears in response to mechanical irritation, too – it can be triggered with a soft brush; damaging stimuli do not evoke the AP; (ii) the extracellularly recorded AP of 30-40 mV spreads to the base of the stigma with the velocity of 18 mm/s in order to make it close; the stigma closes in 6-10 s; (iii) another AP of 80 - 90 mV appears if the pollen has turned out to be respective; if the mechanical irritation is not followed by the corresponding chemical stimulation, the stigma re-opens in 17 - 22 min; (iv) the second AP courses down the style of the pistil at the rate of 29 mm/s and enhances respiration in the ovary; the second AP has been postulated to make the ovary ready for pollination (115). In the same paper the ability to control ovary metabolism by pollen-triggered APs has also been suggested for Lilium martagon, and Zea mays. Similar experiments conducted on Hibiscus rosa-sinensis has shown that either self- or cross-pollination results in a series of 10 to 15 APs propagating down the vascular tissue of the style with a velocity of 13 - 35 mm/s (116). AP-induction is proceeded by a hyperpolarization that takes place 50 – 100 s before AP firing. Only with the passage of AP series is an increase in ovary respiration correlated; neither cold nor wounding are coupled with CO2 increases though they also produce membrane potential changes and moreover cold stimulation is associated with a single AP (116). By analogy to Sinyukhin and Britikov‘s results, it can be concluded that electrical signalling of AP is informative only if accompanied by additional – most probably pollen derived - stimulants. It can be speculated that there must be a signalling cascade leading to pollen recognition, which triggers APs. In case of Hibiscus rosa-sinensis cation efflux and thus membrane hyperpolarization must be involved, while in Incarvillea spp. membrane stretch was suggested to be of crutial importance (115). Since both, negative membrane potential (hyperpolarization) and positive pressure (stretch), are known to activate respective Ca2+-channels (117), they might serve AP initiation. However, the exact sequence of events leading from pollen germination to AP initiation has yet to be deciphered. It is very likely, for example, that receptor like kinases (RLK) known to be involved in pollen-pistil communication (118) might mediate in channel activation, too. An ovary response only to the second AP (chemically-induced AP) greatly resembles a protection system of carnivorous plants against accidental stimulations, and points to the interesting fact that a single electrical change itself may hardly be satisfactory if not backed up by supportive information – a recurrent issue, recently raised by Pyatygin et al. (119).

Mechanical Stimulation and Thigmonastic Movements The movements of plant parts (e.g.: leaves, stamens, stigma, stems, tendrils) caused by touch are referred to as thigmonastic if independent of the stimulus direction and tigmotropic when they follow the stimulus course. Described in the insectivorous plants first (1,112), the


9

thigmonastic movements soon turned out to be a characteristic phenomenon for a few other species: Mimosa pudica (27,30), Biophytum sensitivum (120) and Incarvillea spp. (115). Leaf folding by Mimosa is the best elaborated thigmonastic response that has long been linked with AP propagation (90). It is enough to touch a single pinnate leaflet to trigger an AP and let the thigmonastic movement start, when AP propagation along the entire leaf make the leaflets fold up consecutively. The pathway of AP transmission comprises the elongated cells of phloem and parenchymal cells surrounding both the xylem and the phloem (90,121). The transmission velocity varies enormously from 4 to 40 mm/sec, depending on leaf age and general condition as well as on ambient temperature and humidity (30,90,122). If the AP reaches the pulvinus, another type of AP (pulvinar AP) appears with a latency of 0.2 – 0.4 s (102). The pulvinar AP with the amplitude of 100 – 140 mV arises with a rate of 0.5 – 2 V/s and endures on average 10 s (90,102). Within 0.3 s after generation it propagates throughout the whole pulvinus (102). As a consequence the abaxial (lower) cells of the pulvinus lose turgor vigorously, which causes the leaf drop (85). Time needed to lose water amounts to 0.1 – 0.2 s (122). From the pulvinus the signal (AP) occasionally enters the stem and next ingresses the other pulvini so that the other leaves drop and fold (now the AP moves from the pulvinus up to the pinnate leaflets; thusly, APs have a nature of propagating waves in both basipetal and acropetal direction). The transmission rates in the petiole and the pina-rachis only slightly depend on the direction (basipetal vs acropetal), but they increase with an increase in the number of excitable cells involved or - in other words - with the width of the petiole (90). This means that the extent of excitation transmission and velocity depends on the co-operation of many cells, which manifests itself in such a way that thicker organs transmit the signal wider and faster (30). Accordingly, the transmission along the stems of Mimosa takes place only as a result of the co-operation of a number of cells. The transmission is electrotonic and occurs longwise excitable cells as well as transversely - then ―jumping over‖ an unexcitable tissue separating excitable bundles (90). In the pulvinus, the so called collocytes (adhesive cells) occupying the phloem/cortex interface are responsible for lateral transduction of APs toward motor cells (123). Since folding is under the control of AP, this reaction runs either completely or not at all. With the passage of excitation wave Cl- and K+ ions are released first; they ―drag‖ water out of cells next. When water leaks out, leaf movement begins. The coincidence of Cl- / K+ release to the apoplast of a pulvinus and ―tissue contraction‖ (leaf drop) has been proven with the use of Cl-selective electrodes (102) and radioactive potassium ions (124). However, not all excitable cells ―expel‖ ions to the same extent. Accordingly, the increase in [Cl-]ext is observed only in the lower half of the pulvinus (102,125-126), while the APs are detected in both halves (90,102,127-128). The situation resembles the conditions from Dionaea‘s trap where a loss of turgor is coupled with AP passage but do not embrace all cells excited (but upper epidermis only). Therefore, turgor-losing cells can be viewed as effectors (motor cells), while the other excitable cells as both efferent fibres connecting sensors with effectors and the sensors themselves, as every part of Mimosa‘s leaf is receptive to touch. The slumped leaves return to their starting position after 15 to 30 minutes of recovery (129). This time is needed for restoring ionic gradient and turgoid water status in each pulvini autonomously (130). Leaf folding brings some consequences for Mimosa, among of which an impediment of photosynthesis seems quite obvious (131). Moreover, an AP controlling the leaf movements also triggers phloem unloading of sucrose (132). It appears that with the transmission of excitation through the phloem the flow of assimilates stops, sucrose enters the apoplast and

10


the excited cells shrink (129,132-133). As a matter of fact, the temporal loss of photoassimilates seems to control all movements of Mimosa (nyctinasty, thigmonasty, gravitropism), since they all depend on turgor changes. Should excitation be evoked by phloem injury, then phloem shrinking could serve as a kind of protection against photoassimilate (energy) loss, as well. The latter hypothesis can be partly substantiated by showing that the sugar unloading is a more general response of the excited phloem (134-135). Mechanically triggered APs propagating throughout the length of a pinna-rachis or a peduncle have also been reported in Biophytum sp. (120). The AP of 60 to 100 mV (extracellular recordings) is followed by the absolute refractory period of 20 - 50 s and the relative one of 30 - 70 s. The AP transmission is restricted to the base of the leaf or peduncle; its velocity of is about 2 mm/s; and there is no difference in the velocity between the acropetal and basipetal directions. The mechanism of the transmission is electrotonic and similar to that in Mimosa pudica. Other plants in which mechanical-APs are registered include not only the abovementioned sensitive plants or carnivorous spp. (Dionaea (63), Aldrovanda (91), Drosera (114,136)) but also Pinus (137), Ipomoea, Xanthium, Pisum (138) and algae (139-140). Mechano-stimulation of carnivorous plants is connected with bending of trigger hairs, the organs responsible for prey sensing (sensors). Deviation of the trigger-hair of Dionaea and Aldrovanda or bending of the head of Drosera‘s tentacle results in activation of the stretchactivated channels located in the bending zones. The channels allow Ca2+ entry and hence membrane depolarization (63). In Chara APs can be stimulated by touching (dropping a glass rod on) the node (140) or by pressure changes (139); they appear as a consequence of membrane stretching of the node cells and propagate along intermodal cells, proving that there is an electrical coupling between nodes and internodes. Characean internodal cells can be mechanically stimulated either by direct decompression of the plasma membrane or thanks to osmotic changes of a bath solution. Exchanges from hypertonic to hypotonic media or their accompanying membrane stretching, always induce large membrane depolarization (141) that is accompanied by APs (142). By contrast, APs have been never observed during exchanges from hypotonic to hypertonic solutions (=membrane compression). A link from membrane stretch to AP generation in Chara can be quite straightforward, if stretch-activated Cl-channels are engaged (143). Alternatively, likewise for carnivores, the activation of the mechano-sensitive Ca2+-channels triggered by membrane decompression has been proposed (142-144). Additionally, stretch-activated Ca2+-channels in the chloroplast have also been shown to participate in plasmalemma excitation (145). Because in Acetabularia mediterranea APs accompany pressure regulations in the critical range and their frequency is increasing with turgor raises (146), it seems convincing that APs may constitute a ―valve‖ releasing osmotically active ions (Cl-, K+) and thus lowering turgor, as it is the case in bacteria (147). It has already been suggested that the original function of electrical excitability of biological membranes is related to osmoregulation which has persisted through evolution in plants, whereas the osmotically neutral action potentials in animals have evolved later towards the novel function of rapid transmission of information over long distances (148). As for higher plants, the osmoregulation-hypothesis might be well substantiated by APs induced by wetting dry roots (hypo-osmotic shock). Additionally, such APs initiated in the roots and registered in the stem are suggested to coordinate physiological responses with water availability in the soil (149); the results were further supported in maize (150). In the plumular hook of pea epicotyls, in turn, mechanically evoked APs are proposed to mediate an


11

increase in mechanical durability during stem growth (151). Their involvement in induction of an ethylene release (a hormone that among others inhibits the opening of the pulmular hook and in this way enables the plumule to penetrate soil) has been suggested (151). Growth-associated spontaneous fluctuations of the membrane potential occurring individually or in series have been also recorded in shoots of Ipomoea, Xanthium and Pisum (138). With the use of intracellular recordings they were noted as the putative action potentials of 1-4 s duration, however, their function was never deciphered. The same holds true for spontaneous APs reported in cucumbers and sunflowers (152). More often than not, local membrane potential changes instead of APs appear in the place of growth (apical tips, elongation zones and pollen tubes). Corresponding transmembrane currents seem to control such plant reactions as gravitropism (roots and shoots), thigmotropism (tendrils), chemotropism (pollens), (circum)nutations (roots and shoots), which all together is of great interest for electrophysiology but is not an issue for the present review. Up to this day, for example, the suggestion of AP involvement in geotropic responses (84) has not been experimentally confirmed (87,153). On the other hand, circumnutation-associated APs were shown to appear in sunflowers with 24-h-rhythmicity (154). The same results were independently obtained by Stahlberg et al. who postulated a casual relationship between stem growth and stem spontaneous excitability (152), but the question of the exact role of APs in growth progression has not been answered yet.

Light/Dark - Guided Signalling The existence of the above mentioned circumnutation-associated APs is rather linked with darkness, as those APs predominately occur at nights (152,154), when the membrane resting potential is known to be relatively depolarized (38,94,150,155-161). The boosting effect of light on the plasmalemma polarization can be connected with the stimulating action of photosynthesis on plasma membrane H+-ATPase, which was experimentally shown by the use of PSII inhibitors (156,162). Therefore, the enquiry of whether those APs are light/darkmessage transmitting signals to synchronize dark-induced growth of a plant (152) or just a consequence of membrane depolarization (163) is really hard to be answered, especially that both solutions do not have to be mutually exclusive. The very first response of a plasmalemma to light-on is a short and transient membrane depolarization (if strong enough, leading to AP in excitable cells) followed by a long-running hyperpolarization (light boosting effects as mentioned above). Both responses are associated with photosynthesis, because they are absent in cells deprived of chloroplasts (158), inhibited by DCMU (an electron transport inhibitor) (69,94-95,164-165) and stimulated by CCCP (a proton gradient uncoupler) (164). These data also suggest that electron flow in chloroplasts (either cyclic or non cyclic) is somehow sensed by a plasmalemma (38). The mechanisms of light induced potential changes in excitable cells has been elaborated on lower plants predominately (38,53,73,165). Since approximately a half of alga‘s resting potential is fuelled by ATP (another half by K+-diffusion) and both photosynthesis and respiration are ATP-yielding processes, therefore any transition from darkness to illumination (and vice versa) may be connected with the very temporal and local ―loss‖ of ATP, sufficient enough to be sensed by adjacent plasmalemma H+-ATPase, thusly leading to H+-ATPase inhibition and hence membrane depolarization (14,157,166). Light-induced inhibition of the

12


electrogenic proton pump during the onset of AP has been assessed at 50% - 80% of the resting value (167-168). Another possible explanation of AP initiation by light-on is put forward by Mimura and Tazawa, who have suggested that light-induced chloroplast surface charge is able to influence plasmalemma (164). This is very much consistent with inhibitory effects of DCMU (38). This is also in accordance with previous Tazawa‘s papers which reported that not the stoppage of the pump but membrane depolarization is a necessary condition for the generation of light-induced rapid potential changes (169). Moreover, lightinduced potential changes on thylakoid membranes are long known to precede those occurring on the plasmalemma (165). Like ―thylakoid-voltage‖ influences plasma membrane potential, so electrical excitation of the plasmalemma can modulate events in the thylakoid membrane (170-172). The plasmalemma-chloroplast coupling factors might be again ATP/ADP/Pi, Ca2+ and membrane depolarization itself. Additionally, AP-associated pHcyt changes have been postulated to influence photosynthesis directly (173). Since electrical signals interfere with photosynthesis (107,131,172-178) and photosynthetically active light triggers different membrane potential changes, therefore multifunctional and bilateral communication between plasmalemma and chloroplast must exists, where chloroplast-plasmalemma vicinity enables their mutual interactions (38). Chloroplastic Ca2+ release could be a plausible explanation of membrane excitation under dark (179-180). This Ca2+ flux does not occur immediately after the light-to-dark transition but begins circa 5 min after light off and slowly increases to a peak at 20 to 30 min after the onset of darkness, affecting cytosolic Ca2+ concentration as well (179). Ca2+ influence on membrane proteins (H+-pumps, transporters, channels and various membrane-bound enzymes) is difficult to be summarized in a few sentences, as its aftermaths depend on Caconcentration itself as well as on numerous Ca-binding proteins (kinases, phosphatases, CaM, CBL). However Ca2+-activated Cl--channels or Ca2+-inhibited H+-ATPase seem to suffice to justify induction of APs. Light-induced APs have been so far reported in the moss Physcomitrella patens (94), the liverwort Conocephalum conicum (16,73,181), the bean Phaseolus vulgaris (182) and Dionaea muscipula (96), whereas dark-induced ones in Helianthus annuus (152), Physcomitrella patens (94), the hornwort Anthoceros punctatus (165), the green alga Eremosphaera viridis (183) and Acetabularia spp. (14,53). Recently Shabala et al. have demonstrated in maize seedlings that light exposure in the shots can have a strong impact on root ion transport, visible within a range of seconds to minutes (184). Such fast shoot-root communication must be accounted for with transmittable membrane potential changes. Since light-induced potential changes may be of AP character, therefore APs involvement in the control of root uptake machinery is not excluded, though it needs experimental confirmation. Finally, not only chlorophyll but also other receptors (phytochromes, cryptochromes, phototropins) can mediate the light-induced membrane potential changes (185). As those receptors are cytosolic - membrane bound proteins, their signalling cascade leading to membrane potential changes seems at first glance quite simple (via e.g. light-activated channels (186-187)). Such an attitude, however, may be in most cases misleading, as molecular studies have recently acknowledged the complicated and multilevel nature of lightperception systems in plants (188). In general, they do not cause AP generation (189), hence they are out of interest of this presentation. An exception is the UV-C perception complex in algae known to interfere with visible light to evoke APs (190). Additionally, for a few


13

reasons, two papers of Ermolayeva reporting on phytochrome-mediated membrane depolarization of the moss Physcomitrella patens are worth mentioning as well, although in those papers the light-induced membrane changes have never been named APs (191-192). First of all, the rapid and transient membrane depolarization of 100 mV has shown graded response below and all-or-nothing characteristics above the threshold value. Secondly, the depolarization has been followed by a transient 30 mV hyperpolarization and the refractory period of 12 - 15 min, which reflects AP characteristics. Thirdly, the ionic mechanism of the red-light induced depolarization resembles AP evolution. At last but not least important is the fact that the moss is excitable, thus able to generate APs in response to different stimuli (light, cold, current). The phytochrome evoked potential changes (putative APs) have been shown to initiate the development of primary side branches on caulonemal filaments of Physcomitrella (191). In accordance with this is the further report of Mishra et al. who have demonstrated that an electrical stimulus can probably overcome the requirement of photo-exposure to induce primary leaf formation in etiolated seedlings of Sorghum bicolor (193). Therefore it can be postulated that light-induced APs could be competent signals controlling photomorphogenesis. Still AP-controlled light sensing needs deeper consideration.

Temperature Sensing Although as early as in 1837 Dutrochet observed that rapid cooling leads to an abrupt cessation of protoplasmic streaming in Chara (23), it took almost 100 years to realize that a sudden temperature drops evoke APs in this alga (35). Rapid cooling (unlike gradual cooling) acts as a stimulus upon nearly all plant cells. As a result of temperature drops membrane depolarization takes place (23). In excitable cells, the depolarization develops into an AP, as it is a case of Mimosa pudica (90,129), Biophytum sensitivum (120), Dionaea muscipula (67), Hibiscus rosa-sinensis (116), Zea mays (134), Cucurbita pepo (23,80,194-195), Cucumis sativus and Triticum aestivum (196), Luffa cylindrica (197), Populus trichocarpa (176), Conocephalum conicum (68), Physcomitrella patens [unpublished results] and numerous algae (14,35,197-198), and very likely for Arabidopsis hypocotyls (186). There have been differences in AP duration recorded after cold and other types of stimulation, with cold-AP lasting significantly longer, and no differences seen in AP amplitudes (68,116). Moreover, the lower the temperature, the slower the repolarization, which may simply reflect a dependency of an enzymatic activity of pumps on the temperature (= Q10 coefficient) (194). In unexcitable cell the cold-induced depolarization shapes after a stimulus strength and duration (199), and even if it surpasses the amplitude of 100 mV, it does not develop into an AP (23). Such magnitude originates form an influx of Ca2+ that is driven by a huge cell-interior directed electrochemical gradient (the negative transmembrane potential + the equilibrium potential ECa of circa +100 mV). More detailed experiments have demonstrated that these Ca-increases are adjusted by the rate of cooling irrespective of the absolute value and are ―sensitive‖ to previous stimulation, showing large desensitization (attenuation) (199). Consequently, not each consecutive cold treatment leads to APs in excitable plants (23,195,200) as well as Cainfluxes in unexcitable cells are hardly comparable when successively repeated (201). Since cold-induced Ca2+-flows were of interest of a host of researchers, their existence has been proved with the use of a plethora of experiments, e.g.: radioactive ions (202), voltage measurements (68), current measurements (199), luminescence measurements (186,203-204).

14


As cold-induced calcium increases are the very first measurable cell responses, the coldactivated Ca-channels have been hypothesized to be temperature sensors in plants (205). Moreover, fast accommodation is one of the characteristics of a receptor system whose thresholds depends on the steepness of stimulus rise (195), which perfectly matches coldactivated Ca-currents. However, molecular entities and corresponding genes of Ca-channels have not been found yet, thus the channel-sensor hypothesis awaits verification. Another plausible explanation for cold-induced depolarization is an inhibition of plasmalemma H+-APTase (194-195,206-207). As mentioned above, the same may refer to light action linked with transient membrane depolarization. Both temperature and light are the so called physiological stimuli. As ambient environmental factors they control the whole plant metabolism shaping [ATP]cyt availability. Thus, it is not surprising that under certain circumstances they are able to evoke APs through [ATP]cyt-disturbances, and hence such APs can be named ―metabolic‖ (14). Since light and temperature act on the whole plant at a time, describing all the functions of ―metabolic APs‖ may be very problematic. In the case of cold stimulation, however, APs can be considered as ―hardening signals‖ (119), especially that AP-induced pre-adaptation has already been successfully provided for some plants, namely maize (208), wheat and cucumber (196).

Stress or Damage-associated APs Not only physiological (pressure, light, temperature) but also notorious stimuli (burning, freezing, mashing, cutting) can make Mimosa and Biophytum fold down rapidly (90,120, respectively). Obviously, the sensitive plants can ―feel‖ pain, as Bose postulated already in 1926 (30). 50 years later after Bose‘s publication the view of plants sensing environmental danger became prevailing (149). After all, in many ―not-sensitive‖ species APs have been noted after harsh stimulation, e.g.: pine seedling (137), poplar (176-177), lupine (209), pea (210), broad bean (211), cucumber (212), tomato (213-215), beggartick (216-217), hibiscus (116), sunflower (160), Arabidopsis (218), barley (219), maize (173), liverworts (220), and various species of algae (14,139,221-222). In fact four types of electric signals have been noted in Chara (222) and two in higher plants after severe wounding (160,223-225); in the latter – ―fast‖ APs and ―slow‖ VPs, variation potentials. VPs are generated only if a xylem continuity is disrupted and a subsequent increase in xylem pressure takes place (212). Consequently, at saturating humidity, when xylem tension is negligible, VPs do not appear (225). Accordingly, the speed of conduction is related to the velocity at which water moves in the xylem and amounts from 0 to 7 mm/s (160,214). VPs cannot be evoked by electrical stimulation and are able to pass through the zone of killed plant tissue, which strongly differs them from APs (160). They simply are a manifestation of a pressure wave that makes stretchactivated channels open in living cells adjacent to the xylem (160). They also are responsible for a transient shutdown of plasmalemma H+-ATPase there, probably through [Ca2+]cyt increases (225). As a consequence, two types of responses are recorded at a time after severe wounding – on the shoulder of VP, APs occur (160,223). Since VPs may ―interfere‖ with APs and because they never appear after electrical stimulation (160), thus a depolarizing current (DC) is often a stimulus of choice, when APs are to be explored. With the use of DC the view that excitable tissues act as ―neuroid‖ system was elaborated for: the lupine Lupinus angustifolius (17,19,226-227), the sunflower


15

Helianthus annuus (18,160,224), the cress Arabidopsis thaliana (228), the flytrap Dionaea muscipula (96), the waterwheel Aldrovanda vesiculosa (97), the sensitive plants Mimosa pudica (128) and Biophytum sensitivum (120), the potato spp. Solanum (229), the tomato Lycopersicon esculentum (229-231), the pumpkin Cucurbita pepo (232), the bean spp. Phaseolus (233), the buckwheat Fagopyrum sagittaeum (after (149)), the sorgo Sorghum bicolor (193), the willow Salix viminalis (234), the liverwort Conocephalum conicum (235), and numerous algae (reviewed by (38)). The careful reader must have already noticed, that every time APs are numbered in response to either non-damaging or severe stimulation the same plants are quoted, which simply reflects the fact that in an excitable cell/tissue/organ APs occur with a threshold stimulus but irrespective of the stimulus kind. Thus it is not surprising that DC is a means of evoking APs, that simplifies the experimental procedures, still allowing to deal with AP purposes and functions. The most splendid example is PIN (proteinase inhibitor) expression occurring systemically after wounding (213) as well as after electrical stimulation (229-231), thus proving that APs may control such a process as gene transcription and are meaningful for defence processes (236-237). In general, damage- or DC-evoked APs are linked with growth arrest (197,217), photosynthesis drops (107,131), enhancement of respiration (238-239), induction of ethylene emission (211), JA biosynthesis (86) and ROS generation (after (119)), which altogether resembles responses associated with danger perception (229). It is likely that under unfavourable circumstances plants stop growing and start self-defending, and that APs may synchronize both processes (86,240). Such a scenario perfectly corresponds to damagetriggered APs and repair-associated accomplishments in algae (241). In these taxa, [Ca2+]cyt increases during the passage of an action potential; next, Ca2+ activates the protein kinase that phosphorylates myosin; this inhibits myosin interaction with actin and finally terminates cytoplasmic streaming (241-242). Cessation of streaming, in turn, grants the cell time for controlling damage. Moreover, cessation serves to protect the cell from leakage, while increased [Ca2+]cyt participates in wound-clotting mechanism (241). It is tempting to speculate that phloem clotting, for which increased [Ca2+]cyt is indispensable as well (243), also takes place after damage-induced AP passage and that such a succession of events has preserved in higher plants since algae acquired it. One of the consequences of tissue damage is a loss of turgor pressure that is sensed by adjacent intact cells (221-222), another - a release of molecules which being associated with a cell interior, when released, can serve signalling functions, e.g.: systemin, hydroxyprolinesystemin, PEP, ATP/ADP, acetylocholine, GABA, free amino acids or even KCl (at high concentration). Both stimulations (pressure or chemicals) are known to bring about profound membrane potential changes, but only for wound-associated membrane stretching (221-222) and for a few cytoplasmic compounds (KCl, Gly, Glu and GABA) was an induction of APs reported (172,218-219,244-246). With the discovery of ionotropic glutamtate/glycine receptor genes in Arabidopsis, the quest for their role in plant physiology has begun (247). Though their functioning as Ca-permeable channels has only been indirectly proven, such a scenario fits perfectly to their putative role in AP generation (244). Their high expression in roots (248) may explain why these cells treated with amino acids generate APs that propagate to the leaves, where such APs induce changes in the rates of transpiration and photosynthesis (172). Pathogen attack, which is a quite common insult affecting plant development, is associated with tissue damage, too (249). However, pathogen recognition is most frequently

16


linked to a depolarization of insular characteristics (250). Therefore, in spite of tremendous amplitude (up to 150 mV), duration (over 1 h), and significance for plan survival (251), most of the pathogen-associated membrane potential changes are beyond the scope of this review. Nonetheless, it must be stressed here that AP function has already been suggested to be coupled with local/insular changes in ion concentration (Ca2+, H+, K+, Cl-), which lead to modified activities of enzymes in the cell wall (e.g. pectinase), the plasma membrane (e.g. cellulose synthetase, callose synthetase), and the cytoplasm (e.g. protein kinase), and may be indispensable for protection against injury and pathogen invasion (84,244). Accordingly, for AP-induced PIN expression only action potentials with a complete Ca2+ signature are required (86). Therefore, the notion has been put forward that AP propagation is a nonspecific component of signalling pathway which needs additional messengers to become specific (119). Such an additional role of ions (Ca2+, H+), sugars, aminoacids, nucleotides and phytochormones has long been known; more and more often VP and not-propagable potential changes are being included in the signalling network, too. It can be concluded that transmittable APs are the fastest systemic signal but represent just a part of the effector response (219,252). Quite obviously, there is an urgent call for further examination of APconcurrent effector-sensor ―intermediators‖ and their dependencies on electrical membrane changes in plants (87). So prevailing are APs associated with stress or damage that they should be viewed as a kind of arms. The will to decipher the exact purposes of APs and AP-coupled sensor-effector links forces us to look at plants more carefully. A recent concept of viewing excitable plant cells as neurons is only partly justified (109). It seems like, for example, that plant APs carry no frequency-coded information (119,246). A series of AP occurring after severe wounding (14,218,220) should rather be connected with the leakage of excitatory compounds than with stimulus strength. Alternatively, AP series might fulfil a requirement for additional information, since a single AP means nothing unless followed by supplementary ―instructions‖ (86,105,115). Thus, apart from following AP-associated end responses (e.g. gene expression), dissecting the pathways of AP transmission and generation is equally important, as all these cells (sensors, conductors and effectors) seem to constitute AP-specific ―instructions‖ concurrently.

PATHWAYS OF TRANSMISSION Bundles of phloem with companion cells and living cells of xylem (protoxylem, metaxylem); or the entire organ such as an active trap of Dionaea; or even the whole organism as it is a case of lower taxa (algae, mosses, liverworts); are pathways of AP transmission (88). As for higher plants, the living vascular bundles displaying highly negative membrane potential of circa -200 mV, having numerous plasmodesmata that guarantee good electrical conductivity over long distances, keeping low longitudinal resistance and being relatively insulated from the surrounding cortex (assuring minimal loss of excitation current) are the best suited for systemic and electrotonic transmission (177). Simultaneous acro- and basipetal direction results from the absence of ―rectifying‖ synapses. Instead, architecture of vascular system determines AP reach. Thus, the restricted areas exist, e.g. a base of peduncles of Biophytum sensitivum (120) or leaves of Helianthus annuus, whose vascular architecture


17

hampers APs from entering the petiole (224). In contrast, in Mimosa pudica (90), Vicia faba (238) or Arabidopsis thaliana (228) AP can ingress/leave leaves easily. The transmission along the vascular bundles takes place as a result of the co-operation of a number of cells, hence being preferred in stems rather than in leaves, after all. Moreover, most cells in leaves except conductive bundles are unexcitable in vascular plants but carnivores. Accordingly, no AP has ever been registered from mesophyll cells (except in carnivores), though local changes of a different character appear as a result of adjacent bundle excitation (219,244). Apart from excitation spreading excitable tissues in plants fulfil many other function (e.g. metabolite distribution, metabolite loading/unloading, photosynthesis, secretion, absorption). Since they have stop short of differentiating into nerve-like exclusively, the rate of AP transmission in plant (from 0.5 up to 300 mm/s) lags behind nerve impulse velocities (0.03 – 120 m/s). Still it is enough to shut up an organ within 100 ms or ―excite‖ the whole plant within a few minutes.

HOW TO RECORD AND MEASURE ACTION POTENTIALS Electrode Techniques Electrophysiology - a study of living objects, which deals with voltage, current, capacity, resistance or conductivity measurements and covers an ample variety of scales, beginning from entire organisms through excitable organs and cells to finish at a single channel activity level. Its goal is to describe the electrical properties of the living world. Classical electrophysiology make use of (micro)electrodes either placed outside or inside a living cell (100). The latter allows for the accurate measurement of a resting potential value and AP amplitude, a membrane capacitance, conductance and resistance; the former – for monitoring of AP occurrence, transmission and coincidence with physiological responses (177). With a multi-electrode installation an exact assessment of the transmission rate is possible. Extracellular recordings offer also such an advantage that the measurement can be conducted over several days (246). One must keep in mind, however, that during extracellular recordings electrode arrangement is of great importance for a few reasons: (i) the electrodes must be localized nearby excitable cells; (ii) there must be a link of sufficient resistance between the measuring and reference electrode to record potential drops; (iii) the electrodes must be localized on the way of excitation spread when physiological interdependence is to be worked out (224). With intracellular impalements, the difficulties may also begin when the exact positioning of a measuring electrode is important while working on an intact plant. This problem was solved by Wright and Fisher who used aphid‘s stylets to penetrate the phloem exclusively (253); the procedure was so suitable that it was used by the others, as well (132134). Equally prosperous is the method of placing the measuring electrode into substomatal cavities of the open stomata nearby an AP-conductive tissue (219,244,252). With the use of giant cells the step from intracellular recordings to voltage-clamp technique was taken quite smoothly (see Introduction). Even then, however, two severe problems remained: (i) spatially non-uniform voltage control; (ii) the lack of control over intracellular ionic composition (254). Solution to both problems came along with the patchclamp technique which additionally allowed for a single channel measurements (9,255). AP-

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clamp (76) and Self-clamp (256) techniques, in which an AP is recorded and repetitively replayed as the command voltage to the same cell under voltage control, proved to be reliable with excitable cells. Nowadays the sophisticated system of microstructured chips called a patchliner or planar patch-clamping facilitates an automatic and simultaneous patch-clamp analysis of many cells with high outputs (254). It is very useful for fast screening of channels; it is devoid of noises, very sensitive and designed to display an increased accessibility of the membrane for optical detection techniques (e.g. FRET - Fluorescence Resonance Energy Transfer) (254). Another sophisticated electrode technique is MIFE (Microelectrode Ion Fluxes Estimation) - a selective measurement of ion fluxes appearing near living cells (257), which originated form a vibrating probe (microelectrode) method (258). Both techniques are noninvasive and has a resolution of 2 - 20 micrometer in position and 10 seconds in time, which for membrane potential changes lasting a minute or longer is sufficient to be resolved (100). A typical MIFE measurement implements an ion-selective electrode and assesses the net flux of ions (nmol/m2s) on the basis of a change in ion concentrations (change in voltage of the ion-selective microelectrode) over a small known distance (184). An additional scanning function of a computer-controlled microelectrode position system offers two-dimension resolution via: SVET (Scanning Vibrating Electrode Technique) that can measure voltage gradients down to nV at a minimum speed of approximately 50 ms per scan point; or SIET (Scanning Ion-selective Electrode Technique) that can measure ion concentrations down to picomolar levels but at a slow speed of 500 - 1 000 ms per point so as not to disturb the measured ion gradient.

Optical Methods Optical electrophysiological techniques were established to follow the one- or twodimension distribution of electrical changes occurring in a living cell/tissue/organ. They are grounded in fluorescent techniques and make use of voltage sensitive dyes – the molecules capable of emitting light in response to applied voltage (259). After introduction of one or more such compounds into a cell via perfusion, injection or gene expression, the spatial and temporal patterns of electrical activity may be observed and recorded. Apart from voltage sensitive dyes, ion-selective fluorescent indicators can be engaged to monitor ion concentration changes during excitation. Commercially available Ca2+-, H+-, K+and Cl--indicators [http://www.invitrogen.com/site/us/en/home/References/Molecular-ProbesThe-Handbook.html] can be introduced to excitable cells either through infiltration or by iontophoresis. The latter approach was successfully applied in algae to correlate membrane potential changes such as APs with [Ca2+]cyt-increases (260). One can also imagine breeding of transgenic plants which would express apo-aequorin (a bioluminescent Ca2+-indicator) in excitable tissues exclusively; this is a futuristic idea, however.

Computational Studies If a mathematical model of AP can be built up, its analysis may help to substantiate an experimental hypothesis, which indeed was the case for postulating osmotic changes during


19

APs or for proving intracellular Ca2+ involvement as well as H+-ATPase inhibition during a depolarization phase of APs or for reconstruction the main dynamical features of APs in plants (21,64,80,148,261-264). However, elaboration of such models is always restricted by the volume of experimental data. Nevertheless, modifications of the models could be a tool for theoretical investigation. Recently, an assemble of the number of AP models has been suggested as a means for the analysis of AP propagation (80).

Working on Mutants Since the ion mechanism of APs elaborated on algae turned out to be consistent for all plants, the full knowledge of the channel proteins/genes involved in plant excitability has been on its way. The involvement of voltage-gated channels is unquestionable and surely comprises voltage-dependent Cl-- (56) and K+-channels (265). However, the voltage control over Ca2+-conduits is only assumed. Besides CNGC (Cyclic Nucleotide Gated Channels) and GLR (Glutamtate Receptor Like) nothing is known about the molecular entities of the plasmalemma calcium ―passive conductors‖ (266). Accordingly, stretch-, cold- or lightregulated Ca2+-channels remain as presumptions. No better situation appears with putative genes for intracellular Ca2+-conduits, as there is little direct evidence linking their products to intracellular calcium increases (267). The same holds true for Cl--channels, whose gene identification is in infancy (268). With the recently characterized S-type Cl-channels (SLAC and SLAH - (269-270)) a quest for voltage-gated Cl--conduits has just begun. Light- (186187,271) or stretch-activated anion channels (272) still need to be identified at the genetic level. As for genes and their products voltage-gated K+-channels are unique; they are Shakertype inward (AKT1, AKT2-3, AKT5, AKT6, KAT1, KAT2, silent KC1) and outward (GORK, SKOR) rectifiers, which are very well described and genetically, molecularly and functionally characterized (273). Nevertheless, their involvement in membrane excitability has not been examined in detail. Neither has this been done for any of the mutants of the above mentioned channels. Thanks to enormous progress in genetics, a cornucopia of channel genes and channel mutants is ultimately expected. As most of these mutants are commercially available right away, working on such plants will open new perspectives for electrophysiology.

CONCLUSION Most if not all of the plants possess excitable tissues. Action potentials in plants arose independently of those in metazoan excitable cells, nevertheless some analogies to animal APs can be found (195,274). For instance, they coincide with movement. They occur in mobile excitable organs such as traps/leaves or pistil to function in movement/turgor regulation. Moreover, they are also generated and transmitted in immobile parts of a plant to carry out intercellular and intracellular signalling indispensible for growth, photosynthesis and respiration adjustment, stress/danger perception and self-defence commencement (88). In spite of a lack of purely specialized cells devoted to AP transmission exclusively, plants are able to spread information systemically. This long distance communication is guaranteed by

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electrically coupled plasma membranes of excitable cells constituting conductive bundles. Apart from systemic transmission, AP-associated local signalling accomplished by changes in the subcellular localization of ions (Ca2+, H+, K+, Cl-) and perhaps membrane depolarization itself is equally important (252,275).

ACKNOWLEDGMENTS This work was supported by the Ministry of Science and Higher Education Grant No. N N301 464534.

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Chapter 2

BIOPHYSICAL PROPERTIES UNDERLYING HUMAN NERVE IMPULSE CONDUCTION Susanna B. Park and Matthew C. Kiernan* Prince of Wales Clinical School and Prince of Wales Medical Research Institute, University of New South Wales, Sydney, NSW 2031 Australia

ABSTRACT The molecular and structural organization of the axon has evolved to efficiently support the conduction of nerve impulses. Axonal membrane Na+ and K+ channels, in addition to other voltage-gated channels, ion pumps and exchangers play a critical role in the normal processes of saltatory conduction. The molecular and structural organization of the axon are key factors that determine membrane excitability, providing the basis for action potential generation and effective impulse transmission. A variety of research techniques have provided novel insights into human axonal structure and function at a molecular level, yielding an improved understanding of nerve function in both health and neurological disease states. An overview of the role of specialized axonal excitability techniques in understanding the consequences of abnormal membrane excitability in the clinical realm will be highlighted in this chapter. Through greater understanding of the contribution of axonal ion channel dysfunction and anomalous membrane excitability, it may be anticipated that novel disease-modifying strategies may be developed to be incorporated into the future treatment of neurological diseases.

ABBREVIATIONS AED AIP *

Anti-epileptic drugs Acute intermittent porphyria

Correspondence to: Professor Matthew C. Kiernan, Prince of Wales Medical Research Institute , Barker Street, Randwick, Sydney, NSW 2031, Ph: Int +61 2 9382 2422, Fax: Int +61 2 9382 2437 ; E-mail: [email protected]

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Susanna B. Park and Matthew C. Kiernan ALS ATP Ca2+ CNS DRG IH K+ Kir Kv Mg2+ MMN Na+ Nav NCS PNS TTX τSD

Amyotrophic lateral sclerosis Adenosine Tri-Phosphate Calcium Central nervous system Dorsal root ganglia Hyperpolarization-activated cation conductance Potassium Inwardly rectifying K+ channel Voltage-gated potassium channel Magnesium Multifocal motor neuropathy Sodium Voltage-gated sodium channel Nerve conduction studies Peripheral nervous system Tetrodotoxin Strength-duration time constant

INTRODUCTION The complex structural and molecular organization of the human axon has evolved to effectively support the conduction of nerve impulses. The precise organization of axonal domains into functional zones populated by voltage-gated ion channels, ion pumps and exchangers supports the rapid and accurate transmission of impulses. Since the seminal discoveries of the basis of membrane excitability by Hodgkin, Huxley and colleagues in the 1940s, the development of more recent in vitro and in vivo research techniques have provided important insights into axonal structure and function at a molecular level that have yielded an improved understanding of nerve function in both health and disease. The crucial role of axonal structure and function in determining membrane excitability has been confirmed by the identification of neurological disease states that arise due to aberrant excitability. Recently, the in vivo study of axonal excitability has provided insights into the role of disturbances in membrane potential and ion channel function that underlie neurological disorders. As such, the present chapter will present an overview of the complex structural organization and molecular diversity underlying neurotransmission, to illustrate how an improved understanding of these contributing factors will assist in the development of novel disease-modifying therapies in neurological disease.

IMPULSE COUNDUCTION The action potential consists of a rapid, stereotyped sequence of changes in membrane potential, driven by brief changes in ion flow across the cell membrane (Figure 1; Barnett and Larkman, 2007; Hille, 2001). Resting membrane potential is determined by the relative concentration of ions on each side of the membrane, creating an electrical potential difference

Biophysical Properties Underlying Human Nerve Impulse Conduction

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across the cell membrane. At rest, sodium (Na+) is highly concentrated outside the cell, with high concentrations of potassium (K+) inside. When the membrane potential is depolarized to threshold, resting membrane potential (typically -70 mV) rapidly reverses to +40 mV (Barnett and Larkman, 2007; Hille, 2001). The upstroke of the action potential is driven by an influx of positively charged Na+ ions into the cell. Accordingly, action potential generation can be entirely modeled by Na+ channel function alone (Schwarz et al., 1995) and K+ channel blockade does not affect the generation of action potentials in human axons (Chiu and Ritchie, 1980; Kocsis and Waxman, 1980). Following the upstroke of the action potential, repolarization towards baseline resting membrane potential occurs, driven by the inactivation of Na+ channels, with activation of K+ channels serving to stabilize the membrane potential (Schwarz et al., 1995). However, in human axons, K+ channels play little role in repolarization due to their slow kinetics of activation (Schwarz et al., 1995), instead contributing to the characteristic afterhyperpolarization created when the repolarized membrane potential overshoots the original membrane potential (Baker et al., 1987). The action potential is a regenerative, ‗all or none‘ response, so that once the threshold for excitation is reached, a complete action potential is inevitably produced, which travels down the axon, depolarizing adjacent areas (Hille, 2001).

Figure 1. Schematic diagram of the action potential, demonstrating stereotypical changes in membrane potential over time from a resting potential of -70mV to +40mV.

HISTORICAL PERSPECTIVE In 1939, the first intracellular recording of an action potential was obtained by Hodgkin and Huxley in giant squid axons, which identified reversal of the membrane potential during an action potential. The development of the voltage-clamp technique by Cole and Marmont made possible further studies into the measurement of ions across neural membranes (Cole,

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Susanna B. Park and Matthew C. Kiernan

1949; Marmont, 1949). Voltage-clamp techniques allowed membrane potential to be controlled and permitted the movement of ions to be measured as current (Hille, 2001). By 1952, Hodgkin, Huxley and colleagues had developed a model of impulse conduction using experimental data from voltage-clamp recordings and modeling studies. The Hodgkin and Huxley model described the electrical circuitry underlying the action potential as produced by rapid alterations in Na+ and K+ conductances and has provided the basis for further discoveries about the ionic conductances underlying impulse propagation (Hodgkin and Huxley, 1952; Piccolino, 2002). The development of more sophisticated ‗patch clamping‘ techniques by Neher and Sakmann in 1976 enabled a small ‗patch‘ of membrane to be electrically isolated so that currents could be recorded from single ion channels (Neher and Sakmann, 1976). The subsequent development of high resistance gigaohm seals facilitated vastly improved, low noise recordings (Hamill et al., 1981; Sigworth and Neher, 1980). As such, patch clamping techniques revolutionized electrophysiological research to facilitate the examination of the properties of neuronal and axonal ion channels. Progress in the fields of molecular biology and genetic analysis facilitated the identification of genes involved in producing ion channels. Molecular techniques enabled the cloning and genetic sequencing of the Na+ channel alpha subunit (Noda et al., 1984). Once ion channel recombinant cDNA sequences were identified, plasmid vector expression facilitated the functional expression of ion channels. Site-directed mutagenesis provided the ability to manipulate ion channel sequence to reveal structure-function relationships and explore channel binding sites and gating properties. In K+ channels, site-directed mutagenesis has revealed the specific sequence involved in movement of the K+ channel voltage sensor helix (Larsson et al., 1996). The development of immunohistochemistry techniques permitted the localization of ion channels and proteins in situ, relaying information about the molecular architecture of the axon. Further structural information was generated via X-ray crystallography, although ion channel structures were difficult to obtain due to large hydrophobic domains which precluded crystallization. Using X-ray crystallography, the high resolution structure of the K+ channel was ultimately characterized, revealing the structure of the channel pore and voltage sensor paddles on the exterior of the channel (Jiang et al., 2003). In the peripheral nervous system, the development of nerve conduction studies (NCS) and electromyography as a clinical tool permitted the examination of pathology in vivo. While electrical stimulation of nerves and muscles has a long history, it was not until the late 1940s that electrodiagnostic techniques became prominent (Bonner and Devleschoward, 1995; Dawson and Scott, 1949; Hodes et al., 1948; Weddell et al., 1944). NCS now provide standard clinical assessment of peripheral nerve function, providing information about compound action potential amplitude, latency and thereby conduction velocity. While this information is important in the differentiation of axonal versus demyelinating pathologies, it is relatively non-specific in relation to the mechanisms underlying the development of pathology (Kiernan et al., 2005a). The development of threshold tracking techniques to evaluate the excitability of axons using subthreshold stimulation has provided information regarding axonal ion channel function and membrane potential in vivo (Bostock et al., 1998; Burke et al., 2001; Krishnan et al., 2009). While the assessment of excitability properties, in particular chronaxie and rheobase, had been undertaken since the early 1900s, it was not widespread (Kiernan et al., 2005a; Lapicque, 1909; Weiss, 1901). In 1970, Joseph Bergmans isolated single motor units via surface stimulation and measured threshold changes following


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different experimental maneuvers to alter membrane potential (Bergmans, 1970). While isolating single units is difficult and time consuming, threshold tracking techniques enabled groups of axons of similar threshold to be recorded by ‗tracking‘ the stimulus current required to generate the compound potential (Bostock et al., 1998). With the advent of specialized tracking software and semi-automated protocols, excitability studies have now become a more accessible technique to examine membrane potential and ion channels in vivo. The combination of these techniques has facilitated understanding of the biophysical properties underlying impulse conduction, in particular the structure and function of ion channels, pumps and exchangers in the axonal membrane.

ION CHANNEL STRUCTURE AND FUNCTION Voltage-gated Na+ channels are the most important contributors to neurotransmission. Nine mammalian voltage-gated Na+ channel α-isoforms have been cloned and functionally expressed (see Table 1), sharing considerable similarities in structure, with at least 50% conserved amino acid sequence (Catterall et al., 2005; Goldin et al., 2000; Krafte and Bannon, 2008). A 10th isoform, Nax (genes SCN6A and SCN7A) shares considerable homology with Nav1 class channels, although it is not voltage dependent, being instead activated by changes in Na+ concentration (Hiyama et al., 2002; Watanabe et al., 2002). Nax is expressed in dorsal root ganglia (DRG), trigeminal ganglia, brain circumventricular organs and in non-neuronal visceral tissues and appears to play a role in modulating extracellular Na+ levels (Hiyama et al., 2002; Watanabe et al., 2002). Typically, Na+ channel structure consists of one α subunit of 260 kDa in size in association with auxiliary β subunits (Beneski and Catterall, 1980). Studies in the 1980s revealed the structural composition of the voltage-gated Na+ channel (Noda et al., 1984) with four homologous transmembrane protein domains (I - IV), each domain with six membrane spanning regions (α-helicies S1 – S6) (Catterall et al., 2005). Although the Na+ channel structure has yet to be confirmed by high resolution X-ray crystallography, the 3D structure of the Na+ channel reveals that it is bell-shaped with 4 inlets leading to a central pore (Sato et al., 2001). The S5 and S6 segments of each domain form the Na+ selective pore for ion conduction (Yu and Catterall, 2003). The voltage sensitivity of Na+ channels has been linked to the S4 transmembrane segment, with its helical structure composed of positively charged amino acids with hydrophobic residues (Catterall, 2000; Stuhmer et al., 1989). The different operational states of the Na+ channels are dependent on membrane potential, comprising open, closed and inactivated states (Figure 2). Following sustained depolarization, Na+ channels inactivate, ceasing Na+ current flow. The mechanism of Na+ channel inactivation relates to an inactivation gate located between domains III and IV of the alpha subunit. An intracellular loop formed by the IFM (Ile-Phe-Met) motif located between S3 and S4 domains blocks the flow of the pore in response to sustained depolarization (Catterall et al., 2005; Rohl et al., 1999). The nine voltage-gated Na+ channel α-isoforms are differentiated by their localization, kinetic properties, genetic basis and toxin sensitivities (Table 1; Catterall et al., 2005; Goldin et al., 2000; Krafte and Bannon, 2008).

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Figure 2. Operational states of voltage-gated Na+ channels, with Na+ ions depicted in red. In the closed state, current is not able to flow through the channel. However, depolarization opens the channel enabling Na+ ions to flow through (open state). Following sustained depolarization, channels inactivate, produced by the movement of an intracellular inactivation. Following sustained depolarization, channels inactivate and become refractory, unable to open and pass Na+ ions through. Inactivation is produced by the movement of an intracellular inactivation gate (depicted in blue).

In terms of channel kinetics, Nav 1.1 is slower to activate than Nav1.2, but β subunit expression modulates kinetics to produce a fast, transient rapidly inactivating inward Na+ current from both isoforms (Smith and Goldin, 1998; Xie et al., 2001). Subunit Nav 1.3 demonstrates rapid recovery from inactivation and slow inactivation kinetics, facilitating rapid repriming and the production of ramp currents in response to slow depolarization, which may enable the generation of ectopic activity (Chen et al., 2000; Cummins et al., 2001; Krafte and Bannon, 2008). Nav1.6 displays similar kinetic properties to Nav1.2 and Nav1.3 isoforms (Baker and Bostock, 1997; Burbidge et al., 2002; Chen et al., 2008; Tzoumaka et al., 2000; Whitaker et al., 2001), although inactivation occurs at more positive membrane potentials which may predispose to high frequency repetitive firing (Chen et al., 2008; Rush et al., 2005). Nav 1.7 displays slow kinetics in both activation and inactivation, and is active during slow depolarization when other channel isoforms are inactivated (Elliott and Elliott, 1993). Nav1.8 is inactivated at relatively more depolarized membrane potentials than other isoforms and displays slow inactivation but rapid repriming kinetics (Elliott and Elliott, 1993; Roy and Narahashi, 1992; Sangameswaran et al., 1996). Nav1.8 is important in electrogenesis in unmyelinated neurons, contributing over 80% of the inward current in C –type unmyelinated neurons (Renganathan et al., 2001). Nav1.9 displays a hyperpolarized voltage of activation suggesting that it may be activated at rest and lead to a sustained current (Cummins et al., 1999; Sleeper et al., 2000). Auxillary β subunits have important roles in modulating channel kinetics and gating properties (Catterall, 2000). Four β subunits have been identified (Catterall et al., 2005), each with a transmembrane region consisting of an immunoglobulin-like extracellular domain and small intracellular domain (Isom, 2000; Isom and Catterall, 1996). The modulatory role of β subunits is important - β1 subunits, when co-expressed with Na+ channel α subunits, act to increase the rate of channel inactivation and change the voltage dependence of inactivation (McCormick et al., 1999). Mutations in β subunits are also associated with neurological


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disease, with SCN1B mutations producing forms of epilepsy (Kiernan et al., 2005c; Wallace et al., 1998). There are two main types of Na+ current distinguishable by their kinetics of activation and inactivation. While transient Na+ conductances contribute 98% of total Na+ current and are responsible for action potential generation (Burke et al., 2001; Crill, 1996; Hille, 2001), persistent Na+ conductances have an important influence on membrane excitability. Persistent Na+ conductances have slower gating kinetics and are active at near-threshold membrane potentials (Crill, 1996), demonstrating incomplete inactivation (Baker and Bostock, 1998). Although only representing a fraction of the total Na+ current, persisting Na+ conductances contribute to regulation of excitability due to these factors. Persistent Na+ conductances have been identified in a range of central nervous system (CNS) regions (Kiss, 2008) and also in DRG neurons and peripheral nerve (Baker and Bostock, 1997; Bostock and Rothwell, 1997; Kiernan et al., 2003). It remains unclear if the persistent current arises from a different population of channels to the transient current. However, some studies have suggested that both transient and persistent currents may derive from the same population of channels, demonstrating identical properties of voltage dependence (Taddese and Bean, 2002). Potassium (K+) channels are diverse, with over 100 subunits identified to date (Coetzee et al., 1999), comprising over 75 genes (Jenkinson, 2006). The main families of K+ channels include voltage-gated K+ channels, Ca2+ activated K+ channels, leak K+ channels (tandem pore), and inwardly rectifying K+ channels, grouped according to structure and function (Coetzee et al., 1999; Jenkinson, 2006). Inward rectifier K+ channels have 2 transmembrane domains, while voltage-gated K+ channels and Ca2+ activated K+ channels have 6 transmembrane domains. X-ray crystallography has confirmed the complete voltage-gated K+ channel structure, revealing a tetrameric structure around a central pore composed of hydrophobic residues combined with a similar S4 voltage sensor structure to Na+ channels (Doyle et al., 1998). The transmembrane pore has an extracellular ion selectivity filter, widening to an aqueous pore surrounded by helical hinged voltage sensor paddles (Larsson et al., 1996; Jiang et al., 2003).

Figure 3. Distribution of K+ channels along the axonal membrane with fast K+ channels depicted in black and slow K+ channels depicted in white. Fast K+ channels are clustered at high density in the juxtaparanode (JXPN; shown in orange) adjacent to the paranode (PN). Slow K+ channels are found at the nodes of Ranvier (N; depicted in red) at higher density than at the internode (INT).

Voltage-gated potassium channels form the largest family of K+ channels with 12 subfamilies (Gutman et al., 2005). Voltage-gated K+ channels are involved in modulating neuronal excitability through membrane stabilization, and by controlling repetitive action potential firing (Hille, 2001). There are at least five voltage-gated K+ channels in human

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myelinated nerve, with fast, slow and intermediate activation kinetics (Reid et al., 1999). However, functionally the main types of voltage-gated K+ channel with major impact on nerve function are divided into those with slow and fast kinetics. Fast K+ currents display fast kinetics of activation and inactivation. Fast K+ channels have been linked to the voltage-gated K+ channel isoforms Kv1.1, Kv1.2, and the β subunit Kv β2 (Rasband et al., 1998; Wang et al., 1993) which are excluded from nodal regions but located in high density in the juxtaparanode (Figure 3; Rasband and Trimmer, 2001; Rhodes et al., 1996; Roper and Schwarz, 1989; Wang et al., 1993). Fast K+ currents act to dampen excitability following an action potential to prevent re-excitation and contribute to maintaining resting membrane potential (Chiu and Ritchie, 1984; Waxman and Ritchie, 1993). In classical models of squid axons, fast K+ currents are important in the repolarization of the action potential, producing the downstroke of the action potential, while in human axons, Na+ channel kinetics alone are sufficient to produce repolarization (Schwarz et al., 1995). Gene deletion of Kv1.1 produces epilepsy in mice (Smart et al., 1998) and missense mutations in Kv1.1 in humans produce episodic ataxia and myokymia (Brown and Adams, 1980; Tomlinson et al., 2009). During acute demyelination involving the central or peripheral nervous system, the structural boundaries of the node become disrupted, leading to diffusion of Kv channels away from the juxtaparanode and affecting impulse conduction (Rasband et al., 1998). Slow K+ channels are located at the nodes of Ranvier at much higher density than the internode (Figure 3), with 35% of slow K+ channels activated at resting membrane potential (Devaux et al., 2004; Roper and Schwarz, 1989). However the large size of the internode means that slow internodal K+ channels still make a significant contribution to resting membrane potential. Slow K+ currents have been linked to KCNQ channels, with KCNQ2 channels strongly labeled at the nodes of Ranvier in large fibers in rat sciatic nerve (Schwarz et al., 2006). Blockade of the slow K+ current increases axonal excitability, removing the contributions of spike frequency adaptation (Schwarz et al., 2006). Similarly, the M-current is a classical K+ current with slow activation and produces a sustained current without inactivation which is involved in determining subthreshold excitability and also linked to KCNQ channels (Brown and Adams, 1980; Marrion, 1997; Wang et al., 1998). Slow K+ currents do not contribute to repolarization during the generation of a single impulse due to their slow kinetics. The slow K+ current produces outward rectification which limits ectopic firing during depolarization and is responsible for the reduction in excitability following a short train of impulses (Baker et al., 1987). There are a number of other K+ channel families which contribute to modulating membrane excitability. Inwardly rectifying K+ channels (Kir) have seven subfamilies (Kubo et al., 2005), demonstrating tetrameric structure with two transmembrane spanning segments (Kuo et al., 2003; Nishida and MacKinnon, 2002; Pegan et al., 2005). Kir channels in the nervous system play a regulatory role, modulating membrane excitability. Kir channels produce inward rectification of the membrane potential, carrying an inward K+ current even against a concentration gradient (Lu, 2004). Kir channels are not voltage-dependent per se but depend on the difference between the membrane potential and the K+ gradient (Lu, 2004). During depolarization, the channel pore is blocked by Mg2+, polyamines and other ions, which are removed by hyperpolarization to enable the flow of K+ ions (Bichet et al., 2003). The hyperpolarization-activated cation conductance (IH) is a mixed cation conductance of Na+ and K+ ions, activated by membrane hyperpolarization below -50 mV (Robinson and


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Siegelbaum, 2003). Inwardly rectifying IH has slow and complex gating properties which can vary depending on cell type, with maximal activation at -110 mV (Pape, 1996). Because of these unusual kinetic properties, up to 15% of IH channels are active at resting membrane potential, giving IH an important role in determining and stabilizing resting membrane potential (Pape, 1996; Robinson and Siegelbaum, 2003). Four HCN (Hyperpolarization activated cyclic nucleotide sensitive cation non-selective channels) genes have been identified and are expressed in the heart, brain, peripheral nervous system (PNS) and other sites (Bois et al., 2007). The sodium/potassium ATPase (Na+/K+ pump) is vital to support maintenance of axonal ion gradients and thereby assure continuous nerve function. Ubiquitously expressed across axonal membranes, the Na+/K+ pump functions as both an enzyme and energy dependent ion pump (Dempski et al., 2009). The ion ratio of the pump is fixed and voltage-independent: three Na+ ions are extruded to every two K+ ions imported in to the cell, yielding a net positive electrogenic charge (Rakowski et al., 1989). The pump is energy dependent and requires the catalysis of ATP to exchange ions. The Na+/K+ pump has widespread localization on the axonal membrane, and myelin sheath (Alberti et al., 2007) and has been identified in the nodes of Ranvier (Vorbrodt et al., 1982) and internode (Mata et al., 1991). X-ray crystallography has been utilized to identify Na+/K+ pump structure (Morth et al., 2007; Shinoda et al., 2009; Toyoshima et al., 2000) and has confirmed that the pump is formed as a heterodimer of α and β subunits (Rakowski et al., 1997). The pump exists in two conformational states – E1 and E2 (Figure 4). In E1, ion binding sites are available to cytoplasmic ions (i.e Na+ ions). Ion binding triggers phosphorylation which occludes the ions from the cytoplasm, until conformation changes to the E2 state and Na+ ions are released extracellularly, permitting extracellular K+ ions to bind and reverse the process (Gadsby, 2007).

Figure 4. Conformational states of the axonal Na+/K+ pump. The E1 state has the binding site accessible to intracellular Na+ ions (blue circles) which may trigger phosphorylation via ATP. Phosphorylation induces conformational change to E2 state, releasing 3 Na+ ions extracellularly and allowing binding of 2 K+ ions (red circles).

Activity of the Na+/K+ pump is an important contributor to membrane potential (Morita et al., 1993). The pump is also crucial to the maintenance of low intracellular Na+ concentration (Thomas, 1972), with inhibition of the pump leading to increased intracellular Na+ concentration, which has serious adverse consequences on axonal function. Over-activity of

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the Na+/K+ pump induces hyperpolarization, as occurs following prolonged tetanic stimulation (Morita et al., 1993) or impulse trains (Bostock and Grafe, 1985). Intracellular Ca2+ levels are maintained in a very low range in the cytoplasm to protect against activation of the multitude of Ca2+-associated systems (Steffensen and Stys, 1996). Transport mechanisms are utilized to extrude Ca2+ from the cell, via the Na+- Ca2+ exchanger. This exchanger utilizes the relative ionic concentration gradients to transport 3 Na+ ions into the cell for each Ca2+ ion released, and is independent of energy expenditure (Rasgado-Flores et al., 1989). The exchanger has been localized to neurons, axons and glial cells via immuno-fluorescence (Steffensen and Stys, 1996; Steffensen et al., 1997). Excess Ca2+ accumulation is a common final mechanism of nerve degeneration and damage (LoPachin and Lehning, 1997). Under normal conditions, the exchanger will extrude Ca2+ from the cell, utilizing the Na+ gradient, but in conditions of prolonged membrane depolarization or alterations in the Na+ concentration the exchanger may reverse in function, resulting in axonal damage and cell death (Craner et al., 2004; LoPachin and Lehning, 1997; Stys et al., 1992).

STRUCTURAL AND MOLECULAR ORGANIZATION OF THE AXON The principles of structural organization are similar in CNS and PNS axons (Arroyo and Scherer, 2000). The myelin sheath is crucial for the fast propagation of action potentials in both the PNS and CNS. Composed of lamellar membranes intersected by unmyelinated nodes of Ranvier, the myelin sheath enables salutatory conduction of action potentials from node to node (Hille, 2001). Formed by glial cells (oligodendrocytes in the CNS and Schwann cells in PNS), myelin effectively insulates the axon, reducing membrane capacitance and thereby current leak (Poliak and Peles, 2003; Salzer et al., 2008). In the PNS, each Schwann cell produces one myelinated segment of 300 to 2000 µm in length, divided by unmyelinated nodes of Ranvier of 1 µm length (Reynolds and Heath, 1995; Rydmark and Berthold, 1983). Schwann cells contact the axolemma with an inner membrane and the basal lamina with an outer membrane, providing further stability to maintain axonal structure (Salzer et al., 2008). The Schwann cell also projects microvilli enriched with a range of matrix proteins which directly contact the nodes of Ranvier to provide the nodal microenvironment in the PNS (Peters et al., 1991; Salzer et al., 2008). In the CNS, the equivalent oligodendrocytes myelinate multiple axonal processes (Arroyo and Scherer, 2000). There are also differences in the structure and protein composition of myelin in central and peripheral axons, with the major PNS myelin protein component of protein zero compared to the CNS proteolipid protein (Arroyo and Scherer, 2000; Schiff and Rosenbluth, 1995). Despite the differences between PNS and CNS myelin structure and protein composition, axonal structure is remarkably conserved between central and peripheral axons, delineated into nodal, paranodal, juxtaparanodal and internodal regions (Figure 5; Arroyo and Scherer, 2000). Nodes of Ranvier represent, physically, the smallest contributor to the axonal landscape, measuring only 1 µm wide (Reynolds and Heath, 1995; Rydmark and Berthold, 1983). However, the nodes of Ranvier play a critical role in neurotransmission, containing high densities of voltage-gated Na+ channels estimated up to 1400 channels per um2 (Chiu and Ritchie, 1980; Ritchie and Chiu, 1981; Ritchie and Rogart, 1977).


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The internodal region (between nodes of Ranvier covered by the myelin sheath) makes up the largest total axonal area, up to 1 mm per internode, representing 99.9% of all axonal membrane (Abe et al., 2004; Burke et al., 2001; Salzer et al., 2008). The internode has a low Na+ channel density, less than 25 per um2 (Ritchie and Rogart, 1977). Within the internode, the paranodal region is located directly adjacent to the node and contains septate-like axoglial junctions providing a tight barrier against ion diffusion (Einheber et al., 1997). These paranodal axoglial junctions form the attachment of the myelin sheath to the nodal membrane and are important contributors to define the structure of the axonal nodal region via paranodal myelin attachment loops (Rosenbluth, 2009). The juxtaparanode extends 10-15 μm from the paranode into the internode and is involved in the control of membrane potential with high densities of K+ channels, chiefly Kv1.1, Kv 1.2 and Kvβ2 (Rasband et al., 1998; Rosenbluth, 1976; Salzer et al., 2008; Stolinski et al., 1985; Wang et al., 1993). Nodes of Ranvier contain a complex arrangement of ion channels (Nav, Kv), cell adhesion molecules and cytoskeletal proteins (Schafer and Rasband, 2006). It has long been proposed that voltage-gated Na+ channels were clustered at high density at the nodes in myelinated axons (Dugandzija-Novakovic et al., 1995; Ritchie and Rogart, 1977; Rosenbluth, 1976). The molecular identity of nodal Na+ channels has now been determined to be primarily composed of Nav1.6 subunits, although there are several other isoforms of Na+ channel at the node (Boiko et al., 2001; Caldwell et al., 2000). Na+ channels are anchored at the nodes by a complex of proteins including ankyrin G, neurofascin (NF)-186 and Nr-CAM (Davis and Bennett, 1994; Davis et al., 1996; Kordeli et al., 1990; Srinivasan et al., 1988). In peripheral nodes, the Schwann cell protein gliomedin initiates nodal assembly via binding to the cell adhesion molecule NF-186 (Eshed et al., 2005). Accordingly, NF-186 and NrCAM are the first molecules found at developing nodes of Ranvier (Lambert et al., 1997), and act to bind to ankyrin G proteins which anchor voltage-gated Na+ channels at the node (Arroyo and Scherer, 2000). The paranodal region contains proteins contactin and Caspr with glial NF-155 (Peles et al., 1997; Tait et al., 2000) which help structure the paranodal junction.

Figure 5. Structure of the axon, depicting the node of Ranvier (N; red) with high density of Na+ channels, the paranode (PN; blue) located adjacent to the node, with paranodal axoglial junctions connecting the myelin to axon, the adjacent juxtaparanode (JXPN; orange) and the internode (INT; white) representing 99.9% of the axon under the myelin sheath.

ACTION POTENTIAL INITIATION The axonal initial segment was initially proposed as the site of action potential initiation in the CNS in the 1950s (Coombs et al., 1957; Fatt, 1957; Fuortes et al., 1957). Sophisticated patch clamping techniques have now enabled this hypothesis to be more directly examined,

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by simultaneous recording of action potentials from axonal and somatic sites, demonstrating action potential initiation occurring in the axon (Stuart and Hausser, 1994; Stuart and Sakmann, 1994). Utilizing voltage sensitive dyes, further studies demonstrated that action potential initiation occurs approximately 35 µm from the axon hillock in layer 5 pyramidal neurons (Palmer and Stuart, 2006). However in other cell types, such as Purkinje cerebellar neurons, initiation seems to occur at the first node of Ranvier (Clark et al., 2005). The mechanisms underlying axonal potential initiation in the initial segment have been linked to an increased density of Na+ channels, providing a lower threshold for action potential generation relative to the cell body or dendritic tree (Hille, 2001; Mainen et al., 1995; Rapp et al., 1996). Accordingly, antibody studies have revealed that the initial segment has a high density of Na+ channel staining (Boiko et al., 2003; Inda et al., 2006; Wollner and Catterall, 1986). However, estimates of Na+ channel density from patch clamping studies indicated that Na+ currents were similar in the soma and initial segment (Colbert and Johnston, 1996), suggesting that different biophysical properties of Na+ channels in the axonal initial segment may instead underlie the selection of the site of action potential initiation. Accordingly, Na+ channels in the axonal initial segment display differential voltage dependence of activation from somatic channels (Colbert and Pan, 2002). A recent comprehensive study in rat cortical pyramidal neurons utilized a combined approach of patch-clamping, antibody staining, Na+ imaging and modeling to examine the role of the Na+ channels and the axonal initial segment in action potential initiation (Kole et al., 2008), elegantly demonstrating a 50-fold increased density of Na+ channels in the axonal initial segment compared to the soma and proximal dendrites, and suggesting that increased density of Na+ channels in the initial segment underlies the site of action potential generation. The Na+ channel isoforms Nav 1.1, Nav 1.2 and Nav 1.6 have all been identified in the axonal initial segment (Ogawa and Rasband, 2008). Nav1.6 has been identified as the primary isoform due to electrophysiological properties including the voltage dependence of activation (Kole et al., 2008). A number of K+ channel types are also present at the initial segment, which may have a role in controlling excitability (Ogawa and Rasband, 2008), particularly in determining action potential duration (Kole et al., 2007). The molecular development of a functional initial segment is dependent on ankyrin G protein expression (Hedstrom and Rasband, 2006), but does not require glial support as at the nodes of Ranvier (Schafer and Rasband, 2006). The understanding of the axonal initial segment is evolving as a dynamic structure where transcriptional changes in protein expression may significantly alter excitability and impulse conduction (Ogawa and Rasband, 2008).

DETERMINANTS OF MEMBRANE POTENTIAL Axonal excitability properties are diverse, reflecting the activity of multiple conductances (see reviews by Bostock et al., 1998; Burke et al., 2001; Kiernan et al., 2005a; Krishnan et al., 2008b; Krishnan et al., 2009; Lin et al., 2006). Resting membrane potential is primarily determined by the contributions of active ionic conductances near rest and the activity of the Na+/K+ pump (Burke et al., 2001). Axonal excitability techniques have been developed in order to probe membrane potential and ion channel function in vivo, via a variety of experimental procedures.


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Strength-duration properties describe the relationship between stimulus strength and stimulus duration in producing a compound response (Figure 6A). As the stimulus duration becomes longer, reduced stimulus strength is required to produce a response. Classically, the lowest stimulus required to produce a response (for a stimulus of infinite width) is termed rheobase and chronaxie reflects the stimulus duration corresponding to double the rheobasic current. Strength-duration time constant (τsd) is an apparent membrane time constant which equates to chronaxie according to Weiss‘ law, representing the relationship between stimulus intensity and width (Bostock, 1983; Bostock and Rothwell, 1997; Weiss, 1901). The demonstration of a linear relationship between stimulus duration and stimulus charge (Bostock, 1983; Mogyoros et al., 1996) confirmed the predictions of Weiss‘ law (1901). τsd relates to nodal properties, reflecting persistent Na+ conductances which are active near threshold (Bostock and Rothwell, 1997). Sensory axons display a longer τsd than motor axons (Bostock and Rothwell, 1997; Mogyoros et al., 1996), reflecting differences in the expression of persistent Na+ currents. Accordingly, it has been estimated that persistent Na+ current makes up 2.5% of the total Na+ current in sensory axons compared to 1% in motor axons, reflecting the greater susceptibility of sensory axons towards ectopic activity as less driving current is required to produce activity (Bostock and Rothwell, 1997; Mogyoros et al., 1996).

Figure 6. A) Strength-duration time constant demonstrated as the negative intercept of the linear relationship between threshold charge and stimulus width, equating to chronaxie as per Weiss‘ law. B) Recovery cycle of excitability, characteristic sequence of excitability changes following an impulse, with reduced excitability (refractoriness) up to 3 ms interstimulus interval, followed by a period of increased excitability (superexcitability) peaking at 5-7 ms and subsequently reduced excitability (subexcitability). C) Threshold electrotonus, depicting waveforms in response to prolonged subthreshold polarizing current (100ms), with hyperpolarizing direction plotted in the bottom quadrant and depolarizing direction plotted in the upper quadrant.

Following impulse conduction, there are significant changes in excitability which occur in a stereotypical fashion (Figure 6B). Due to the kinetics of transient nodal Na+ channels following an action potential, the axon becomes refractory for 0.5 – 1 ms. During this period the axon is unable to generate subsequent action potentials (Burke et al., 2001; Hodgkin and Huxley, 1952). For a further 3 ms, axons become relatively refractory and less excitable as voltage-gated Na+ channels recover from their inactivated state (Bergmans, 1968; Kimura et al., 1978). However, the passive capacitative charge on the internodal membrane following impulse conduction (Baker et al., 1987; Barrett and Barrett, 1982) produces a depolarizing afterpotential, increasing membrane excitability (a period termed superexcitability) peaking at

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5-7 ms after the impulse (Burke et al., 2001; Kiernan et al., 1996; Lin et al., 2000). Due to the slow kinetics of slow K+ channels activated during impulse generation, following the superexcitability period, membrane excitability again becomes reduced (Baker et al., 1987; Lin et al., 2000). This characteristic pattern of excitability fluctuations following an action potential is termed the recovery cycle of excitability (Burke et al., 2001; Kiernan et al., 1996). Threshold electrotonus utilizes long subthreshold polarizing currents to assess the properties of the internode, which accounts for 99.9% of the axonal membrane (Baker, 2000; Burke et al., 2001). Threshold electrotonus curves portray a complex sequence of excitability changes reflecting underlying changes in membrane potential that develops with membrane polarization (Figure 6C). The initial fast deflections of threshold electrotonus are proportional to the applied current in both depolarizing and hyperpolarizing directions, reflecting polarization of the nodal membrane. Further changes in the waveform result from modulation of internodal conductances produced by the slow spread of current into the internode (Baker et al., 1987; Bostock et al., 1998; Burke et al., 2001). In response to depolarizing current, slow activation of K+ channels produces a rectification of the threshold towards baseline. When the depolarizing current ceases, threshold quickly returns to baseline before ‗overshooting‘ and subsequently returning to baseline, due to slow K+ channel deactivation and repolarization of the internode (Bostock and Rothwell, 1997; Burke et al., 2001). Hyperpolarizing current produces an equivalent waveform morphology, but with larger threshold change, as polarization is not limited by activation of a slow K+ conductance as in the depolarizing direction (Bostock et al., 1998; Burke et al., 2001). Hyperpolarizing threshold electrotonus demonstrates inward rectification towards threshold produced by slow activation of IH by hyperpolarization (Bostock et al., 1998; Pape, 1996). When the current is ceased, threshold similarly undershoots baseline levels due to slow IH kinetics of deactivation and the reactivation of slow K+ channels (Burke et al., 2001). The excitability parameter current-threshold relationship also reveals accommodation to polarization with outward rectification in response to depolarization produced by K+ channel activation (Kiernan and Bostock, 2000; Lin et al., 2006) and inward rectification in response to hyperpolarization due to IH activation.

EXCITABILITY STUDIES IN THE CLINICAL REALM The role of axonal ion channels, pumps and exchangers in maintaining nerve function may be reflected by the disease states in which abnormalities in axonal function have been identified. Axonal excitability studies have been utilized in the clinical setting to provide insights into the role of ion channel dysfunction and membrane potential disturbances in producing neurological disease states.

Metabolic Neuropathy Nerve dysfunction may be induced by disorders of metabolism, most commonly impairment of glucose metabolism or kidney function. Peripheral nerve damage is a common consequence of impaired glucose tolerance and diabetes mellitus, often presenting as a


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sensorimotor polyneuropathy (Tracy and Dyck, 2008). Peripheral nerve complications of noninsulin dependent diabetes mellitus are very common, with objective signs of neuropathy in 59% of patients in large population-based studies (Dyck et al., 1993). The severity of neuropathic symptoms appears closely aligned to the duration of exposure to hyperglycemia (Dyck et al., 1993). The effects of hyperglycemia on peripheral nerve function have been linked to a combination of vascular and metabolic factors (Obrosova, 2009). Hyperglycemia activates the polyol pathway, leading to oxidative stress and subsequent nerve damage (Chung et al., 2003; Greene et al., 1999). Abnormal axonal excitability in diabetic neuropathy has long been identified (Horn et al., 1996). In established diabetic neuropathy, there are a number of abnormal excitability findings in motor axons: reduced strength-duration time constant, ‗fanned in‘ threshold electrotonus, and reduced refractoriness (Kaji et al., 2000; Kitano et al., 2004; Krishnan and Kiernan, 2005; Krishnan et al., 2008a). This constellation of findings has been attributed to axonal depolarization due to Na+/K+ pump dysfunction combined with reduction in nodal Na+ gradient. Metabolic changes in the activity of the Na+/K+ pump would reduce pump function, leading to depolarization of membrane potential and increased intra-axonal Na+ levels (Kiernan and Bostock, 2000; Lin et al., 2002). Reductions in Na+/K+ pump activity have been linked to diabetic neuropathy in animal models (Greene et al., 1987). Accordingly, axonal excitability studies have established that depolarization of motor axons occurs in established diabetic neuropathy (Kitano et al., 2004; Krishnan and Kiernan, 2005). Experimental studies have demonstrated decreased Na+ permeability and gradient at the nodes of Ranvier (Brismar et al., 1987), which may underlie changes in recovery cycle parameters (Krishnan and Kiernan, 2005). Measures of Na+ channel function improve with insulin treatment (Kitano et al., 2004), suggesting that reduced Na+ nodal driving current is amenable to treatment. Aldose reductase therapy also improved measures of nerve excitability, with increased SDTC indicating normalized persistent Na+ channel activity (Misawa et al., 2006). Accordingly, the degree of hyperglycemia has also been found to influence abnormalities in strength duration time constant (Misawa et al., 2005). Further studies of Na+/K+ pump function in diabetic neuropathy have utilized maximal voluntary contraction to produce activity-dependent hyperpolarization and subsequent Na+/K+ pump over-activation (Krishnan et al., 2008a). The Na+/K+ pump becomes over-activated following activity to reduce the high levels of intra-axonal Na+ that accumulate. As the Na+/K+ pump exchanges three Na+ ions for every two K+ ions, over-activation of the pump tends to result in axonal hyperpolarization with an excess of positive charge removed from the axon (Rakowski et al., 1989). Patients with diabetic neuropathy demonstrate reduced axonal hyperpolarization following maximal voluntary contraction compared to controls, suggestive of impairment in Na+/K+ pump function (Krishnan et al., 2008a). Uremic neuropathy is the second most common form of metabolic neuropathy, occurring in 90% of end-stage kidney disease patients requiring dialysis (Krishnan and Kiernan, 2009; Laaksonen et al., 2002), resulting in a length-dependent polyneuropathy with sensorimotor involvement (Krishnan and Kiernan, 2007; Krishnan and Kiernan, 2009). Chronic renal impairment often coexists with diabetes mellitus, further complicating the clinical picture. Axonal excitability studies have permitted the examination of the effects of toxic metabolites on nerve function in vivo in this clinical setting. In patients with chronic renal failure, axonal excitability measurements revealed significant axonal depolarization which was corrected by

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hemodialysis (Kiernan et al., 2002b; Krishnan et al., 2005b). Subsequent studies demonstrated that axonal depolarization was widespread in chronic renal failure, in upper (Kiernan et al., 2002b) and lower limb motor axons (Krishnan et al., 2005b) and in sensory axons (Krishnan et al., 2006b). Parameters were highly correlated with serum K+ levels, suggesting that hyperkalemia was responsible for uremic neuropathy (Bostock et al., 2004; Kiernan et al., 2002b). Previously, it was hypothesized that ‗middle molecules‘ which could not be effectively removed by hemodialysis membranes were responsible for axonal toxicity in renal disease (Vanholder et al., 1994). However, these more recent excitability findings demonstrated that K+ was the likely agent responsible for peripheral nerve dysfunction in chronic renal impairment; and that serum K+ levels should be normalized as much as possible to reduce the risk of neuropathy in the kidney disease population. Another group of metabolic disorders, the porphyrias are rare genetic disorders of heme metabolism, resulting from mutations causing enzyme deficiencies in the synthesis of porphyrin metabolites and producing a constellation of symptoms including abdominal pain, psychosis, neuropathy, and skin symptoms (Albers and Fink, 2004). Porphyric neuropathy develops into severe motor and co-existent autonomic neuropathy in 10 – 40% of patients, although the mechanisms underlying neuropathy remain unclear (Albers and Fink, 2004). Acute Intermittent Porphyria (AIP) is most common form of genetic porphyria, resulting from porphobilinogen deaminase enzyme deficiency (Bylesjo et al., 2009; Deybach and Puy, 2003). In a large cohort of AIP patients, axonal excitability studies demonstrated changes in motor axonal function suggestive of reduction in the inwardly rectifying cation conductance (IH) (Lin et al., 2008). Importantly, these changes occurred in AIP patients without clinical or electrophysiological evidence of porphyric neuropathy, suggesting that deficits in IH may represent an early sign of metabolic deficiency. In acute porphyric neuropathy, the axonal membrane was depolarized, suggesting that severe energy derangement could produce Na+/K+ pump dysfunction and subsequent membrane depolarization.

Toxic Neuropathy Neurotoxic marine poisoning produces a large spectrum of neurological and gastrointestinal symptoms. Ciguatera is the most common form of marine poisoning, arising from ciguatoxins which accumulate through the food chain. Ciguatoxins act via Na+ channels by shifting the voltage dependence of activation towards more hyperpolarized potentials (Mattei et al., 1999). Ciguatera poisoning produces a range of symptoms including gastrointestinal problems and neurological symptoms including paresthesia, allodynia, and paradoxical temperature reversal (Cameron and Capra, 1993; Isbister and Kiernan, 2005). While these symptoms are acute and occur within 48 hours of intoxication, chronic symptoms can persist intermittently when triggered by certain substances or activities (i.e. alcohol, exercise, food). Axonal excitability studies in patients with chronic ciguatera sensitization revealed normal ion channel function (Vucic and Kiernan, 2008), suggesting that there is no persistent defects in axonal Na+ channel function in chronic ciguatera poisoning (Cameron et al., 1991). Puffer fish poisoning is the most common cause of death from marine intoxication (Isbister et al., 2002), resulting from high concentrations of the potent Na+ channel blocking agent tetrodotoxin (TTX). Puffer fish poisoning results in numbness and paresthesia


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progressing to weakness, paralysis and respiratory failure. Axonal excitability studies performed in patients suffering acute intoxication with TTX revealed significant abnormalities in excitability, with reduced strength-duration time constant and refractoriness related to Na+ channel blockade; and reductions in superexcitability and threshold electrotonus parameters related to alteration of the relationship between membrane potential and threshold (Kiernan et al., 2005b). Mathematical modelling of these results established that these effects could be reproduced by a 50% reduction in Na+ current, demonstrating for the first time a characteristic pattern of abnormalities in axonal excitability caused by blockade of Na+ channels (Kiernan et al., 2005b). Toxic neuropathy may also arise as a side effect of medications. Chemotherapy-induced neurotoxicity is a common and significant side effect of cancer treatment, which may develop with some of the most commonly used chemotherapies (Park et al., 2008). Oxaliplatin is a platinum-based chemotherapy, utilized in colorectal cancer, one of the most common forms of cancer worldwide (Center et al., 2009). Oxaliplatin produces two forms of neurotoxicity, with acute neurotoxicity developing immediately following infusion, characterized by sensory and motor symptoms triggered by cold exposure (Gamelin et al., 2002). With increasing cumulative doses, a chronic sensory neuropathy develops, leading to functional deficits and limiting treatment success.

Figure 7. Characteristic changes in sensory excitability with oxaliplatin treatment in a single patient, with threshold electrotonus depicted on the left and recovery cycle on the right, demonstrating increases in hyperpolarizing threshold electrotonus and reduction in refractoriness post-oxaliplatin as depicted by arrows. Pre-oxaliplatin recordings are depicted in red and post-oxaliplatin recordings in black (following five months of oxaliplatin treatment).

Axonal excitability studies undertaken in oxaliplatin-treated patients revealed that acute neurotoxicity relates to a channelopathy of axonal Na+ ion channels. Studies in patients following oxaliplatin treatment demonstrated alterations in recovery cycle parameters in both motor and sensory axons (Kiernan and Krishnan, 2006; Krishnan et al., 2005a; Krishnan et al., 2006a; Park et al., 2009a) consistent with modulation of Na+ conductances. Accordingly, in vitro studies have demonstrated oxaliplatin-induced effects on Na+ channels in a variety of experimental settings (Adelsberger et al., 2000; Benoit et al., 2006; Grolleau et al., 2001;

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Webster et al., 2005). However, longitudinal studies of sensory axonal excitability in patients over 6 months of oxaliplatin treatment revealed a different pattern of excitability change, associated with widespread axonal degeneration (Figure 7; Park et al., 2009b). Importantly, these changes occurred significantly earlier than changes in classical measures of axonal function, peak amplitude and latency, suggesting that they may provide an early marker of axonal dysfunction in chronic oxaliplatin-induced neurotoxicity. In addition, the magnitude of excitability change was greatest in patients with the most severe neurotoxic symptoms, suggesting that sensory excitability parameters may represent a sensitive biomarker of oxaliplatin–induced neurotoxicity.

Motor Neuron Disorders Motor neuron diseases are progressive neurological disorders that affect peripheral motor neurons leading to paralysis and death. Amyotrophic lateral sclerosis (ALS) is universally fatal, clinically characterized by fasciculations, cramps, progressive weakness and respiratory involvement. Axonal excitability studies have revealed increased strength-duration time constant in motor axons in patients with ALS (Mogyoros et al., 1998; Vucic and Kiernan, 2006; Vucic and Kiernan, 2009), suggesting that upregulation of persistent Na+ conductances may support the generation of ectopic motor activity underlying fasciculations. In addition, threshold electrotonus waveforms have demonstrated abnormalities in the depolarizing direction in patients with ALS, with less accommodation to depolarization (Bostock et al., 1995; Kanai et al., 2006; Nakata et al., 2006; Vucic and Kiernan, 2006), which has been linked to reductions in axonal K+ conductances (Kanai et al., 2006). The combination of enhanced persistent Na+ current with reduced K+ conductance may facilitate ectopic activity underlying the generation of fasciculations and cramps. Importantly, axonal excitability studies have established significant differences in the pattern of peripheral abnormalities in ALS and other motor nerve disorders. Multifocal motor neuropathy (MMN) is a slowly progressive inflammatory motor nerve condition characterized by conduction block, leading to asymmetric weakness of limbs. Axonal excitability studies revealed widespread axonal hyperpolarization distal to the site of conduction block (Kiernan et al., 2002a), while no abnormalities were noted away from the site of block (CappelenSmith et al., 2002). The mechanism of axonal hyperpolarization in MMN has been linked to over-activation of the axonal Na+/K+ pump distal to the site of block. Such distal Na+/K+ pump dysfunction may be produced as a consequence of Na+/K+ pump failure, increased Na+ concentration and subsequent depolarization at the site of conduction block (Kiernan et al., 2002a; Krishnan et al., 2009). Studies of MMN patients utilizing maximal voluntary contraction to fatigue muscles revealed the development of activity-dependent conduction failure mediated by excessive hyperpolarization during activity, supporting the theory that axonal hyperpolarization produces conduction block in MMN (Kaji et al., 2000). These findings suggest that ectopic activity and fasciculations in MMN are mediated by a substantially different mechanism to those in ALS, with depolarized lesions surrounded by hyperpolarized axon producing ectopic activity rather than upregulation of persistent Na+ conductances (Kiernan et al., 2002a).


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ABERRANT EXCITABILITY IN NEUROLOGICAL DISEASE Through greater understanding of the contribution of axonal ion channel dysfunction and anomalous membrane excitability, novel disease-modifying strategies may be developed for the treatment of neurological disease states. Genetic mutations in voltage-gated ion channels have been implicated in a number of neurological disorders (see Table 1), suggesting that modulation of excitability may be an important strategy in the development of disease modifying therapies for neurological disorders. Accordingly, a number of current medications for neurological conditions utilize ion channels as molecular targets. Many antiepileptic drugs (AEDs) target ion channel function as a primary mechanism of action. Drugs including carbamazepine and valproate act to preferentially block Na+ channels during prolonged activation and at depolarized membrane potentials (Rogawski and Loscher, 2004). This enables AEDs to inhibit high frequency discharges without affecting normal impulse conduction, thus preserving neurotransmission while inhibiting seizure activity. The novel AED retigabine utilizes a new ion channel target, the K+-mediated M current. The Mcurrent produces a sustained outward current, which stabilizes the membrane potential (Delmas and Brown, 2005). Retigabine is an M-current enhancer, acting to shift the voltage dependence and increase channel opening (Tatulian and Brown, 2003; Tatulian et al., 2001; Wuttke et al., 2005). Retigabine appears to bind to S5 and S6 domains of the KCNQ channel, stabilizing the open channel state, which reduces electrical excitability and the propensity for seizures (Wuttke et al., 2005). Retigabine is selectively neurally active, and does not affect cardiac K+ channels which possess different S5 residues to neural channels (Rogawski and Bazil, 2008). Retigabine may also be useful as a membrane stabilizer in neuropathic pain (Passmore et al., 2003). Na+ channels also play a role in multiple sclerosis, with demyelination disrupting the nodes of Ranvier and leading to increased expression of Na+ channels along the axon (Bostock and Sears, 1978; Foster et al., 1980; Waxman, 2006). While Na+ channels perform a supportive role to ensure conduction of impulses along demyelinated axons, increased Na+ influx may also result in axonal degeneration (Stys et al., 1992; Waxman, 2006). Nav1.6 subunits are upregulated in damaged axons and carry a more persistent Na+ current, suggesting that they are associated with sustained Na+ entry into the neuron and subsequent axonal degeneration (Boiko et al., 2001; Craner et al., 2004; Rush et al., 2005). The role of Na+ channel reorganization in multiple sclerosis raises the possibility that modulating the activity of voltage-gated Na+ channels could affect disease course, preventing axonal loss and further disability (Waxman, 2008). Accordingly, studies of currently available Na+ channel blockers phenytoin and flecainide have demonstrated some benefit in experimental models of multiple sclerosis (Bechtold et al., 2004; Lo et al., 2003).

CONCLUSION The development of research techniques to probe axonal structure and function in both in vitro models and in vivo human axons has provided important insights into the role of biophysical properties in controlling axonal function. Dysfunction of voltage-gated ion channels has been implicated in a number of neurological disorders. Future challenges remain

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to identify novel channel modulating agents which selectively target particular channel isoforms. Further research into the biophysical properties underlying impulse conduction will inevitably assist in understanding the complex interplay between axonal structure, ion channel function and membrane excitability.

ACKNOWLEDGMENTS The support of the National Health and Medical Research Council of Australia (Project grant number 570233), the Sydney Foundation for Medical Research and an Australian Postgraduate Award (SP) are gratefully acknowledged.

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Chapter 3

PHYSIOLOGICAL IMPLICATIONS OF ACTION POTENTIAL IN CHARACEAN CELL: EFFECTS ON PH BANDS AND SPATIAL PATTERN OF PHOTOSYNTHESIS Alexander A. Bulychev* and Natalia A. Krupenina† Department of Biophysics, Faculty of Biology, Moscow State University, Moscow, 119991 Russia

ABSTRACT Most plants generate propagating action potentials (APs) upon injuries or other stimuli. The functional significance of APs is intriguing but still unclear, except for a few cases of insectivorous and sensitive plants. In characean algae, close relatives of higher plants, the membrane excitation exerts marked effects on spatial heterogeneity of chloroplast and plasmalemma functions. The light-dependent ―pH bands‖ in characean internodes are highly sensitive to AP generation. The spatial pattern of apoplastic pH collapses transiently after membrane excitation, indicating temporal inhibition of H+pump activity in acid zones and of counter-directed passive H+ flows in alkaline areas. The plasmalemma conductance in the alkaline regions decreases several fold during postexcitation period in parallel with the drop of apoplastic pH, while the conductance in acid regions is barely affected. The blockade of high pH channels permeable to H+ (OH–) seems to be the key event in the AP impact on pH pattern and cell electrogenesis. Imaging of chlorophyll fluorescence in resting Chara corallina cells revealed the patterns of photosynthetic activity and non-photochemical quenching, which are finely concerted with the pH bands. Unlike temporal decline of the pH bands after AP propagation, heterogeneity of photosynthesis and fluorescence quenching was temporally enhanced in the post-excitation period. The enhancement might be related to opposite changes in cytosolic pH following the AP-induced cessation of counter-directed H+ fluxes in the alkaline and acid cell regions. Effects of AP on photosynthetic pattern differed strikingly in the absence and presence of the herbicide methyl viologen (MV). Under natural * †

E-mail address: [email protected], E-mail address: [email protected]

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Alexander A. Bulychev and Natalia A. Krupenina conditions, the spatial heterogeneity of photosynthesis was enhanced after AP owing to stronger inhibition in chloroplasts of alkaline cell regions with minor changes in acid regions. By contrast, the effect of a single AP on photosynthesis in the presence of MV was most pronounced in the acid regions and led to irreversible smoothing of the spatial pattern. These and other results indicate that MV cannot permeate the composite membrane barrier (plasmalemma + chloroplast envelope) under resting conditions but gains access to its interaction sites within the chloroplast during or after AP generation. The gated ion channels might provide a pathway for permeation of physiologically active amounts of MV across the plasmalemma.

INTRODUCTION The action potential (AP) of excitable plant cells is a physiological signal involved in regulation of osmotic balance, gene expression, and other cell functions. The most spectacular phenomena related to occurrence of AP are observed upon mechanical stimulation (touching, wind blowing) of mimosa (Mimosa pudica) leaves and upon touching, at least two times in series, of a sensitive trichome of Venus flytrap (Dionaea mascipula) leaf. Closing of mimosa leaves and of the flytrap lobes occurs with a surprisingly fast rate unexpected for the majority of usual plants. This behavior is initiated by rapid generation and propagation of AP, which is followed by differential loss of cell water on different sides of particular stem regions (Sibaoka, 1969). The physiological significance of rapid movements is evident for insectivorous plants, e.g., Dionaea. It is thought that the leaf folding in mimosa may restrict evaporative water losses during strong wind and may be helpful as a defense from herbivores, because leaf shrinkage exposes stem prickles and makes the branch appear leafless. Action potentials develop also in most other plants, although they do not produce visible movements. Slight movements of leaves upon distant application of mechanical or flame stimuli can be detected with sensitive techniques. The AP transmission was observed in tomato, pumpkin, and sunflower plants upon cold and mechanical stimulation. Electrical signaling in plants was surveyed in a number of reviews (Wayne, 1994, Davies, 2006, Stahlberg, 2006, Fromm & Lautner, 2007; see also Chapter 1 in this book). Propagating electrical signals, including AP, often originate upon plant injury and may participate in plant protection against wounding. For example, plants rapidly respond to attack of herbivorous insects by producing insect-deterring substances, e.g., proteinase inhibitors (Rhodes et al., 2007). The information about injury of one leaf is rapidly transmitted to all parts of the plant. The conduction rates of plant action potentials are in the range from 0.1 to 20 cm/s (Fromm, 2006, Favrea & Agosti, 2007). The velocity of AP transmission along the characean internode is about 1.5 cm/s when the cell is submerged in artificial pond water. Ionic fluxes associated with AP in plants are mostly known. The propagation of AP involves Ca2+ influx into the cytoplasm across the plasma membrane through voltage-gated channels, followed by chloride efflux through Ca2+-activated channels, and the delayed potassium efflux (Lunevsky et al., 1983, Beilby, 2007). The supposed role of AP in osmotic regulation is related to large Cl– and K+ effluxes from the cytoplasm to the apoplast during cell excitation. The short-term Ca2+ influx at the initial stage of AP generation does not compensate for the osmolyte efflux. Thus, during AP some cells may lose appreciable quantities of osmotically active substances and change their turgor. The loss of cell turgor

Physiological Implications of Action Potential in Characean Cell:…

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may account not only for leaf movements but also for closing of stomata upon signal transmission from injured roots (Songjie et al., 2006). Among recent discoveries shedding new light on physiological role of electrical signaling in plants, the long-lasting effects on photosynthesis are particularly interesting (Koziolek et al., 2003, Bulychev et al., 2004, Lautner et al., 2005). It was found that heat injury of a leaf in several plant species, such as Mimosa, Populus, and Zea mays, provokes transient inhibition of photosynthesis in distant leaves. However, the assignment of photosynthesis inhibition to propagation of AP is often compromised by the ability of vascular plants to transmit both electrical and hydraulic signals (Fromm, 2006). Furthermore, two types of electrical signals are known to propagate along the conducting tissues after heat injury: AP and variable potentials (Stahlberg & Cosgrove, 1997). Unlike AP characterized by comparatively uniform amplitude and fast propagation, variation potentials are distinguished by variable depolarization amplitude, longer duration, and a slower spreading velocity (Davies, 2006). The inhibitory influence of variation potentials on photosynthesis has long been noted (Van Sambeek & Pickard, 1976). The complications arising from different nature of transmitted signals can be avoided by monitoring the photosynthetic activity of individual excitable cells that are capable of generating AP in a controlled and reproducible manner upon passing a short pulse of transmembrane electric current. Excitable giant cells of characean algae are particularly suitable for such measurements because their chloroplasts are immobile and arranged as a single layer. An emerging and largely unexplored area is influence of cell membrane excitation on spatial patterns of photosynthesis and ion fluxes (Bulychev et al., 2004, Krupenina et al., 2008). The green cells and tissues are capable of reversible transitions between uniform and spatially heterogeneous distribution of photosynthetic activity upon changes of light conditions. When the leaf is illuminated after a period of dark adaptation, uniform images of chlorophyll fluorescence and photosynthetic characteristics are replaced by mosaic images showing damping oscillations (Siebke & Weis, 1995a, 1995b, Baker et al., 2001, Schurr et al., 2006). The mechanisms involved in light-dependent generation of heterogeneous areas in photosynthetic objects remain poorly understood. However, it has been found that the spatial self-organization of photosynthesis is closely related to generation of nonuniform electrochemical gradients for protons (ΔμH+) across the thylakoid and plasma membranes (Bulychev et al., 2005, Krupenina & Bulychev, 2007). In characean algae the positions of cell areas with low photochemical activity of photosystem II (PSII) coincide with the locations of H+ entry zones, where the apoplastic pH (pH on the outer cell surface, pHo) is almost three units higher than in the cell areas with active photosynthesis. The propagation of AP exerts differential influence on photosynthetically active and inactive cell regions (Bulychev & Kamzolkina, 2006); it alters both the photosynthetic and electrochemical (pHo, transmembrane ΔμH+) patterns. Apparently, the signaling role of AP is mediated, among other factors, by changes in cytoplasmic and apoplastic pH, and by modulation of bioenergetic events in thylakoid membranes. This work examines cardinal changes in spatial organization of photosynthetic activity and H+ membrane transport in the excitable plant cell upon generation of a pulse-wise electrical signal, AP. Interrelations between fundamental cell processes, such as membrane excitation, photosynthesis, and spatial pattern formation in vivo are also considered. Characean algae, which are close relatives of higher plants, represent the most suitable model

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Alexander A. Bulychev and Natalia A. Krupenina

system for this purpose, because they combine all aforementioned basic processes at the cell level.

SPATIAL PATTERN OF H+-PUMP AND H+ LEAK ACTIVITIES AND ITS TRANSIENT DECAY UPON MEMBRANE EXCITATION Proton transport across the plasma membranes plays a crucial role in regulation of cytoplasmic pH, electrogenesis, mineral nutrition, and cell turgor of plant cells (Palmgren, 1998, Tazawa, 2003). The electrochemical gradient ΔμH+ created by the plasma membrane (PM) H+-pump provides the driving force for accumulation of mineral nutrients, such as K+, Cl–, and NO3– and benefits to photosynthesis of aquatic plants inhabiting weakly alkaline stagnant waters (Walker et al., 1980, Miedema et al., 1992, Plieth et al., 1994). Local acidification of the apoplast to pH 6.3–6.7 increases the content of the neutral species CO2, which readily passes through the membranes unlike poorly permeable charged species HCO3– and CO32–. Depending on specific cell function, ΔμH+ generators and ΔμH+ consumers are either distributed smoothly over the organ or cell surface or produce a nonuniform pattern. In submerged leaves of some water plants such as Potamogeton and Elodea, the morphologically lower leaf side actively extrudes H+ to the unstirred layers of the outer medium during illumination, while the upper leaf side produces strong light-dependent alkalinization near the surface (Miedema et al., 1992, Miedema & Prins, 1992). Nonuniform spatial distribution of PM H+-pumps and sinks is particularly evident in characean algae. Under continuous light, the internodal cells of these algae produce zones of H+ extrusion (acid zones with pH ~6.5) alternating with spatially separated alkaline regions (pH 9.5–10) (Lucas & Nuccitelli, 1980, Bulychev et al., 2001b). The number of acid and alkaline zones increases with light intensity. At high light intensity ~400 µE m–2 s–1 the periodic length between alkaline bands is about 7 mm. In acid zones the pH on the outer cell surface (pHo) was found to shift additionally to values as low as 6.1 when the PM H+-pump was activated by fusicoccin, whereas pHo in alkaline peaks was not significantly altered upon this treatment (Bulychev et al., 2005). On the other hand, the local inhibition of PM H+-ATPase after intracellular injection of a peptide that competitively binds to 14-3-3 proteins induced rapid pHo increase in the formerly acid region, in consistency with the expected inhibition of H+ extrusion. These findings provide evidence that the H+ efflux in the acid regions is driven by the light-regulated PM H+ATPase. The H+-pump activity is high in acid areas, is low in alkaline zones, and is smoothly distributed over the cell in darkness. Measurements with a vibrating microprobe revealed electric currents flowing in the extracellular medium between the acid and alkaline zones (Lucas & Nuccitelli, 1980, Fisahn et al., 1992). The outward direction of current in acid zones indicates its association with ATPase-driven H+ extrusion. In the alkaline cell zones, the electric current with a density of 20–60 μA/cm2 is directed inward. It is known that the PM conductance of characeaen cells increases considerably at high pH of the external medium (Bisson & Walker, 1980, Beilby et al., 1993). A very high conductance observed at pH 10–11 was assigned to the so-called "high pH channels" supposedly permeable to H+ or OH–. Under physiological conditions, these


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channels account for unusually high area-specific membrane conductance in the alkaline cell regions of illuminated cells (Walker et al., 1980). These data underlie the hypothesis that the PM H+-ATPase is a generator of outward current and that the inward current in alkaline regions is carried either by H+ influx or OH– efflux. By analogy with the notion of circulating H+ fluxes in energy-coupling membranes of chloroplasts and mitochondria, the inward current is conventionally considered here as a result of passive H+ entry into the cytoplasm, even though H+ influx cannot be distinguished from the OH– efflux (Beilby & Bisson, 1992). In contrast to the notion of passive H+ (OH–) uniport through the high pH channels, the alternative view is that alkaline zones result from operation of electroneutral OH–/HCO3– antiporter (Shimmen et al., 2003, Shimmen & Wakabayashi, 2008). It was assumed for a long time that pH banding in characean cells is controlled mostly, if not exclusively, by illumination conditions. However, the membrane excitation was found to override the influence of continuous light, so that the pattern of pHo disappears temporally after propagation of a single AP, despite the ongoing illumination (Bulychev et al., 2004, Eremin et al., 2007, Krupenina et al., 2008). Figure 1 illustrates changes in pHo profile along the internodal cell of Chara corallina upon membrane excitation evoked with a pulse of electric current (10 μA, 150 ms) at time t = 5 min. The three-dimensional graph (Figure 1a) was obtained by repeated measurements of longitudinal pH profiles along the internodal cell with a scanning pH microelectrode before and after cell excitation. In the beginning of experiment, the pHo profile was composed of few alkaline peaks and acidic zones. After AP generation, the pHo pattern decayed within 5–10 min, giving rise to a smooth pH distribution. The decay was roughly similar to that evoked by darkening but it began earlier after AP than after light–dark transition (Bulychev & Kamzolkina, 2006).

Figure 1. Collapse and recovery of longitudinal pHo profile in illuminated Chara corallina cell after triggering an action potential (AP). (a) Time–space diagram reflecting the dynamics of pHo after AP generation at the time point marked with a zigzag arrow (t = 5 min). (b) Two-dimensional representation of temporal decline and subsequent recovery of pH bands after AP propagation. The dotted line at t = 5 min marks the moment of AP generation. The color codes for pH in (a) and (b) are identical. Photon flux density 10 µE m–2 s–1.

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The time course of the pH profile smoothing after membrane excitation or darkening is presumably limited by the rate of H+ diffusion. The diffusion proceeds between acid and alkaline regions, as well as between these regions and the bulk solution. When visualized with pH indicator phenol red, the alkaline areas appear as spherical spots with a radius of about 3 mm; see e.g., (Krupenina et al., 2008). The unstirred layer of such thickness was also inferred in earlier studies (Walker et al., 1980). The characteristic time of pH smoothing after AP or darkening can be estimated from the diffusion equation x2 = 2Dt, where x is the distance between the centers of alkaline and neighboring acid regions, equal also to the thickness of unstirred layer, and D ≈ 9.3∙10–5 cm2/s is proton mobility in water (Serowy et al., 2003). Taking x = 3 mm, we obtain t ≈ 8 min, which is close to the experimental values. Thus, the decay of pH pattern after membrane excitation seems to reflect the diffusion-limited H+ redistribution around the cell after cessation of H+-pump activity and of passive inward H+ flows across the plasma membrane. It appears that the cell excitation temporally inhibits both the ATPase-driven active H+ efflux and the passive H+ influx (OH– efflux) in different cell regions. Following a transient decay, the pH pattern started recovery and was nearly restored in about 30 min after AP generation. The recovery of pH bands was promoted by elevation of external Ca2+ concentration in the range 0.05–2 mM and by the increase in actinic light intensity (Eremin et al., 2007). The dynamics of pH pattern is also shown in Figure 1b, which depicts the data as a two-dimensional graph. The color code is the same as in Figure 1a. Alternating areas in different colors on the left side of the diagram represent the initial pH profile composed of acid and alkaline zones. At a time moment marked with dotted line (t = 5 min), the cell was electrically stimulated and generated a single AP. In subsequent 5–10 min, the alkaline zones disappeared temporally; they reappeared later by the end of the experiment. It should be noted that the AP-induced pH changes in the acid regions are much smaller than those in alkaline regions and remain unresolved in Figure 1. The typical amplitudes of APinduced pH increase in acid zones are 0.2–0.3 pH units (Krupenina et al., 2008).

POST-EXCITATION DROP OF MEMBRANE CONDUCTANCE IN ALKALINE AREAS AND ITS ROLE IN THE COLLAPSE OF PH BANDS The immediate suppression of an inward H+ flux in the alkaline cell regions after AP generation can be employed as a means to clarify the mechanism of H+ (OH–) transport in the alkaline cell regions. By measuring the membrane conductance and pH changes in particular cell regions before and after cell excitation it is possible to discriminate whether the transmembrane H+ transport in the alkaline zones is electroneutral or electrogenic and whether this transport is affected by AP directly or indirectly (through inhibition of the H+pump). The rapid cessation of H+ influx after AP should not affect the membrane conductance in the case of electroneutral transport (H+/HCO3– symport or OH–/HCO3– antiport) but the conductance changes are expected to occur in the case of uniport. The membrane conductance of specific cell regions can be assessed under space clamp conditions that assure uniform membrane potential on a small area of cell surface. Space clamping is usually attained through isolation of a small cell region from the rest of the cell by means of


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insulating gaps (Lunevsky et al., 1983). The size of isolated cell part should be smaller than the cable length. The cable length of resting characean internodes under dim light ranges from 15 to 30 mm. These values represent a very rough approximation, because they were obtained under assumption that internode electrical properties are homogeneous over the cell length (Smith, 1983). However, the membrane conductance is strikingly nonuniform in illuminated cells, even though it is uniform in darkened internodes. According to Smith and Walker (1983, 1985), the membrane conductance (Gm) in acid zones is about 1 S/m2, whereas Gm in alkaline zones ranges from 5 to 15 S/m2, increasing with external pH. In our study, the requirement of homogeneous current density over selected membrane regions was fulfilled by isolating a narrow (3 mm) cell region. This distance is less than the cable length values, which are 3–5 and 10–15 mm for alkaline and acid regions, respectively, in Chara cells (Smith & Walker, 1983). The current flow was accomplished through extracellular electrodes, while the membrane potential and its changes were measured with intracellular capillary microelectrodes. We measured resistance (Rm = 1/Gm) of the selected cell region by passing square pulses of current (0.5–1 μA, pulse duration 180–360 ms) at a frequency of 2.5 or 1.25 Hz; these pulses induced hyperpolarizing shifts of the membrane potential in the central compartment (Bulychev & Krupenina, 2009). Small voltage drops on a series resistance (resistance of external medium and of a salt bridge) were measured prior to insertion of a microelectrode into the cell and were digitally subtracted in the final records. The Rm values were expressed in kΩ∙cm2. For comparison with previously published conductance values in alkaline and acidic regions, we calculated Gm, and expressed these values in S/m2. The AP generation was evoked by single pulses of depolarizing current (4–6 μA, 100–200 ms). When the cell was placed in a three-compartment chamber, the isolated central cell region was able to produce alkaline or acid areas, although formation of high and low pH zones took longer time than in unconstrained cells (Bulychev & Krupenina, 2009). Figure 2a shows changes in plasma membrane potential (Vm) and membrane resistance (Rm) induced by AP generation in the alkaline cell region. In the resting cell exposed to continuous light, the alkaline cell region was moderately depolarized (Vm of about –170 mV). The hyperpolarizing Vm shifts, induced by a train of inward current pulses, appeared in records as a wavy band whose width is proportional to Rm values. The upper edge of this band represents Vm. The Rm values in the alkaline region of a resting cell were low, yielding after recalculation a high membrane conductance (8.32 ± 1.1 S/m2, n = 19). This value is consistent with the range of 5–15 S/m2 determined in an earlier work (Smith & Walker, 1983, 1985) for alkaline zones of illuminated Chara cells. After AP generation, the Rm increased several fold (by a factor of 7.5 in Figure 2a) within about 40 s. The membrane conductance decreased accordingly to the average value of 1.79 ± 0.6 S/m2 (n =19). The increase in Rm was paralleled by a large (50–60 mV) hyperpolarization of the plasmalemma Vm. The AP-induced changes in Rm and Vm were fully reversible following prolonged rest periods. The initial state was restored after at least 15 min from the moment of cell excitation.

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Figure 2. Excitation-induced changes of plasma membrane potential Vm and resistance Rm in selected regions of C. corallina cell exposed to continuous blue light (100 µE m–2 s–1) and prolonged (30 min) darkness. Rm values are proportional to Vm shifts induced by square pulses of hyperpolarizing electric current flowing through a space-clamped cell region. The strength of current pulses was 1 µA in (a-c) and 0.5 µA in (d). (a) AP-induced inactivation of membrane conductance (increase in Rm) in the alkaline cell region of illuminated cell; (b) different patterns of Vm and Rm changes induced by two APs in the alkaline region after a 20-min rest period in continuous light; (c) post-excitation changes in Rm and Vm induced by AP in the acid region of illuminated cell; (d) elimination of post-excitation Rm and Vm transients in the former alkaline region after 30-min incubation in darkness.

Figure 2b shows that the second AP induced in 30 s after the first one had a different shape and extent. The AP amplitude was higher owing to the hyperpolarized resting potential, and there was no additional post-excitation hyperpolarization. Furthermore, the pattern of Rm changes was also different: Rm decreased during AP and returned rapidly to values observed in the absence of the second excitation. There was no additional increase in Rm after the second AP. Different patterns of Vm and Rm changes associated with the first and subsequent cell excitation were also evident after triggering the second AP in 1–3 min after the first one. Figure 2c represents Rm and Vm measurements before and after AP generation in the acid region of an illuminated cell. In resting cells exposed to continuous light, Rm in the acid areas was about twice higher than that in alkaline regions under similar conditions. After AP generation, Rm increased by about 30% of the initial value. The post-excitation hyperpolarization was either small (< 20 mV) or absent. Figure 2d shows that darkening of the cell for 30 min was followed by a several-fold increase in Rm of the resting cell, which indicates, accordingly, a strong decrease in


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membrane conductance Gm. The mean value of Gm in the formerly alkaline regions of darkened cell was 0.58 ± 0.09 (n = 4), i.e., almost 15 times lower than the mean Gm for the alkaline areas of illuminated cells. The triggering of AP in the darkened cell was not accompanied by the post-excitation increase in Rm and caused no hyperpolarization. The Rm in the darkened cell decreased during AP but returned to the initial level shortly after the end of AP. The average ratio of Gm values measured in the resting cell before AP and 50–100 s after AP was 0.98. In dark-adapted cells the membrane conductance of the formerly acid regions was low and close to that of formerly alkaline regions. The Rm changes associated with AP in darkened ―acid regions‖ were similar to those shown in Figure 2d. After a 30-min dark adaptation, the AP generation induced neither the post-excitation hyperpolarization nor the increase in Rm. It should be noted that the effects of membrane excitation resembled in some respects the effect of darkness. Both treatments elevated the plasmalemma R m, although the increase in Rm was stronger upon darkening than after AP generation. In addition, both treatments induced the cell hyperpolarization (Figure 3). The AP-induced hyperpolarization developed faster than the similar voltage shift induced by darkening.

Figure 3. Hyperpolarization transients induced in C. corallina internode by the light-dark transition and by the membrane excitation of illuminated cell. The membrane potential Vm was measured with capillary microelectrodes. The depolarization upstroke during AP is not shown in full for scaling reasons. Arrows off and on designate the moments when light was switched off and on, respectively. Zigzag arrow marks the moment of triggering AP by an electric stimulus.

POST-EXCITATION CHANGES IN PH AND MEMBRANE PROPERTIES REVEAL ELECTROGENIC UNIPORT IN ALKALINE ZONES In order to get insight into the origin of AP-induced conductance changes, it is helpful to compare the kinetics of Rm transients with changes of membrane potential Vm and external

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pH (pHo). Figure 4 shows such a comparison for the case of space-clamped alkaline cell regions. The amplitudes of hyperpolarizing Vm excursions induced by periodic pulses of constant current (like those shown in Figure 2) were recalculated to Rm values and plotted as a function of time (solid squares, curves 1) together with other parameters measured (Vm, pHo). It is seen from Figure 4a that the post-excitation increase in Rm developed in parallel with large hyperpolarization (ΔVm). The excitation-induced increase in Rm was also accompanied by a strong decrease in external pH near the cell surface (Figure 4b, curve 2). However, the peak of Rm was attained much earlier than the minimum of pHo. Furthermore, the slow reversal of Rm started 1–2 min after cell excitation, when the pHo continued to decrease. Thus, the Rm kinetics did not follow the pHo change, indicating that the conductance change is not a consequence of pHo decrease but, most probably, is the cause of H+ flux cessation. Changes in Rm, Vm, and pHo were reversible: all parameters returned to their initial values within about 15 min at irradiances of 100–400 μE m–2 s–1. The recovery took longer time at lower irradiance. The results presented in Figures 2–4 provide evidence that the AP generation transiently lowers pHo in alkaline zones in parallel with large hyperpolarization of PM and with severalfold decrease in membrane conductance. By contrast, in cell regions producing acid zones, the AP generation was followed by a small increase in pHo (data not shown), concomitant with a slight decrease in Gm and insignificant hyperpolarization. The results suggest that the smoothing of pH pattern after AP in whole cells involves the suppression of passive electrogenic H+ (OH–) transport in the alkaline regions, which coincides with and might result from the rapid inactivation of ―high pH channels.‖ At the same time, H+ extrusion in the acidic zones was also blocked after AP. Since local acidification of the medium in unstirred layers is an indicator of the H+-pump activity, it is evident that the increase in pHo after AP in the acid zones originates from inhibition of the PM H+-pump. Although the H+-pump is a driving source of extracellular currents, the suppression of passive H+ flux in the alkaline regions after AP was clearly caused by the Gm decrease, not by the change in the driving force. The inward-directed driving force, ΔμH+ increased actually along with the drop in pHo and membrane hyperpolarization. Thus, the cessation of H+ influx in alkaline zones cannot be a secondary event arising from the H+pump inhibition. On the other hand, the AP-induced Gm decrease in the alkaline cell regions in vivo might contribute to the inhibition of H+-pump activity. According to some reviews and research studies (Shimmen, 1994, Tazawa, 2003, Spanswick, 2006), the conductance of electrogenic H+-pump is comparable to the conductance of passive diffusion pathways. Hence, the pump cannot be considered as an ideal current source, and the pump current should be sensitive to the conductance of ion channels. In this case, the inactivation of high pH channels would diminish the pump current. The membrane excitation in characean cells was mostly analyzed under low light conditions ensuring spatially uniform distribution of PM properties (Lunevsky et al., 1983, Beilby & Bisson, 1992, Berestovsky & Kataev, 2005). This may explain why the large inactivation of PM conductance in alkaline regions after AP remained undiscovered until recently. The pH band formation in characean internodes requires photon flux densities above the threshold ~5 μE m–2 s–1 (Bulychev et al., 2003). Smith and Beilby (1983) examined the membrane conductance in unconstrained Chara cells exposed to sufficiently high irradiance (50 μE m–2 s–1).


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Figure 4. Excitation-induced Rm changes in the alkaline region (symbols in traces 1) compared with changes of (a) membrane potential Vm and (b) pH near the outer cell surface (curves 2). ΔVm indicates the post-excitation hyperpolarization.

They observed the AP-induced decrease in Gm by 30–40% within about 30 s and attributed these changes to inactivation of the H+-pump conductance. The conductance changes illustrated in Figures 2 and 4 are almost an order of magnitude higher. Nevertheless, the kinetics of conductance changes in our experiments was similar to those described for the whole cell in the absence of space-clamped conditions. These changes seem to have a common origin and reflect primarily the inactivation of channel conductance in the alkaline cell regions. The effect of cell excitation on Gm in alkaline cell regions was found to mimic the influence of prolonged darkness. Both the AP and dark incubation caused a large reduction of Gm in parallel with Vm hyperpolarization. The conductances of formerly acid and alkaline cell regions became almost equal after 30-min incubation in darkness, while longer dark incubation (1–2 h) might be needed to attain completely uniform Gm distribution (Smith & Walker, 1983). The possible reason for similar effects of excitatory stimulation and darkening on membrane conductance is that both treatments elevate the cytoplasmic Ca 2+ level (Berestovsky & Kataev, 2005, Johnson et al., 2006), which might affect ionic permeabilities of PM. The AP-induced hyperpolarization was found to correlate with the decrease in Gm; it was absent or small in the acidic zones. We suppose that Vm of alkaline cell regions under resting conditions in continuous light is shifted toward the equilibrium potential for H+ (EH), in similarity with the original hypothesis put forward by Kitasato (1968, 2003). The inactivation of H+-conducting channels after AP is expected to shift Vm in the direction of Nernst potential for K+ (EK), which is more negative than EH. Furthermore, an abrupt decrease in Gm after AP might elevate the electrogenic component of Vm (the product of pump current and passive membrane resistance), provided the increase in resistance of the passive pathway is larger than the decline in pump current. The post-excitation hyperpolarization, observed previously in Chara globularis, was regarded as a unique property of this species (Shimmen, 1994). Our results indicate that the post-excitation hyperpolarization is not confined to this particular species. The main requirement for its appearance in C. corallina is heterogeneous spatial distribution of pHo and

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Gm. This heterogeneity is restored in continuous light during prolonged rest periods (≥ 15 min) after previous cell excitation. At shorter periods between stimuli, the profound effect of excitation on Gm is damped and can be overlooked. In higher plant leaves, the propagation of electric signals along the plant also induced transient hyperpolarization (Zimmermann et al., 2009). In contrast to our conclusions, the hyperpolarization in higher plants was ascribed to activation, rather than inhibition of the electrogenic H+ pump, because it was prevented by the pretreatment with orthovanadate, an inhibitor of PM H+-ATPase. However, it is reasonable to expect that after-hyperpolarization in Chara is also sensitive to H+-pump inhibitors since the AP-induced inhibition of H+-pump can be only observed on the background of active H+-pump. The results of parallel measurements of Rm, Vm, and pHo led us to conclude that the origin of high pHo in alkaline zones of Chara cells cannot be attributed to functioning of H+/HCO3– symport or OH–/HCO3– antiport. In the case of electroneutral symport or antiport, the cessation of H+ (OH–) transport should have affected the pHo without simultaneous decrease in Gm. Thus, the idea is substantiated that the active H+ transport and counterdirected passive H+ flux in whole cells are spatially separated but coordinated by means of extracellular currents carried in the bulk solution by dominant ions (Walker et al., 1980, Bulychev & Krupenina, 2008a). Considering the functional role of spatially separated zones with active H+ extrusion and passive conductance, the passive H+ transport noncoupled to symport or antiport of nutrient ions might seem wasteful. However, the large distance between zones of H+ extrusion and passive H+ leak can be favorable, because it allows the cell to lower pH over a large areas (broad acid zones) approaching pK~6.3 for CO2/HCO3– equilibrium. This shift enriches the apoplast with the dissolved CO2 and facilitates permeation of this photosynthetic substrate into the cytoplasm. Such lowering of pH would have been hampered or weakened if the proton leak channels were distributed homogeneously over the cell membrane. The supposed functional significance of the membrane areas with passive H+ leak is related to the high conductance of these areas (Gm values more than tenfold higher than in darkened cells). As already noted above, Gm changes in alkaline zones might regulate the H+ pump activity by providing adjustable load for this electromotive source. From this point of view, the minimal width and the number of alkaline zones are determined by the required pump current satisfying the cell demand in photosynthetic CO2 acquisition. It is interesting in this context that the outward pump current in acid zones (~10 μA/cm2) (Lucas & Nuccitelli, 1980) corresponding to H+ efflux ~100 pmol cm–2 s–1 is comparable with the average rate of CO2 fixation by characean internodes in saturating light (40 pmol cm–2 s–1) (Lucas, 1975). This implies that a considerable portion of extruded protons is used for HCO3– to CO2 conversion and for subsequent utilization of carbon dioxide in photosynthesis. Thus, the role of H+ pump in algal cells inhabiting weakly alkaline environments is not restricted to accumulation of mineral nutrients but also includes the supply of membrane-permeable substrate of photosynthesis. It is even more important that this PM function is sensitive to electrical signals (AP) propagating along the cell under stressful treatments. The AP-induced retardation of PM H+pump might be considered as a manifestation of down regulation of cell metabolism upon the perception of stress signal. On the other hand, temporal suppression of H+ conductance after AP and the temporal shift of membrane potential to the level more negative than E K (Figures 2a, 2b) might redirect the remaining part of pump current to its circulation through K+


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channels. By this means, a partial loss of K+ after AP can be overcome, because K+ would accumulate in the cytoplasm during the period of hyperpolarization.

COORDINATION OF PH BANDS AND PHOTOSYNTHETIC PATTERN IN RESTING CELLS In resting illuminated cells, the alternate pattern of acidic and alkaline zones (pH banding) is mirrored by the spatial pattern of photosynthetic activity of chloroplasts packed densely in a thin layer under the plasma membrane (Bulychev & Vredenberg, 2003, Krupenina et al., 2008). Chloroplasts in Chara are immobile and fixed in the immediate proximity to the plasmalemma; therefore, their environment might undergo alterations during AP in association with the transmembrane ion fluxes. Changes in cytosolic Ca2+ concentration are presumed to be particularly high during AP, as Ca2+ enters from the medium through voltage-gated channels and is released from intracellular stores (Lunevsky et al., 1983, Thiel et al., 2002, Wacke et al., 2003, Berestovsky & Kataev, 2005). According to various estimates, the cytosolic Ca2+ concentration might increase from about 100 nM to 20 μM during AP. The transient cessation of counter-directed area-specific H+ fluxes after AP may cause opposite shifts of cytoplasmic pH in the alkaline and acidic cell regions. Photosynthetic rates can be assessed from chlorophyll fluorescence measurements on microscopic regions of the chloroplast layer using pulse-amplitude-modulated (PAM) fluorometry and the saturation pulse method (Schreiber, 2004). The method is based on comparison of chlorophyll fluorescence yield in vivo under weak to moderate actinic light and under high-intensity light pulses. Saturating pulses fully reduce the primary quinone acceptor Qa, thus inhibiting the photochemical activity of photosystem II (PSII) and enhancing energy losses to fluorescence and dissipation to heat. By comparing modulated fluorescence before and during the saturation pulse (F and Fm', respectively), one can evaluate the quantum yield of PSII reaction from the formula Y' = (Fm' – F)/Fm' = ΔF/Fm'. Under constant light intensity the parameter ΔF/Fm' is proportional to the rate of linear electron flow. Another useful characteristic obtained with this method is nonphotochemical quenching (NPQ). It is calculated from the equation: NPQ = (Fm – Fm')/Fm', where Fm is maximal fluorescence ever observed during the saturation pulse for the given sample (Fm is usually measured in dark-adapted materials) and Fm' is maximal fluorescence in the sample exposed to actinic light (Fm' < Fm). The above expression for NPQ is analogous to Stern–Volmer equation, according to which the parameter (Fm/Fm '– 1) is proportional to the concentration of quencher. The lower values of Fm' compared to Fm reflect the increased proportion between thermal and radiative dissipation of chlorophyll excitations. The increased thermal losses are related directly and indirectly to acidification of the thylakoid lumen and ΔpH formation (Finazzi et al., 2004). Thus, the NPQ parameter can be used as an indicator of the thylakoid pH gradient. This noninvasive method is widely used for studies of photosynthetic activity in intact plant leaves but its application to microscopic objects (individual cells or cell parts) is still quite rare (Goh et al., 1999, Snel & Dassen, 2000). It was revealed with PAM microfluorometry that electron transport rates through PSII are low in cell regions producing alkaline zones (pH 9–10) and are high in cell areas that acidify the apoplast to pH ~6.5 (Bulychev et al., 2001a, Bulychev & Vredenberg, 2003).

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Furthermore, analysis of NPQ pattern in Chara cells provided evidence that the thylakoid ΔpH is large in the cell regions producing alkaline peaks and is low in the regions with active PM H+-pump (Krupenina & Bulychev, 2007). The feedback relations between the H+-pump operation and photosynthetic rate might include the control of H+-pump activity by cytosolic contents of ATP and protons as the substrates for PM H+-ATPase (Palmgren, 1998, Tazawa, 2003). An important factor in these relations is different permeation rates of CO2, HCO3–, and CO32– across the membrane, as well as uneven distribution of these inorganic carbon forms along the cell with spatially distributed H+-pump and H+ leak activities. In CO2 sufficient acid regions, CO2 assimilation is facilitated and associated with ATP consumption, which lowers the thylakoid ΔpH and affects the dynamic balance between ΔpH and photosynthetic electron transport. The low ΔpH implies that the amount of protons displaced from the stroma and the cytoplasm into the lumen is small and has no significant influence on cytoplasmic pH (Hansen et al., 1993). At low ΔpH electron transport is unrestricted and allows effective ATP supply within the chloroplasts, which keeps sufficient cytosolic ATP content for operation of the PM H+-pump. Accumulation of mitochondria in photosynthetically active regions (Foissner, 2004, Braun et al., 2007) may contribute to the sufficiency of cytosolic ATP content. These conditions seem optimal for operation of the PM H+-pump. By contrast, in CO2-deficient alkaline regions, the thylakoid ΔpH is high (Krupenina & Bulychev, 2007), because ATP synthesis proceeds slowly when ATP-consuming reactions of CO2 fixation are suppressed. Accumulation of H+ in the lumen at the expense of protons taken up from the stroma and the cytoplasm elevates the cytoplasmic pH, thus inhibiting H+ extrusion from the cytoplasm (Hansen et al., 1993). The build up of large ΔpH in thylakoids suppresses electron flow (photosynthetic control) and diminishes the efficiency of PSII operation. Together with a dramatic increase in H+ conductance of PM at high pHo (Bisson & Walker, 1980, Beilby et al., 1993, Miedema & Prins, 1993), these interactions provide feedback loops that provoke coordinated patterns of extracellular pH and photosynthesis. The interactions between the plasma membrane and chloroplasts are probably important for the adjustment of photosynthesis to variations in environmental conditions. Now it becomes increasingly clear that the influence of PM on chloroplast functions is not limited to the H+-pump-mediated supply of CO2 for photosynthesis. Electron transport in chloroplasts is strongly affected by the PM excitation. Physiological consequences of AP generation, e.g., photosynthesis suppression, are orders of magnitude more durable compared with AP duration and its transmission time along the cell.

DISPARATE EFFECTS OF MEMBRANE EXCITATION ON PHOTOSYNTHETIC AND PH PATTERNS Based on the established relation between the PSII quantum yield and pHo under steadystate conditions, one might expect that the pH decrease in alkaline zones after AP would promote photosynthesis owing to the increased CO2 supply. However, in contrast to this reasoning, the AP generation was followed by an increase in fluorescence quenching NPQ and a decrease in ΔF/Fm' (Bulychev & Kamzolkina, 2006, Krupenina & Bulychev, 2007). The AP-induced quenching was interpreted as energy-dependent quenching qE caused by the


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increase in thylakoid ΔpH and lumen acidification. Fluorescence microscopy data indicated that the correlation between local pHo and photosynthesis is disrupted after an AP. This prediction was verified with a powerful technique of pulse-amplitude-modulated (PAM) imaging of chlorophyll fluorescence. The application of this method unveiled spatially resolved changes in photosynthetic fluorescence parameters upon the membrane excitation (Krupenina et al., 2008). Figures 5a and 5b show dynamics of ΔF/Fm' and NPQ in a single C. corallina cell under low intensity continuous illumination before and after AP generation. Before the AP the heterogeneity of ΔF/Fm' in the chloroplast layer along the cell length was weak but obvious (Figure 5a, the upper image taken at t = 0 min). After triggering an AP with a pulse of electric current, there was a pronounced decrease of ΔF/Fm' in alkaline regions (from ~0.55 to 0.4– 0.37), whereas this parameter did not change and remained at ~ 0.65 in broad acidic regions. Figure 5b shows respective AP-induced changes of NPQ in the same experiment. In the resting state at the given irradiance, the cell displayed no discernible pattern of nonphotochemical quenching. However, the electrically stimulated AP gave rise to the formation of pronounced NPQ pattern. The minimum of ΔF/Fm' and the maximum quenching were observed 6–8 min after the AP. Figures 6a and 6b show the AP-induced changes in ΔF/Fm' and NPQ as two-dimensional images with the color codes corresponding to those in Figures 5a and 5b. The time point marked with dotted lines and zigzag arrows corresponds to the moment when the AP was triggered by an electric stimulus. It is seen that the decrease in ΔF/Fm' was transient and followed by its reversal towards the initial values. The NPQ profiles were almost flat before membrane excitation and acquired a pronounced pattern after eliciting the AP. This periodic profile appeared temporary after an AP and returned toward the initial profile thereafter. It should be noted that the diagrams in Figures 6a and 6b differ substantially in their initial parts: the ΔF/Fm' profile was heterogeneous even before excitation, whereas the NPQ profile was almost flat. Another conspicuous feature is sharp boundaries between the regions of high and low NPQ and ΔF/Fm' at positions near 16 and 31 mm along the cell length. One may assume that interactions between chloroplasts located on different sides of these borders are limited or absent. A possible morphological barrier that restricts chloroplast interactions is a helical line separating counter-directed flows of streaming cytoplasm. It is possible that sharp shifts in photosynthetic characteristics at very close distances are attributed to the border between oppositely directed cytoplasmic streams. The results presented in Figures 5 and 6 and their comparison with Figure 1 demonstrate that the generation of a single AP enhances the banding patterns of NPQ and photosynthetic electron transport in the chloroplasts of C. corallina cells, in contrast to the concurrent suppression of the banding pattern of extracellular pH. On the first sight, the opposite effects of AP on photosynthetic and pH patterns seem unexpected because these patterns are strictly coordinated under resting conditions in the light and disappear concurrently in darkness. However, the effects of AP on the PM H+-transport and on chloroplast functional activity are mediated by different pathways (Bulychev & Kamzolkina, 2006) having in common only the initial step, i.e., a 10- to 100-fold increase in cytosolic Ca2+ concentration during AP. Furthermore, the coordination between local pH in the external medium and photosynthetic activity can be disrupted by some experimental treatments, e.g., microinjection of phosphorylated peptides preventing physiological interactions of 14-3-3 proteins with the PM H+-pump (Bulychev et al., 2005). The discovery of opposite impacts of AP propagation

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on functional patterns attributed to the plasmalemma and the chloroplast layer opens new prospects in studies of intracellular signaling interactions.

Figure 5. Images of PSII quantum yield (ΔF/Fm') and non-photochemical quenching (NPQ) in C. corallina cell in the resting state and at various periods after triggering an AP. The excitatory stimulus was applied at t = 0 min. (a) Spatial dynamics of the AP-induced ΔF/Fm' changes. The color bar at the bottom indicates the ΔF/Fm' values multiplied by 100. (b) Spatial dynamics of NPQ changes. The color bar at the bottom indicates NPQ/4 values multiplied by 100.

Figure 6. Spatiotemporal changes of AP-induced ΔF/Fm' (a) and NPQ (b) after AP generation in C. corallina cell. The moment of excitatory stimulation is marked with dotted lines and zigzag arrows. Note that local changes of both patterns are temporal and reverse to the initial states. The color codes are identical to those in Figures 5a and 5b.


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The observation that the AP generation intensifies separation of the chloroplast layer into areas with high and low photosynthetic electron flow rates (Figures 5, 6) adds to the list of documented phenomena induced by propagating electric signals in plants from various taxonomic groups. Apart from changes in turgor pressure, induction of proteinase inhibitor synthesis, and stimulation of respiration (see recent reviews (Davies, 2006, Shimmen, 2006, Fromm & Lautner, 2007)), these include temporal inhibition of the H+-pump and high pH channel activity (Bulychev & Krupenina, 2009). The significance of AP as a multifunctional signal is thus emphasized. The discovered sharpening of the photosynthetic profile after AP propagation (Figure 6) may offer an explanation to the still open question of how the Chara cell ―memorizes‖ the positions of pH bands and reestablishes alkaline bands after AP at their initial locations. At elevated Ca2+ concentrations in the outer medium (0.5–2 mM), the pHo pattern is not completely eliminated after AP and may serve as a template during reappearance of the pH profile. At low Ca2+ concentrations (≤ 0.1 mM) the external heterogeneity was not observed after AP generation, and reappearing pH bands shifted slightly from their initial positions. Nevertheless, the displacements of band positions were small (< 1 mm), implying that, apart from external factors, internal heterogeneity (e.g., banding of photosynthetic activity) may impose restrictions on the location of rearising bands (Eremin et al., 2007). The results of chlorophyll fluorescence imaging provide direct evidence in favor of this assumption. Indeed, the spatial distribution of photosynthetic activity becomes strongly heterogeneous after AP (Figure 6). The rate of noncyclic electron flow, being comparatively low in the alkaline cell regions, turned even lower after an AP, whereas in the acidic cell regions it was not significantly affected. A tentative primary trigger for the temporal smoothing of heterogeneous pH profile is the increase in the cytosolic Ca2+ concentration during AP from about 100 nM to the peak level as high as 6–40 μM (see (Berestovsky & Kataev, 2005) and references therein). A Ca2+mediated inhibition of the PM H+-pump in the acidic regions during AP seems likely, since Ca2+ is capable of binding to divalent cation-binding site in 14-3-3 proteins, thus impairing interactions of 14-3-3 with the H+-ATPase and, consequently, disturbing the H+-pump activity (Sehnke et al., 2002). The inhibition of H+-ATPase activity in the acidic bands concurrent with the cessation of H+ influx in the alkaline cell regions after an AP might cause opposite shifts in cytoplasmic pH (pHcyt) in different cell regions. The cessation of continuous H+ inflow in the alkaline cell regions after AP should disturb the pH balance and elevate pHcyt, while in the acidic cell regions a decrease of pHcyt would occur. It is conceivable that the ionic changes occurring after an AP favor Ca2+ uptake by chloroplasts of the ―alkaline‖ regions, since Muto et al. (1982) observed that the light-induced Ca2+ uptake by intact chloroplasts was stimulated by about 80% upon a shift of external pH from 6.5 to 8.0. Therefore, one may expect that the stromal Ca2+ concentration would increase to a larger extent after AP in the alkaline cell regions than in the acidic regions. Elevation after AP of stromal Ca2+ level by the light-dependent Ca2+ uniport is thought to suppress CO2 fixation and ATP consumption (Krupenina & Bulychev, 2007). The suppression of ATP consumption and synthesis would result in thylakoid energization (ΔpH increase) and energy-dependent quenching, provided some form of energizing (ΔpHgenerating) electron transport is maintained. The increase in ΔpH would be higher in chloroplasts featuring low H+ conductance of the thylakoid ATPase than in chloroplasts with high H+ conductance. One possibility for maintenance of an energizing electron flow is that

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the inhibition of assimilating (CO2-dependent) electron flow is accompanied by stimulation of electron flow to oxygen with the formation of superoxide, consequent dismutation to molecular oxygen and hydrogen peroxide, which eventually is reduced to water via noncyclic electron transport, catalyzed by ascorbate peroxidase. This electron transport pathway is known as Mehler–ascorbate peroxidase cycle (Schreiber et al., 1995) or water–water cycle (Asada, 1999). The operation of this pathway creates a high ΔpH at the thylakoid membranes, thereby serving as an effective means for down-regulation of PSII. It should be noted that inhibition of pH banding by the AP and darkness are not equivalent, even on the phenomenological level. The transition from light to darkness eliminates functional patterns (H+ transport and photosynthetic quantum yield) at the plasma membrane and the chloroplast layer. In contrast, triggering of AP eliminates only the H+ transport pattern at the plasma membrane but enhances the heterogeneity in the chloroplast layer.

EFFECT OF ACTION POTENTIAL ON LIGHT-INDUCED ABSORBANCE CHANGES OF CHLOROPHYLL P700 Considering strong effects of AP on chlorophyll fluorescence, quantum yield of PSII reactions, and linear electron transport, one may suppose that changes in electron flow should be also manifested in the reactions of PSI. Absorbance changes reflecting the redox transitions of the oxidized form of chlorophyll P700 in the reaction centers of PSI are suitable to follow such reactions. In commercially available instruments, the absorbance changes of oxidized P700 form (P700+) are monitored at 810–830 nm with respect to a reference wavelength (870 nm). The differential dual-wavelength mode allows measurements of lightinduced P700 oxidoreductions with minimum signal distortion due to other processes. The technique is described in detail in several research and technical papers (Klughammer & Schreiber, 1994, 2008). Measurements of P700+ absorption in individual cells are complicated by low content of P700 chlorophyll (in comparison with total chlorophyll content). Micromethods for such measurements are still unavailable, while application of standard equipment is hindered by a small projective area of a single cell in the measuring beam cross-section. In our studies the sample area was increased by parallel adjustment of eight isolated internodes placed at a close distance to each other. Fixed position of cells in the chamber was provided by narrow slits in the partition between two neighboring compartments. The slits were filled with silicone grease for electrical insulation of two compartments. Excitatory current pulses were applied between electrodes placed in these insulated compartments of the measuring chamber. Redox transitions of chlorophyll in the reaction center of PSI (P700) were followed from differential absorbance changes at 810 and 870 nm (∆A810 signal). The measurements were performed with a PAM-101 recording system (modulation frequency 100 kHz) combined with a two-wavelength emitter–detector unit ED-P700DW (Walz, Germany). A branched fiber-optic light guide was used to deliver measuring and acting light to the sample and to direct transmitted IR light to the detector. Internodal cells were placed between the mirrored support and the end of the light guide cable, so that the measuring beam passed the cells in the forward and reverse directions (reflectance mode).


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Figure 7. Absorbance changes ΔA810 in C. corallina cells induced by two sequential pulses of white light (150 µE m–2 s–1) under resting conditions, in the post-excitation period, and after pretreatment with the ionophore A23187. The cells were bathed in artificial water containing 0.1 mM Ca2+ (a, b) and in water with 1 mM Ca2+ (c, d). The increase in absorbance at 810 nm with respect to that at 870 nm (ΔA810) corresponds to accumulation of chlorophyll P700 oxidized form, P700+. (a) Identical kinetics of ΔA810 induced in the dark-adapted cells at rest (curve 1) and 40 s after AP stimulation in darkness (curve 2); (b) ΔA810 signals in cells exposed continuously to background white light (3 µE m–2 s–1) under resting conditions (curve 1) and 40 s after AP generation (curve 2); (c) the same as (b) except for elevated Ca2+ concentration (1.0 mM) in artificial pond water; (d) ΔA810 transients in cells continuously exposed to background white light at 1 mM Ca2+ in the medium without ionophores (curve 1) and under similar conditions in the presence of 10 μM A23187 (curve 2). Note similar modifications of ΔA810 in the post-excitation period and after pretreatment with A23187, provided the cells were exposed to continuous background light. The cells were kept in darkness (D) between measurements or stayed under continuous background light (L).

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During ∆A810 measurements the cell samples were irradiated with white light from a Luxeon LXK2-PWN2-S00 light-emitting diode (Lumileds, United States) at a photon flux density of 150 µE m–2 s–1. In the intervals between ∆A810 measurements, the cell parts positioned under the light guide were kept in darkness or exposed to weak background white light (3 µE m–2 s–1) obtained from a Schott KL-1500 illuminator (Germany). Traces shown in Figure 7 represent averaged curves from four measurements, each made with eight cells. Figure 7a shows ∆A810 signals arising in response to a series of two white light pulses after 5-min dark exposure with and without the suprathreshold electric stimulation of cells 40 s prior to measurement. The choice of 40-s interval between triggering AP and measurements was based on our previous experience, because the strongest quenching of Fm' fluorescence occurred after such period. When the cells were kept in darkness prior to measurements (Figure 7a), identical kinetics of ∆A810 signals were observed, both with and without AP generation. Different shapes of ∆A810 signals in response to the first and the second light pulses result presumably from light-dependent activation of the electron carriers on the acceptor side of PSI (ferredoxin-NADP reductase) and of Calvin cycle enzymes (Schansker et al., 2003). This photoactivation is known to accelerate P700 oxidation due to stimulation of electron efflux from P700 to available acceptors. The lack of AP effect on ∆A810 in predarkened cells is fully consistent with observations that AP-induced fluorescence changes appear only in illuminated samples but not in darkness (Krupenina & Bulychev, 2007). Figure 7b illustrates a similar experiment when the analyzed cell regions were continuously exposed to weak background white light. The ∆A810 signals measured in illuminated resting cells (curve 1) and in the same cells tested 40 s after AP generation (curve 2) differed significantly in the response to first light pulse. In pre-excited cell the transient minimum between the first and the second peaks of P700 oxidation was less pronounced and P700 photooxidation developed faster than in the resting cells. The ∆A810 responses to the second pulse were nearly identical before and after the membrane excitation. Different shapes of ∆A810 responses at rest and after excitation (curves 1, 2) indicate either a faster electron flow in the acceptor side of PSI after AP propagation or retardation of electron flow between PSII and PSI. The second alternative seems preferable, as it is consistent with the results of fluorescence measurements. The retardation of PSII-driven electron flow after AP generation is well documented (Krupenina & Bulychev, 2007, 2008). The suppression of electron flow depends largely on generation of thylakoid ∆pH that restricts the rate of plastoquinol oxidation by the cytochrome b6f complex. The results of Figure 7 represent the first observation of AP impact on electron transport related to oxidoreductions of the primary donor in PSI reaction center, chlorophyll P700. According to the hypothetical scheme of AP influence on electron transport (Krupenina & Bulychev, 2007), the increase in cytosolic Ca2+ content during AP gives rise to Ca2+ uptake by illuminated chloroplasts and to respective accumulation of Ca2+ in the stroma. The chloroplast envelope is endowed with light-dependent Ca2+ uptake system that is inactive in darkness (Muto et al., 1982, Kreimer et al., 1985). The elevation of stromal Ca 2+ content is known to inhibit the ATP-consuming reactions of CO2 fixation (Johnson et al., 2006). In turn, this inhibition would increase the thylakoid ∆pH and suppress electron transport between two photosystems. The supposed involvement of Ca2+ was checked in our experiments by the treatment of Chara cells with the ionophore A23187 that exchanges divalent cations against protons. It is known that the cytosolic Ca2+ level increases in plant cells treated with this


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ionophore (Jones et al., 1998). One may expect that effects of AP generation and A23187 treatment on ∆A810 transients should be similar in illuminated cells. The results shown in Figures 7c and 7d prove this similarity. Experiments were performed at elevated Ca2+ level (1 mM) in the medium with the purpose to increase the efficiency of the ionophore treatment. Figure 7c shows that the effect of AP on ∆A810 kinetics was clearly evident in the presence of 1 mM Ca2+ and was largely similar to that observed at 0.1 mM Ca2+. In pre-excited cells exposed to the background white light, the photooxidation of P700 was manifested stronger in response to the first light pulse than in the resting cells. Figure 7d shows ∆A810 signals observed in the resting cells exposed to background illumination in the absence and presence of the ionophore A23187. It is seen from Figures 7c and 7d that the influence of calcium ionophore on ∆A810 was equivalent to the influence of preliminary AP generation. The ionophore-induced modification of P700 photooxidation kinetics cannot be ascribed to elimination of ∆pH at the thylakoid membrane, because the dissipation of ∆pH by other protonophores (nigericin, monensin in combination with valinomycin) was shown to inhibit the secondary wave of P700 oxidation (Bulychev et al., 2008), in contrast to the faster onset of secondary P700 oxidation under the action of A23187. These results substantiate the calcium hypothesis of AP influence on photosynthesis.

EVIDENCE FROM ΔA810 FOR AP-TRIGGERED PERMEATION OF METHYL VIOLOGEN INTO PLASTIDS OF AN INTACT CELL The AP generation in an intact cell diminishes the effective quantum yield of PSII reactions and increases nonphotochemical losses of chlorophyll excitations (dissipation of light energy as heat), which is manifested as a transient decrease in maximal chlorophyll fluorescence Fm' or NPQ increase (see Figures 5, 6). The largest increase in NPQ after AP generation was observed on cells treated with a dicationic artificial electron acceptor methyl viologen (MV) (Bulychev & Krupenina, 2008c). In the presence of MV, unlike physiological conditions, the AP-induced increase in NPQ was irreversible under constant irradiance, i.e., it developed only once, in response to triggering the first AP. Incubation of resting Chara cells in the presence of MV had no discernible effect on chloroplast functioning in vivo, which indicates that the resting cells possess effective barriers for MV permeation from the external medium into the chloroplasts. On the other hand, the pathways of photosynthetic electron transport were strikingly modified after a single AP generation in the presence of MV. The chlorophyll fluorescence data indicated that MV became accessible acceptor within the chloroplast stroma immediately after the electric pulse generation at the cell membrane (Bulychev & Krupenina, 2008b). A reasonable assumption is that the impact of AP on chloroplast functioning might be complex and include changes in membrane permeability of the plasmalemma–chloroplast envelope system to artificial charged substances such as MV. Oxidized form of MV is a divalent cation with effective length and width of 12 and 6 Å, respectively. Substances of such dimensions can permeate through the Ca2+ channels of characean cells (G.N. Berestovsky, personal communication).

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Figure 8. Kinetics of chlorophyll P700 oxidation in dark-adapted C. corallina cells induced by a pulse of white light (150 μE m–2 s–1) before (a) and after (b) a single excitatory stimulation in the presence of methyl viologen (MV). (a) Consistent kinetics of ΔA810 for three sets of experimental conditions: (i) nontreated resting cells, (ii) once stimulated cells in the absence of MV, and (iii) resting cells incubated for 30 min in the presence of 0.2 mM MV. For each set of experimental conditions ΔA810 were measured in four replicates at 6-min intervals. The average curve for three sets of records is presented with standard errors between the treatments. (b) Kinetics of ΔA810 after generation of a single AP in the presence of 0.2 mM MV; the averaged curve was measured in four replicates at 6-min intervals after AP generation. Upward and downward arrows designate the moments when light was switched on and off.

However, it is not yet known if biological cell membranes can increase their permeability to MV in response to short-term physiological depolarization. The recognition of a possible role of AP in permeation of biologically active substances into the cytoplasm and organelles is not only important for understanding the intracellular interactions but has also a practical aspect, because methyl viologen (1,1‘-dimethyl-4,4‘ bipyridinium chloride, known also as paraquat) is an efficient herbicide acting on PSI in chloroplasts. Methyl viologen is known to accept electrons from iron-sulfur centers on the acceptor side of PSI competing with the natural acceptor ferredoxin; it diverts electron flow from the assimilating pathway and from the PSI-driven cyclic route to the reactions associated with the production of reactive oxygen species and membrane destruction (Ivanov et al., 1998). There are numerous ways to verify the hypothesis that MV cation does not penetrate into chloroplasts of resting Chara corallina cells within tens of minutes but enters plastids and is incorporated into photosynthetic electron-transport chain immediately after generation of a single AP on the electrically excitable membrane. The onset of MV-mediated photoreactions in chloroplasts in vivo can be detected from the induction changes in the redox state of chlorophyll P700 in PSI reaction centers. It is known that MV effectively removes electrons from PSI, thereby causing fast oxidation of P700 in the light. Figure 8 shows changes of P700 redox state in dark-adapted (5 min) C. corallina cells, which were induced by the pulse of white light upon sequential succession of four sets of


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experimental conditions: (1) resting cells in the absence of MV; (2) cells stimulated once prior to repeated measurements of ∆A810 during subsequent 30-min period, (3) resting cells incubated for 30 min in the presence of 0.2 mM MV; and (4) cells incubated in the presence of 0.2 mM MV and stimulated once prior to repeated measurements of ∆A810 during subsequent 30-min period. The kinetics of ∆A810 transients for the first three sets of experimental conditions were almost identical (Bulychev & Krupenina, 2008d). The averaged curve for all these treatments is shown in Figure 8a together with bars designating standard errors between the treatments. Illumination of dark-adapted resting cells in the absence or presence of MV, as well as after stimulation of a single AP in the absence of MV, induced a rapid peak of P700 oxidation followed by the reduction stage and subsequent second wave of P700 oxidation. Such ΔA810 kinetics is also characteristic of some higher plants and cyanobacteria. The intermediary P700+ reduction is related to the arrival of electrons from PSII following plastoquinone reduction, while the second wave of P700 oxidation is thought to arise from the release of restrictions for electron transport on the acceptor side of PSI (Schansker et al., 2003, Bulychev et al., 2008). Thus, ∆A810 transients in resting cells incubated in the absence or presence of MV showed no discernible difference. The AP generation in a dark-adapted cell in the absence of MV had no appreciable influence of ∆A810, in consistency with Figure 7a. By contrast, the kinetics of ΔA810 induction curve was modified rapidly and irreversibly in the presence of MV after triggering a single AP with an electric stimulus (Figure 8b). In this case switching the light on was accompanied by rapid oxidation of P700 within about 100 ms without the stage of intermediary P700 reduction. Rapid oxidation of P700 reflects the capacity of MV as a very effective electron acceptor at the PSI level. The essential similarity of ΔA810 signals for resting cells in the absence and presence of MV in the medium suggests that permeation of MV into chloroplasts in vivo was prevented by effective membrane barriers, such as the plasmalemma and the chloroplast envelope. Since AP generation did not influence the ΔA810 signals in the absence of MV but immediately modified ΔA810 in its presence, it is reasonable to suppose that the passage of MV towards the chloroplast thylakoids was facilitated abruptly during or after AP. The generation of a single AP was sufficient for the delivery of MV into chloroplasts in effective concentrations.

TRIGGERED ENTRY OF MV ELIMINATES THE PHOTOSYNTHETIC PATTERN THROUGH CHLOROPLAST ENERGIZATION IN THE ACIDIC CELL AREAS Evidence for the involvement of MV in photochemical reactions of chloroplasts in vivo can be also derived from chlorophyll fluorescence because MV-supported electron flow induces strong energization of thylakoid membranes. Electron transport from water to O2 via MV generates ΔpH, which is not properly utilized since O2 photoreduction proceeds without the use of ATP. Thus, permeation of MV from the medium into chloroplasts should be accompanied by excess thylakoid energization, energy-dependent quenching, and the respective decrease in quantum efficiency of PSII. Unlike physiological situation, the quenching associated with MV permeation might occur both in alkaline and acid cell regions.

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Figure 9 shows light response curves for the quantum yield of electron transport in PSII (ΔF/Fm') and for NPQ in the acidic cell regions in the absence and presence of MV. Under control conditions (open squares) ΔF/Fm' remained high over a broad range of light intensities, decreasing at photon flux densities above 70 μE m–2 s–1. The addition of MV to a final concentration as high as 0.2 mM and subsequent 30-min incubation of cells in the presence of MV did not cause any significant change in the light curves for ΔF/Fm' (solid circles). However, after AP generation the light curve has changed considerably. The effective efficiency of PSII decreased after AP at a wide range of photon flux densities and remained high only at very low light intensities (triangles). Similar strong changes were observed in the light curves of non-photochemical quenching NPQ. As can be seen in Figure 9b, in the absence of MV, as well as in the presence of MV prior to cell excitation, NPQ was low, increasing only at the highest light intensity used. By contrast, after generation of a single AP, strong non-photochemical quenching developed at moderate and high photon flux densities, and the NPQ light curve shifted strongly towards low intensities. These results provide direct evidence that MV-mediated energization of chloroplast membranes developed rapidly and irreversibly after generation of a single AP at the plasma membrane.

Figure 9. Light-response curves for (a) quantum efficiency of PSII-driven electron transport (ΔF/Fm') and (b) non-photochemical quenching (NPQ) in chloroplasts of acidic regions of C. corallina cells that were incubated in the absence of MV (squares), in the presence of 0.2 mM MV at rest (circles), and after triggering a single AP in the presence of 0.2 mM MV (triangles).


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Figure 10. Spatiotemporal dynamics of ΔF/Fm' (a, c) and NPQ coefficient (b, d) in C. corallina cell, induced by AP generation under control conditions (a, b) and after incubation of the same cell in the presence of 0.45 mM MV (c, d). The moment of triggering an AP is marked with dotted lines.

Effects of AP on PSII-driven electron transport and fluorescence quenching in the absence and presence of MV in the outer medium are best illustrated from the dynamics of ΔF/Fm' and NPQ images in the resting state and after cell excitation (Figure 10). The upper panels show the AP-induced changes in NPQ and ΔF/Fm' patterns under physiological conditions, and the lower panels show AP-triggered changes in the same cell after 30-min incubation in the presence of 0.45 mM MV. In the absence of MV, the effects of AP on ΔF/Fm' and NPQ were similar to those shown in Figures 5 and 6. Prior to AP generation, the quantum efficiency was comparatively high (ΔF/Fm' ~0.65) in broad acidic regions and was lower in alkaline regions (Figure 10a). The cell excitation led to the transient retardation of electron transport (decrease in ΔF/Fm') in the regions with low activity of PSII (alkaline regions) and had no appreciable effect on PSII-driven electron transport in regions with higher ΔF/Fm' values (acidic regions). The ΔF/Fm' pattern became more contrast temporally (appearance of spots with yellow and red false colors) and later returned to its original state. It is seen in Figure 10b that, prior to cell excitation at a given light intensity, NPQ was low and spatially uniform throughout the cell. However, after triggering an AP, strong quenching

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developed in the same regions where inhibition of PSII activity was manifested. The increase in NPQ was temporal and eventually replaced by the release of quenching. Next, the same cell was incubated for 30 min in the presence of 0.45 mM MV. After this incubation, the heterogeneity of ΔF/Fm' distribution over the cell was clearly evident (Figure 10c, left side of the diagram, t < 2 min). The regions of high PSII efficiency (ΔF/Fm' ~ 0.59) alternated with regions of low ΔF/Fm' (0.25–0.35). The range of ΔF/Fm' changes in the spatial profile of the resting cell was larger in the presence of MV than in its absence. The increased heterogeneity of photosynthetic parameters was also observed in the spatial profiles of NPQ (Figure 10d, left side of the diagram, t < 2 min). Low NPQ values were observed in the acidic zones of resting cells, while NPQ levels were as high as 0.7–1.2 in the alkaline regions. The generation of AP in the presence of MV at t = 2 min was accompanied by rapid and irreversible changes in ΔF/Fm' and NPQ patterns. In broad regions with high rates of PSII electron flow (ΔF/Fm' ~ 0.6), the AP propagation caused a sudden decrease in ΔF/Fm'. At the same time, the AP propagation induced smaller changes of ΔF/Fm' in the alkaline regions. The strong AP-induced decrease of ΔF/Fm' in the regions with active photosynthesis and small changes of this parameter in the regions with low photosynthetic activity caused rapid flattening of ΔF/Fm' spatial profile in the post-excitation period. In the presence of MV, the NPQ profiles also underwent irreversible smoothing after AP propagation (Figure 10d). At t < 2 min, the NPQ profile was very sharp, with NPQ values ranging between 0 and 1–1.3. Following the AP generation, NPQ values increased strongly (from 0–0.1 to 0.7–1.0) in the acidic regions but remained largely unaffected in the alkaline regions, where NPQ values were already high prior to excitation. As a result the NPQ profile along the cell length became rather flat in the post-excitation period. Strong AP-induced quenching of chlorophyll maximal fluorescence Fm' provides evidence that MV gained access to the chloroplast interior (stroma) immediately after AP propagation along the internode. Moreover, a comparatively weak effect of AP on chloroplasts of alkaline regions in the presence of MV suggests that MV might have permeated into the chloroplasts of these regions during prolonged incubation under resting condition, while the chloroplasts of the acid regions remained inaccessible for this agent in the resting cell. By inspecting ΔF/Fm' and NPQ images induced by AP in the absence and in the presence of MV one may suppose that chloroplasts located in broad acidic zones are insensitive to MV treatment unless an AP is triggered. At the same time, chloroplasts located in the alkaline zones seem to be less protected against MV permeation under resting conditions, which was manifested in high NPQ in these cell regions after long (30 min) incubation of resting cells in MV-containing medium. Obviously, the AP generation abruptly increases the accessibility of chloroplasts for the electron acceptor and herbicidal agent MV, which rapidly switches photosynthetic electron flows from the assimilating pathway to the MV-catalyzed photoreduction of O2 and associated reactions.

CONCLUSION The results obtained with pH microelectrodes, Imaging PAM fluorometer, and P700 absorbance measurements (ΔA810) on individual cells of Chara corallina have proven that spatial patterns of photosynthetic electron transport and proton flows across the plasmalemma


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and thylakoids are highly sensitive to a single electrical excitation of the plasma membrane. The effects of AP propagation on photosynthesis and H+ transport are durable —two orders of magnitude longer than the electrical signal itself — and extend up to 30 min. The AP generation disrupted strict coordination between photosynthesis and the apoplastic pH, established under continuous light prior to excitation. This disruption was evident from the temporal decay of the pH bands in parallel with an enhancement of spatial heterogeneity for NPQ and quantum yield of PSII-dependent electron flow. The decay of pH bands after AP was found to originate from inactivation of high conductance in the alkaline cell regions and from concurrent inhibition of the PM H+-pump in the acidic regions. The influence of AP on photosynthetic electron flow, first observed from measurements of chlorophyll fluorescence, was also manifested in the effect of AP on the kinetics of P700 photooxidation.

Figure 11. Tentative scheme of the reaction chain leading from membrane excitation to changes of photosynthetic pattern in illuminated C. corallina cell. See text for explanation. The gradient colors of external medium in the acid and alkaline zones correspond to yellow and red staining of pH indicator phenol red in these zones.

The emerging scheme of AP-triggered phenomena in photosynthesizing excitable cell (Figure 11) should consider separately the reaction sequences occurring in functionally different cell regions. The starting event during AP, common to all cell regions, is nearly a 100-fold elevation of cytoplasmic Ca2+ level due to opening of voltage-gated Ca2+ channels in the plasmalemma (Kikuyama & Tazawa, 1983, Sanders et al., 2002, Berestovsky & Kataev, 2005) and due to Ca2+ release from intracellular stores (Wacke & Thiel, 2001, Wacke et al., 2003). The calcium burst would inhibit (presumably through modulation of Ca2+-binding

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proteins (Kinoshita et al., 1995, Rutschmann et al., 2002)) the PM conductance in the alkaline regions and the PM H+-pump in the acidic regions. Thus, the Ca2+ signal would act in combination with elevated cytoplasmic pH in the alkaline regions where passive H+ influx was blocked after AP and would act in combination with lowered cytoplasmic pH in the regions where H+-pump activity was arrested. According to opposite shifts of cytoplasmic pH, the light-dependent Ca2+ uptake by chloroplasts would be higher in the alkaline regions than in the acidic regions (Krupenina et al., 2008). Hence, the Ca2+-mediated inhibition of the Calvin cycle reactions is expected to be stronger in the alkaline regions. The ensuing decrease in ATP consumption would cause area-specific over-energization of thylakoids (increase in thylakoid ΔpH), enhancement of non-photochemical quenching, and retardation of linear electron transport (Krupenina & Bulychev, 2007). The negative influence of elevated stromal [Ca2+] on photosynthesis can be overcome through the removal of excess Ca2+ from the stroma by means of Ca2+/H+ antiporter located at the thylakoid membrane (Ettinger et al., 1999, Johnson et al., 2006). Such an exchange would reactivate the Calvin cycle reactions in parallel with lowering of thylakoid ΔpH and the respective release of non-photochemical quenching. In the presence of hydrophilic biologically active agents, e.g., MV, the influence of AP on photosynthesis might be additionally mediated by permeability changes of the plasma membrane. It appears that MV can permeate through voltage-gated Ca2+ channels in the plasmalemma. Thus, generation of a single AP is accompanied by entry of MV into the cell in amounts sufficient for redirection of electron transport from native assimilating pathway to the photoreduction of O2 catalyzed by MV. Although this work revealed a series of new physiological phenomena associated with AP propagation in excitable plant cells, the functional significance of these striking changes remains to be determined. One may speculate that different behaviors of external pH pattern and intracellular photosynthetic pattern in response to cell excitation provide flexibility for cell adaptation to the environment, depending on the severity of stress underlying AP generation. If triggering of the AP is not accompanied by changes in cell position and lighting conditions, the enhanced photosynthetic pattern would serve as a template for the recovery of coordination between pHo and photosynthetic bands. However, if AP generation was accompanied by cell reorientation due to agitation of water or mechanical deformation of algae, the altered lighting conditions would rearrange the distribution of photosynthetic activity along the cell. In this case the capacity of the AP to override the effect of illumination on pH bands can be useful as a necessary step in rearrangement of the pH banding pattern that serves to adjust CO2 acquisition (the CO2/HCO3– ratios) to particular illumination conditions of the natural environment.

ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research. We are grateful to Drs. M.R.G. Roelfsema and U. Schreiber for their kind offer of the laboratory facilities at Würzburg University and for their help with fluorescence imaging experiments.


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Chapter 4

ACTION POTENTIAL PRODUCTION: AN ION CHANNEL DEPENDENT PROCESS Richard Hahin* Biological Sciences Department, Northern Illinois University, DeKalb, IL 60115, USA

ABSTRACT Action potentials are produced as a consequence of opening (activation) and closing (deactivation) of ion channel proteins that are distributed in cell membranes. In human nerve and skeletal muscle cells the principal ion channels responsible for action potential (AP) production are voltage- dependent sodium (Nav) and potassium (Kv) channels; however voltage dependent calcium channels (Cav) do play essential roles in AP production in cardiac pacemaker and ventricular cells. A number of different homologous types (isoforms) of Nav , Cav, and Kv displaying altered properties are differentially found in various excitable cells to produce APs that differ in character. Nav , Cav, and Kv possess specialized structural features (voltage sensors) that enable them to sense voltage changes and respond to those changes by kinetically altering their states to allow ions to selectively flow through the membrane channel via a structural pore region. A number of agents act to bind to the channels and act to alter their properties and thus alter AP production. Nav acts as specific target for a number of animal and plant toxins. Binding of the toxins to the channels act to alter the size, shape and conduction velocity of the AP. Nonspecific binding of a wide number of other chemical agents to Nav act to cause changes in AP production and properties. APs have been mathematically modeled using several different approaches; however the most widely used method was developed by Hodgkin and Huxley (1952) and continues to be used in predicting AP behavior in simulation programs.

*

[email protected]

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Figure 1. Action potential. Figure 1 shows an action potential elicited by a current pulse (upper record) applied to a node of Ranvier of a single mylenated neuron obtained from a frog (Rana pipiens) sciatic nerve.

INTRODUCTION Action potentials (APs) are electrical potential changes that occur in the plasma membranes of excitable cells such as neurons and typically propagate along the axons to distant locations to signal other cells. Figure 1 illustrates a typical AP elicited by a pulse of current and recorded from a single myelinated axon. The AP displays an upstroke from the resting potential to a peak and decays back down to the resting value in the downstroke. APs are produced as a consequence of the opening and closing of ion channels distributed along excitable cell membranes. Excitable cells are capable of AP production and propagation and are found in a number of tissues in humans and other animals. Excitable cells in humans include heart, neurons, and muscle. The size, shape and properties of the APs produced in each of the above cell types depend on the distribution, density, and properties of the ion channels found in their respective membranes. In order to best understand the properties, production, and propagation of APs it is important to describe the ion channel proteins that play a central role in the process.

EARLY WORK: ION CHANNEL ISOLATION AND PURIFICATION OF NA+ AND CA CHANNELS In the early 1950‘s AP production and propagation was mathematically predicted to arise as a consequence of time and voltage-dependent changes in the membrane conductance to both sodium (Na+) and potassium (K+) ions (Hodgkin and Huxley, 1952d). At the time their work suggested that only two types of putative membrane pores or channels, selectively

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permeable to Na+ and K+, were necessary for the production of APs. The mathematical framework they used to describe the conductance changes they observed also suggested that channels could exist in different functional states, including open, closed, and inactive states. Their work also suggested that ion channels selectively transport particular ions over others and can exist in and make kinetic transitions between a number of states. The channel states typically can be lumped into closed, open or inactivated states and this is best illustrated by kinetic models developed for Na+ channels (Armstrong & Bezanilla, 1977; Goldman and Hahin, 1978, Armstrong 2006). Hodgkin and Huxley‘s work caused a flurry of experimentation designed to identify the molecules responsible for the voltage and time dependent conductance changes observed during AP production. Early work using agents that typically altered amino acids (Eaton et al., 1978) or proteins showed that the Na+ or K+ conductance could be modified. This suggested the putative channels or pores were membrane proteins. Putative Na+ channels were found to be made non-conducting (blocked) by two specifically acting high affinity toxins, tetrodotoxin (Narahashi et al., 1964) and saxitoxin (Narahashi et al. 1967). These agents proved to be valuable in isolating and characterizing the Na+ channel protein. Agnew et al. 1978 used tritiated tetrodotoxin ([3H]TTX)to isolate and purify sodium channel proteins from membranes of Electrophorus electricus by membrane solubilization techniques and gel filtration chromatography. Na+ channel proteins bound by tritiated saxitoxin ([3H]STX) were isolated after being solubilized from neuronal synaptic membranes (synaptosomes) from rat brain using centrifugation techniques and gel filtration chromatography (Goldin et al., 1980). The STX binding-protein isolated also was reconstituted into phospholipid vesicles and shown to exhibit ion transport. Barchi et al. (1980) also used [3H]STX to purify Na+ channel protein from rat skeletal muscle. Using a similar approach, [3H]nitrendipine, which blocks calcium channels, was used to purify calcium channels from skeletal muscle (Curtis and Catterall, 1984). The isolated and purified calcium protein complex was found to consist of several polypeptide subunits including a pore forming α subunit (Curtis and Catterall, 1984). Later work showed that both Na+ and Ca2+ channels show similarities in structure and function with both channels possessing a large α subunit consisting of 4 repeated domains and auxiliary subunits.

MOLECULAR GENETIC CHARACTERIZATION OF CHANNEL PROTEINS Using an alternate approach, K+ channel proteins were identified via their genes (Tempel et al., 1987; Kamb et al., 1988; Pongs et al., 1988), and this approach led to the discovery of many ion channel protein subunits that assemble to form functional potassium channels that play a key role in and alter the characteristic properties of APs. The characteristic α1 subunit amino acid sequence of the calcium channel in skeletal muscle that constitutes the pore forming region of the channel was obtained by cloning and sequence analysis of DNA complementary (cDNA) to its messenger RNA (Tanabe et al. 1987). Calcium channel α1 subunits found in other cell types (e.g. cardiac, brain) were identified thereafter (Mikami et al., 1989; Williams et al., 1992). These and other similar molecular genetic studies led to a clearer understanding of the similarities and structural characteristics of the voltagedependent channel proteins. Molecular genetic, structural and electrophysiological studies

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revealed that voltage-gated Na+, K+, and Ca2+ channels have similar functional and structural properties. The amino acid sequences of the Na+, K+, and Ca2+ protein channels are evolutionarily related and comprise a part of a protein superfamily (Dayhoff, 1976) or gene superfamily which includes other voltage-gated cation selective ion channels.

DIVERSITY OF CHANNEL PROTEINS There is a large diversity of Na+, K+, and Ca2+ channels that transport cations. In addition to the cation-selective channels, there are voltage-gated Cl- channels that play roles in modifying AP production and properties. The diversity of channels appears to derive from a primordial gene and evolutionary changes and selection processes. The voltage-dependent Ca2+ (Cav) and Na+ channel (Nav) gene/protein families each contain an α subunit polypeptide which contains 4 internal repeated domains (I-IV) that each contain six transmembrane αhelices (S1-S6) and a pore (P) loop between S5 and S6 (Figure 2; Conley and Brammar, 1999). The nomenclature for these channels has been standardized to identify the major permeant ion (Ca2+, Na+, or K+), an identifier (subscript) that specifies the principal way the channel is activated (e.g. v-voltage, Ca-calcium,) a number that identifies the gene subfamily corresponding to the channel, followed by a second number (preceded by a period) that specifies the particular channel (isoform) (Catterall et al. 2005). Nav α polypeptide subunits possess four repeated domains and are expressed with other smaller subunits β1-β4 (Catterall et al. 2005) to form a number of channel isoforms. Figure 2 shows the membrane organization of Na+ channel subunits. There are nine Nav channel isoforms (Nav1.1-1.9) found in mammals (Catterall et al., 2005). Nav channels display much less functional diversity than their Cav and Kv counterparts. However, Nav channels play a central role in AP production. Similar to Nav channels, the Cav α polypeptide subunits are typically expressed with other polypeptide subunits (α2/δ, β and γ) to produce many functionally distinct subtypes of channels. The Cav channels selectively conduct Ca2+ ions when the cell membrane is depolarized. When activated, Cav channels lead to a number of intracellular events including transmitter release and muscle contraction. In some instances they play a key role in action potential production. Kv channels display the greatest diversity because they can be expressed as channel proteins with 4 identical subunits, 4 different subunits, or a combination of identical or different subunits. In addition, there are a number of types of pore forming subunits that are expressed in cells that can combine to form a functional channel leading to a multiplicity of channels. The Kv channels are multimers of transmembrane polypeptides subunits. There are 5 classes of K+ channels (Gutman et al. 2003). The first exists as a tetramer of a subunit that possesses 6 transmembrane helices and one pore-forming P region. The Kv channels are included in the first class of K+ channels and consist of 8 members defined by the subfamilies of genes that encode the proteins (Kv1-Kv6; Kv8 and Kv9). The second class of K+ channels (e.g. inward rectifier and KATP channels) are not opened in response to membrane voltage depolarization, but may be activated by an intracellular agent such as ATP, are comprised of a tetramer of subunits that possess two transmembrane helices and a P region (Gutman et al.


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2003). Another third class of K+ channels is a tetramer of subunits with 7 transmembrane helices and represents large conductance Slo or Ca2+ activated BK channels that play important roles in various physiological processes (Gutman et al. 2003). These channels can be activated by voltage, Ca2+, or intracellular agents (Salkoff et al. 2006; Cui et al. 2009). Another class of K+ channels is a dimer of two subunits; the first is a six transmembrane helix with a P region segment connected to a two transmembrane helix with a P region and the second subunit is an 8 transmembrane helical region with 2 P regions (Gutman et al. 2003). The fifth class of K+ channels are the two pore domain channels (K2P) which is a dimer of a 4 transmembrane helical segment with 2 P regions. When initially discovered, this class of K+ channels was recognized to play a crucial role in maintaining and modifying the resting K+ conductance of cells (Lesage and Lazdunski, 1999) in addition to other important roles. Later work clarified more of the roles the K2P channels play in various physiological processes (Lotshaw, 2007). This large diversity of ion channels provides various types of cells to produce and alter AP production in many different ways.

Figure 2. Transmembrane organization of sodium channel subunits. The primary structures of the subunits of the voltage-gated Na+ channels are illustrated transmembrane-folding diagrams. Cylinders represent probable α-helical segments. Bold lines represent the polypeptide chains of each subunit, with length approximately proportional to the number of amino acid residues in the brain sodium channel subtypes. The extracellular domains of the β1 and β2 subunits ar shown as immunoglobulin-like folds. ψ, sites of proable N-linked glycosylation; P, sites of demonstrated protein phosphorylation by protein kinase A (circles) and protein kinase C (diamonds); shaded, pore-lining S5-P-S6 segments; white circles, the outer (EEDD) and inner (DEKA) rings of amino residues that form the ion selectivity filter and tetrodotoxin binding site; ++, S4 voltage sensors; h in shaded circle, inactivation particle in the inactivation gate loop; open shaded circles, sites implicated in forming the inactivation gate receptor. Sites of binding α- and β-scorpion toxins and a site of interaction between α and β1 subunits are also shown. Figure reprinted with permission from Catterall, Goldin and Waxman, 2005; © ASPET.

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HODGKIN-HUXLEY PREDICTIONS OF ACTION POTENTIALS +

APs were recorded and shown to be related to the influx of Na and efflux of K+ in nerve cells early on in the study of neuronal excitability (Rothenberg, 1950; Keynes and Lewis, 1951). However, the landmark studies of Hodgkin, Huxley and Katz (1952) and Hodgkin and Huxley (1952a-d) characterized the properties of the membrane conductance of K+ and Na+ that was needed to produce AP behavior in squid giant axons. Hodgkin and Huxley developed a quantitative mathematical description of APs and their equations predicted many of the properties of APs quite well. Hodgkin and Huxley modified and used a negative feedback voltage control system (voltage-clamp) first developed by Cole (1949) and Marmont (1949), to record ionic currents over a region of axon membrane that was kept uniformly isopotential (space-clamped) over the membrane area. By employing internal axial wire voltage sensing and current passing electrodes, external electrodes, a guard system to isolate a region of axon membrane, and a voltage-clamp, Hodgkin and Huxley recorded sodium and potassium currents from squid giant axons at various membrane potentials and characterized their kinetic changes as a function of membrane potential. All other currents that were detected were lumped together as a ―leak‖ current and were considered an ohmic conductance.

Figure 3. Voltage-clamp current records. Voltage-clamp current records obtained from an isolated single myelinated nerve frog node of Ranvier. The myelinated nerve fibers were voltage-clamped using a modified version of the Dodge and Frankenhauser (1958) potentiometric voltage-clamp method. The lower set of records represents a sequence of voltage-clamp pulses spaced 10 mV apart from an initial hyperpolarizing prepulse potential (≈ -120 mV). The holding potential (≈ -80 mV) was set so that steady-state sodium channel inactivation was 0.75. The upper traces represent nodal ionic currents recorded at each potential.


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When the axon membrane voltage was voltage-clamped and currents were recorded, depolarizing potentials activated both Na+ and K+ currents when applied as a step from an initial hyperpolarized holding potential. In a typical voltage-clamp current record to a depolarizing voltage step from the resting potential, an initial inward Na+ current was followed by the delayed appearance of an outward K+ current. The voltage-clamp technique has undergone many alterations, improvements and has been applied to many different cells other than giant axons of squid and continues to be used. An example of a family of Na+ and K+ currents recorded at a set of voltages using the voltage-clamp using an isolated node of Ranvier from a myelinated axon is shown in figure 3. Hodgkin and Huxley bathed axons in a medium that was Na+ free and this allowed the time-delayed K+ currents to be studied in isolation (Hodgkin and Huxley, 1952a). However, Na+ currents elicited by depolarizing steps exhibited an initial activation followed by an inactivation to small values. Hodgkin and Huxley (1952b,c, &d) mathematically modeled the initial activation of Na+ and K+ conductances using normalized, unitless, variables m, and n respectively. Since a depolarization caused an initial increase in Na+ conductance with only a short delay it was modeled as a product of a maximum conductance, , and m3, while the + . Inactivation much more delayed increase in K conductance was modeled similarly as of the Na+ conductance was modeled by 1-h, where h represented the active fraction of conductance (Hodgkin and Huxley, 1952c). Each of the variables was described by a first order differential equation (eq. 2-4). If the membrane potential was not controlled using negative feedback, non-propagating membrane APs could be recorded over the membrane area. Under this condition no axial current flows and membrane APs were then predicted by setting the membrane current to 0 and solving for V with a depolarizing initial condition (V = V0; caused by an initial exciting current) using the following equations: (1) where

(2) (3) (4)

(5)

(6) (7)

(8)

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Figure 4. Computed membrane action potential at reduced temperature. The upper curve represents the solution of equation (1) using an initial depolarization of 15 mV and a temperature of 6oC. The lower curve represents a membrane action potential recorded at 9.1oC (axon 14). Figure reprinted with permission from Hodgkin and Huxley, 1952d; © Wiley-Blackwell.

(9) (10) = 120, = 36, = 0.3 mS/cm2 and VNa, VK, and Vl = 55, -72, and and CM = 1µF/cm2, -49.4 mV respectively. Hodgkin and Huxley assumed that the inside potential was 0 and recorded membrane potential externally as a displacement from a resting value. This convention is no longer used and their original equations have been modified (equations 5-10) so the membrane potential is an absolute value and the external potential used as a reference ground potential so that at rest V = -60 mV. The ionic currents were modeled as ohmic conductances that pass current equally well in both directions multiplied by a driving force (V-Vx) for current. Experimental support for this supposition was obtained for both K+ and Na+ currents when the squid axons were bathed in a solution with normal sea water ion concentrations (Hodgkin and Huxley, 1952b). The variables, n and m modeled the voltage- and time-dependent activation of K+ and Na+ currents and h represented the inactivation of Na+ currents. In their model, activation and inactivation of Na+ currents were two independent processes. The predicted membrane APs Hodgkin and Huxley obtained were similar to experimentally recorded APs (Hodgkin and Huxley, 1952d). Figures 4 and 5 show a comparison between computed and experimentally recorded membrane APs that Hodgkin and Huxley obtained at two different temperatures. To


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obtain their results at the two different temperatures, Hodgkin and Huxley used an experimentally determined temperature coefficent (Q10 = 3.0) to adjust the rate constants for permeability changes.

Figure 5. Computed membrane action potential at room temperature. The upper curve represents the solution of equation (1) using an initial depolarization of 15 mV and a temperature of 18.5oC. The lower curve represents a membrane action potential recorded at 20.5oC (axon 11). Figure reprinted with permission from Hodgkin and Huxley, 1952d; © Wiley-Blackwell.

Figure 6. One dimensional cable and equivalent distributed RC network. The upper RC network model assumes the RC elements are distributed uniformly and is infinite in extent. To obtain the values of resistances and capacitance used in mathematical nerve models the following relations are used:

;

; and

.

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If the axon is considered to be well represented by an infinite distributed RC network (Figure 6) or a one dimensional cable then propagated APs can be predicted by the following equation: (11) where m, n, and h and their parameters are described by equations 2-10, a is the radius of the axon, and Ri is the specific resistance of the axoplasm. Equation 11 can be equivalently expressed as: (12) Hodgkin and Huxley (1952d) did not solve this partial differential equation, but solved a simpler ordinary differential equation by making the following assumption:

(13)

Figure 7. Computed propagated action potential. The upper curves represent the solution of eq. (11) with the assumption that

to produce

the following ordinary differential equation:

and

= 10.47 ms-1 at 18.5oC. Panel B is the identical solution of eq. (11) shown in panel A

except that a slower time scale was used. Panels C and D represent tracings of propagated APs recorded at 19.2oC using the same time scales as panels A and B. Figure reprinted with permission from Hodgkin and Huxley, 1952d; © Wiley-Blackwell.


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where θ represents the conduction velocity. The conduction velocity used was obtained by an iterative procedure that identified a value that produced an AP that converged to the value of (the termination of the AP). the resting potential as The APs that were predicted using these equations were quite similar to experimentally obtained APs and this was especially so for membrane APs (Figure 4-5). By making the assumption in equation 13, APs were made to propagate with a uniform and constant conduction velocity. This would only occur if the axon could be represented by a one dimensional cable with uniform properties throughout its extent; however nerve fiber axons are not one dimensional cables and display ionic currents that can be faithfully represented by the three currents (INa, IK and Il) displayed in equation 11-12. Therefore the predictions (Fig 7) of propagated APs only approximated experimentally recorded APs. Simulations of AP activity were made using a finite difference approximation to the partial differential equation of equation 12 (Cooley and Dodge, 1966). To obtain a conveniently solvable set of equations, the axon was divided up into small segments so that the potential could be considered uniform over each segment and the membrane current was equated to the difference in entering and leaving axial currents. Boundary conditions were used to simulate a stimulating electrode current placed in the middle of the axon to initiate APs. The RC network used in the simulation was also terminated at both ends with a short circuit; since this was an unrealistic assumption, they carried out computations over only a limited spatial extent of the RC network to minimize errors. If constant currents over the range 3-8 µA were applied to the theoretical axon, repetitive propagating APs were observed. At the point of stimulation each repetitively observed AP diminished in size so that the number of computed APs observed varied from 2 (3.0 µA) up to 9 (3.4 µA) over the time period the calculations were made (Cooley and Dodge, 1966). Thus a theoretical HodgkinHuxley axon does not exhibit the repetitive properties that many cells possess. However, the form of equation 12 provides a clue to how repetitive activity can become spontaneous (pacemaker activity) or modulated. Equation 12 is a very useful equation that describes how the axial voltage gradient (electric field) changes in response to capacitive and ionic currents and can be expressed in a simpler form to show that APs produced in a nerve cell axon highly depend on the ionic Na+, K+ and leak currents described by Hodgkin and Huxley. The Na+ and K+ ionic currents characterized and mathematically modeled by Hodgkin and Huxley (1952d) are not the only time dependent and nonlinear currents that can cause AP production. Any ion channels that contribute to the ionic current can contribute to the AP. Thus AP production and properties can be modified by the presence of voltage and ligand gated channels. To show this more explicitly, equation 12 is shown below in a simpler form: (14) Also intracellular or extracellular neuromodulators that act to alter the ion channels behavior will also play a key role in the production and pattern of activity in time. In addition, any ion exchange transport processes that produce a current (electrogenic) such as the Na-K pump or Na-Ca exchanger (Powell et al. 1993) should be included, so equation 14 should be modified:

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(15) The activation of sodium channels to produce the upstroke of the AP in many cells is not the only way APs are produced. Voltage-dependent calcium channel activation may also produce similar potential changes and have been observed in a number of animal cells. The essential property of the ion channel currents in equation 15 is their initial voltage-dependent opening to cause an inward current followed by a delayed outward current. Since Ca 2+ and Na+ are both distributed across cells so that their external concentrations are much greater than their internal concentrations, the opening of channels permeable to either or both of these ions can produce the needed net inward current to produce the upstroke of APs. The inactivation of the inward-current carrying channels followed by the delayed opening of channels that produce an outward current produces typical APs.

GENERALIZED MATHEMATICAL MODEL SIMULATE ACTION POTENTIAL BEHAVIOR If distance and time are expressed as dimensionless variables X and T by dividing actual distances by a characteristic length or space constant and an RC time constant respectively, the Hodgkin-Huxley model and other models that predict APs can be expressed in the following way: (16) for i = 1,…n

(17)

The Hodgkin-Huxley model requires three additional variables (Mi = m, n, and h) while some other AP models require less, such as the model used by FitzHugh (1961)which uses only one variable described by equation 17. The equations represented by 17 are the voltagedependent ion channel currents, electrogenic pump currents and any other voltage-dependent processes that cause ion currents.

MORRIS-LECAR PREDICTIONS OF VOLTAGE OSCILLATIONS IN BARNACLE MUSCLE CELLS Not all oscillatory potentials such as APs are produced as a consequence of an activation of voltage-dependent Na+ and K+ currents and this was observed in muscle cells of the barnacle (Morris and Lecar, 1981). Using space-clamped muscle cells, the spiking behavior of these cells could be described by equations similar to that employed by Hodgkin and Huxley:


111 (18) (19) (20)

where (21) (22) (23) (24) where , , = 8,3,40 mS/cm2 respectively, , are 1/15 and 0.1, while the equilibrium potentials are VK,VCa, and VL = -70,120, and-50 mV. I represents an applied stimulatory current. In the Morris and Lecar model, Ca2+ plays a similar role to Na+ in the Hodgkin and Huxley model. In this model Ca2+ current does not inactivate like Na+ current does in the Hodgkin-Huxley model. This model produces AP-like repetitive voltage oscillations. Similarly, in the heart Ca2+ plays a key role in producing a repetitive pacemaker AP. A number of ionic currents including IK, ICa, and a current carried by Na+ and K+ referred to by a number of names (Ih, If, IQ, and IAR) play principle roles in producing spontaneous repetitive membrane APs.

MODELING AP BEHAVIOR IN THE HEART: VENTRICULAR AND SINO-ATRIAL PACEMAKER CELLS DiFrancesco and Noble (1985) developed a mathematical model of cardiac Purkinje cell action potentials that used a number of ion channels and other processes that produced currents including the Na+-K+ pump, a Na+-Ca2+ exchanger, and a calcium pump. Similar models that described AP behavior in cardiac cells were developed by Rasmusson et al. (1990) and Luo and Rudy (1991; 1994). The approach in their models was to solve an equation similar to the equation used by Hodgkin and Huxley (1952d) where the interior of the cell is considered isopotential or space-clamped and no propagation occurs; however the number of currents included was greatly expanded. The basic equation used by Luo and Rudy (1994) was:

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Where Iionic specifies a number of ion channel currents and other currents including: INa (fast Na+ current; Nav 1.5, similar to INa in eq. 1), ICa (cardiac L-type channels; Cav1.2), a number of K+ currents; IK, a time-dependent current and two time-independent terms, a nonspecific Ca2+ activated cation current, currents contributed by the Na+-K+ pump, a Ca2+ pump, and the Na+-Ca+ exchanger in heart ventricular cells, Ca2+ uptake by network sarcoplasmic reticulum (NSR), release of Ca2+ by the junctional sarcoplasmic reticulum (JSR), translocation of Ca2+ from the NSR to the JSR, and release of Ca2+ from the JSR. The mathematical model used by Luo and Rudy (1994) also used more realistic descriptions of currents through channels than that originally used by Hodgkin and Huxley in 1952; Ca 2+ channels are permeable to Na+ and K+ as well as Ca2+ and the contributions of each of the ions was handled via their model by assigning permeability ratios to the various cations. In addition not all the currents through channels can be modeled as ohmic conductors that pass inward and outward currents equally well, so Ca2+ currents were modeled using a modified version of the constant field equation. The constant field equation better models currents that rectify:

(26) where represent in inside and outside concentrations of ion X (Ca2+, Na+, K+, etc.) and F, V, R, and T correspond to the Faraday, voltage, the Universal gas constant and absolute temperature, respectively. Matusuoka et al. (2003) and Sarai et al. (2003) used a common set of equations (Kyoto model) to describe ion channel and exchanger activity to predict AP behavior in sinoatrial node and ventricular cells. In their mathematical model a number of inward (INa, ICaL, ICaT, Ist, and Iha) and outward (IK1, IKr, IKs, and Ito) ion channel currents were described. A number of other currents (background; IbNSC, IKpl, Il(Ca), IKATP, and ICab) were also included in their mathematical model as well as the Na+/K+ pump and Na+/Ca2+ exchanger, sarcoplasmic reticulum (SR) Ca2+ transport and the ryanodine receptor (RyR) channel activity (Matusuoka et al., 2003; Sarai et al., 2003). Some of the ion channel currents that were modeled (Ist, and Iha) were found only in sinoatrial node cells and play a role in producing spontaneous pacemaker APs and were not included in AP simulations for ventricular cells (Matusuoka et al., 2003). Since a model for sarcomere shortening was also included in their system of equations, parameters for equations representing SR Ca2+ fluxes were altered to fit experimental observations for the Kyoto model. Using an approach similar to that used by Luo and Rudy (1994), the Kyoto model also used permeability ratios to partition the flux of ions through channels into identifiable components (K+, Na+, and Ca2+). The constant field equation (eq 24.) was used to calculate the various current components in the Kyoto model. Thus, this fairly comprehensive model simulates SA node and ventricular AP changes in various external Ca2+ and K+ concentrations, shows reduction of intracellular ATP production causes AP shortening in ventricular cells, and show the properties of some of the ion channels are essential for SA


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node spontaneous AP generation. Using the Kyoto model, Sarai et al. (2003) suggest that ICaL (Cav1.2), the deactivation of a delayed rectifier current, IKr, and Ist play important roles in spontaneous AP generation. Although the majority current of Ist is carried by Na+ in the Kyoto model, it is not clear what channel carries this current. Studies of the rat heart showed that a number of sodium channels (Nav1.1,Nav1.5- Nav1.7) were expressed in the SA node; however Nav1.1 and Nav1.6 were the principal channel α-subunits found and reduction in their numbers contributed to heart failure-induce SA node dysfunction (Du et al., 2007). Currents carried by these channels may well describe INa and Ist in the Kyoto model. The current Iha in the Kyoto model is carried by K+ and Na+ and also contributes to the production of spontaneous pacemaking in the SA node and has been given several names including If, IQ, and IAR by various investigators. These channels are activated at hyperpolarizing potentials and by intracellular cyclic adenosine monophosphate (cAMP) (DiFrancesco and Borer, 2007). There are four isoforms of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels and HCN4 is the most abundantly expressed form in SA node cells ((DiFrancesco and Borer, 2007). The presence of these channels in the SA node aptly illustrates how AP activity can be modulated by changes in an intracellular modulator. Intracellular cAMP concentrations can be reduced via the use of agents such as β-adrenergic blockers that will alter AP production via changes in HCN4 channels.

SYNAPTIC ACTIVITY PRODUCES ACTION POTENTIALS AND CELL GEOMETRY INFLUENCES REGENERATIVE BEHAVIOR APs generated in the initial segment or soma of neurons are typically the product of the synaptic currents caused by the release of neurotransmitters onto the dendrites and soma of the cell. Net inward cationic currents produced by the binding of the neurotransmitters to ligand-gated channels and their subsequent opening act to depolarize the cell and produce APs. The currents produced may act as a synaptic drive to produce repetitive AP activity. Any equations that simulate neuronal AP behavior must include synaptic currents to successfully reproduce or emulate experimental data. The synaptic inputs also may occur along dendrites and the dendritic branching patterns (dendritic trees) of various nerve cells varies depending on where the cell is located in the central nervous system. A mathematical model of a nerve cell exhibiting dendritic branching was developed by Rall (1962) and helped contribute to an understanding of how dendritic synaptic input currents alter the potential distribution along the neuron. To obtain his model, Rall (1962) made several simplifying assumptions: the soma and dendritic membranes were considered to have uniform electrical properties and composed of passive components; the soma membrane was considered isopotential throughout its extent and modeled as a lumped impedance; the dendritic tree was represented by cylindrical trunks and branches; extracellular potential gradients were considered to be negligible compared to intracellular counterparts. In each cylindrical element the following differential equation was used: (27)

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where V represents changes in membrane potential from a steady-state resting value, T = t/τ is a dimensionless unit of time relative to a characteristic membrane (RC) time constant, τ, and X = x/λ is a dimensionless unit of distance relative to characteristic length or space constant, λ. The equation is quite similar to equation 12 used by Hodgkin and Huxley (1952d) and can be made equivalent if the sum of the currents produce a potential change V. Also boundary conditions were used to insure continuity of currents and potentials at branch points (Rall, 1962). If a generalized length constant was defined as

where λ depends upon the branch diameter, and x is distance along the axis of the trunk and branches from the soma origin, then the potential changes occurring along the dendritic tree could be obtained by solving the partial differential equation shown below (eq. 26) (28) if the branching pattern satisfies the following relationship (29) where K is a constant, di represents the diameter of the ith branch found at L(Rall, 1962). In the special case were K =0, the differential equation is reduced to a form (eq 25) that describes potential changes along a uniform cylindrical membrane (equivalent cylinder). Thus, if the branching pattern of a dendritic tree follows Rall‘s power law (equation 29), the potential changes along the tree can be mathematically described by considering a simple equivalent cylindrical membrane model. In order to determine if equivalent cylinders and one-dimensional cable models adequately describe nerve axon membranes, Rall (1969) also solved Laplace‘s equation for the distribution of potential inside and outside a membrane cylinder enclosing and surrounded by an internal resistive and homogeneous medium. Radial and angular potential changes along the cylinder occur much faster (angular time constants were 10,000 times smaller than RmCm) than changes along the central axis for cylinders whose lengths are large compared to their radii (Rall, 1969). Similarly for membrane cylinders with a long central axis compared to their radii, time constants describing nonuniformities in potential along the axis agreed well (differences were less than 1%) with those obtained using one-dimensional cable theory. If all dendritic branching were assumed to be symmetrical bifurcations that satisfy equation 27 with K =0, then an equivalent cylinder model could be used to describe the potential response at the soma to current injected at a branch terminal (Rinzel and Rall, 1974). Using a dendritic tree model of 6 trunk cylinders originating from a soma followed by two orders of symmetrical branches, Rinzel and Rall (1974) showed that the voltage response time course at the soma produced by a simulated synaptic current becomes increasingly delayed to its peak value, slowed in its decay and attenuated with increasing distance from the current injection location. These predictions were analogous to observations made earlier using


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models of motor neurons (Rall, 1960). Using similar dendritic tree models it was possible to conclude that the shape and time course of experimental observations of synaptic depolarizations, excitatory post synaptic potentials (EPSPs), observed at the soma of cat spinal motor neurons was consistent with a wide distribution of synaptic inputs over dendrites and the soma (Rall et al. 1967). The EPSP‘s rapid rise to the peak was produced by synaptic input to the soma, but the slowly decaying phase of the EPSP suggested dendritic synaptic inputs contributed to the shape of the EPSP. The rapidity of the rise to a peak, amplitude, decay to the resting potential and duration of the EPSP will act to open voltage-dependent Na+ and Ca2+ channels and if a sufficient number of channels are opened an AP or a sequence of APs will be produced.

AP SIZE, SHAPE AND PROPAGATION VELOCITY DEPENDS UPON NERVE CELL GEOMETRICAL PROPERTIES Most nerve APs are typically initiated at sensory neuron terminals or at the initial segment of the soma of the cell via synaptic transmission events distributed to the dendrites and soma of neurons. APs are distributed to other cells via axons that may decrease in their diameter along their extent and also may branch. Goldstein and Rall (1974) used computational methods to gain insight into AP changes produced by a number of geometrical changes in axon properties including changes in diameter (tapering or flaring) and branching. The mathematical model they used to simulate APs was: (28) (29) (30) The model used was a specific case of the general model in equations 16-17 (Goldstein and Rall, 1974) and employed dimensionless variables for time, T, and voltage, V. Goldstein and Rall (1974) used a number of sets of rate constants, (k1-k7), to simulate APs in squid, lobster and crab axons and can be found in their paper. The model used is a simpler model of APs than the Hodgkin-Huxley model because the rate constants (k1-k7) are not voltagedependent quantities. The voltage-dependent rate constants (αm, βm, αn, βn,,αh, and βh ) used in the Hodgkin-Huxley (1952d) model possess a voltage dependence that are defined by equations 5-10. APs were found to increase in amplitude and velocity and change shape as they approached a sealed end in a cylindrical axon model (Goldstein and Rall, 1974). As the AP approached the end, it shortened its width and increased its amplitude. This result is expected for an axon with uniform ion channel distributions and electrical properties along its length. As Goldstein and Rall (1974) point out, the axial current diminishes by flowing outwardly via a large area of surface membrane, but the size of the surface membrane decreases

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dramatically at the end of the axon, thus dramatically increasing the membrane current density causing AP amplitude and propagation velocity increases. APs also would be predicted to change when encountering a step change in radius. APs are predicted to change their shape, decrease their width, increase in size, upon entering a region of reduced radius, and continue to propagate from that location with a reduced conduction velocity but virtually identical peak height (Goldstein and Rall, 1974). Similarly, APs are predicted to change their shape, increase their width, decrease in size, upon entering a region of increased radius, and continue to propagate from that location with an increased conduction velocity and slightly greater peak height. If the step increase (3.5 fold increase) in radius was large enough, Goldstein and Rall (1974) showed propagation was eliminated. The diameter of a nerve axon changes along its length and APs propagate longitudinally along axons to produce cell to cell communication. To simulate changes in axonal radius axially along the axon, Goldstein and Rall (1974), used a generalized length parameter, λtaper, that relates how the length constant differentially changes with x. Taper was defined so that r2 λtaper eKZ, where Z is a dimensionless measure of length along axon axis and defined via the relation dZ = dx/ λtaper. In most cases changes in radius were small compared to changes in distance along the axis of the axon, so some of their simulations used the following approximation: r = r0e2KZ/3, where r0 is the initial radius prior to tapering or flaring. Since equation 28 only applies to propagation along a cylinder, to mathematically model APs along an axon axis with changes in radius along its length required the addition of an extra term that includes the taper parameter K (

to the left side of equation 28 (Goldstein and Rall,

1974). When K is positive, the axon increases its radius (flare) along its axial length as opposed to a negative K which represents an axon that decreases its radius (taper) along its axis. If model axons showed taper or flare that followed r2 λtaper eKZ, Goldstein and Rall (1974) showed that AP velocity was linearly dependent upon the actual distance, x, following the equation:

(31)

where β is a constant, λ0 is the length constant at the beginning of the axon (prior to a change in radius), τ is the time constant, and K is the taper parameter. The shape of the AP in time did not change if the taper followed r2 λtaper eKZ (Goldstein and Rall, 1974). If K was too large (>5), propagation was eliminated. Since axons also may branch and AP propagation can fail or change at the junction, Goldstein and Rall (1974) also simulated AP propagation at branch points. To simulate propagation in either direction they defined a geometric ratio: (32) where da represent the diameter of the branch along the direction of approach of a branch point, while the dis represents the diameters of the ith other branches and the summation is over all the other branches(Goldstein and Rall, 1974). For ease of computation all branches


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were assumed to possess a length of at least one length constant. When the GR =1, APs propagate from the parent axon to the branches as if there were no branching because the system of conductors can be modeled as an equivalent cylinder and the branching pattern follows Rall‘s power law (equation 29). If GR is less than one, the other branches correspond to an equivalent cylinder that has a smaller diameter than the parent or approaching branch (Goldstein and Rall, 1974). Similarly, if GR is greater than one, the diameter of the equivalent cylinder of the other branches will be greater than the parent or approaching branch. Thus branching is quite analogous to step changes in diameter of an axon and this explains why AP propagation may fail at branch points. The geometric ratio provides a way to describe the degree of impedance matching of the equivalent parent RC network and the branching RC network. Grossman et al. (1979) recorded APs in a branching axon of the lobster. The branching axon had a GR of nearly 1 and APs were recorded in the parent axon and both branches when stimulated at high frequency (50 Hz). Repetitive stimulation at 50 Hz caused a progressive decrease in AP amplitudes in the parent and daughter branches until conduction was blocked in the larger branch at 4.5 sec followed by a block in the smaller branch at 8.5 sec. During the repetitive stimulation period the shapes of the APs also changed in time (Grossman et al., 1979a). Despite the fact that GR was nearly 1 and RC network impedances at the branch point were nearly equivalent AP conduction failure occurred. In order to explain the results, Grossman et al., 1979b) performed another set of experiments to test whether their results could be explained by stimulation-induced changes in extracellular K+ concentration. Using a modified segmented model of an axon based on the Hodgkin-Huxley equations designed to study the behavior of branching and tapering on AP behavior, Parnas and Segev (1979) showed that AP propagation block should occur simultaneously in both the smaller and larger branches. In order to explain the differential block of AP conduction into the larger diameter branch differential changes in external K+ concentrations during stimulation had to be introduced into the equations (Parnas and Segev, 1979).

AP PRODUCTION AT SYNAPSES REQUIRES THE PRESENCE OF VOLTAGE-DEPENDENT ION CHANNELS APs were first recorded in dendrites of cerebellar Purkinje cells from the alligator, Caiman slerops, following stimulation of presynaptic parallel fiber APs (Llinas and Nicholson, 1971). A dye, Procion yellow, was used to verify the location of the dendritic intracellular recording site. Figure 8 shows examples of the APs recorded by Llinas and Nicholson (1971). Wong et al. (1979) showed that synaptically elicited APs could be initiated at dendrites and showed that only the fast component of APs was blocked by the Na+ channel blocker tetrodotoxin (TTX) suggesting that voltage-dependent Na+ and Ca2+ channels may well be present in the dendritic tree. Microfluorimetric imaging of pyramidal cells in brain slices showed that voltage-dependent Ca2+ channels were present in dendrites (Regehr et al. 1989.)

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Figure 8. Action potentials recorded from Purkinje cell dendrites from the alligator cerebellum. APs were recorded using intracellular microelectrodes filled with 3 M KCl and K citrate exhibiting d-c resistances between 10-20 megohms. Local stimulation of the cerebellar cortex (Loc) stimulates parallel fibers that synapse on and excite Purkinje cells. APs could be recorded at 50 to 350 µm from the surface in the molecular layer. Dendritic AP recordings could be identified using the dye Procion yellow that was injected into the cells at the recording location. Panels A-D show APs recorded in a dendrite with increasing levels of Loc stimulation from A to D. The arrows indicate the time of Loc stimulation. Figure 8 panels A-D were reprinted with permission from Llinas and Nicholson, 1971. © American Physiological Society.

The theoretical studies conducted by Rall and his collaborators helped contribute insight into AP initiation at the dendrites and soma of nerve cells. Segev and Rall (1988) used a compartmental mathematical model to study how action potentials could be produced on dendritic spines in the dendritic tree of a model neuron. Using modified versions of the Hodgkin-Huxley equations to describe excitable membrane properties, Segev and Rall (1988) concluded that the anatomical arrangement of a dendritic spine, including its stem and head, provided a unique way to maximize dendritic membrane depolarization if voltage-dependent channels were located on the spine head. Later experimental work verified this prediction (Segev and Rall, 1998). Infrared differential interference contrast microscopy studies have shown that dendrites of neurons typically contain voltage-dependent ion channels including K+, Na+ and Ca2+ channels (Markram and Sakmann, 1994; Stuart et al., 1997). Many different types of Ca2+ channel isoforms are found in brain cells. In a pharmacological study of hippocampal guinea


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pig brain slices, granule cells were found to possess L-type (Cav1), P, and N-type (Cav2), Ca2+ channels (Eliot and Johnson, 1994). In another study (McKay et al. 2006) designed to identify the distribution of T-type (Cav3) Ca2+ channels in the soma and dendrites of rat neurons, all three types of T-type channels Cav3.1, Cav3.2 and Cav3.3 were found in the soma, but only Cav3.3 was found in the distal dentrites. Using brain slices from the somatosensory cortex of rats, simultaneous dendritic and somatic potential recordings were made from pyramidal neurons following synaptic stimulation of the cells (Stuart et al., 1997). APs could be initiated either first in the soma or the dendrites depending upon the location of synaptic stimulation. Somatic APs also propagated back into the dendrites and activated Ca2+ channels in the dendrites (Stuart et al., 1997). When occasional dendritic APs could be elicited without evoking somatic APs, recordings at the soma revealed that the potential changes were greatly attenuated signals (Stuart et al., 1997) consistent with earlier theoretical computational studies. The large repertoire of voltage-dependent ion channels found in the soma and dendrites of neurons provide a framework of currents to produce a diverse array of repetitive AP behavior.

SENSORY TRANSDUCTION, TEMPERATURE GATED CHANNELS, MECHANICALLY GATED ION CHANNELS AND APS APs are also produced as a result of sensory transduction processes mediated by specialized receptor ion channels. Animals typically possess a wide array of responses to sensory signals including touch, pressure, temperature and balance. Primates typically possess a greater sensory repertoire than other animals and can also experience both discriminative and crude touch, kinesthesia, position sense, linear and angular acceleration and the special senses of hearing, vision, taste, and smell. For some sensations, vision, taste and olfaction, light or chemical signals are detected via the activation of G protein-coupled receptors (GPCRs) that lead to ion channel activation and voltage changes. The mammalian olfactory system has the capacity to detect a large number of odorous molecules and pheromones. Mammals possess a diverse set of sensory receptors and they have been classified into several categories which include the odorant receptors (Fleisher et al., 2009). Odorant receptors are characterized by seven membrane spanning trans-membrane regions. Odorant binding to the receptors activates them and they interact with an heterotrimeric G protein which acts to stimulate adenylyl cyclase and increases in cAMP and ultimately opening of cyclic nucleotide-gated ion channels that are permeable to Ca2+ to cause a voltage change. The mode of action of odorant receptors in producing voltage changes in cells parallels the action of rhodopsin which is activated by light. Temperature sensation is critical for organisms and temperature and pressure are related in the sense of touch. In order to detect temperature, changes in temperature must be converted to voltage changes. Changes in temperature can be detected by a set of ion channels that represents a subset of a larger class of ion channels, transient receptor potential (TRP) channels, whose first member was light sensitive and discovered in Drosophila (Dhaka et al., 2006). A subset of TRP channels are temperature sensitive (thermoTRP) and include TRPA1, TRPM8, and TRPV1-TRPV4 (Dhaka et al., 2006). Most of these channels also respond to a number of plant compounds and some of the TRPs can be identified by the different

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substances that activate them. TRPA1 is activated by several compounds including the active ingredients of garlic (allicin), cinnamon (cinnamaldehyde), and wasabi (Dhaka et al., 2006). TRPV1 is activated by capsaicin found in hot peppers, while camphor activates TRPV1 and TRPV3 (Moqrich et al. 2005) and menthol derived from mint activate TRPM8 (Bandell et al. 2006). Each of the thermoTRPs are activated over different temperature ranges causing some of the thermoTRPs to respond to cold (TRPM8) while the others respond to warm temperatures. TRPV1 and TRPV2 are also believed to play a role in responding to noxious signals (Dhaka et al, 2006) and TRPV1 is stimulated by low pH, and other substances found in the inflammatory response including bradykinin and prostaglandins (Tominaga and Caterina, 2004). The thermoTRPs possess 6 transmembrane regions and functional channels exist as tetramers (Moiseenkova-Bell and Wensel, 2009); however their mechanism of activation is unclear. Some of the thermo-TRPs (TRPV1, TRPV3, and TRPM8) can be weakly activated by voltage and their ability to sense temperature appears to be related to shifts in their voltage-dependence with changes in temperature (Nilius et al. 2005). These channels act to produce inward cation currents principally carried by Ca2+ to produce a membrane depolarization. If it is large enough to activate Na+ channels, APs will be produced. Bautista et al. (2007) developed a set of TRPM8 deficient (TRPM8-/- ) mice and recorded APs obtained from a skin-saphenous nerve preparation in normal (TRPM8+/+ ) and TRPM8-/mice during the application of a range of decreasing temperatures (32-2oC) to the skin receptors serving the nerve. The percentage of small diameter C fibers that serve temperature sensitivity was dramatically reduced in its AP firing rate in TRPM8-/- mice when compared to normal wild-type animals. A review of TRPV1, TRPM8 and TRPA1 channels (Stucky et al., 2009) suggests that these channels do not simply mediate heat, cold and pungency, but serve many roles including cold detection, cold pain, and hypersensitivity for TRPM8, heat, acid, and inflammatory agent receptivity for TRPV1, and response to pungent agents, nociception, inflammation, and oxidative stress for TRPA1. In order to detect sensory signals that are associated with mechanical forces mechanotransduction or the conversion of mechanical energy into electrical energy must occur. Mechanotransduction plays essential roles in plants and very simple animals such as bacteria and protists (e.g. Paramecium). Mechanotransduction typically acts to convert deformations or strains such as membrane stretch into voltage changes. Hearing, touch and proprioception are believed to be mediated by mechano-electrical (MeT) channels. In the nematode, Caenorhabditis elegans, neurons that respond to touch, MeT channels are composed of pore-forming subunits (MEC-4 and MEC10) and additional subunits MEC-2 and MEC6(Cueva et al, 2007). MEC-4 and MEC-10 show a similarity with amiloridesensitive epithelial Na+ channels (ENaCs) and degenerins and are all considered to be part of a (DEG/ENaCs) superfamily of proteins (Syntichaki and Tavernarakis, 2004). In many neurons in C. elegans propagated APs are not produced and signaling is rendered by electrotonic decrement along the neurons. However, a set of interneurons, RMD, in C. elegans that interconnect with muscle cells and are involved with nose-stimulation-induced movement, and forward and backward motion have been shown to exhibit Ca2+-dependent APs upon stimulation (Mellem et al. 2008) that conduct in a Na+ free solution. The nose of C. elegans is exquisitely sensitive to touch and when the animal encounters an obstacle, touch receptor sensory neurons respond to the obstacle and cause it to reverse its direction of movement (Syntichaki and Tavernarakis, 2004). The APs in RMD neurons are likely quite


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similar to those required in muscle cells in C. elegans. APs recorded in pharyngeal muscle of C. elegans were shown to be generated by three voltage-dependent ion channels, a T-type Ca2+ channel (CCA-1), an L-type Ca2+ channel (EGL-19), and a K+ channel (EXP-2). Thus, even in the tiny nematode, APs can be produced in response to activation of mechanoreceptor activation and cause essential movements. APs created by activation of sensory reception act as essential signaling agents. Their frequency of appearance and change in frequency typically signals the intensity and properties of the sensation. Ion channels also act to introduce currents that can modulate AP firing frequency. An example of this was observed in dorsal root ganglion (DRG) neurons which serve a central role in many sensory modalities. Different populations of DRG neurons express distinct sets of ion channels (Waxman et al., 1999; Wood et al., 2004; Wang and Woolf, 2005). Using cultured DRG cells obtained from rats, Coste et al. (2007) identified the role low voltage-activated (LVA) currents such as LVA T-type Ca2+ and NaN (Nav1.9) Na+ channels play in various subpopulations of DRG neurons. Activated Nav1.9 channels act to produce a long lasting Na+ current at small depolarizing voltages that enables APs to be produced at smaller depolarizing voltages and causes repetitive AP bursting behavior (Herzog et al. 2001; Baker et al., 2003; Coste et al., 2004). Using various pharmacological tools to block various ion channels Coste et al. (2007) were able to categorize different types of DRG cells. Cells were also subjected to mechanical stimulation in steps to assay for the presence of any mechanico-sensitive currents. C-type neurons possessed Nav1.9, Nav1.8, T-type Ca2+, and TRPV1 channels and mechanical stimulation elicited ion channel currents. Aδ-like neurons contained Nav1.9, Nav1.8 , amiloride-sensitive T-type Ca2+, TRPV1 channels and showed no mechanically-induced ion channel currents. D-hair cells possessed Nav1.8, amiloridesensitive and resistant T-type Ca2+, channels and mechanically-induced currents, but had no TRPV1 channels. Aα/β-like neurons had Nav1.8, amiloride-sensitive and resistant T-type Ca2+, channels and mechanically-stimulated currents, but had no TRPV1 channels. Thus Coste et al. (2007) showed that different populations of DRG neurons possess a varied set of ion channels that enables them to transmit APs in different patterns associated with particular sensory modalities. Thus an alteration in the types of ion channels producing the current I ion channels in equation 15 will produce different AP shape and response patterns in neurons. The two most important channel types that govern AP behavior are Nav and Cav since they provide the net inward current to drive the membrane potential to its peak value and inactivate to contribute to the falling phase. Na+ channels play a greater role in producing the upstroke of most APs, while Ca2+ channels act to broaden APs. Any agents that alter the kinetic and conductive properties of these channels will alter APs.

NAV CHANNELS PLAY A KEY ROLE IN APS IN NEURONS AND OTHER CELLS When activated by depolarizing events such as excitatory synaptic potentials (ESPs) or receptor potentials Na+ channels typically provide the inward current required to drive the membrane potential to its peak value during the upstroke of the AP. Na+ channels can exist in a number of closed, open and inactivated states and the various voltage-dependent transitions between the states provide a means to model the activation, deactivation and inactivation of a

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population of channels. The original Hodgkin and Huxley model assumed that the activation and inactivation processes were independent; however it became clear over time that the inactivation of a channel was coupled to its activation inconsistent with two independent processes for activation and inactivation (Goldman & Schauf, 1972; Armstrong and Bezanilla, 1977; Goldman & Hahin, 1978; Aldrich et al. 1983; Horn and Vandenberg, 1984; Vandenberg and Bezanilla, 1991). A five state model was found to be the minimum number of states to adequately fit the macroscopic Na+ currents and the delays that preceded channel opening (Hahin and Goldman, 1978). A study of single channel Na+ currents showed that a five state model acceptably fit the data and eliminated the Hodgkin-Huxley m3h model. In order to fit all available data (single channel, macroscopic currents, and gating charge movements) a 9 state model with 5 closed states, three inactive states and one open state was required (Vandenberg and Bezanilla, 1991). Based on the 4 domain structure of the sodium channel, macroscopic and gating currents and fluorescence changes that correlated with channel gating Armstrong (2006) proposed a 19 kinetic state model with two open conducting states. Multistate kinetic models that explain the gating process of Na+ and other channels more thoroughly than the Hodgkin-Huxley model will provide better tools to predict AP and other experimentally observed signaling behavior in excitable cells. However, the simplicity of the Hodgkin-Huxley model has caused it to be the most used approach to simulate APs.

CAV CHANNEL PROPERTIES CAN BE ALTERED BY AGENTS THAT BIND TO THE CHANNELS L-type Ca2+ channels are responsible for producing the current, ICaL, in cardiac muscle. The properties of single L-type Ca2+ channels could be distinguished from other Ca2+ isoforms by their single channel conductance, open lifetime, and the voltage range that they begin to open (activate). In chick dorsal root ganglion cells, Fox et al. (1987) identified Ltype, T-type, and N-type Ca2+ channels. The L-type Ca2+ channels were activated at more positive cell membrane potentials (>-10 mV), inactivated very little, and had a much larger single channel conductance than T-type Ca2+ channels. L-type Ca2+ channels are preferentially blocked by dihydropyridines, such as nifedipine, nitrendipine, and diltiazem (Bean, 1985). Dihydropyridines are not selectively acting agents and can act on other Ca2+, Na+, and K+ channels at high enough concentrations to cause their block. A polypeptide toxin obtained from the venom of Conus geographus (ω-conotoxin GVIA) acts to block N-type Ca2+ channels and was used to characterize the properties of T-type Ca2+ channels (Fox et al., 1987). Two other types of Ca2+ channels, P/Q and R, were characterized electro physio logically and pharmacologically (Bean and Mintz, 1994). A polypeptide toxin (ω–Aga IVA) obtained from the funnel-web spider Agelenopsis aperta was shown to block P/Q-type Ca2+ channels (Llinas et al., 1989). ω–Aga IVA was shown to block synaptic transmission at the squid giant synapse without altering the presynaptic AP and block Ca2+ dependent APs in cerebellar Purkinje cells (Llinas et al., 1989).


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Figure 9. Action potential block by saxitoxin. Panel A shows a compound AP from a desheathed frog sciatic nerve recorded via the single sucrosegap technique. Panel B shows the kinetics of AP attenuation after 1 nM STX was applied to the nerve. APs were stimulated and recorded at 1 minute intervals and each trace was delayed in appearance to show the rate of block.

NAV CHANNEL PROPERTIES CAN BE ALTERED BY AGENTS THAT BIND TO THE CHANNELS Since Na+ channels play a principal role in APs, agents that can bind to them and alter their properties will significantly alter either AP size, shape or their production. A number of animals have the capabilities to produce chemical defense agents that can specifically bind to and alter the properties of a number of Na+ channels. The best studied agents are TTX and STX. Both of these substances bind with high affinity to the majority of Na+ channels (Nav1.1-1.4, Nav1.6-1.7) with effective concentrations for 50% block (EC50) in the range of 16 nM. Some Na+ channels (Nav 1.5, and Nav1.8-1.9) are quite resistant to block by TTX and exhibit EC50s in the range of 1-60 mM. Both of these toxins block Na+ currents (Fig 9-10) without affecting their kinetics (Hahin and Strichartz, 1981) so the AP height decreases without large shape changes as the toxins block channels after application of the toxins to the bath. Ellliott and Quilliam (1964) applied the local anesthetic procaine to rabbit pre- and post ganglionic superior cervical ganglion cells and found APs were decreased and lengthened with increasing concentrations of procaine. Local anesthetics (LAs) act to block Na+ channels by binding to and interacting with the channel. However, unlike TTX and STX their binding is quite dependent on the state of the channel therefore the LAs are expected to alter AP properties to a greater extent. Since they are amines they can typically be in a protonated or neutral state depending on the pH of the solution. In the unprotonated state they are freely lipid soluble. A number of the LAs block Na+ channels to a greater degree each time the channels are opened. The increased ability to block with each stimulus has been called frequency-dependent or use-dependent block (Courtney, 1975). Thus AP block becomes progressively greater in the presence of use-dependent LAs; an effect not observed with TTX or STX..

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Figure 10. Sodium current block by saxitoxin. Panel A shows the kinetics of sodium current block after the application (indicated by an arrow) of 5 nM STX to the node of Ranvier of a frog myelinated nerve fiber. Each current record was elicited every 19 seconds by a test pulse to 10 mV from a holding potential of -120 mV and delayed along the axis to illustrate the kinetics of block. Delayed rectifier K+ currents were blocked by the addition of 12 mM tetraethylammonium to the bath.

Binding of LAs also shows a voltage-dependence that causes a greater degree of block at large depolarizing potentials that open channels to the maximum extent (Strichartz, 1973). This led to the hypothesis that the LAs bind in a state-dependent manner either via a route through the membrane in an unprotonated state or the channel pore when protonated with different affinities of binding to open, closed and inactivated states of the channel (Hille, 1977). LA binding acts to stabilize the inactivated state and the anesthetic must unbind to relieve the block. Wang et al (2004) have shown that LAs can block open, closed and inactivated states of Na+ channels. Agents that are most likely to have the greatest effect on AP size, shape and repetitive properties alter either one, or a combination of any of the following channel properties: statetransition kinetic rates, conductance, and activation or inactivation voltage-dependence. Examples of these agents are the α- and β-scorpion toxins, and lipid soluble plant alkaloid toxins: aconitine, veratridine, batrachotoxin, and grayanotoxin. The α-scorpion toxins act to bind to a set of amino acid residues (site 3; Tejedor and Catterall, 1988; Rogers et al., 1996) on Na+ channels and cause a large decrease in inactivation. There are over 85 α- and α-like scorpion toxins and each scorpion can produce a number of toxin variants which show strong sequence similarity. When applied to neurons they act to greatly prolong APs (Schmitt and Schmidt, 1972; Rochat et al, 1979; Borneman and Hahin, 1993). Figure 11 shows how an αscorpion toxin greatly prolongs APs and the underlying Na+ current inactivation process. The β-scorpion toxins modify the activation process and shift their voltage-dependence so that channels can open at the resting potential causing current induced or spontaneous repetitive firing of APs (Cahalan, 1975).


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Figure 11. Scorpion α-toxins greatly prolong APs by modifying Na+ channel inactivation. Panel A shows compound APs obtained from a frog sciatic nerve prior to (leftmost record) and after (denoted by an arrow) the application of 100 nM of an α-toxin isolated from Mesobuthus martensii Karsch (MESMA). Panel B shows Na+ currents before (indicated by a C) and after (time after toxin addition indicated) the addition of MESMA 11(2) to rat skeletal muscle (Nav1.4) α subunits expressed in HEK cells. Current records obtained 5 and 10 min after toxin addition did not differ or was slightly changed from control currents respectively. Each of the current records was elicited by a voltage-clamp pulse protocol shown above the current records. Figure modified from Chen et al. (2002).

The plant alkaloids and other similar acting compounds are much more complicated in their actions and therefore would alter APs more profoundly and alter their production. These agents act to shift the voltage-dependence of activation so that channels are open at the resting potential and keep Na+ channels open longer in addition to their changes in channel

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conductance and the selectivity for cations (reviewed by Catterall 1980; Khodorov, 1985; Hille et al. 1987; Ulbricht, 1998.) The agents preferentially bind to an open channel and modify the channel so that fast inactivation is virtually eliminated. Aconitine and batrachotoxin binding to the open state of the Na + channel is very long lasting and act as very potent activators of the channels, while other similarly acting agents (veratridine, DDT, pyretrins) bind and unbind more quickly (Hille, 2001). The shift of the voltage-dependence to more hyperpolarizing voltages will act to cause these agents to induce spontaneous AP production, while their ability to eliminate inactivation will prolong the APs. There are also a large number of other substances that alter Na+ channels. Many of the substances act non-specifically to alter the channel by blocking it or additionally altering its voltage-dependent kinetic behavior. Alkanols act to block Na+ channels and cause alterations in their kinetics to cause AP block (Kondratiev and Hahin, 2001). In addition a large number of aliphatic hydrocarbons exhibiting a wide range of octanol/water partition coefficients also acted to block Na+ channels to cause AP block. Alkanol and the aliphatic hydrocarbon block of APs could be predicted as a function of the molecule‘s intrinsic molar volume, polarity, hydrogen binding acceptor basicity and donor acidity (Kondratiev and Hahin, 2001; Hahin et al., 2008).

CONCLUSION The large diversity of ion channels found in membranes provide excitable cells with a large repertoire of AP behavior. The APs produced act as a means to communicate from one cell to another. This is very easily seen in neurons in the mammalian central nervous system (CNS). The ion channels observed in CNS cells produce currents that cause a wide range of AP shapes and repetitive behavior (Bean, 2007). In addition many of the voltage-dependent channels can be modified by molecules (neuromodulators) to change their properties and alter signaling behavior. Nonuniform distributions of the various channels along the neuron or excitable cell also cause AP behavior to occur that can not simply predicted by model axons that assume a uniform distribution of channels along the whole extent of the cell. Since many of the channels are voltage-dependent, voltage drives many different types of channels to interactively work in concert to produce signaling behavior. The signaling carried by APs that is produced ensures that humans and other animals can experience an incredible array of sensations and produce complex behaviors.

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Chapter 5

AFFERENT OUTPUT IN MAMMALIAN TASTE CELLS: A ROLE OF ELECTRICAL EXCITABILITY IN MEDIATING TRANSMITTER RELEASE Roman A. Romanov1, Olga A. Rogachevskaja1, Marina F. Bystrova1, and Stanislav S. Kolesnikov1,* 1

Institute of Cell Biophysics, Russian Academy of Sciences, Institutional Street 3, Pushchino, Moscow Region, 142290, Russia

ABSTRACT Although mammalian taste cells are epithelial by nature, cells of the type II and type III are electrically excitable and capable of firing action potentials in response to electrical and chemical stimulation. In hair cells and photoreceptors, sensory stimuli elicit gradual receptor potentials that govern directly, that is, without stimulating action potentials, release of the afferent neurotransmitter glutamate. Given this fact and that taste cells have no axons, physiological significance of the electrical excitability for taste transduction and encoding sensory information is unclear. Most likely, action potentials facilitate transmitter release, both ATP in type II cells and 5-HT in type III cells, although by different mechanisms. The ATP release is mediated by hemichannels, do not require a Ca2+ trigger, and is gated by membrane voltage. Meanwhile, 5-HT secretion is driven by intracellular Ca2+ and involves VG Ca2+ channels. This work is focused on molecular mechanisms of ATP release from type II cells and on a role of action potentials in mediating their afferent output. Electrical excitability is a fundamental property of neuronal and muscle cells and certain other cells, which generate all-or-none electrical signals, action potentials (APs), basically in response to an external stimulation of sufficient strength. AP serves to spread excitation over the entire surface of a muscle cell, thus triggering and synchronizing its contraction. In neurons, the elongated axon serves to transmit information in the form of APs over long distance in a non-decremental manner, while coming in the synaptic *

Corresponsing author. E-mail: [email protected]

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Roman A. Romanov, Olga A. Rogachevskaja, Marina F. Bystrova et al. terminal, the AP triggers and shapes neurotransmitter release. Despite being epithelial in nature (Stone et al., 1995) and having no axons, taste cells are electrically excitable. Pioneer intracellular recordings from taste buds of the salamander Necturus (Roper, 1983) provided the first evidence for electrical excitability of taste cells. It is now well documented that in vertebrates, taste cells generate APs not only on electrical stimulation, but also in response to apically applied chemical stimuli (Behe et al., 1990; Avenet, Lindemann, 1991; Cummings et al., 1993; Varkevisser, Kinnamon, 2000; Yoshida et al., 2006). To generate APs, taste cells should possess a certain repertoire of ion channels, such as voltage-gated (VG) Na+ and K+ channels, in combination with a high input resistance, the feature allowing small depolarizing ionic currents to produce large effects on the membrane potential. As demonstrated in earlier studies, the needed membrane properties are indeed characteristic of taste cells (Herness, Gilberson, 1999; Bigiani, 2002). Since the detailed analysis of ion permeability of the taste cell plasma membrane is beyond the scope of the present work, ion channels are considered here in two specific aspects: in context of taste cell identification and in relatedness to excitability of taste cells and to their afferent output. Note that certain sensory cells, such as vertebrate photoreceptors and hair cells in the Corty organ, which have no axons, do not produce APs, thus questioning why those are generated by taste cells. The likely possibility is that despite the absence of axons, taste cells need APs to control afferent output. As related to the further discussion, we provide below a brief overview of mechanisms mediating neurotransmitter discharge.

SYNAPTIC TRANSMISSION Discontinuous and Graded Synapses Although in common synaptic transmission involves discontinuous transmitter release triggered by presynaptic APs, there are graded-potential synapses (Juusola et al., 1996). Vertebrate photoreceptors and their second order neurons (bipolar cells), auditory and vestibular hair cells respond to external stimulation with graded potentials (Sterling, Matthews, 2005). These cells have short or no axons and a characteristic synaptic topology to provide dynamic coding of graded presynaptic signals into tonic transmitter release. Their socalled ribbon synapses, which contain an organelle, synaptic ‗ribbon‘, invariably use glutamate as the primary transmitter (Sterling, Matthews, 2005). The advantage of APs is a reliable transmission of information over long distances, while graded potentials, which can only operate over a short distance, allow for a higher bandwidth and information capacity (Juusola et al., 1996), the feature important for sensory information processing. For example, blowfly photoreceptors gradually transmit information through chemical synapses to large monopolar cells with the rate of nearly 2000 bits/s (de Ruyter van Steveninck, Laughlin, 1996), while for spiking neurons, estimates of maximal neurotransmission rates give at least fivefold lower values (de Ruyter Van Steveninck, Bialek, 1988; Bialek et al., 1991; Kjaer et al., 1994). The pivotal processes mediating transmission in both spiking and graded synapses seem to be basically similar.

Afferent Output in Mammalian Taste Cells:…

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Ca2+-dependent Exocytosis Synaptic transmission is initiated when AP triggers a Ca2+ transient in a presynaptic terminal that stimulates synaptic vesicle exocytosis. After exocytosis, synaptic vesicles undergo endocytosis followed by their recycling and refilling with neurotransmitters for a new round of exocytosis (Sudoff, 2004). The principle Ca2+-dependent mechanism, which couples AP to the discontinuous transmitter release is well detailed (reviewed in Evans, Zampony, 2006; Lisman et al., 2007). During the initial depolarizing phase, AP initiates rapid opening (for ~ 0.1 ms) of VG Ca2+ channels primarily of P/Q- and N-type (Wu et al., 1999; Iwasaki et al., 2000; Reid et al., 2003), which, however, usually transport a small Ca2+ current because its electrochemical driving force is low at high positive membrane voltage settled by open VG Na+ channels. Largely responsible for synaptic delay, the second stage is associated with the repolarizing phase of AP, during which, the driving force increases, thereby strongly augmenting the Ca2+ influx. There is, however, evidence that in certain synapses, vesicular exocytosis may be a one-stage process, given that substantial and quick Ca2+ entry may occur at the peak of AP (Sabatini, Regehr, 1996; McDonough et al., 1997). Presumably, fast K+ channels preclude too high depolarization of the plasma membrane by VG Na+ channels, thereby retaining high enough driving force for Ca2+ influx (Sabatini, Regehr, 1999). Calcium-dependent exocytosis at ribbon synapses involves largely L-type Ca2+ channels (Juusola et al., 1996; Sterling, Matthews, 2005). External Ca2+ enters the synaptic terminal and stimulates fusion machinery (Südhof, Rothman, 2009) with high cooperativity, as is the case with CNS synapses (Mintz et al., 1995; Borst, Sakmann, 1999; Wu et al., 1999). In ribbon synapses of hair cells and retinal bipolar cells, vesicular exocytosis exhibits a steep dependence on free cytosolic Ca2+ with the Hill coefficient of up to 5 (Heidelberger et al., 1994; Beutner et al., 2001). The physiologically relevant rate of vesicle release from bipolar cell terminals is likely to occur at 20–50 M free Ca2+ (Heidelberger, 2001). By contrast, exocytosis in photoreceptor synapses, which varied with Ca2+ influx in nearly linear manner (Wu, 1985; Naka et al., 1987), that is, with cytosolic Ca2+ (Thoreson et al., 2004), is stimulated at a much lower level of intracellular Ca2+ (~ 1 M) (Rieke, Schwartz, 1996; Thoreson et al., 2004).

Nonconventional Mechanisms Growing evidence points out that in addition to quantal synaptic signals, transmitters may provide diffusion signals by being released in unconventional ways. A non-vesicular release of transmitters, occurring presumably due to the reversal of transporters, has been reported for several cellular preparations (Paton, 1973; Schwartz, 1987; Taylor, Gordon-Weeks, 1991, Warr, et al., 1999). The main inhibitory neurotransmitter GABA is well documented as releasable from neurons and glial cells with non-vesicular mechanisms (reviewed by Koch, Magnusson, 2009). Several different release modes have been reported for the neurotransmitter/neuromodulator ATP, including exocytosis, the ABC transporter, and a number of ATP-permeable ion channels (Bodin, Burnstock, 2001; Lazarowski et al., 2003; Dale, 2008).

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CELL POPULATION IN THE MAMMALIAN TASTE BUD The taste bud arising from the local epithelium is composed of several dozens of elongated taste cells and few rounded basal cells. Taste cells undergo continuous renewal throughout life, with life span of 10-14 days on average, developing from a population of basal cell progenitors (Beidler, Smallman, 1965; Farbman, 1980; Delay et al., 1986; Stone et al., 1995). Based on distinctions in their morphological characteristics, taste cells have been classified into three core subclasses: type I, II, and III (Finger, Simon, 2000). Cells distinguished by their morphology are also different in their molecular and functional features. Type II cells are generally considered as primary chemosensory cells as they express two structurally distant families of G-protein coupled receptors (GPCRs), T1R and T2R, and downstream signaling effectors for bitter, sweet, and umami taste. Three closely related GPCRs from the T1R family originate at least two dimeric receptors. The heterodimer of T1R2 and T1R3 functions as a promiscuous sweet receptor, while T1R1 and T1R3 form a broadly turned L-amino acid sensor. The T2R family includes nearly 30 GPCRs that distinguish bitter ligands. Although sweet-, umami- and bitter-sensitive taste cells represent separate subpopulations within the type II subgroup, they employ basically the same transduction pathway involving activation of phospholipase C 2, IP3 production and release of Ca2+ from intracellular stores, activation of Ca2+-dependent cation channels TRPM5, membrane depolarization, and release of afferent transmitter, most likely ATP (reviewed in Chandrashekar et al., 2006; Sugita 2006; Roper 2007; Vandenbeuch, Kinnamon, 2009). Surprisingly, type II cells do not form classical chemical synapses with afferent nerve endings but utilize ATP-permeable channels for ATP secretion (discussed below). Taste cells of the type III, also referred to as synaptic cells, represent the only population of taste bud cells, which form recognizable synapses with afferent nerve terminals (Murray, 1986; Yang et al., 2007). Evidence implicates them in sensing acids that elicit sour taste: (i) Exclusively type III cells express PKD2L1 (Kataoka et al, 2008) and presumably PKD1L3 (Ishimaru et al., 2006; LopezJimenez et al., 2006), the channel subunits forming a cation channel activated by acids (Ishimaru et al., 2006; Ishii, 2009); (ii) Mice lacking cells expressing PKD2L1 are completely devoid of taste responses to sour stimuli (Huang et al., 2006). In addition, the extracellular Ca2+-sensing receptor is expressed in a subset of type III cells, enabling them to respond to amino acids (Gabriel et al., 2009; Bystrova et al, 2010). Therefore, type III cells can also serve as an amino acid sensor. Although type I cells are commonly considered as supportive (e.g. Lindemann, 1996), to all appearance, they can perform several functions. By expressing amiloride-sensitive Na+ channels (Vandenbeuch et al., 2008), type I cells can evaluate saltiness of a taste pore medium associated with the presence of NaCl, thus mediating the amiloride-sensitive mode of the salty taste (DeSimone, Lyall, 2006; Yoshida et al., 2009). Physiological studies of P2X2/P2X3-null mice showed that animals deficient in these ionotropic purinoreceptors lack neuronal and behavior responses to tastants of all taste modalities, implicating extracellular ATP in mediating afferent output in the taste bud (Finger et al., 2005). Reportedly, solely type I cells express nucleotide triphosphate diphosphohydrolase (NTPDase) 2, the enzyme hydrolizing extracellular ATP (Bartel et al., 2006). Moreover, NTPD2 is apparently coexpressed with the glutamate/aspartate transporter GLAST (Lawton et al., 2000) that is


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responsible for glutamate clearance by glial cells (Gadea, Lopez-Colome, 2001; Kanai, Hediger, 2004). These findings suggest that type I cells may control a spatial and temporal profile of transmitters released by type II cells, thus serving a glia-like function.

ELECTRICAL PROPERTIES OF TASTE CELLS Basic Electrophysiological Characteristics Multiple recordings from individual taste cells (n ~ 2000) convinced us that irrespective of their origin from circumvallate, foliate, or fungiform papilla, taste cells could be classified into three subgroups based on sets of voltage-gated (VG) currents they exhibited (Figure 1AC, left panels). With 140 mM KCl in the pipette and 140 mM NaCl in the bath, certain cells, called further as of the type A, showed inward TTX-blockable VG Na+ currents, noninactivating outward currents with relatively slow activation, and characteristic inward tail currents recorded on membrane re-polarization (Figure 1A, left panel). The second group of taste cells, the electrophysiological type B, also exhibited TTX-sensitive VG Na+ currents and outward currents activating quickly and inactivating to some extent (Figure 1B, left panel). The third group, type C, showed solely outward VG currents and no VG Na+ currents (Figure 1C). A small fraction (~ 2-4%) of elongated cells in preparations of dissociated taste buds showed no VG currents (not illustrated). When taste cells were dialyzed with a CsCl-based solution to suppress outward K+ currents, the difference between their primary electrophysiological profiles was even more profound. It was especially elucidative in experiments, wherein the patch pipette was filled with 140 mM KCl in the tip (~ 1 mm) and with 140 mM CsCl in the bulk (Figure 1D right upper insert). Under these recording conditions, a cell was dialyzed shortly with KCl that was then substituted for CsCl. In taste cells that exhibited type A-like WC currents in the very beginning of the recordings (Figure 1D, left panel), large outward and tail currents were observed even 15-40 min later (Figure 1D, right panel), although Cs+ rather than K+ was expected to be the most abundant cytoplasmic cation at that time. These outward currents are largely mediated by weakly selective connexin hemichannels (Romanov et al., 2007, 2008). Taste cells assigned to the type B showed large VG outward currents immediately after the WC formation (Figure 1E, left panel), which however disappeared in few minutes. In contrast, VG Na+ currents were mostly unaffected by the Kin/Csin substitution (Figure 1E, right panel). In taste cells of the type C, outward currents were suppressed dramatically upon the Kin/Csin substitution (Figure 1F). These observations indicate conclusively that in cells of the type B and type C, outward currents are normally transported by K+ channels. Thus, the above data pointed to the existence of three basic subpopulations of taste cells that are distinct electrophysiologically. This inference was validated by more detailed analysis of ionic currents in mouse taste cells.

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Figure 1. Whole-cell (WC) currents recorded from taste cells can be classified into three subfamilies. (A, B, C) Representative families of VG integral currents (left panels) elicited by 100 ms voltage pulses varied as indicated (upper insert in A) and corresponding I-V curves (right panels). (A, B, right panels) Sustained current ( ) and VG Na+ current (▲) versus membrane voltage. (C) Representative WC currents that were recorded from a cell showing no VG Na+ currents (left panel) and the corresponding I-V curve ( , right panel) for the sustained current. (D) Representative WC currents recorded sequentially from a type A cell soon after the establishing the WC mode and 15 min later. The patch pipette (upper right insert) was filled with a complex intracellular solution allowing for the replacement of K+ in the tip with Cs+ within 10 min. (E, F) Substitution of K+ for Cs+ dramatically suppressed outward VG currents in taste cells of the type B and type C. (D, E, right panels). In all cases, cells were held at -70 mV, perfused with a bath solution containing 140 mM NaCl, and dialyzed with 140 mM KCl (A-C) or with 140 mM KCl/CsCl (D-F). (Modified after Romanov, Kolesnikov, 2006).

Miscellaneous Currents VG Ca2+ Channels Both high and low voltage activated Ca2+ currents have been reported in previous studies of rodent taste cells that were not identified (Behe et al., 1990; Furue, Yoshii, 1997; Noguchi et al., 2003). In our experiments, activity of VG Ca2+ channels, which were predominantly of the L-type, was seen in type B cells but neither in type A cells nor in type C cells (Romanov,


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Kolesnikov, 2006). Although with 1 mM Ca2+ in the bath, VG Ca2+ currents were detectable in nearly 60 % of cells tested, apparently every Fluo-4 loaded taste cell of the type III exhibited Ca2+ transients in response to depolarization, indicating that VG Ca2+ channels are functional in most, if not all, type III cells (Romanov et al., 2008).

Delayed Rectifier K+ Current The presence of delayed rectifier K+ channels in non-identified taste cells of the rat has been reported in previous works (Behe et al., 1990; Chen et al., 1996). These channels are largely responsible for TEA-blockable VG outward K+currents in taste cells of the type B and type C (Figure 1E, F) but have small contribution to VG outward currents in type A cells (Figure 1D, upper current traces). Transient Potassium Current (IA) The IA current was originally described in non-identified rat taste cells, where it contributed to the falling phase of APs (Chen et al., 1996). We recorded this 4-AP-sensitive VG current solely in type B cells of the mouse but never in cells of the type A and C (Romanov, Kolesnikov, unpublished observations). Hypolarization-activated Current (Ih) The Ih current has been documented first in non-identified rat taste cells (Stevens et al., 2001). We observed Cs-sensitive Ih-currents in virtually all cells of the type B, provided that those were assayed with the perforated patch approach. In contrast, cells of the type A and type C never exhibited such currents, indicating that cationic CNH channels are not functional in these cells (Romanov, Kolesnikov, 2006). Inward Rectifying (IR) K+ Current Earlier studies have revealed IR K+ channels in non-identified rodent taste cells (Sun, Herness, 1996; Stevens et al., 2001; Noguchi et al., 2003). In our experiments (Romanov, Kolesnikov, 2006), an increase of external K+ concentration shifted the reversal potential of integral currents positively and enlarged the inward component recorded at negative voltages. Such observations are conventionally considered as indicative of IR K+ channel activity. While in cells of the type A and type C, the rise in bath K+ affected mostly the inward currents, in type B cells, it augmented both the inward and outward currents. Since an electrochemical driving force for an outward K+ current decreases as external K+ increases, such a K+ dependence of the outward component suggests an active role for external K+, including the modulation of K+ channel gating (Yellen, 2002) and the direct gating of cation channels by K+ ions (Kolesnikov, Margolskee, 1998). Thus for type B cells, the contribution of IR K+ channels to integral currents is uncertain. Ca2+-gated K+ Current (ICa) This current first was isolated in non-identified rat taste cells as being apamin-blockable and dependent on bath Ca2+ (Chen et al., 1996). We observed an apamin-sensitive K+ current in type B cells, but not in cells of the type A and type C (Romanov, Kolesnikov, unpublished observations). Nifedipine also suppressed this current presumably by blocking L-type Ca2+ channels, which largely mediate VG Ca2+ influx in type B cells.

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TRPM5-mediated Current Reportedly, cation channels TRPM5 are expressed in taste cells to mediate bitter, sweet, and umami transduction (Perez et al., 2002; Zhang et al., 2003). Given that these channels are poorly selective among monovalent cations, gated by cytosolic Ca2+ (Liu, Liman, 2003; Pra7witt et al., 2003), and highly thermosensitive (Q10 ~ 8, Talavera et al., 2005), TRPM5mediated currents were searched for as Ca2+- and temperature-dependent ones. Such currents were found solely in type A cells (Romanov et al., 2007). Ca2+-gated Cl- current. Ca2+-gated Cl- currents were found solely in type C cells, where these channels are involved in Ca2+ signaling and stimulated by a variety of agonists, particularly ATP, which mobilize intracellular Ca2+ (Kim et al., 2000).

CORRELATION BETWEEN ELECTROPHYSIOLOGICAL PROPERTIES AND EXPRESSION OF MARKER PROTEINS As described above, three subpopulations of taste cells, type A, type B, and type C, which were initially distinguished on the basis of simple set VG currents, are basically distinct by their electrophysiological properties. We therefore inferred that these electrophysiologically determined subgroups of taste cells represent functionally separate cell subpopulations, which might directly relate to the morphologically defined cellular subclasses, namely, to type I, type II, and type III. The first supportive, albeit indirect, evidence was provided by Medler and co-authors (2003), who recorded from individual taste cells isolated from transgenic mice that express GFP under promoter of the G-protein gustducin, which is specifically expressed in a subpopulation of type II cells. They reported that gustducin-positive cells identified by their green fluorescence exhibited no VG Ca2+ currents, small VG Na+ currents, and noninactivating outward currents, as is the case with type A cells. We also used this animal model and found that gustducin-positive cells are exclusively of the type A (Romanov et al., 2007). Using single-cell RT-PCR, we also showed that TRPM5 and phospholipase C 2, two markers specific for type II cell, are expressed in taste cells of the type A (Romanov et al., 2007). Thus, morphologically defined type II and electrophysiological type A represent the same subpopulation of taste cells. Type III cells are the only taste bud cells that form classical presynaptic structures (Roper, 2006). It therefore can be expected that these taste cells possess fusion machinery and VG Ca2+ channels. Indeed, the presynaptic protein SNAP-25 and -subunits of L-type Ca2+ channels are expressed in cells, which lack G-protein coupled taste receptors and the downstream effectors PLC 2 and TRPM5, that is, most likely in type III cells (Clapp et al., 2006; DeFazio et al., 2006). These findings suggest that type III is identical to type B, because VG Ca2+ channels are functional in type B cells only. As having no alternative, type I and type C should represent the same cell subpopulation. Recently, we profiled expression of certain marker proteins at the level of individual taste cells (Bystrova et al., 2010) and found that the markers were distributed among taste cells, which were identified electrophysiologically, in complete correspondence with the following relation: type I = type C, type II = type A, and type III = type B. Thus, individual taste cells can indeed be ‗fingerprinted‘ by their VG currents (Figure 1).


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EXCITABILITY OF TASTE CELLS As mentioned above, taste cells of the type II and type III utilize different sets of ion channels, including VG Na+ channels that are apparently presented by different isoforms in the particular cell type (Gao et al., 2009). Type III cells express a variety of channels rather characteristic of neuronal cells, wherein they are used to shape APs (delay rectifier and transient K+ channels), to establish interspike intervals (transient K+ channels), to generate slow afterhypolarization (Ca2+-gated K+ channels), and to mediate slow depolarization and pacemaker activity (cationic CNH channels). In type II cells, the set of classical regeneratory channels includes solely VG Na+ channels and delay rectifier K+ channels. Thus, it is clear a priory that electrical excitability of type II and type III cells should be different.

Figure 2. Electrical excitability of taste cells of the type III and type II. (A) Families of VG currents recorded from assayed cells, thus defining one as of the type III (upper current traces) and another as of the type II (bottom current traces). In both cases, perforated patch technique under the voltage-clamp mode was employed. The cells were perfused with a bath solution containing 140 mM NaCl, and dialyzed with 140 mM KCl. (B) Bursts of APs generated by the type III cell as in (A, upper traces) in response to 500 ms pulses of the depolarizing current of different values, as indicated. (C) Set of APs generated by the type II cell as in (A, bottom traces) in response to the 800 ms graded stimulation by the depolarizing current, as indicated. (D) Single APs generated by the type III cell (left panel) shown in (B) and by the type II cell (right panel) shown in (C). In (B-D), the cells were assayed under the current clamp mode.

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Figure 3. Bitter responses of type II cells. (A) Change in a resting current in response to a mix of bitter compounds (100 M cycloheximide + 1 mM denatonium benzoate + 3 mM sucrose octaacetate). The cell was held at -70 mV, perfused with a bath solution containing 140 mM NaCl, and dialyzed with 140 mM CsCl. (B) Gradual response to denatonium accompanied by APs was generated by a cell assayed under zero current clamp mode with 140 mM NaCl in the bath and 140 mM KCl in the patch pipette. In both cases, the perforated patch approach was used.

When stimulated by a step-like depolarizing current (5-25 pA), type III cells generated either single AP or a burst of the variable number of APs, depending on a current value (Figure 2B). A typical AP was very fast (t1/2 = 1.5-1.8 ms) and invariably accompanied by deep afterhyperpolarization (Figure 2B and Figure 2D, left panel). Cells of the type II typically generated single AP on a step-like depolarizing current (5-40 pA) (not shown), while graded stimulation usually produced 2-4 APs that were relatively slow (t1/2 = 3.5-4.2 ms) (Figure 2C and Figure 2D, right panel). It thus appears that in taste cells of the particular type, mechanisms underlying electrical excitability are adjusted to kinetically different stimulation, that is, to relatively slow, perhaps, bell-like generatory potentials in type II cells (Figure 3) and to pulse-like potentials in type III cells.

NEUROTRANSMITTERS OPERATIVE IN THE TASTE BUD Physiological evidence and data of molecular biology and immunohistochemistry indicate that cell-to-cell signaling in the taste bud can involve multiple first messengers and their receptors, including such classical neurotransmitters/neuromodulators as glutamate, serotonin, acetylcholine, GABA, АТР, noradrenaline, cholecystokinin, vasoactive intestinal


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peptide (reviewed by Roper, 2006, 2007; Herness, Zhao, 2009). It is unclear why the peripheral taste organ needs so many first messengers, and which physiological processes they are involved in. Studies performed within the last years, especially the demonstration that tastants stimulate release of serotonin and ATP from taste cells, highlighted the serotonergic and purinergic systems as directly related to taste transduction.

Serotonin Serotonin (E5-hydroxytryptamine (5-HT)) has long been considered as a very likely candidate for being an afferent neurotransmitter in the peripheral taste organ based on the following evidence. Using different staining techniques, the presence of serotonin in a subset of Type III taste cells has been demonstrated for different mammalian species (Nada, Hirata, 1975; Uchida, 1985; Fujimoto et al., 1987; Kim, Roper, 1995; Yee et al., 2001). Consistently, the Na-dependent 5-HT transporter has been identified in taste cells (Ren et al., 1999). The data of RT-PCR and immunostaining suggest that 5HT1a receptors are expressed in taste cells, while 5-HT3 receptors are present in nerve fibers innervating taste buds (Kaya et al., 2004). Serotonin has been found to decrease Ca2+-gated K+ currents and VG Na+ currents in nonidentified taste cells (Herness, Chen, 2000). Moreover, serotonin can be released by taste buds, presumably from type III cells, on taste stimulation and on depolarization elicited by bath KCl (Huang et al., 2005). However, as demonstrated in crucial behavioral tests, genetically modified mice lacking the 5-HT3 subunit showed no deficit in taste perception of stimuli representative of different taste modalities (Finger et al., 2005). Thus, afferent transmission from taste cells to nerve fibers is hardly relied on release of serotonin that is rather employed as a cell-to-cell messenger within the taste bud.

ATP Several lines of evidence suggest a pivotal role of purinergic signaling system in taste bud physiology. The early works revealed that cells in different taste papillae express a variety of metabotropic ATP receptors of the P2Y type (Kataoka et al., 2004; Bystrova et al., 2006; Hayato et al., 2007), certain of which are coupled to the phosphoinositide cascade and Ca2+ mobilization (Baryshnikov et al., 2003). The immunohistochemical evidence points out that ionotropic P2X2 and P2X3 receptors are present in gustatory nerve endings innervating taste buds (Bo et al., 1999). Transcripts for P2X2, P2X4, and P2X7 receptors were found in mouse fungiform papillae, and the expression of the P2X2 protein was confirmed with immunostaining (Hayato et al., 2007). Recordings of electrical activity of taste nerves in P2X2/P2X3 double knock-out mice and behavior studies of these animals have provided fundamental insights into the role of purinergic signaling in taste bud physiology. Finger et al. (2005) showed that P2X2/P2X3 null mice lacked all neuronal responses to taste stimuli of all qualities and had dramatically reduced behavioral responses to sweet, bitter, and umami substances. These findings implicate ATP and P2X2/P2X3 receptors in mediating taste signal output to the gustatory nerve. Consistently with such a role for the nucleotide, bitter substances have been shown to stimulate ATP secretion from lingual epithelium containing taste cells (Finger et al., 2005).

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RELEASE OF SEROTONIN AND ATP FROM TASTE CELLS Serotonin The release of serotonin from mouse taste buds was first assayed by Huang and coworkers (2005) by employing a cellular biosensor: bath serotonin was detected with Fura-2loaded CHO cells transfected with high-affinity 5-HT2C receptors coupled to Ca2+ mobilization. When taste cells in an assayed taste bud were depolarized by 50 mM KCl, the nearby sensor, which was irresponsive per se to this stimulus, generated a marked Ca2+ transient, indicating strong serotonin release initiated by taste cell depolarization. Removal of bath Ca2+ completely inhibited effects of KCl, showing that Ca2+ influx was necessary and sufficient to stimulate serotonin release. Bitter cycloheximide and saccharin also stimulated transmitter release that persisted to some extent in the absence of extracellular Ca2+, presumably due to that the tastants stimulated Ca2+ release from intracellular store (Huang et al., 2005). Interestingly, nearly one third of serotonin releasing cells co-released norepinephrine in a Ca2+-dependent manner (Huang et al., 2008). Given the strong dependence of serotonin release on bath Ca2+ and that KCl-produced depolarization stimulates high Ca2+ influx via VG Ca2+ channels solely in type III cells (Huang et al., 2005, Romanov et al. 2008; Roberts et al., 2009; Bystrova et al., 2010), there may be little doubts that just type III cells release serotonin with exocytosis as the predominant mechanism.

ATP ATP secretion from mouse taste cells was also assayed with a cellular biosensor (Romanov et al., 2007; Huang et al., 2007). This approach was modified by us in that taste cells were concurrently examined with the patch clamp technique and Ca2+ imaging, thus allowing one to identify taste cells electrophysiologically, to controllably stimulate them by depolarizing voltage pulses, and to correlate a rate of secretion with a change in cytosolic Ca2+ (Romanov et al., 2007, 2008). We used COS-1 cells loaded with the Fluo-4 as an ATP biosensor capable of detecting ATP at 100 nM and higher. These cells endogenously express P2Y receptors coupled to Ca2+ mobilization so that a local variation in bath ATP can be monitored with Ca2+ transients in the COS-1 cytoplasm. The advantage of this P2Y-based sensor is that removal of external Ca2+ only weakly affects its responses to bath ATP, enabling one to analyze coupling of Ca2+ influx to ATP secretion with Ca2+ imaging. Figure 4A exemplifies representative recordings of intracellular Ca2+ in COS-1 cells (right panels) placed nearby assayed taste cells identified by their VG currents (left panels). As indicated, depolarization from the holding potential of -70 mV to 10 mV (Figure 4A, upper-right panel) stimulated detectable ATP release solely in a cell of the type II (Figure 4A, upper current and fluorescent traces). Among taste cells isolated from circumvallate and foliate papillae, most (>80%) of robust cells of the type II released ATP (n~200), while ATP efflux was never detected in cells of the type I and type III. Somewhat similar results were reported by Huang et al., (2007), who used Ca2+ imaging but a different cellular ATP biosensor to assay secretion of ATP in mouse taste cells.


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Figure 4. Subtype specific release of ATP from taste cells. (A) Correlations between electrophysiological characteristics of taste cells (left panels) and responses of the ATP biosensor, a Fluo-4 loaded COS-1 cell (right panels). Only taste cells classified to the type II by their integral currents (upper-left traces) released ATP upon depolarization, while electrically stimulated cells of the type III (middle-left traces) or type I (bottom-left traces) never released ATP detectable with the ATP biosensor (right panels). The upper inserts indicate command voltage used for cell identification (left panel) and for the stimulation of ATP release (right panel). A relative change in fluorescence intensity is expressed as F/F0, where F0 is a value of Fluo-4 emission measured just before cell stimulation. (B) ATP release on electrical stimulation of type II cells is not accompanied by a change in intracellular Ca2+. The 5 sec depolarization (upper insert) of the taste cell produced well resolved outward and tail currents (upper trace), did not affect cytosolic Ca2+ (middle trace) but triggered ATP release, thereby stimulating the ATP sensor (bottom trace). In all cases, currents/voltage were recorded with 140 mM KCl in the pipette and 140 mM NaCl in the bath using the perforated patch approach.

Thus in the mammalian taste bud, different taste cells are responsible for release of serotonin (type III cells) and ATP (type II cells).

MECHANISM OF ATP RELEASE Voltage and Ca2+ Dependence As mentioned above, there are several pathways mediating ATP secretion, including ABC transporters, ATP permeable ion channels, and exocytosis driven by a local rise in intracellular Ca2+. When the intracellular Ca2+ trigger was eliminated both by decreasing extracellular Ca2+ to 100 nM and by loading type II cells with the fast Ca2+ chelator BAPTA (10 mM), the ATP secretion was not affected significantly (Romanov et al., 2007). In complimentary experiments, wherein taste cells were concurrently assayed with the patch

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clamp technique and Ca2+ imaging and by using the ATP sensor, depolarization of type II cells elicited negligible deviations of free Ca2+ in their cytoplasm but triggered well detectable ATP efflux (Figure 4B). These observations indicate that the vesicular mechanism contributes negligibly to the ATP secretion. In a search for an alternative mechanism, we studied voltage dependence of ATP secretion. Serial depolarization of Type II cells typically elicited multiple and well reproducible responses of the ATP sensor (Figure 5A), demonstrating the high fidelity of secretory machinery. As a function of voltage held on the taste cell membrane, ATP sensor responses showed a steep bell-like dependence at 2 s depolarization (Figure 5B) that is inconsistent with the weakly-rectifying I-V curves characteristic of ABC transporters (Abraham et al., 1993). On the other hand, a number of ion channels with markedly nonlinear I-V curves have been reported to mediate ATP secretion in a variety of different cells. Examples include certain anion channels (Sabirov et al., 2001; Bell et al., 2003), P2X7 receptors (Suadicani et al., 2006), connexin (Cotrina et al., 1998; Stout et al., 2002) and pannexin (Bao et al. 2004; Locovei et al. 2006a) hemichannels. The P2X7 receptors and anion channels could be excluded for the reason that the former are not functional in type II cells, while anion channel blockers affected ATP secretion weakly, if at all (Romanov et al., 2007). Thus, connexin/pannexin hemichannels remained as the most likely conduit of ATP release.

Figure 5. Dependence of ATP secretion on membrane voltage. (A) Sequential responses of the ATP biosensor elicited by 2 s depolarization of the same taste cell from the holding potential of -70 mV to the voltage indicated above the traces. (B, C) Normalized response of the ATP-sensor (●,) versus voltage clamped on the plasma membrane of an assayed taste cell. To elicit ATP responses, cells were depolarized for 2 s (B) or for 100 ms (C). The responses were normalized to a value of the maximal response. The experimental data are presented as a mean SD (n=5-8). In (B, C), the continuous curves represent computer simulations of ATP sensor responses (Romanov et al., 2008). The recording conditions as in Figure 4.


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Connexin versus Pannexin Taste cells of the Type II express multiple junctional proteins, including pannexin 1 (Px1) and several connexins (Cx) (Romanov et al., 2007; Huang et al., 2007), which alone or in combination can mediate ATP secretion. Huang et al. (2007) speculated in favor of Px1hemichannels as a conduit of ATP release based on that Px1 is the most abundant gapjunction protein in type II cells, compared to Cx30 and Cx43, and that 5 M carbenoxolone, a potent blocker of Px1-hemichannels at this concentration, severely diminishes ATP secretion elicited by tastants. We relied mostly on mimetic peptides and biophysical methods and inferred that Cx-based chemichannels mediate ATP efflux stimulated by depolarization of type II cells (Romanov et al., 2007, 2008). Kinetically, Px1- and Cx-hemichannels are different. The former activate and deactivate quickly and inactivate slowly (Bruzonne et al, 2003, 2005). The Cx hemichannels activate and deactivate slowly and exhibit no inactivation (Valiunas, 2002; Bader, Weingart, 2004; Bruzonne et al, 2005) as is the case with the channels responsible for VG outward currents in Type II cells (Figure 1A, left panel). One more argument in favor of Cx-hemichannels as the main conduit of ATP efflux was provided by the analysis of ATP release from type II cells stimulated by voltage pulses of different durations. The model of transient VG ATP efflux through Cx hemichannels predicts that for prolonged electrical stimulation, ATP release should be a bell-like function of depolarizing voltage, while for relatively short depolarization, one should follow a Langmuir isotherm-like dependence (Romanov et al., 2008). Such bifurcation is indeed characteristic of a voltage dependence of ATP release exhibited by electrically stimulated cells of the type II (Figure 5B, C). Since subtype specific blockers for Cx- and Px- hemichannels are not available even for recombinant connexons/pannexons, while natural hemichannels can function as heterooligomers (Mese et al., 2007) with peculiar sensitivity to blockers, it is difficult to unambiguously distinguish between Cx- and Px-mediated pathways in natural cells. Nevertheless, Cx mimetic peptides and the Px1 mimetic peptide 10Px1 exhibit high enough specificity to certain recombinant Cxs and to Px1, respectively (Chaytor et al., 1997; Leybaert et al., 2003; Martin et al., 2005; De Vuyst et al., 2006; Pelegrin, Surprenant, 2006, 2007). We used mimetic peptides as a relatively specific probe of hemichannel activity and found that the Cx peptide 43GAP26 mutually inhibited VG outward currents and depolarization-driven ATP release in type II cells, while 10Px1 was ineffective (Romanov et al., 2007, 2008). These observations and other findings led us to the conclusion that the same hemichannels are responsible for both VG outward currents (Figure 1A, left panel) and for ATP secretion. It was shown particularly that the channels involved are ATP permeable. Given that hemichannels are weakly selective and permeable to small molecules up to 1 kDa (Goodenough, Paul, 2003) and that ATP can aggregate with different ion species, we simplify the analysis by dialyzing and perfusing cells with solutions containing exclusively MgATP, which were adjusted to pH 7.4 by adding the equimolar quantity of Mg(OH)2. Such a solution should contain mostly Mg2+ and MgATP2- ions and a negligible quantity of other species. Particularly, with 50 mM MgATP + 50 mM Mg(OH)2 in a solution, calculations gave that at pH 7.4 and 25 oC, it should contain 21.0 mM MgATP2-, 21.1 mM Mg2+, and 28.9 mM Mg2ATP. For 12.5 mM MgATP + 12.5 mM Mg(OH)2, 7.04 mM MgATP2-, 7.1 mM Mg2+ and 5.42 mM Mg2ATP should be present in a solution.

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Figure 6. VG currents in taste cells dialyzed and perfused with MgATP. (A) Representative whole-cell (WC) currents (n=4) recorded from the same cell perfused with 50 mM MgATP + Mg(OH)2 (middle panel) and with 12.5 mM MgATP + Mg(OH)2 (bottom panel). The currents were recorded with 50 mM MgATP + Mg(OH)2 in the recording pipette. Taste cells were patched in the bath solution containing 140 mM NaCl that was substituted for 50 mM MgATP + Mg(OH)2 after obtaining the WC mode. (B) Voltage-current curves generated with 50 mM (●) and 12.5 mM () MgATP + Mg(OH)2 in the bath. With 50 mM MgATP + Mg(OH)2 both in the recording pipette and in the bath, WC currents did not reverse at 0 mV, as membrane voltage was not corrected for the liquid junction potential of about 10 mV between solutions containing 140 mM NaCl and 50 mM MgATP + Mg(OH)2, respectively. Nearly the same junctional potential arose across the boundary between the solutions containing 140 mM NaCl and 12.5 mM MgATP + Mg(OH)2. Since the life-time of stable WC preparations was very short with high MgATP + Mg(OH)2 in the pipette, neither serial resistance nor cell capacitance was compensated for in the presented recordings.

With 50 mM MgATP + 50 mM Mg(OH)2 both in the recording pipette and in the bath, the VG outward currents were still observed in type II cells, indicating that the channels involved were permeable to MgATP2- and/or to Mg2+ (Figure 6A, middle panel). The reduction of extracellular MgATP + Mg(OH)2 from 50 mM to 12.5 mM led to a small increase in the inward component of the WC current, slightly decreased its outward component, and shifted the reversal potential Vr of the VG current positively by nearly 4 mV (Figure 6A, B). These observations suggest that the plasma membrane is slightly more permeable to MgATP2- compared to Mg2+. Thus, hemichannels carrying VG outward currents in Type II cells are indeed permeable to ATP well enough to mediate ATP secretion. Reportedly, Px1-hemichannels are gated by intracellular Ca2+ with the micromolar halfeffect concentration (Locovei et al., 2006b). Their activity should therefore be negligible in electrically stimulated Type II cells, where intracellular Ca2+ apparently remains at the low level (Figure 4B). This inference is consistent with the key role of Cx hemichannels in mediating ATP release in electrically stimulated type II cells. In contrast, taste stimulation can produce both a marked Ca2+ transient in their cytoplasm (Huang et al., 2007) and membrane depolarization. Hence, the principle difference between depolarization-triggered ATP efflux and tastant-elicited ATP secretion is that the former is apparently governed by a single factor, i.e. by membrane voltage, while taste stimulation initiates both depolarization


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and intracellular signaling, at least Ca2+ signaling. In light of the mentioned dualism of taste transduction, the following is noteworthy. One of the key elements of taste transduction cascade is the Ca2+-gated cation channel TRPM5 (Perez et al., 2002), given that neuronal and behavior responses to bitter, sweet, and umami stimuli are dramatically diminished in TRPM5-null mice (Chandrashekar et al., 2006; Damak et al., 2006). Apart from thermosensitivity (Talavera et al., 2005), the only conceivable function of these channels in the transduction process is to convert an initial Ca2+ signal elicited by a taste stimulus into membrane depolarization. Note that removal of Ca2+impermeable TRPM5 should negligibly affect Ca2+ signaling in type II cells, which express TRPM5. Therefore, the collapse of taste transduction as a whole in TRPM5 knock-outed taste cells can be rationally explained only if membrane depolarization, rather than Ca 2+ transients, is a key factor governing release of the afferent neurotransmitter ATP. Thus, although a relative contribution of the VG pathway, most likely Cx-based, and a Ca2+-dependent mechanism, perhaps Px1-mediated, to ATP secretion triggered by taste stimulation remains uncertain, the voltage dependence of ATP release (Figure 5) appears to be the pivotal factor in transmission of sensory information from type II cells to gustatory nerve endings.

CONCLUSION The conventional point of view is that taste cells generate APs to drive the release of neurotransmitter onto the afferent nerve (e.g., Herness, Gilbertson, 1999). Meanwhile, retinal rods and cones as well as auditory hair cells, which also have no axons, provide examples of afferent transmission that is based on tonic release of neurotransmitter glutamate under control of graded generator potentials (Sterling, Matthews, 2005). Glutamate also serves as the principal afferent neurotransmitter in olfactory sensory neurons, which have axonal projections to the olfactory bulb and generate APs to convey sensory information distantly. All these non-taste sensory cells used classical chemical synapses and the exocytotic mechanism for glutamate release. The afferent transmission in mammalian taste cells is distinct from that in either of the mentioned sensory cells. Bitter, sweet, and umami sensitive cells of the type II, which utilize ATP instead of glutamate to transmit sensory information, do generate APs but do not form classical chemical synapses, relying on ATP-permeable hemichannels for ATP secretion. In contrast, considered as sour sensors, taste cells of the type III form presynaptic structures and use APs to govern exocytosis of serotonin, a signaling role of which is still debatable. Given apparently normal taste perception of mice deficient in 5HT3 receptors presumably operative in the gustatory nerve (Finger et al., 2005), serotonin hardly serves as a type III cell-specific neurotransmitter that mediates afferent output to the gustatory nerve. To account for the observations that bitter and sweet compounds, which are primarily recognized by type II cells, can stimulate serotonin release from type III cells (Huang et al., 2005) it was hypothesized that taste stimulation of type II (receptor) cells initiates secretion of ATP, which acts on both afferent terminals and type III (presynaptic) cells (Huang et al., 2007). If P2X2/P2X3 receptors, which originally have been located to afferent nerve terminals (Bo et al. 1999), also operate in type III cells, the dramatic impact of P2X2/P2X3 knock out on bitter, sweet, and umami taste could partly be attributed to the disruption of proper

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communications, mediated by ATP and these P2X receptors, between cells of the type II and type III. However, our observations strongly argue against such a possibility, given that type III cells are irresponsive to micromolar ATP at least in circumvallate and foliate papillae (Bystrova et al., 2010). Why is afferent output in taste cells so markedly distinct from that in other sensory cells? Although at the moment there is no clear answer, the likely possibility is that unlike the retina or main olfactory epithelium, the peripheral taste organ is subjected to a strong mechanical disturbance accompanying eating. Whatever the reason, AP seems to be an obligatory intracellular event in a transduction pathway, should ATP and ATP-permeable channels be chosen to mediate afferent output in taste cells of the type II. Indeed, being mediated by transduction channels TRPM5, gradual generator potentials elicited by tastants should not depolarize taste cells above 0 mV, the voltage being close to the reversal potential of a TRPM5-mediated current under physiological conditions. Meanwhile, characteristic of ATP secretion is its steep dependence on membrane voltage with the high apparent thresholds of about -10 mV and 0 mV obtained at prolonged and short electrical stimulations, respectively (Figure 5B, C). If a taste stimulus would evoke gradual depolarization without AP, even sustained depolarization below -10 mV would fail to effectively stimulate ATP release (Figure 5B). Brief generatory potentials would be entirely unable to release ATP (Figure 5C). Thus, with the secretory mechanism relying on hemichannels, a graded taste response is apparently inappropriate for governing afferent output. In contrast, being triggered by moderate depolarization above the threshold of about -40 mV, each AP would stimulate the release of a more or less universal ATP quantum by depolarizing a taste cell to nearly 50 mV for ~ 4 ms, the weakly variable voltage and duration (Figure 3B). With this all-or-nothing strategy, encoding of taste information is reduced to the generation of a train of APs, which, for instance, lasts proportionally to stimulus intensity. In our experiments, the resting potential in type II cells ranged from -53 ÷ -36 mV and was -43 mV on average, with 140 mM KCl in the recording pipette and 140 mM NaCl in the bath. A similar value (~ -45 mV) was obtained by Medler et al. (2003) for mouse taste cells that showed VG Na+ currents and no VG Ca2+ currents, thus being of the type II. At such resting potential, a fraction of non-inactivated VG Na+ channels in resting type A cells is high enough to generate marked APs (Figure 3B), thus mediating the AP-based mechanism supposed above.

ACKNOWLEDGMENTS This work was partly supported by the Program ―Molecular and Cell Biology‖ of the Russian Academy of Sciences.

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Chapter 6

METHODOLOGIES TO UNRAVEL CARDIAC STRUCTURE AND FUNCTION COMPLEXITY AT CELLULAR AND TISSUE LEVEL Ioanna Chouvarda and Nicos Maglaveras Lab of Medical Informatics, Aristotle University of Thessaloniki, Greece

ABSTRACT This chapter aims to elaborate on different aspects of current biomedical modeling and processing approaches, with respect to questions at a certain analysis scale of cardiac system. Three examples are discussed, referring to different problems and levels of detail at microscopic scales. Ways of modelling and extraction of characteristics of the underlying processes are presented, corresponding to medically interesting conditions. These examples are illustrated by use of experimental data and simulated experiments data. The proposed approaches offer the basis for discussion on further perspectives towards possible integrative approaches.

1. INTRODUCTION The heart is a complex system, with evident structure and function interplay, as well as multiple scale interactions, both in normal conditions and in disease. Constituting a challenging modeling target, cardiac function has been extensively studied during the past years. Multilevel cardiac analysis and modeling, from molecule and cell to organ, and even inter-organ interaction, actually create an excellent paradigm within the virtual physiological human context, which can shine light on the complex cardiac mechanisms and explain the phenomena of health and disease towards translational research and eventually personalized health. A realistic reproduction of cardiac function requires the description of electro physiological and mechanical function coupled with the description of anatomy, which

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Ioanna Chouvarda and Nicos Maglaveras

implies detailed models, mathematical and geometric, respectively, along with experiments to tune model parameters, and actual clinical data for the model evaluation. In this sense, cardiac modeling is a highly multidisciplinary task. This chapter presents biomedical processing methods that can be employed to answer different questions at microscopic cardiac scales. The main aim is to elaborate on different aspects of current biomedical modeling and processing approaches, with respect to questions and answers that can be given at a certain analysis scale. In this context, scale-specific examples are discussed with respect to the cardiac system and to different levels of complexity. Ways of modeling and extraction of characteristics of the underlying processes are presented, in medically interesting conditions, from basic methods examining propagation at cellular level to overall characterization of organ function under disease or medication. When considering the heart in microscopic scale, i.e., focusing on the action potential issues, there are multiple factors to be taken into account, including ionic conditions and cell function, stimulus rate structural properties and heterogeneity. The way these factors interact, or whether each factor acts independently and complementary, in health and disease or vulnerability to arrhythmias, how these issues are reflected in observable biosignals, create important topics, towards the question of structure and function interaction and complexity.. Starting from the basic cardiac mechanisms in microscopic scales, the first question addressed concerns 1D propagation and the location of activity. Methods are presented for the estimation of the electrode distance from the active fiber. In 2D propagation, addressing the question ―How does propagation take place‖, methods for estimating the propagation wavefront in cases of complex zig-zag propagation are discussed. Furthermore, propagation characteristics in the 2D case are analysed in different combinations of pacing and ionic conditions reflecting diseased situations. These examples are illustrated by use of experimental data and simulated experiments data. Finally, besides discussing the proposed approaches, questions are raised in each case and further perspectives are highlighted towards possible integrative approaches that would combine such multiple level methods for diagnosis and treatment enhancement.

2. BACKGROUND Nowadays, 3D models integrating both electrophysiological and mechanical properties have been proposed [0], and can be supported by the computational power offered via parallel computing or computational grid technologies [0]. Nevertheless, detailed two-dimensional modeling is still of value for the biomedical community, towards simulating various propagation conditions and gaining insight on the properties of tissue activation. Adopting a model for a cardiac simulation needs to bear in mind that ionic currents have different behavior, as illustrated in the following example. The ionic current models used were the Beeler-Reuter (BR), Luo-Rudy (LR) and Ebihara-Johnson (EJ) [3][4][5]. The BR and LR in the fast inward current (Ina) formulation exhibit one activation gating variable (m) and two inactivation gating variables (h,j), while the EJ model exhibits one activation (m) and one inactivation (h) variable.

Methodologies to Unravel Cardiac Structure and Function Complexity…

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Figure 1. Example 2D testbeds for the investigation of cardiac propagation under different conditions. An example setup for a 2D simulation is depicted in Figure 1. Following the 2D monodomain model of cardiac muscle , each cell is simulated as 4 longitudinal elements/cell (3 cytoplasmic and 1 junctional) and the 2D tissue is simulated as a rectangular grid of 40x200 such elements, which corresponds to 40x50 cells. Regions of scar tissue are defined, which do not allow propagation of action potential, thus introducing tissue heterogeneity causing zigzag pathways, and enabling the study in conditions of rotating waves. Such a framework can be a testbed for examining different questions, depending also on the ionic properties assigned to each node. A variety of ionic current models has been defined during the last decades, specifying the cellular function under normal conditions or disease, and for different anatomic parts. Many of these models are available online in standard xml descriptions [2].

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Figure 2. Current: Normalised Ionmin values in the area of interest, in cartesian coordinates, for the 3 models. setup A and setup B defined above.


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The kinetics of the BR model are much slower when compared with the LR and EJ models, and this may play a role in the behaviour of the propagating wavefront especially in regions of high anatomical and functional complexity such as the bifurcation sites in an infracted cardiac tissue. A close examination at the variation of Ionmin in the area of interest, which corresponds to an area where the wave is initially planar, then starts rotating until it gets again planar, reveals differences in the behavior of the three models. Near the turning point (20,80), in BR model Ionmin decreases, while LR and EJ have an abrupt increase close to the turning point (see Figure 1). Specifically, in setup A, the maximum Ionmin value for BR model is at point (25, 62), ), at the beginning of the rotation, while point (20,82), just in front of the barrier, holds the maximum Ionmin value. In setup B, point (17, 62), at the beginning of the rotation, has the maximum Ionmin value, while point (21, 82), just beside the barrier holds the maximum Ionmin for LR and EJ models. As shown in Figure 2, the behavior of Ionmin in LR-EJ models is quite similar, but quite distinct from that of BR model. A different dependence of current on radius and angle in relation with the rotating front is evident, and specifically, in the former case current is decreasing, while in the latter case it is abruptly increasing in the vicinity of a propagation barrier. It is thus evident that working with appropriate simulation setups can facilitate research on effect of propagation barriers [6], wavefront curvature [7], on arhhythmiogenic tissue and reentry conditions [8], while modelling a disease like atrial fibrillation [9] and comparing results with experimental ones constitutes a huge progress towards understanding the physiologic cardiac mechanisms under different conditions . In fact, there is a series of questions that can be investigated by this kind of simulations and by analysis of Action Potentials, Ionic Currents and the extracellular potentials or electrograms produced respectively. The evaluation of these investigations can then take place via experimental recordings in similar conditions. The propagation properties and the wavefront morphology in specific conditions are among the most important issues in which computational model studies gave significant insight, as to the way in which tissue inhomogeneities, due to tissue infarction, fibrosis, altered ionic properties, affect the activation of tissue and contribute to the initiation and continuation of arrhythmias, constituting vulnerable conditions for reentrant wave arrhythmias. The degree of fractionation of electrograms, in terms of multiple deflections instead of the biphasic wave expected in normal conditions, is another indirect way to express the inhomogeneity of the underlying tissue. Furthermore, the ionic conditions that quantitatively express a specific disease, such as ischemia or atrial fibrillation, the altered mechanisms of propagation and how they are mapped to the overall behavior can be studied via a combination of computer simulations and clinical validation. Finally, it has to be highlighted that computer modeling plays a significant role in understanding the effect of interventions and medication on the conditions generating cardiac malfunction. In the following, three cases will be presented, exhibiting modeling methodologies and the use of biomedical signal processing in understanding the mechanisms of cardiac propagation in normal and pathologic conditions. The examples presented refer both to structure and function related problems, as well as to their interplay.

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3. ESTIMATING THE LOCATION OF ACTIVITY An important problem for treatment of tachycardias using high-frequency catheter ablation is the estimation of the distance between an isolated myocardial bundle and ablation electrode based on the recorded electrogram which forms the extracellular potential generated by the bundle. It is an important issue from a basic as well as a clinical point of view. It can help decide whether a deflection is remote or local, which is crucial for the construction of activation maps. It is true that most of the cardiac muscle does not resemble a bundle. However, a number of electrophysiologic pathologies giving rise to tachy-arrhythmias are based on the presence of small myocardial bundles [10]. But also in the healthy heart discrete bundles are present, like for instance the HIS bundle. The location of the HIS bundle with respect to a catheter is often required to avoid its ablation or just to ablate it. In ablation, when this distance is too large, ablation cannot be successful. The problem complexity is high, due to factors such as noise, unknown histology and pathophysiology of the underlying tissue, and, more importantly, incomplete knowledge of the spatial distribution of the membrane currents and of the dipole model that is applicable. Electrogram amplitude and configuration change with distance from the bundle, which constitutes distance estimation from the recorded electrogram a possible hypothesis. This is an 1D problem , and it can serve as an example in order to present a possible approach, illustrating a methodology for the solution of an inverse problem.

Basic Formulations The mathematical description of the extracellular field generated by electrical activity in an excitable fiber in an unbounded volume conductor depends on assumptions made about the sources and propagation properties as well as the source-field relationship. The main factors affecting the extracellular field shape and properties are the (a) Propagation velocity, (b) Source strength and length, related to the amplitude and spatial extent of the source and (c) Distance of the field point from the surface of the tissue. The electrical source strength in the case of an activated fiber is its transmembrane current. It has to be noted that, in real situations, neither the parameters of propagation for a specific bundle nor the distance of recording are a priori known. The electrode potential Ve measured at a point y is computed as a volume integral over the cardiac tissue (equation 1).

(1) The extracellular potential at a distance z from the propagation axis can be expressed as the convolution of the current source with a distance function, which acts as a low-pass filter. Thus, extracellular potentials are low-passed versions of the source. The larger the distance, the smoother the extracellular potentials (Figure 3).


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(a)

(b) Figure 3. (a) The setup: recordings in the XZ plane at various distances from the bundle, (b)Electrograms at various distances from myocardial bundle (0–660 μm from the surface), in steps of 0.06 mm starting from the surface of the tissue. Distance is expressed in μm. It is obvious that maximum value and slope decreases with distance.

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An Approach towards Solving the Inverse Problem Having as a basis Equation 1, which expresses the extracellular potential as a function of current source and distance, a parameter estimation approach can be used for this type of inverse problem> The first step would then be to define the mathematical models of electrical sources. Following, a robust parameter estimation method and appropriate cost functions that express estimation error would be required. Finally, after testing of the method with the predefined models for artificial data, experimental data evaluation can take place.

Models of Electrical Sources Some possible functions that can be adopted as models of the current source are depicted in Table1. Each model has different properties. For example, the multipole model is not spatially continuous. The triangular model has singularities only at the edges of the linear segments. The Morita model is continuous, however its adoption is more computationally intensive. Model selection is an important, as each one will result in extracellular potentials with different properties. For example, the bipolar source is expected to produce a higher spectral content than the triangular source, and thus the generated electrograms will also include higher frequencies. Model Parameter Estimation and Cost Functions Since the function that describes the extracellular potential is a non-linear function of the parameters in general, non-linear estimation methods have to be used. Parameter estimation based on the shape of the waveform is generally handled with a non-linear least square method. These methods try to find a set of parameters that minimize the square error between the data waveform and the waveform produced by the model, using this set of parameters. Stochastic methods (simulated annealing, genetic algorithms) produce better results than deterministic methods (Levenberg-Marquardt, Steepest Descent etc.) in complex optimization problems (where local minima are present). In the present study, simulated annealing method was adopted for parameter estimation [12]. Based on the physical idea of metal annealing and minimum energy state, the mathematical annealing algorithm uses a cooling schedule, where temperature falls with time. The cost function that has to be minimized can be flexibly selected, and parameter constraints can be introduced. The basic Time-Domain features to be used are the Euclidean distance between the waveform produced by the model and the real waveform and the Euclidean distance between the simulated and real signal derivatives. Time derivative is an important feature regarding distance estimation, because it depends on both the distance of recording and current source properties. The combination of these features constitute the LS cost function depicted in Table 2. On the other hand, taking into account the time-frequency characteristics of the electrograms, Wavelets have a strong resemblance to electrograms, as they can both be biphasic and band-limited signals. Electrograms at different distances are relevant to Wavelet Functions at different scales, since the bigger the distance the smoother the electrogram. The combination of square errors of all the detail wavelet components corresponds to the ―WT‖ Cost Function, as expressed in Table 2.


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Table 1. Examples of potential functions modeling a current source Bipolar Source

Im(x) k {d(x l) d(x l)}

Multipole Source

Im(x) k1 d(x dl1 ) k2 d(x dl2 ) k3 d(x dl3 ) k4 d(x dl4 ) ...

Triangular Source

k (x / l 2), [-2l,-l) k x / l, [-l,l] k (x / l 2), (l,2l]

Im(x)

Morita Function Source

1 e g1 x 1 1 e g2 x 1 eg1 x *t x0

Im (x) x

Table 2. Cost functions for the optimization problem Least square const function (LS)

Wavelet least square cost function (WT)

(equation 2)

(equation 3)

Method Evalaution Testing Cost Function and Distance with Artificial Data Artificial data were constructed, using 2-pole and Morita functions, and the corresponding electrograms, in order to test the ability of the optimization setup to estimate the model parameters. Concerning the performance of the model – cost function combinations, dipole source model is best combined with LS cost function, while for Morita model, WT cost function leads to better estimation, as depicted in Figure 4. Overall, the best estimation of distance and radius are succeeded with the Morita model and the WT cost function. In all cases, estimation error increases with distance. error of estimated radius 0.03 0.02 0.01 0 -0.01 -0.02 2-pole LS

2-pole WT

Morita LS

Morita WT

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mean distance estimation error 0.06 0.05 0.04 0.03 0.02 0.01 0 2-pole LS

2-pole WT

Morita LS

Morita WT

Figure 4. Estimation results with artificial data, a) mean error of the estimated bundle radius (real value=0.35 μm), b) mean distance estimation error.

Limitations of the Approach – Artificial Data Study a) Noise Problem: Tests with artificial data corrupted by gaussian noise (noise standard deviation = 10% of signal maximum) reveals that noise might affect dramatically the estimation outcome. Wavelet-based cost function is more sensitive to noise than LS (time-domain) cost function. b) Velocity mismatch problem: Velocity v is related to the scaling of axis X (x= v t), and thus it is important for signal morphology. Recording distance has a similar effect on signal morphology as velocity, therefore velocity error is expected to affect distance estimation. Besides, as observed in initial tests, velocity is a parameter that cannot be safely estimated by use of a single recording. The error caused by inappropriate conduction velocity was investigated by generating artificial waveforms using v =0.89 m/s as propagation velocity, and assuming slightly different velocities during distance estimation (v1=0.99 m/s and v2=0.79 m/s). As expected, when a bigger velocity is assumed (e.g. v1=0.99 m/s), estimated distance is bigger than the actual one, as a counterbalance. The opposite takes place in case of smaller velocity (e.g. v2=0.79 m/s). Estimation error is introduced in the other model parameters as well. c) Model mismatch problem: Estimation error increases (compared to the correct model case) for small recording distances where source topology details are more important. Therefore, selection of an appropriate source model is crucial in order to achieve the desired accuracy in small distances.

Is the Approach Close to Reality? Evaluation with Experimental Data After evaluation of the method capabilities and limitations with artificial data, the method was applied to the experimental electrogram data. The experimental scheme includes recordings along a line perpendicular to a small bundle (trabeculae) in steps of 0.06 mm. Estimating distance with error lower than 0.06 mm, i.e. the recording step in our experiments, constitutes the major goal of the experimental evaluation.


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0.07 0.06 0.05 0.04

Mean Std

0.03 0.02 0.01 0 2pole LS

2pole WT

partly triang LS

partly triang WT

Morita Morita LS WT (a)

(b) Figure 5. (a) Experimental data and distance estimation results, mean and standard deviation per model and cost function, (b) Distance error for different distances.

Both cost functions (LS and WT) and source models (2-pole and Morita) have been tested for signals taken at distances 0-0.60 mm from the surface of the bundle, in steps of 0.06mm. Quantitative results are summarized in Figure 5a. The evolution of error with distance (for each model/cost function) combination is displayed in Figure 5b. Morita source model combined with WT cost function is the most accurate choice for distance estimation.

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Specifically, mean relative error (error / distance %) is less than 3 % and mean absolute error is less than 0.02 mm, while in any case error does not exceed 0.05mm. Other parameters are also estimated in a stable way, without any systematic deviations. The next best estimation scheme is the combination of 2-pole model with LS cost function, having mean absolute error around 0.035 mm. However, error is increased at small distances, reaching 0.1mm at the surface of the bundle. A general observation is that 2-pole model is best matched with LS cost function, while Morita model with WT cost function.

Discussion on the Problem and Methods The work described constitutes an approach towards solving a category of inverse problems related to cardiac conduction, following a set of assumptions, to deal with its illposed nature, i.e. the fact that conduction velocity and transmembrane current density/ distribution are unknown. The proposed models follow the assumption of point sources activated along an axis. In a real bundle, the distribution of current consists a 3D problem [13] which would need a more complex modeling approach, be it an ensemble of point sources, or a continuous disk of activation propagating along the third dimension. The variation of current source properties on the plane of activation and with respect to the distance from the perimeter, as well as tissue properties anisotropy [14] would have to be taken into account. In case conduction velocity is not a constant but a model parameter to be estimated, the estimation setup requires a more sophisticated approach, including the employment of multiple simultaneous recordings as input.

4. PROPAGATION CHARACTERISTICS AND ACTIVATION MAPPING Two-dimensional Propagation and Electrogram Fractionation When looking at the microscopic properties of cardiac activation, one may assume for simplicity a two-dimensional cardiac tissue, which corresponds to a discrete grid, consisting of a set of nodes , either in terms of recording sites or active sources, i.e. cells, or cell patches. In this case, a major question concerns the spatiotemporal properties of activation, including the determination of activation time in each location, and the overall form of the propagating wavefront, i.e. an activation map depicting the isochronal lines of activation within the area of interest. The latter is especially important in cases of infarction, where propagation may follow a zigzag pathway, due to the tissue inhomogeneities introduced by the inactivated areas of infracted tissue. In infarcted tissue, normal cells mix with scar tissue, and force a zig-zag course of the electric impulse, increasing the possibilities for the formation of dangerous reentrant waves. The location of the surviving tissue completing an arrhythmogenic circuit is important to determine, especially when ablation is applied. Comparison of electrograms recorded simultaneously from multiple neighboring locations may provide information on the heterogeneity of the intercellular coupling. In normal homogeneously coupled tissue, simultaneously recorded unipolar electrograms from


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multiple sites during uniform propagation of electric impulse are biphasic electrograms, with little variation between sites. Electrograms recorded from regions of heterogeneously coupled tissue exhibit a variation in morphology, due to the variation in myocardium electrical properties. Typically, they are fractionated and polyphasic, indicating complex and irregular depolarizations. Extracellular potentials sum up potentials generated by membrane currents from all the myocardial cells. When proximal areas are not simultaneously activated, multiple desynchronized deflections are recorded in electrograms. Thus, when fractionation occurs, electrograms tend to have decreased peak-to-peak values, bandwidth and minimum derivative, while duration and number of inflections is increased. Ellis et al. [15] have studied coefficients of variation that are sensitive to coupling heterogeneity, in terms of statistical variation, rather than unique identifiers of the distribution of intercellular currents.

Activation Maps and Classic Methods For the construction of an activation map, fractionated electrograms must be processed in such a way so as to filter out the remote activation components and extract the local source signals, and eventually the local activation characteristics, which however, may exhibit significant spatiotemporal variation, especially in infarcted tissue. Contribution of activated sources to the electrogram decreases with distance between source and recording site, but cells further away may contribute significantly to the extracellular recording amplitude, if they are activated simultaneously and thus consist a ‗big‘ source. In multiphasic electrograms, where the magnitude of each deflection depends on both the distance of recording and the size of the bundle, it is a complex task to distinguish among electrogram deflections coming from local or distal activation. The classic criterion to distinguish local from remote activation is the time derivative. The point of maximal negative derivative in the extracellular potential is often used as the activation time. The ratio of the second to first derivative has also been used as a local activation criterion, since second derivative falls more rapidly with distance [16]. Derivative criteria may exhibit problems in robust, being prone to noise, or even missing waves which are masked by other bigger simultaneous waves. Besides, these criteria stand for the cases of constant velocity and uniform propagation. When velocity changes in magnitude or direction, the situation becomes more complicated and more versatile methods are required. Comparison of the activation time map generated by various methods has been presented by Maglaveras et al.[17]. In their work they conclude that the most reliable way to estimate local activation time in practice is the zero-crossing of the transmembrane current. Therefore, approximating as much as possible this approach using electrograms, e.g. by Laplacian spatial filtering, can produce quite accurate results [18].

Methods to Distinct Local and Distal Sources The relation between the electrogram and the activating sources can be formulated as follows:

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(4) Taking into account the real blurring effect of extracellular recording, spatial filtering may suppress the distant deflections and produce an accurate estimation of the local source. The transmembrane current source for each time step can be ideally estimated by deconvolving the extracellular potentials with the distance kernel. In this case, assuming equal number of sources and electrogram recording sites, the relation between electrograms and current sources can be expressed as follows:

(5) or Ve=A*Im, where Ve is the vector of extracellular potentials, A is the symmetric square matrix with distance weights, and Im is the vector of current sources for one time step. A direct inversion, or system solution, can result in the estimation of Im. Alternatively, a wavelet-based method that takes into account temporal and spatial information for the suppression of distant activity and enhancement of local activity, and eventually the detection of the local activation time based is described here [19]. The method is based on Wavelet shrinkage, a general method for denoising and inverse filtering [20]. The basic idea is to estimate interference, i.e. distant components, at each wavelet scale, and then remove it by the proposed spatiotemporal wavelet filtering. Estimation of the ―interference‖ is based only on spatial information of the current setting. The algorithm is not based on the comparison of the multiple deflections recorded in a single electrode, but rather on the comparison of the morphology of a single deflection as recorded in many electrodes. The rationale is that, activation is simultaneously recorded by all the electrodes, however, it is recorded with the highest amplitude and highest frequency components in the nearest local recording. Taking advantage of this characteristic, distant recordings are suppressed and local ones are enhanced. The outcome of this procedure is an estimate of the transmembrane current. The mathematical formulation is depicted in equation 6.

(6)


Wi,scj(t)

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is the wavelet coefficient at node , at scale sc and at time point t. Weights

aij are related to relative distances among grid points. Spatial neighborhood selection depends on grid density. Increase of parameter n, leads to bigger enhancement of local activity. Then, for each grid point the steps followed are as follows.

for each electrogram at grid point , Wavelet transform, for each scale and each time step, spatial wavelet filtering of all electrograms, based on equation X, and reconstruction of the electrograms from the filtered wavelet coefficients. The first term of the denominator in equation 6 corresponds to the local recording while the second term corresponds to the components recorded at the neighboring grid points. Lowfrequency components may be recorded by all electrodes with almost the same strength, whereas high-frequency components are more localized. When the activity recorded at a certain grid-point and time step is distant, the denominator of gets much bigger than the nominator and, thus, the distant component is suppressed, while in the opposite case it is enhanced. This principle is illustrated in Figure 6, presenting the first two scales of an electrogram before and after filtering. Even in the finer scale, distant deflections are present with peaks comparable to the local one. However, after Wavelet filtering which isolates local deflections by spatial comparisons, only local deflections are present. It must be pointed out that the shape of local component is almost intact, as if a simple windowing procedure was applied.

Figure 6. Wavelet Coefficients of an electrogram. d1-d2: First and Second scale Wavelet Coefficients. di'-d2': Filtered Versions of d1 and d2.

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Testing Framework and Results Simulated data have been used for this work, in order to test and compare different methods for a structure of known complexity and behavior. Simulated experiments also allowed us to control the number of extracellular measurements to be used during the estimation procedure. The 2-D monodomain model of cardiac muscle was used. A rectangular sheet of cells was simulated with a grid of 30 160 elements, which corresponds to 30x40 cells. Each cell consisted of four longitudinal elements (three cytoplasmic and one junctional). Elements were coupled by resistances. Both Beeler–Reuter and Luo–Rudy models have been used for ionic kinetics kinetics The grid intervals were 10 μm transversely and 25 μm longitudinally and time step was 5μsec. The setup is conceptually depicted in Figure 7.

s Figure 7. The simulated setting used. Two barriers at columns 10 and 20 force the wavefront to follow a zigzag path, expressed by the isochronal lines, which are parallel in normal conduction and curved which changing density during rotation . Dotted lines mark the area of interest.

The extracellular electrograms were calculated at the surface of the tissue. Extracellular potential calculations were made in a grid, with 10 μm transverse interval and 100 μm longitudinal interval, corresponding to one recording per cell. Sparser grids were also tested. During simulation, transmembrane current was stored for the grid-points in the region of interest. Activation times were also calculated using transmembrane current criteria. Current waveforms and activation maps were used for comparison with the ones estimated by the methods described in this work. In Figure 8, the actual polyphasic electrogram and transmemembrane current are depicted, as well as the current approximations calculated by Laplacian, Direct Deconvolution and Wavelet-filtering method.


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Figure 8. Comparison of waveforms at grid-point (16, 40), which is between the two barriers. Extracellular potential, Current sources estimated by Wavelet , Deconvolution and Laplacian are presented simultaneously. All signals are scaled to the same range, for comparison purposes. grid 40 x 100 μm. Transmembrane current is the waveform labeled as ―Current.‖

In general, direct deconvolution method works better if the number of estimated sources is not much smaller than the actual number of sources, even if interpolation is used to produce a dense grid of electrograms. The same stands for the calculation of the Laplacian. This is probably due to the fact that deconvolution is based on a detailed model of current sources. On the other hand, Wavelet method is less sensitive on assumptions concerning the number of sources, since the method is based on very simple ―observations‖ about the characteristics of local and distant sources and not the actual equations that describe the extracellular field. This fact constitutes Wavelet method a more realistic approach, also producing smaller activation time error in various setups, as compared to direct deconvolution method (see Fig 9a).

Discussion on the Problem and Methods At a microscopic scale, methods for estimating the activation time in a 2D inhomeogeneous cardiac tissue are presented, along with the effect of grid and of the

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underlying ionic properties. In this work, we make the assumption of discrete point current sources and point electrodes at a known distance from the tissue in an unbounded medium. The effect of electrode size, having a diameter equaling at least 100 m, thus integrating activity from at least ten cells, is not taken into account. In a recent work, Farina et al [20] have elaborated on a similar approach in a work proposing a new class of spatial filters for surface electromyographic (EMG) signal detection. These filters are based on the 2D spatial wavelet decomposition of the surface EMG recorded with a grid of electrodes and inverse transformation after zeroing a subset of the transformation coefficients. In recent works, electrograms have been extensively used to characterize tissue fractionation and fibrosis. Jaquement [22] has employed realistic temporal and spatial filtering and has studied changes to electrogram waveforms with realistic temporal and spatial filtering with respect to microscale obstacles. According to their findings, conduction velocity and electrogram amplitude and degree of fractionation can be used to discriminate the nature of the substrate and characteristics of fibrosis, giving rise to slow conduction. They also studied the effect of electrode size and found that when a larger electrode was used, electrogram amplitude was smaller and fractionation increased in a substrate-dependent way.

5. COMPLEX INTERPLAY AND DISEASE In this section, in a simulation setup, the activation and propagation differences induced by hyperkalemia and ischemia are investigated, in combination with other underlying factors. Taking into account the importance of these ionic conditions, the purpose of this work is to investigate the way that different factors of spatial heterogeneity (functional and structural) interact and formulate the tissue activation and propagation characteristics. The factors taken into account are ischemia, including hyperkalemia, stimulus rate and structural complexity. Hyperkalemia, a condition of increased extracellular potassium elevation, is present in different conditions (medication, stress, diabetes, ischaemia), and has also been reported in diabetic hearts, but also as a result of physical stress such as exercise. Furthermore, it may be induced by medication in chronic heart failure treatment. Hyperkalemia effects on action potential duration, by decreasing it, reducing cell excitability. It depolarizes the membrane potentials of cells, which affect voltage-gated channels, towards channel inactivation and increased refractoriness, with fibrillation or ectopy as a possible result. Myocardial ischemia, i.e. lack of oxygenated blood for the myocardium, leads to extracellular potassium accumulation. However, myocardial ischemia involves other mechanisms, besides hyperkalemia, namely acidosis and hypoxia, involving alterations in sodium and calcium conductivity and potassium concentrations. Both conditions, hyper kalemia and ischemia, alter the excitability and refractoriness characteristics of the tissue and are therefore considered as factors increasing vulnerability to the development of reentrant arrhythmias, a major cause of sudden cardiac death.


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(a) These differences are also illustrated in Figure 9b, which compares the consequences in activation time error when shifting to a less dense grid, for the deconvolution and the wavelet method, and for two types of ionic currents associated with different dynamics.

(b) Figure 9. Comparison of activation time error. (a) between wavelet and deconvolution method (WTDEC), for Beeler-Reuter and Luo Rudy ionic models (BR-LR), for thick and sparser grids of electrograms. (b) for each method-ionic model combination, difference in error when moving to sparser grid. br: Beeler-Reuter, lr: Luo Rudy ionic current models, 1x4 stands for grid 10 x100 μm 1x4 stands for 40 x100 μm (1 electrogram per 4 cells transversally).

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Simulation Setup In this context, using LR I ionic model [23], two components of ischemia were modeled: increased extracellular potassium , and acidosis, which was expressed as a decrease of sodium and calcium conductivity as expressed in Table 3. The third component of acute ischemia, hypoxia, was not taken into account. Table 3. Hyperkalemia and Acidosis Expression in Luo Rudy I Model Acidosis

moderate ischemia Severe ischemia

The second factor taken into account was stimulus rate. The rate at which recurrent stimuli reach an arrhythmiogenic tissue also affects activation characteristics. The most prominent effect of decreasing the pacing period is shortening of APD, which is an important factor in arrhythmogenesis. Heterogeneity of APD and the resulting dispersion of refractoriness across a tissue wall could provide the substrate for reentrant arrhythmias. Therefore, the interplay between these ionic conditions and pacing frequency needs further study. In this study, extracellular stimulus was a square pulse periodically applied, while intermittent burst pulse protocols were also tested.

Activation Features The macroscopic features of the cells used for assessment are: a) Action Potential Duration (%90 APD), which is crucial for the alterations in refractory period, blockades and arrhythmias , b) Action Potential Upstroke (maxAP), as the maximum Action potential value, c) upstroke velocity , i.e. maximum Action Potential slope (maxAPslope), which along with (b) is related to the spatial properties of conduction and local impedance, and, d) Minimum (negative) value of the ionic current, Ionmin, a basic morphological feature strongly affecting the membrane current and the excitability, which is supposed to change due to heterogeneity, and specifically decrease in the infarcted regions. These two factors were combined with a tissue presenting structural heterogeneity, and thus consisting a possible arrhythiogenic substrate. A rectangular sheet of cells was simulated with a grid. Regions of scar tissue were defined in order to introduce heterogeneity. Considering a rotating propagation wave, due to infracted tissue, we took a closer look at the model kinetics in the area of rotation. Experiments were repeated with different combinations of pacing and ionic parameters, i.e. varying moderate and severe hyperkalemia and ischemia levels. For each grid point, a series of features were calculated for further analysis for each grid point reflecting different characteristics of the cellular activation. The behavior of the action potential and ionic current features in this simulated tissue area is examined, in each protocol.


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The main idea was to investigate the dispersion of functional heterogeneity in the neighborhood of the structurally inhomogeneous tissue, in relation to the ionic and stimulation parameters. Such a structural and functional inhomogeneity might indicate an area of increased vulnerability, under certain conditions. The methodology and the main findings are presented below.

Figure 10. Features for Activation and propagation analysis.

A way to view possible differences in the area of wavefront rotation is a representation in polar coordinates (see Figure 11), with respect to the rotation ―tip‖, in a small distance around the obstacle forcing the propagation wave rotation. In this manner, the behavior in the four areas of rotation is investigated, as regards the activation and repolarisation feature changes.

90 deg

ROTATION

START ROTATION

0 deg 180 deg

360 deg

270 deg AFTER ROTATION PLANAR WAVE

PLANAR WAVE

Figure 11. The four areas of the region of interest with respect to rotation of wavefront.

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Figure 12. Mean values per pacing for various hyperkalemia levels. Up (APD, maxAP), Down (maxAPslope, minIonCur). Pacing is expressed as multiples of the normal APD.

Figure 13. Feature based clustering. Scheme A and B.


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Figure 13. Feature based clustering. Scheme A and B. (Continued)

These two factors were combined with a tissue presenting structural heterogeneity, and thus consisting a possible arrhythiogenic substrate. A rectangular sheet of cells was simulated with a grid. Regions of scar tissue were defined in order to introduce heterogeneity. Considering a rotating propagation wave, due to infracted tissue, we took a closer look at the model kinetics in the area of rotation. Experiments were repeated with different combinations of pacing and ionic parameters, i.e. varying moderate and severe hyperkalemia and ischemia levels. For each grid point, a series of features were calculated for further analysis for each grid point reflecting different characteristics of the cellular activation. The behavior of the action potential and ionic current features in this simulated tissue area is examined, in each protocol. The main idea was to investigate the dispersion of functional heterogeneity in the neighborhood of the structurally inhomogeneous tissue, in relation to the ionic and stimulation parameters. Such a structural and functional inhomogeneity might indicate an area of increased vulnerability, under certain conditions. The methodology and the main findings are presented below.

Analysis of Hyperkalemia and Pacing Overall, the simulated ischemic cells are characterized by reduced ADP, slower APD upstroke and upstroke velocity, and less negative ionic current peak. In both schemes, ADP is

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decreased with pacing frequency, but the relative effect of pacing is more evident in normal than in ischemic tissue. There is also a decrease of APD upstroke and velocity, and ionic current peak with pacing frequency, however, unlike APD, the relative effect is more obvious in ischemic than in normal cells. Some more detailed effects are depicted in Figure 2, indicating that relevance of the cell activation to pacing for normal cells is very different from that of ischemic cells [24].

Complex Factors - Spatial Inhomogeneity In order to express the overall differences induced by the pacing and Ko conditions, all the <pacing, level of ischemia> cases were clustered in terms of the four-feature vector (APD, MaxAP, MaxAPslope and MinIonCur), and a dendrogram of the clusters produced was visualized, by use of manova and manovacluster Matlab methods (Figure 3). In both schemes, three main clusters were produced; roughly corresponding to ischemia levels. For scheme A, the first cluster includes normal cells with normal pacing, the second includes light ischemia and/or high pacing, and the third severe ischemia or average ischemia. In scheme B, the three clusters include respectively: a) normal cells and light hyperkalemia, b) average hyperkalemia, and c) severe hyperkalemia. It is interesting that in scheme B, which has less structural inhomogeneity, severely ischemic clusters are more distinctly separated, so are moderate ischemic clusters, while in scheme A there is more fragmentation and interrelation of ischemia and pacing.

Hyperkalemia vs Ischemia and Spatial Patterns In order to assess the degree to which the ionic and pacing conditions in focus introduce spatial heterogeneity in terms of variation of the features under examination, potentially affecting arrhythmogenesis, we consider four regions with different rotation properties: a) in the first region near the stimulus, where propagation wavefront is planar, b) near the tip of the barrier where it starts rotation, c) near the barrier tip where it turns, and d) in the last area moving away from the rotation tip towards plain rotation again. Differences among feature values in different regions are analysed in the following and depicted in Figure 14. Regarding APD, AP upstroke and velocity, in the ischemic case rather than the hyperkalemic case, there are more relative spatial differences among the mean values in the rotation regions as compared to the initial planar wavefront region. The actual differences in APD are small. However in minIonCur feature the spatial differences are higher in hyperkalemia (See figure 14 left). In all cases, feature values are not restored in the last region (restored planar wave). Furthermore, standard deviation values are higher in hyperkalemia rather than in ischemia for all features (See figure 14 right). It is characteristic that in the ischemic setup, MinIonCur variation is decreasing in the rotation area, while it is increasing in hyperkalemia. Besides the spatial differences among regions, the homogeneity in a local scale was investigated, in terms of spatial correlation analysis, using the following equation:


cn (l)

1 N

N

xˆn (l)xˆn (l 1)

1

1 N

N

xˆn (l)

2

, xˆn (l) x(l)

x

n

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(7)

1

l spatialdisplaceme nt,n a given time The spatial correlation among neighboring fibers is depicted in Figure 15. For AP upstroke and velocity, the spatial correlation is lower in the hyperkalemic rather than in the ischemic setup, and the gradient relates with ionic conditions. In Min Ionic Current, the spatial correlation is low overall, however higher in hyperkalemia than ischemia. In all cases, the values fall with distance more smoothly than exponential law, indicating that there are overall complexities, and areas of different spatial correlation [[25]. The two methods presenting spatial variations of feature values give different results, since they refer to different geometry, polar and parallel lines respectively. When comparing the mean values and standard deviations of the different rotation areas, the wave rotation is taken into account in a whole region, while spatial correlation of features in parallel fibers would reflect a planar propagation and different among adjacent fibers.

Discussion on the Problem and Methods Action potential duration dispersion is governed by a wide variety of factors including short and long term rate dependence, ionic current heterogeneity, and electrotonic loading. The mechanisms of rate-dependent phenomena in a heterogeneous and ischemic tissue are important for determining the heart's response to rapid and irregular pacing rates, be it an arrhythmia or an attempt for cardioversion. We have shown that the changes in the spatial activation properties largely depend on a combination of ischemia and fast pacing, and these factors interact in a nonlinear manner. The analysis shows that activation features are mostly affected by level of ischemia and secondarily by pacing frequency, the differences in the latter being dependent on ischemia level [26]. In increased ischemia, the effect of steady fact pacing is attenuated, although this does not happen in a premature stimulus. Both in ischemia and hyperkalemia, there are variations in all features in the rotation areas, but the spatial variation and the patterns of excitability/repolarisation produced are different. These factors of increased heterogeneity may induce vulnerable spatiotemporal states. Methods to characterise spatial inhomogeneity with respect to the underlying mechanisms is considered of special importance both in microscopic and macroscopic scales, for the explanation of vulnerable conditions to arrhythmias, e.g. in atrial fibrillation. New insight could be given by the examination of the disorder of spatial patterns in different conditions by use of formal spatial or spatiotemporal complexity methods, such as recurrence plots or other nonlinear dynamics tools. In this work, activation and repolarisation features were based on action potential and ionic current morphological characteristics. The introduction of other features directly related to cell membrane gate-dynamics could also be of value. A challenge would be to combine the quantitative features to a qualitative vulnerability index, which would have added value from a clinical viewpoint.

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AP upstroke, mean per area normalised to mean of initial planar area 1.7 hyp fast hyp slow 1.6 isc fast isc slow 1.5 1.4 1.3 1.2 1.1 1 initial planar

3

start rotation

end rotation

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AP Upstroke, std per area

2.5 2 1.5 1 hyp fast 0.5 hyp slow isc fast isc slow 0 initial planar start rotation

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MinIonCurrent, mean per area normalised to mean of initial planar area 1.2 hyp fast hyp slow isc fast isc slow 1.15

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1 initial planar

start rotation end rotation MinIonCurrent, std per area

after rotation

24 22

hyp fast hyp slow isc fast isc slow

20 18 16 14 12 10 initial planar

start rotation

end rotation

after rotation

Figure 14. For AP Upstroke and MinIonCurrent, (left) the mean values per area (before, start, end, after rotation) normalized to the mean value of the initial area, (right) standard deviation per area, K 8.1

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spatial correlation between fibers, AP Upstroke

0.7

Hyp 8.1 Isc 8.1 Hyp 9.4 Isc 9.4

0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 1

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2

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spatial correlation between fibers, MinIonCur 0.25 Hyp 8.1 Isc 8.1 Hyp 9.4 Isc 9.4

0.2

0.15

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0 1

1.5

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Figure 15. Feature spatial correlation between fibers 1 to 4 nodes apart.

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It is important to link these simulation results with experimental recordings, e.g. with electrogram recordings, and clinical findings, and thus, to link electrogram features with the underlying regional ionic/structural conditions, e.g. the level of ischemia or atrial remodelling. In this direction, Vigmont et al [26] have studied methods to derive ADP or APD changes from extracellualr recordings, via the indirect calculation of activation recovery interval (ARI). This might be significant, for example in order to map atrial repolarization, in terms of functional and structural heterogeneity [28].

6. CONCLUSION AND FUTURE DIRECTIONS The methods presented elaborate on microscopic scales cardiac propagation problems. While activation and repolarisation properties in a microscopic scale is important for understanding basic properties in health and disease, studying arrhythmogenic conditions in realistic human models [29], and reproducing disease-like conditions can help in interpreting the overall physiological mechanisms of cardiac diseases, towards enhancing diagnosis and treatment . In order to deal with the cardiac physiology as a whole, mechanisms at multiple scales have to be taken into account [30], [31], from proteins to cells and organs, and even organ to organ interaction, for example interaction between cardiac and autonomic nervous system. The Physiome paradigm [32] has been proposing methods and strategies towards integrating models at multiple spatiotemporal scales. Such integrative approaches include formal representations of the partial knowledge, e.g.. xml-based description of each model. While models exist for various scales, the scale-to-scale link is still under investigation, especially regarding the function and structure in the microscopic domain, i.e., the sub-cellular mechanisms. A further challenge would be to move from static to quasi-static or conditions, i.e., model for changing or dynamic conditions. One of the open goals in cardiac modeling concerns the study of medication effect, towards enhancing the methods for drug discovery. Progress in multiscale modeling will allow the detailed and personalized interpretation of disease mechanisms in complex cardiac diseases, such as atrial fibrillation, also opening the way to optimized and personalized treatment strategies and map the findings to improved eHealth solutions.

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Henriquez CS, Papazoglou A., Using Computer Models to Understand the Roles of Tissue and Membrane Dynamics in Arrhythmogenesis, Proc IEEE 1996; 84: 334-54. K.I. Vegoudakis, V. Koutkias, A. Malousi, I. Chouvarda, N. Maglaveras, ―A Generic Grid Interface and Execution Framework for Biomedical Applications‖, 8th IEEE International Conference on BioInformatics and BioEngineering (BIBE 2008), Athens, Greece, October 8-10 2008 http://www.physiome.org Beeler, G.W. and Reuter, H.: Reconstruction of the action potential of ventricular myocardial fibres, Journal of Physiology, 1977, 268, 177-210.

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Ioanna Chouvarda and Nicos Maglaveras Luo, C. H. & Rudy, Y., A dynamic model of the cardiac ventricular action potential. I. Simulation of ionic currents and concentration changes, Circ. Res, 1994,74, 1071-96. Ebihara L and Johnson E A., Fast sodium current in cardiac muscle. A quantitative description. Biophysical Journal, 1980, 32: 779-790. Maglaveras N, Van Capelle FJL. ,Effects of Barriers on Propagation of Action Potentials in Two-dimensional Cardiac Tissue, J Electrocardiol, 1995; 28: 17-31. Fast, V.G., Kleber, A.G. Role of wavefront curvature in propagation of cardiac impulse. Cardiovasc Res, 1997, 33(2), 258–271. De Bakker, J.M. T., F. J. L.Van Capelle,M. J. Janse, S. Tasseron, J. T. Vermeulen, N. de Jonge, and J. R. Lahpor, Slow conduction in the infarcted human heart, ―ZigZag‖ course of activation, Circulation, 1993, 88:915–926. Vigmond EJ, Ruckdeschel R, Trayanova N., Re-entry in a morphologically realistic atrial model, 2001; J. Cardiovas. Electrophysiol. 12 (9): 1046 – 1054. de Bakker JMT and van Rijen HVM, Electrocardiographic manifestation of anatomical substrates underlying post–myocardial infarction tachycardias, Journal of Electrocardiology, 2007, 40(6), Supp1, , pp S21-S25. Chouvarda I., Maglaveras N., Pappas C., Van Capelle F.J. and J. de Bakker, Estimation of distance between a unipolar recording electrode and a myocardial bundle based on signal characteristics, Ann Biomed Eng 32, 2004, p. 1336-47. Kirkpatrick, S., C. D. Gelatt Jr., M. P. Vecchi, Optimization by Simulated Annealing, Science, 220, 4598, pp: 671-680, 1983. Plonsey, R., and R. C. Barr, Interstitial potentials and their change with depth into cardiac tissue. Biophys. J., 1987, 51:547–555. Panfilov, A., and J. P. Keener, Generation of reentry in anisotropic myocardium. J. Cardiovasc. Electrophysiol., 1993 4(4):412–421. Ellis WS, Eisenberg SJ, Auslander DM, Dae MW, Zakhor A, Lesh MD, Deconvolution: a novel signal processing approach for determining activation time from fractionated electrograms and detecting infracted tissue, Circulation 1995; 94: 2633-40. Anderson K. P., Walker R., Ershler P. R., Fuller M., Dustman T., Menlove R., Karwandee SV, and RL Lux, Determination of local myocardial electrical activation for activation sequence mapping: A statistical approach, Circ. Res., 1991, vol. 69, no. 4, pp. 898–917. Maglaveras N., de Bakker JM, van Capelle FJ, Pappas C, and MJ. Janse, Activation delay in healed myocardial infarction: A comparison between model and experiment, Amer. J. Physiol., 1995, vol. 269 (Heart Circ.Physiol., vol. 38), pp. H1441–H1449. Gezelowitz DB, Use of laplacian to extract local activation from epicardial electrograms, in Computers in Cardiology. Los Alamitos, CA: IEEE Comput. Soc. Press, 1996, pp. 129–132. Chouvarda I, Maglaveras N, de Bakker J, van Capelle FJL, and C. Pappas Deconvolution and wavelet based methods for membrane current estimation from simulated fractionated electrograms, IEEE Trans. Biomed Engng, 2001, vol. 48(3), pp. 294-301. Chipman H., Kolaczyk E., and R. McCulloch, Adaptive bayesian wavelet shrinkage, J. Amer. Stat. Assoc., 1997, vol. 92, pp. 1413–1421.


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[21] Farina D, Kamavuako EN, Wu J, and F Naddeo, Entropy-Based Optimization of Wavelet Spatial Filters, IEEE Trans BME, 2008, Vol. 55, No. 3, pp 914 – 922. [22] Jacquemet V and CS. Henriquez, Genesis of complex fractionated atrial electrograms in zones of slow conduction: A computer model of microfibrosis, Heart Rhythm, 2009, Volume 6, Issue 6, Pages 803-810. [23] Shaw R.M.;Rudy Y, Electrophysiologic effects of acute myocardial ischemia: a theoretical study of altered cell excitability and action potential duration, Cardiovascular Research, 1997;35(2), pp. 256-272. [24] Zhang H, Zhang ZX, Yang L, Jin YB. and Huang YZ., Relevance of Ventricular Electrical Dispersion to Arrhythmogenesis in Ischemic Myocardium: – A Simulation Study, Gen. Physiol. Biophys, 2005, 24:365-380. [25] Vasconcelos DB, Lopes SR, Viana RL, Kurths J., Spatial recurrence plots, Physical Review E 2006;73, pp. 056207-1 : 056207-10. [26] Chouvarda I, and N Maglaveras, Hyperkalemia vs Ischemia effects in fast or unstable pacing : a cardiac simulation study - HCI 2009 , LNCS5620- Digital Human Modelling, pp 492-501. [27] Vigmond EJ; Tsoi V; Yin Y; Page P; Vinet A, Estimating atrial action potential duration from electrograms. IEEE Trans Biomed Eng 2009 May;56(5):1546-55. [28] Turner I; L-H Huang C; Saumarez RC, Numerical simulation of paced electrogram fractionation: relating clinical observations to changes in fibrosis and action potential duration. J Cardiovasc Electrophysiol, 2005 Feb;16(2):151-61. [29] Kuo SR, Trayanova NA., Action potential morphology heterogeneity in the atrium and its effect on atrial reentry: a two-dimensional and quasi-three-dimensional study, Philos Transact A Math Phys Eng Sci. 2006 Jun 15;364(1843):1349-66. [30] Plank G, Zhou L, Greenstein JL, Cortassa S, Winslow RL, O'Rourke B, Trayanova NA., From mitochondrial ion channels to arrhythmias in the heart: computational techniques to bridge the spatio-temporal scales, Philos Transact A Math Phys Eng Sci. 2008 Sep 28;366(1879):3381-409. [31] Jalife J, Atienza F, López-Salazar B, Delpón E, Sánchez-Quintana D, Bernad A and J Almendral, Molecular, cellular and pathophysiological mechanisms of human atrial fibrillation, Nature Clinical Practice Cardiovascular Medicine - CNIC Edition, MARCH 2009 VOL 6 NO 3, pp 15-21. [32] Hunter P and P Nielsen, A Strategy for Integrative Computational Physiology, Physiology 2005, 20: 316-325.



Chapter 7

THE ELUSIVE D-CURRENT: SHAPING ACTION POTENTIALS IN THE DENDRITES? Xixi Chen and Daniel Johnston Center for Learning and Memory, The University of Texas at Austin, TX, USA

ABSTRACT Most neurons host a complex combination of various K+ currents. These K+ currents differ from each other in voltage- and time- dependent kinetics, and contribute to different aspects of action potentials. The D-current was first discovered in adult pyramidal cells in the hippocampus. This K+ current activates quickly at subthreshold voltages and inactivates slowly, contributing to a long delay before action potential firing, hence its name. A prominent pharmacological feature of the D-current is its high sensitivity to 4-amino-pyridine (4-AP). With this pharmacological tool, we studied the contribution of the D-current to the waveforms of back-propagating action potentials (bAPs) in the dendrites of hippocampal CA1 pyramidal neurons. We performed dendritic, whole-cell recordings from the dendrites of CA1 pyramidal neurons, with extracellular stimulation of the axons of these neurons in the acute slice preparation. Bath application of low concentration 4-AP (50 µM) led to a dramatic increase of the afterhyperpolarization following the bAPs. This increase can be completely eliminated by the GABAb receptor antagonist, CGP55845 (5 µM). This result indicates that D-current contributes significantly to the regulation of GABA release from interneuron axon terminals. In terms of the waveform of bAPs we did not observe any significant change in amplitude or initial dV/dt that‘s caused by 4-AP, at all the locations along the dendrites. However, at locations farther than 200 µm away from the soma, 4-AP did cause a small but significant increase in the half-amplitude duration of bAPs. A similar, 6-16% contribution of D-current was also observed by other groups, in terms of action potential after-depolarization and threshold for Ca2+ spikes, in both hippocampal and neocortical neurons. We would like to argue that the D-current makes a small but significant contribution to the shape of dendritic action potentials. The more prominent role played by D-current in the hippocampal circuit, however, may be the regulation of presynaptic neurotransmitter release.

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INTRODUCTION The activation and inactivation kinetics determine how a particular type of K+ current regulates neuronal excitability (Johnston and Wu, 1995). Among the voltage-dependent K+ currents, both the A-type and the D-type inactivate during a sustained depolarizing voltage pulse. Whereas the A-type K+ current inactivates with a time-constant of tens of milliseconds, the D-type K+ current usually takes hundreds of milliseconds to inactivate (Storm, 1990). Original descriptions of the D-type K+ current include fast, subthreshold activation, slow inactivation and high sensitivity to 4-amino-pyridine (4-AP). These properties of the Dcurrent differentiate it from the A-current and other voltage-dependent K+ currents, both biophysically and pharmacologically. Because of its fast, subthreshold activation, the Dcurrent would be activated at the beginning of a depolarizing current injection, oppose the depolarization, and contribute to a long delay before action potential firing. The D-current thus gets its name because of this ―delay‖ (Storm, 1988).

MOLECULAR IDENTITY OF CHANNELS UNDERLYING THE D-CURRENT The concept of the D-current evolved over the years with advances in molecular biology and pharmacology. Besides 4-AP, alpha-dendrotoxin was also found to block the D-current with high affinity (Wu and Barish, 1992). Among the four Kv families of K+ channels, it is widely believed that the Kv1 family of K+ channels, Kv1.1 and Kv1.2 in particular, and possibly in association with some subunit, underlie the D-current (Coetzee et al., 1999). While the pharmacology of these channels agrees well with properties of the D-current, their biophysics doesn‘t always match that of the original D-current. The ―D‖ in ―D-type K+ current‖ now often refers to dendrotoxin sensitivity. The D-current and its physiological roles are more often identified by the use of low concentration 4-AP and dendrotoxin, than by biophysical criteria.

SUBCELLULAR LOCALIZATION OF D-CURRENT AND THE KV1 FAMILY OF K+ CHANNELS IN THE HIPPOCAMPUS D-current contributes to important aspects of neuronal excitability in the hippocampus. This was demonstrated in both adult and developing neurons, in both CA1 and CA3 regions of hippocampus, and in acute and cultured preparations (Storm, 1988; Wu and Barish, 1992; Lüthi et al., 1996). All of these early studies described the D-current as a component of the whole-cell K+ currents, with recordings at the soma. With advances in patch-clamp techniques and differential interference contrast (DIC) microscopy, dendritic, isolated patch recording became the method-of-choice for physiological studies of ion channel distribution. It was soon discovered that the A-type K+ current has an increasingly higher density along the apical dendrites of CA1 pyramidal neurons (Hoffman et al., 1997). Compared to other types of K+ currents in the dendrites, the D-current is ―elusive‖, because it is not present in the

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recordings as frequently or as consistently as the A-type or the delayed-rectifier (DR)-type K+ currents (Bekkers, 2000; Bekkers, 2000; Korngreen and Sakmann, 2000; Chen and Johnston, 2004). In terms of physiological effects, the putative D-current may contribute to setting the threshold for dendritic Ca2+ spikes, as dendrotoxin application makes it easier for the cell to fire Ca2+ spikes (Golding et al., 1999). In addition, somatic action potential afterdepolarization also seems to be regulated by D-current, again based on results from dendrotoxin application (Metz et al., 2007). D-current with these effects seems to localize in the proximal part of the dendrites (Metz et al., 2007). Similar effects have also been demonstrated in cortical neurons (Bekkers and Delaney, 2001). All of these studies point to a small but significant contribution of D-current to the total K+ current in the dendrites, in the range of 6~16%. Immunohistochemistry studies of Kv1 channel protein distribution yielded results that are mostly in agreement with the physiological data. Some Kv1.2 was found to reside in the apical dendrites of CA1 pyramidal neurons (Sheng et al., 1994), but are also present in axon terminals of principal neurons in the hippocampus (Sheng et al., 1993; Monaghan et al., 2001). Kv1.1 and Kv1.4 are mostly in axon terminals, with very little presence in the dendrites (Sheng et al., 1993; Monaghan et al., 2001).

TRANSLATIONAL REGULATION OF KV1.1 IN THE DENDRITES AND ITS IMPLICATIONS While the axonal localization of Kv1.1 was gradually becoming the dogma, it was discovered, quite unexpectedly, that Kv1.1 mRNAs are actually present in the dendrites. The translation of the Kv1.1 protein is suppressed in an m-TOR pathway dependent manner, hence the low protein level in dendrites under most conditions (Raab-Graham et al., 2006). This finding implies that the Kv1.1 protein level, therefore the availability of D-current in the dendrites, can be a point of dynamic regulation under certain physiological conditions.

D-CURRENT REGULATES PRESYNAPTIC RELEASE We looked into the physiological role of D-current in CA1 pyramidal neuron dendrites with dendritic, whole-cell recordings in acute hippocampal slices (Figure 1) from adult rats. To record back-propagating action potentials (bAPs), we stimulated the axons of the CA1 pyramidal cells while recording from the dendrites at various distances from the soma. To isolate the bAP from fast synaptic events, we routinely bath-applied CNQX (10 µM) to block AMPA/Kainate type glutamate receptors, APV (50 µM) to block NMDA type glutamate receptors, as well as bicuculline (10 µM) and picrotoxin (10 µM) to block GABAa receptors. To study the regulatory role of D-current, we applied 50 µM 4-AP in the bath. We saw a large increase of after-hyperpolarization (Figure 1C). This hyperpolarization has a slow time course and can be completely eliminated by bath-applied GABAb receptor antagonist CGP55845 (5 µM). We reason that 4-AP, by blocking presynaptic D-current, may have caused an increase of presynaptic neurotransmitter release from axon terminals. While the routes for fast

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synaptic transmission were all blocked, the transmitters could still activate the slow receptors (for example GABAb). This may have happened for both glutamate and GABA. In our experiments, the GABAb effects appeared to be the most prominent. What we saw as an increase of bAP after-hyperpolarization was actually an increase of slow IPSP via GABAb receptors. Indeed, axons from some interneurons in hippocampus do originate from close to the CA1 pyramidal soma and innervate distal parts of the CA1 pyramidal neuron dendrites (Sik et al., 1995). G-protein activated, inwardly rectifying K+ (GIRK) channels that underlie the GABAb-mediated hyperpolarization have also been localized to the dendrites of these neurons (Andrade et al., 1986; Chen and Johnston, 2005).

D-CURRENT REGULATES DENDRITIC BAP WAVEFORM Our later experiments on dendritic bAPs were all performed in the presence of blockers for both fast and slow synaptic transmission (CNQX, APV, bicuculline, picrotoxin and


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CGP55845). Under these conditions, bAPs can be isolated without contamination from synaptic events. As before, we studied the role of D-current in bAP waveform by applying 50 µM 4-AP in the bath. We recorded bAPs at various distances from the soma. We did not observe any significant change in amplitude or initial dV/dt produced by 4-AP at any of the measured locations along the dendrites. However, at distance more than 200 µm from the soma, 4-AP did cause a small but significant increase in the half-amplitude duration of bAPs (Figure 2).

CONCLUSION In light of our results and data from other groups (see above) we would like to argue that the D-current makes a small but significant contribution to the shape of dendritic action

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potentials at distal locations. The more prominent role played by D-current in the hippocampal circuit, however, may be the regulation of presynaptic neurotransmitter release. It should be noted that all the physiological studies so far have been performed without any manipulation of local protein translation. As discussed above, it is possible that if local translation is promoted, more Kv1.1 channels will become available and lead to an increased presence of D-current in the dendrites. Such mechanism may have profound physiological and/or behavioral significance.

REFERENCES Andrade, R., Malenka, R. C., & Nicoll, R. A. (1986). A G protein couples serotonin and GABAB receptors to the same channels in hippocampus. Science, 234(4781), 1261-5. Bekkers, J. M. (2000). Distribution and activation of voltage-gated potassium channels in cell-attached and outside-out patches from large layer 5 cortical pyramidal neurons of the rat. J Physiol, 525 Pt 3, 611-20. Bekkers, J. M. (2000). Properties of voltage-gated potassium currents in nucleated patches from large layer 5 cortical pyramidal neurons of the rat. J Physiol, 525 Pt 3, 593-609. Bekkers, J. M., & Delaney, A. J. (2001). Modulation of excitability by alpha-dendrotoxinsensitive potassium channels in neocortical pyramidal neurons. J Neurosci, 21(17), 655360. Chen, X., & Johnston, D. (2004). Properties of single voltage-dependent K+ channels in dendrites of CA1 pyramidal neurones of rat hippocampus. J Physiol, 559(Pt 1), 187-203. Chen, X., & Johnston, D. (2005). Constitutively active G-protein-gated inwardly rectifying K+ channels in dendrites of hippocampal CA1 pyramidal neurons. J Neurosci, 25(15), 3787-92. Coetzee, W. A., Amarillo, Y., Chiu, J., Chow, A., Lau, D., et al. (1999). Molecular diversity of K+ channels. Ann N Y Acad Sci, 868, 233-85. Golding, N. L., Jung, H. Y., Mickus, T., & Spruston, N. (1999). Dendritic calcium spike initiation and repolarization are controlled by distinct potassium channel subtypes in CA1 pyramidal neurons. J Neurosci, 19(20), 8789-98. Hoffman, D. A., Magee, J. C., Colbert, C. M., & Johnston, D. (1997). K+ channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons. Nature, 387(6636), 869-75. Johnston, D., & Wu, S. M. -. (1995). Foundations of Cellular Neurophysiology. Cambridge, MA: MIT Press. Korngreen, A., & Sakmann, B. (2000). Voltage-gated K+ channels in layer 5 neocortical pyramidal neurones from young rats: subtypes and gradients. J Physiol, 525 Pt 3, 621-39. Lüthi, A., Gähwiler, B. H., & Gerber, U. (1996). A slowly inactivating potassium current in CA3 pyramidal cells of rat hippocampus in vitro. J Neurosci, 16(2), 586-94. Metz, A. E., Spruston, N., & Martina, M. (2007). Dendritic D-type potassium currents inhibit the spike afterdepolarization in rat hippocampal CA1 pyramidal neurons. J Physiol, 581(Pt 1), 175-87.


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Monaghan, M. M., Trimmer, J. S., & Rhodes, K. J. (2001). Experimental localization of Kv1 family voltage-gated K+ channel alpha and beta subunits in rat hippocampal formation. J Neurosci, 21(16), 5973-83. Raab-Graham, K. F., Haddick, P. C., Jan, Y. N., & Jan, L. Y. (2006). Activity- and mTORdependent suppression of Kv1.1 channel mRNA translation in dendrites. Science, 314(5796), 144-8. Sheng, M., Liao, Y. J., Jan, Y. N., & Jan, L. Y. (1993). Presynaptic A-current based on heteromultimeric K+ channels detected in vivo. Nature, 365(6441), 72-5. Sheng, M., Tsaur, M. L., Jan, Y. N., & Jan, L. Y. (1994). Contrasting subcellular localization of the Kv1.2 K+ channel subunit in different neurons of rat brain. J Neurosci, 14(4), 2408-17. Sik, A., Penttonen, M., Ylinen, A., & Buzsáki, G. (1995). Hippocampal CA1 interneurons: an in vivo intracellular labeling study. J Neurosci, 15(10), 6651-65. Storm, J. F. (1988). Temporal integration by a slowly inactivating K$^+$ current in hippocampal neurons. Nature, 336(6197), 379-81. Storm, J. F. (1990). Potassium currents in hippocampal pyramidal cells. Prog Brain Res, 83, 161-87. Wu, R. L., & Barish, M. E. (1992). Two pharmacologically and kinetically distinct transient potassium currents in cultured embryonic mouse hippocampal neurons. J Neurosci, 12(6), 2235-46.

INDEX A accessibility, 88 accommodation, 14, 40, 44 accuracy, 166 acetylcholine, 140 acid, viii, 6, 7, 31, 63, 66, 68, 69, 70, 71, 72, 73, 74, 76, 86, 88, 90, 91, 95, 99, 101, 118, 122, 134, 152, 154 acidity, 124 acidosis, 174 active oxygen, 91 active transport, 2 acute intermittent porphyria, 48, 54 adaptation, 14, 34, 65, 71, 89 adenosine, 111 adhesion, 37, 50, 59 adjustment, 19, 76, 80 ADP, 12, 15, 177, 183 afebrile, 59 afferent nerve, 134, 147 age, 4, 9, 150 agent, 42, 43, 47, 51, 88, 100, 118 algae, viii, 4, 10, 12, 13, 14, 15, 16, 18, 19, 63, 65, 66, 89, 91 algorithm, 164, 170 alkaloids, 123 ALS, 28, 44, 60 alternative, 67, 82, 138, 144 alters, 46, 55, 65 alveolar type II cells, 61 amiloride, 118, 119, 134, 149 amino acids, 15, 31, 99, 134 amplitude, x, 2, 6, 9, 13, 16, 17, 30, 43, 65, 70, 75, 77, 94, 113, 162, 168, 170, 174, 187, 191 amyotrophic lateral sclerosis, 48, 53, 55, 60 anatomy, 158 anesthetics, 121, 127 animals, vii, 1, 3, 4, 5, 7, 10, 98, 117, 118, 121, 124, 134, 141 anisotropy, 167 annealing, 164 antibody, 38

anticonvulsant, 61 Arabidopsis thaliana, 15, 17, 92 argument, 145 Aristotle, 157 arrhythmia, 183 arteries, 150 aspartate, 134, 152 assessment, 17, 31, 93, 175 assignment, 65 assimilation, 76, 96 assumptions, 4, 111, 162, 167, 172 astrocytes, 154 ataxia, 34, 60 ATP, ix, 5, 11, 12, 14, 15, 28, 35, 76, 80, 82, 85, 89, 93, 100, 110, 131, 133, 134, 138, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154 atria, 153 atrial fibrillation, 161, 183, 184, 186 atrium, 186 atrophy, 60 attachment, 37, 129 Australia, 27, 46, 52 autonomic nervous system, 183 autonomic neuropathy, 42 availability, 10, 14, 189 axons, vii, ix, x, 29, 30, 31, 34, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 52, 53, 54, 55, 56, 57, 58, 59, 98, 102, 103, 104, 107, 113, 114, 124, 128, 131, 132, 147, 187, 189 B bacteria, 10, 118 bandwidth, 132, 168 barley, 14 barriers, 83, 85, 161, 171, 172 basal lamina, 36 basicity, 124 behavior, ix, 64, 97, 102, 107, 108, 109, 110, 111, 115, 117, 119, 120, 124, 134, 141, 147, 160, 161, 171, 175, 176 Belgium, 47

200

Index

bending, 10 bicarbonate, 96 binding, ix, 12, 30, 35, 37, 50, 54, 61, 79, 89, 97, 99, 101, 111, 117, 121, 122, 124, 125, 126, 128 bioelectricity, 3, 4 biosynthesis, 15 biotic, vii, 1, 5 blocks, 32, 99 blood, 174 bradykinin, 118 brain, 31, 35, 57, 59, 99, 101, 115, 116, 117, 149, 155, 193 brainstem, 149 branching, 111, 112, 113, 115, 126 breeding, 18 burning, 14 C cables, 107 calcium, viii, 5, 14, 19, 55, 60, 83, 89, 91, 92, 93, 94, 97, 99, 100, 108, 109, 125, 126, 127, 128, 129, 149, 150, 151, 152, 153, 154, 174, 192 calyx, 149, 155 cancer, 43 capillary, 69, 71 carbon, 74, 76 cardiac muscle, 5, 120, 159, 162, 171, 184 cardiac pacemaker, viii, 97 carrier, 153 catheter, 162 cation, 8, 28, 35, 42, 56, 57, 79, 84, 100, 110, 118, 134, 135, 137, 147, 153 C-C, 54 cDNA, 30, 56, 59, 99 cell death, 36, 51 cell line, 49, 61, 150 cell membranes, viii, 84, 92, 94, 97, 98 cell signaling, 140, 149 cell surface, 65, 66, 68, 72, 73 cellulose, 16 central nervous system, 33, 111, 124 cerebellum, 116 channel blocker, 6, 46, 115, 144 chemotherapy, 43, 56 chemotropism, 11 China, 95 chlorophyll, viii, 12, 63, 65, 75, 77, 79, 80, 81, 82, 83, 84, 85, 88, 89, 93, 94, 95 chloroplast, viii, 10, 12, 63, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 88, 91, 92, 93 CHO cells, 59, 142 chromatography, 99 chronic renal failure, 42, 53, 54 ciguatera, 43, 48, 60 circulation, 75 classes, 100 clinical assessment, 30 cloning, 30, 48, 57, 99 closure, 6, 7

clustering, 57, 178 clusters, 54, 179 CNS, 28, 33, 36, 38, 52, 59, 124, 133 CO2, 8, 66, 74, 76, 77, 80, 82, 90, 93, 96 codes, 67, 77, 78 coding, 132, 154 cohort, 42, 51 colorectal cancer, 43, 48 communication, 7, 8, 12, 20, 114, 151, 154 community, 158 companion cell, 16 complexity, 158, 160, 162, 171, 174, 183 complications, 41, 51, 54, 65 components, 47, 110, 111, 126, 127, 164, 168, 170, 174 composition, 17, 31, 36, 50 compounds, 15, 16, 18, 117, 123, 140, 147, 150 computational grid, 114, 158 computer simulations, 144, 161 concentration, x, 2, 4, 12, 15, 16, 18, 29, 31, 34, 36, 44, 68, 75, 79, 81, 86, 92, 93, 115, 126, 137, 145, 146, 155, 184, 187, 188 conduction, vii, ix, 3, 14, 27, 28, 30, 31, 34, 36, 38, 40, 44, 45, 46, 48, 49, 50, 52, 53, 55, 61, 64, 97, 107, 114, 115, 126, 127, 128, 166, 167, 171, 174, 175, 184, 185 conductivity, 17, 174 conductor, 126, 162 configuration, 162 Congress, 93 construction, 162, 168 consumers, 66 consumption, 76, 80, 89 contamination, 191 continuity, 14, 112 control, vii, x, 1, 5, 7, 8, 9, 10, 11, 12, 14, 15, 17, 19, 37, 53, 76, 86, 87, 92, 102, 123, 126, 132, 135, 147, 153, 154, 171 control condition, 86, 87 conversion, 74, 93, 118 cooling, 13, 164 correlation, 3, 50, 77, 179, 180, 182 cortex, 9, 16, 116, 117 cortical neurons, 189 counterbalance, 166 couples, 133, 153, 192 coupling, 7, 10, 12, 67, 142, 168 critical analysis, 153 crystallization, 30 culture, 47 cystine, 155 cytochrome, 82 cytoplasm, 4, 16, 35, 36, 64, 67, 74, 75, 76, 77, 84, 142, 144, 146 D danger, 3, 14, 15, 19 death, 3, 43, 44, 174 decay, 67, 68, 89, 112 decomposition, 174

Index deconvolution, 172, 173 defects, 43, 51 defence, vii, 1, 5, 15, 19 defense, 64, 121 deficiency, 42 delivery, 85 demyelination, 34, 45, 48 dendrites, x, 38, 48, 56, 59, 111, 113, 115, 116, 117, 127, 129, 187, 189, 191, 192, 193 dendritic spines, 116 denoising, 170 density, 7, 33, 34, 37, 38, 53, 66, 67, 69, 82, 98, 114, 167, 170, 171, 189 derivatives, 129, 164 desensitization, 13 destruction, 84 detection, 18, 118, 151, 170, 174 diabetes, 41, 42, 49, 174 diabetic neuropathy, 41, 48, 51, 52, 54 differentiation, 30, 56 diffusion, 11, 34, 37, 68, 72, 95, 133 digestion, 7 direct observation, 129 disability, 45 discharges, 45 disorder, 51, 183 dispersion, 175, 183 displacement, 104 dissociation, 127 distribution, 17, 18, 46, 47, 48, 49, 57, 60, 61, 65, 66, 67, 73, 74, 76, 79, 87, 89, 92, 98, 111, 112, 113, 117, 124, 162, 167, 168, 189 diversity, 28, 49, 100, 101, 124, 127, 192 DNA, 99 domain structure, 56, 120 down-regulation, 80 Drosophila, 117, 127, 128, 129 drug discovery, 184 drugs, 28, 45, 57, 126 dualism, 147 durability, 11 duration, vii, x, 1, 2, 6, 11, 13, 16, 28, 38, 39, 41, 43, 44, 47, 55, 65, 69, 76, 113, 148, 168, 174, 183, 185, 187, 191 dyes, 18, 38 E eating, 148 ECM, 49 ectoderm, 154 Education, 20 elaboration, 19 electric current, 2, 65, 66, 67, 70, 77 electrical conductivity, 16, 107 electrical properties, 17, 69, 95, 111, 113, 168 electricity, 3 electrodes, 5, 9, 17, 69, 80, 102, 170, 173 electromyography, 30, 47

201

electron, 11, 75, 76, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94 electrons, 84, 85 elongation, 11, 46 EMG, 174 emission, 15, 143 employment, 167 encoding, ix, 59, 131, 148 energy, 10, 35, 36, 42, 67, 75, 77, 80, 83, 85, 93, 118, 164 environment, 14, 75, 76, 89 enzymatic activity, 13 enzymes, 5, 12, 16, 82 epidermis, 7, 9 epilepsy, 33, 34, 49, 52, 60 epithelium, 134, 141, 148, 151, 154 equating, 39 equilibrium, 13, 73, 74, 109 erythrocytes, 153 estimating, 158, 173 ethylene, 11, 15 evoked potential, 13 evolution, 10, 13, 126, 167 excitability, vii, viii, ix, 1, 2, 4, 6, 10, 11, 19, 27, 28, 31, 33, 34, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 53, 54, 55, 56, 58, 96, 102, 125, 131, 132, 139, 140, 174, 175, 183, 185, 188, 192 excitation, vii, viii, ix, 1, 3, 4, 5, 6, 7, 9, 10, 12, 16, 17, 18, 29, 34, 47, 52, 54, 61, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 81, 82, 86, 88, 89, 90, 91, 92, 93, 96, 125, 127, 131 exercise, 43, 174 exocytosis, 133, 142, 143, 147, 149, 151, 154 experimental autoimmune encephalomyelitis, 47 experimental condition, 84, 85 exposure, 12, 13, 41, 43, 82 extraction, x, 157, 158 extrusion, 66, 72, 74, 76 F failure, 44, 115 family, 34, 50, 61, 103, 128, 129, 134, 149, 152, 153, 188, 193 fatigue, 45 febrile seizure, 58, 59 feedback, 5, 76, 102, 103 fertilization, 5 fibers, 34, 46, 55, 116, 118, 141, 180, 182 fibrillation, 174 fibrosis, 161, 174, 185 fidelity, 144 filters, 174 filtration, 99 fires, 7 fish, 43, 52, 53 fixation, 74, 76, 80, 82, 94 flame, 64 flexibility, 89 fluctuations, 11, 40

202

Index

fluorescence, viii, 36, 50, 63, 65, 75, 77, 79, 80, 82, 83, 85, 86, 88, 89, 90, 93, 94, 95, 120, 138, 143 focusing, 158 Ford, 149 freezing, 14 functional analysis, 28, 48, 49 fusion, 133, 138, 154 G ganglion, 47, 48, 58, 59, 61, 119, 120, 121, 126 gel, 99 gene, 5, 15, 16, 18, 19, 49, 52, 60, 64, 100, 127, 149, 155 generation, viii, 7, 9, 10, 12, 15, 16, 27, 29, 32, 33, 34, 38, 40, 44, 49, 53, 63, 64, 65, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 92, 111, 148 genetic disorders, 42 Germany, 20, 81 germination, 8 gland, 7 glial cells, 36, 59, 133, 135 glucose tolerance, 41 glutamate, ix, 131, 132, 134, 140, 147, 151, 152, 155, 189 glycine, 15, 151 glycosylation, 101 goals, 184 grants, 15 graph, 67, 68 gravity, 6 Great Britain, 4 Greece, 157, 184 grids, 172, 173 groups, x, 31, 79, 187, 192 growth, vii, 1, 3, 5, 11, 15, 19, 94, 95, 155 guard cell, 93 H hair cells, ix, x, 119, 131, 132, 133, 147 health, viii, 27, 28, 158, 183 heart failure, 111, 174 heart rate, 126 heat, 65, 75, 83, 95, 118, 128 height, 114, 121 heme, 42 hemodialysis, 42 herbicide, viii, 64, 84 heterogeneity, viii, 63, 74, 77, 79, 80, 87, 89, 95, 158, 159, 168, 174, 175, 179, 183, 186 hippocampus, x, 187, 188, 189, 190, 192, 193 histology, 162 homeostasis, 6 homogeneity, 95, 179 hormone, 11 host, x, 13, 187 human brain, 46, 48, 49, 61 humidity, 9, 14 hydrocarbons, 124 hydrogen, 80, 124

hyperglycemia, 41 hyperkalemia, 42, 174, 175, 177, 179, 180, 183 hypersensitivity, 118 hypothesis, 10, 14, 19, 38, 60, 67, 73, 83, 84, 122, 162 hypoxia, 174 I identification, ix, 19, 28, 30, 50, 132, 143 identity, 37 IFM, 31 illumination, 7, 11, 66, 67, 77, 83, 90, 91 image analysis, 94 images, 65, 77, 86, 88, 95 imbalances, 2 immunoglobulin, 33, 101 immunohistochemistry, 30, 140 immunoreactivity, 155 in vitro, 28, 43, 46, 193 in vivo, 28, 30, 39, 42, 46, 54, 55, 60, 66, 72, 75, 83, 84, 85, 193 indication, 7 indicators, 18 induction, 8, 11, 12, 15, 79, 84, 85, 94 infarction, 161, 168 infinite, 39, 105, 106 inflammation, 118 information processing, 132, 154 ingestion, 53 inhibition, viii, 2, 11, 14, 19, 36, 55, 63, 65, 66, 68, 72, 74, 79, 80, 82, 86, 89, 93, 94, 95, 125, 129, 149 inhibitor, 11, 15, 74, 79 inhomogeneity, 161, 175, 179, 183 initial state, 69, 78 initiation, 8, 12, 38, 49, 55, 56, 116, 129, 161, 192 injuries, viii, 63 insects, 64 insertion, 69 insight, 71, 113, 116, 158, 161, 183 instruments, 80 insulation, 80 insulin, 41 integration, 150, 152, 193 interaction, viii, 15, 51, 64, 101, 158, 183 interactions, 12, 76, 77, 79, 84, 157 interdependence, 17 interface, 9 interference, 116, 170, 188 interneuron, x, 187 interneurons, 118, 190, 193 internode, 33, 34, 35, 37, 40, 64, 69, 71, 88 interval, 6, 39, 82, 172, 183 intoxication, 43 intuition, 3 inversion, 169 ion channels, vii, viii, ix, 1, 5, 28, 30, 31, 37, 40, 43, 45, 46, 52, 54, 57, 64, 72, 97, 98, 99, 100, 101, 107, 109, 110, 116, 117, 118, 119, 124, 126, 132, 133, 139, 143, 144, 153, 186

Index ions, ix, 2, 4, 5, 6, 9, 10, 13, 16, 18, 20, 29, 30, 32, 35, 36, 41, 74, 96, 97, 98, 100, 108, 110, 127, 129, 137, 145 iron, 84 irritability, 21 ischemia, 161, 174, 175, 179, 180, 183 isolation, 68, 103 I-V curves, 136, 144 K Keynes, 102, 127 kidney, 41, 42, 54 kinetic model, 92, 99, 120 kinetics, x, 2, 29, 32, 33, 34, 40, 46, 71, 73, 81, 82, 83, 84, 85, 89, 121, 122, 124, 125, 160, 171, 175, 187, 188 L labeling, 47, 193 lack of control, 17 latency, 9, 30, 43 lateral sclerosis, 28, 44 leakage, 15, 16 leaks, 9 lesions, 45 liberation, 5, 96 life span, 134 lifetime, 120 ligand, 107, 111 light conditions, 65, 73 linear function, 164 links, 16 local anesthetic, 121 localization, 20, 30, 32, 35, 46, 52, 60, 61, 151, 152, 154, 155, 189, 193 locus, 129 long distance, ix, 10, 16, 20, 95, 132 lumen, 76, 77 luminescence, 13 M machinery, 12, 133, 138, 144 mammalian brain, 126, 154 management, 51 manipulation, 192 mapping, 185 matrix, 36, 169 measurement, 17, 18, 30, 82 measures, 41, 43, 51, 53 mechanical properties, 158 media, 10 median, 53, 54 medication, 158, 161, 174, 184 membrane permeability, 2, 4, 7, 84 membranes, 2, 4, 5, 10, 12, 30, 35, 36, 42, 52, 65, 66, 67, 80, 85, 86, 98, 99, 111, 112, 124, 125, 127, 128 mental retardation, 60

203

mesophyll, 7, 17 messenger RNA, 99 messengers, 5, 16, 140, 154 metabolism, 8, 14, 41, 42 Mg2+, 28, 35, 145, 146 mice, 34, 61, 118, 128, 134, 138, 141, 147, 150, 153 microinjection, 79 micrometer, 18 microscopy, 57, 58, 77, 95, 116, 188 mitochondria, 67, 76, 92, 93 mobility, 68 model system, 66, 91 modeling, x, 30, 38, 157, 158, 161, 164, 167, 184 models, 19, 34, 41, 46, 105, 108, 109, 110, 112, 113, 126, 152, 158, 159, 160, 161, 163, 167, 171, 173, 183, 184 molar volume, 124 molecular biology, 30, 52, 140, 188 molecular oxygen, 80 molecules, 15, 18, 37, 42, 50, 57, 99, 117, 124, 145, 152 morphology, 40, 134, 161, 166, 168, 170, 186 morphometric, 58 mosaic, 65 motion, 118 motor neurons, 44, 113 movement, 2, 3, 7, 9, 19, 30, 32, 54, 95, 118 mRNA, 193 mucin, 50 multiple factors, 158 multiple sclerosis, 45, 49, 61 muscles, vii, 1, 3, 7, 30, 45 mutagenesis, 30, 125 mutation, 60 myelin, 35, 36, 37, 46, 47, 57, 58 myocardial infarction, 184, 185 myocardial ischemia, 174, 185 myocardium, 168, 174, 185 myocyte, vii myosin, 15 N NaCl, 134, 135, 136, 139, 140, 143, 146, 148, 149, 155 NCS, 28, 30 negativity, 3 nematode, 118 nephropathy, 51 nerve fibers, 51, 57, 60, 102, 141 nervous system, 28, 34, 50, 56, 60, 128 Netherlands, 94 network, 16, 105, 106, 107, 110, 115 neural development, 150 neurobiology, 57, 96, 151 neuroinflammation, 55 neurological disease, viii, 27, 28, 33, 41, 45 neuronal cells, 139 neuropathy, 28, 41, 42, 43, 44, 46, 48, 50, 51, 52, 53, 54, 56 neuropeptides, 151 neurophysiology, 60 neuroprotection, 61

204

Index

neuroscience, 54 neurotoxicity, 43, 51, 53, 56 neurotransmission, 28, 31, 37, 45, 132, 154 neurotransmitter, ix, x, 131, 132, 133, 141, 147, 151, 188, 190, 192 New England, 51 New South Wales, 27 Nobel Prize, 5 node of Ranvier, 37, 38, 50, 54, 57, 58, 98, 102, 103, 122 nodes, 10, 33, 34, 35, 36, 37, 38, 41, 45, 48, 50, 51, 53, 56, 58, 129, 168, 182 noise, 30, 162, 166, 169 non-insulin dependent diabetes, 41 nonlinear dynamics, 183 nonsense mutation, 52 norepinephrine, 142 North America, 60 nucleotides, 16, 150, 152 nucleus, 5 nutrients, 66, 75 nutrition, 66 O observations, 3, 82, 110, 112, 135, 137, 144, 145, 146, 147, 172, 185 olfaction, 117 oligodendrocytes, 36 one dimension, 106, 107 optic nerve, 55 optimization, 164, 165 organ, x, 2, 7, 15, 16, 17, 18, 66, 132, 141, 148, 157, 158, 183 organelles, 6, 84 organism, 2, 16 oxidation, 82, 83, 84, 85 oxidative stress, 41, 49, 51, 118 oxygen, 80 P pacing, 158, 175, 177, 179, 183, 185 pain, 14, 42, 46, 49, 51, 52, 56, 118, 129 paralysis, 43, 44, 56 parameter, 40, 75, 77, 88, 114, 163, 164, 166, 167, 170 parenchymal cell, 9 partial seizure, 59 partition, 80, 110, 124 passive, viii, 19, 40, 63, 67, 68, 72, 74, 89, 91, 111 pathogens, 6 pathophysiology, 53, 162 pathways, 16, 46, 72, 78, 83, 94, 127, 129, 143, 145, 159 PCR, 138, 141 PEP, 15 peptides, 79, 145, 152, 153 perfusion, 18 peripheral nervous system, 30, 34, 35, 58, 60 permeability, ix, 4, 41, 84, 89, 105, 110, 128, 132 permeation, viii, 64, 74, 76, 83, 84, 85, 88, 92

personal communication, 84 pH, v, viii, 63, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 88, 89, 90, 91, 92, 93, 94, 95, 118, 121, 145 pharmacology, 47, 125, 188 phenol, 68, 90 phenytoin, 46 phloem, 9, 15, 16, 17 phosphoinositides, 51 phosphorylation, 35, 101 photons, 91 photooxidation, 82, 83, 89 photosynthesis, viii, 9, 11, 12, 15, 17, 19, 63, 65, 66, 74, 76, 77, 83, 88, 89, 91, 93, 94, 95 physiology, 3, 15, 20, 47, 141, 183 pistil, 8, 19 plants, vii, viii, 1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 25, 63, 64, 65, 66, 74, 79, 85, 91, 92, 94, 95, 96, 118 plasma, vii, ix, 1, 5, 10, 11, 12, 16, 20, 64, 65, 66, 68, 69, 70, 75, 76, 80, 86, 88, 89, 91, 92, 93, 94, 96, 98, 132, 133, 144, 146 plasma membrane, vii, ix, 1, 5, 10, 11, 12, 16, 20, 64, 65, 66, 68, 69, 70, 75, 76, 80, 86, 88, 89, 91, 92, 93, 94, 96, 98, 132, 133, 144, 146 plasmid, 30 platinum, 43 PM, 47, 66, 72, 73, 74, 75, 76, 78, 79, 89 Poland, 1 polarity, 124 polarization, 11, 40, 53, 135 pollen, 8, 11 pollen tube, 11 pollination, 8 polypeptide, 99, 100, 101, 120, 125 population, 33, 41, 42, 48, 51, 119, 134 porphyria, 28, 42, 50 potassium, viii, 4, 5, 9, 28, 29, 34, 35, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 97, 98, 99, 102, 126, 127, 128, 129, 151, 155, 174, 192, 193 power, 112, 115, 158 prediction, 77, 116 pressure, 2, 8, 10, 14, 15, 79, 117 probe, 3, 18, 39, 46, 94, 145 production, vii, viii, 7, 32, 51, 84, 93, 97, 98, 100, 101, 107, 110, 111, 121, 123, 134 promoter, 138 propagation, viii, 6, 7, 9, 16, 19, 30, 36, 59, 63, 64, 65, 67, 74, 79, 82, 88, 89, 95, 98, 109, 114, 115, 125, 129, 158, 159, 161, 162, 166, 168, 169, 174, 175, 176, 179, 182, 183, 184, 192 prostaglandins, 118 protein kinase C, 101 protein kinases, 155 proteinase, 15, 64, 79 protein-protein interactions, 56 proteins, vii, viii, 1, 6, 12, 19, 30, 36, 37, 54, 61, 66, 79, 89, 91, 95, 97, 98, 99, 100, 118, 128, 138, 145, 149, 154, 183 proteolipid protein, 36

Index protocol, 123, 175 protons, 65, 74, 76, 83, 150 psychosis, 42 pulse, vii, 65, 67, 69, 75, 77, 82, 83, 84, 85, 92, 93, 94, 98, 122, 123, 140, 175, 188 pumps, viii, 2, 12, 13, 27, 28, 31, 40, 51, 66, 95, 126 purification, 125 pyramidal cells, x, 52, 56, 115, 128, 187, 189, 193 Q questioning, x, 132 quinone, 75 R radius, 68, 106, 114, 161, 165 rain, 54, 61 range, 10, 12, 33, 36, 42, 64, 68, 69, 86, 88, 107, 118, 120, 121, 124, 172, 189 reaction center, 80, 81, 82, 84 reactive oxygen, 84 reagents, 126 reasoning, 77 receptors, 12, 117, 118, 126, 134, 138, 140, 141, 142, 144, 147, 149, 150, 151, 152, 153, 154, 189, 192 recognition, 8, 15, 84 reconstruction, 19, 170 recovery, 9, 32, 40, 41, 43, 44, 47, 53, 67, 68, 72, 89, 183 rectification, 34, 40, 52, 55, 56 recurrence, 183, 185 recycling, 133 redistribution, 68 regulation, x, 5, 19, 33, 47, 58, 64, 66, 75, 94, 187, 189, 192 relationship, 3, 11, 39, 40, 43, 47, 52, 112, 162 relatives, viii, 63, 66, 155 relevance, 177 remodelling, 183 renal failure, 42 repetitive behavior, 124 reproduction, vii, 1, 5, 158 residues, 31, 33, 45, 101, 122, 125 resistance, ix, 16, 17, 30, 69, 70, 74, 106, 132, 146, 149 resolution, 18, 30, 31, 52, 55, 58, 60, 91, 94 respiration, 8, 11, 15, 19, 79 respiratory, 43, 44 response time, 112 responsiveness, 4, 155 resting potential, 2, 4, 5, 7, 11, 17, 29, 70, 98, 103, 107, 113, 122, 123, 127, 148 retardation, 75, 82, 86, 89 reticulum, 60, 110 retina, 148, 155 retinopathy, 51 rhodopsin, 117 rhythmicity, 11 risk, 42 rods, 147, 155 room temperature, 105

205

Royal Society, 3, 49 Russia, 63, 131 S SA node, 110, 111, 129 saccharin, 142, 149 sample, 75, 80, 81 saturation, 75, 94 scaling, 71, 166 scar tissue, 159, 168, 175 sclerosis, 45 search, 144 secretion, ix, 7, 8, 17, 131, 134, 141, 142, 143, 144, 145, 146, 147, 148 security, 49 seedlings, 12, 13 seizure, 45 selectivity, 33, 50, 101, 124, 125 self-organization, 65, 91 semi-permeable membrane, 4 sensation, 117, 119, 126 sensing, 3, 6, 10, 13, 14, 52, 102, 134, 150, 151 sensitivity, x, 2, 31, 118, 145, 155, 187, 188 sensitization, 43, 60 sensors, ix, 9, 10, 14, 16, 97, 101, 147 sensory modalities, 119 separation, 79 sequencing, 30, 125 serotonin, 140, 141, 142, 143, 147, 151, 152, 154, 155, 192 serum, 42 severity, 41, 50, 89 shape, ix, x, 70, 92, 97, 98, 113, 114, 119, 121, 122, 126, 139, 149, 162, 164, 170, 187, 192 shaping, 14 shares, 31 sharing, 5, 31, 155 shock, 10, 95 shoot, 12 sign, 42 signal transduction, vii, 1, 6, 95 signaling pathway, 150, 155 signalling, vii, 1, 3, 5, 7, 8, 12, 15, 16, 19, 94, 149, 150 signals, ix, 6, 11, 12, 13, 14, 64, 65, 74, 75, 79, 81, 82, 83, 85, 92, 93, 94, 95, 117, 118, 119, 131, 132, 133, 152, 164, 167, 168, 172 similarity, 73, 83, 85, 118, 122 simulation, ix, 97, 107, 159, 160, 161, 172, 174, 183, 185 sinoatrial node, 110 skeletal muscle, viii, 52, 60, 97, 99, 123, 125, 126, 129 skin, 42, 50, 118, 128 SLAC, 19 smoothing, viii, 64, 68, 72, 79, 88 SNS, 46, 49, 50 sodium, viii, 4, 28, 29, 35, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 97, 98, 99, 101, 102, 108, 111, 120, 122, 124, 125, 126, 127, 128, 129, 150, 151, 174, 184 software, 31

206

Index

soil, 10 somata, 127 spatial information, 170 specialization, 47 species, 4, 6, 7, 9, 14, 65, 66, 74, 84, 141, 145 specificity, 145 spectrum, 42, 51, 60 speed, 14, 18 spinal cord, 55, 58 spine, 116, 129 standard deviation, 166, 167, 179, 181, 182 standard error, 84, 85 stigma, 8 stimulus, vii, 1, 2, 5, 6, 7, 8, 13, 14, 16, 31, 39, 71, 77, 78, 85, 91, 121, 142, 147, 148, 158, 174, 175, 179, 183 stoichiometry, 57 strategies, viii, 27, 45, 56, 184 strength, vii, ix, 1, 2, 13, 16, 39, 41, 43, 44, 47, 70, 131, 162, 170 stress, 3, 16, 19, 75, 89, 174 stretching, 10, 15 stroma, 76, 82, 83, 88, 89 structural characteristics, 99 subgroups, 135, 138 substitution, 135 substrates, 76, 184 sucrose, 9, 121, 140 sulfur, 84 Sun, 46, 93, 137, 150, 155 supply, 75, 76, 77 suppression, 48, 68, 72, 75, 76, 78, 80, 82, 170, 193 survival, 16 susceptibility, 39 Sweden, 48 swelling, 154 switching, 85 symbols, 73 symptoms, 41, 42, 43, 54 synapse, 116, 120, 149, 153, 154, 155 synaptic transmission, 113, 120, 132, 152, 154, 190, 191 synaptic vesicles, 133 synchronization, 5 syndrome, 58 synthesis, 42, 76, 79, 80 T targets, 45, 57 temperature, 3, 4, 9, 13, 14, 43, 48, 104, 105, 110, 117, 118, 126, 138, 164 tension, 14 terminals, 55, 113, 133, 134, 147, 151, 189 therapy, 41, 56 thigmotropism, 11 threshold, vii, x, 1, 2, 7, 13, 15, 29, 31, 33, 38, 39, 40, 41, 43, 44, 47, 73, 148, 187, 189 tissue, 3, 7, 8, 9, 14, 15, 17, 18, 151, 158, 159, 160, 161, 162, 163, 167, 168, 172, 173, 174, 175, 177, 183, 185 tobacco, 93

tonic, 132, 147 topology, 132, 166 toxicity, 42, 60 toxin, 32, 47, 120, 122, 123, 128, 129, 153 tracking, 31, 47 transcription, 15 transduction, ix, 9, 117, 131, 134, 137, 141, 147, 148, 150, 151, 153, 154, 155 transformation coefficients, 174 transition, 11, 12, 67, 71, 80, 122 transitions, 65, 80, 81, 95, 99, 119 translation, 189, 192, 193 translocation, 110 transmembrane region, 33, 118 transmission, vii, viii, 1, 2, 6, 7, 9, 10, 16, 17, 20, 27, 28, 64, 65, 76, 94, 126, 132, 133, 141, 147, 152, 155 transpiration, 15 transport, 11, 36, 60, 65, 66, 68, 72, 74, 76, 78, 80, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 99, 100, 107, 110, 126, 133, 155 transport processes, 107 trees, 111 triggers, ix, 8, 9, 12, 35, 132, 133 turgor, 5, 6, 7, 9, 10, 15, 19, 65, 66, 79 turtle, 153 U underlying mechanisms, 183 uniform, 17, 65, 68, 69, 73, 86, 107, 111, 112, 113, 124, 168, 169 United States, 82 UV, 12 V vacuole, 4 validation, 161 values, vii, 1, 2, 66, 68, 69, 70, 71, 72, 74, 75, 77, 78, 86, 88, 103, 105, 132, 139, 160, 168, 177, 179, 180, 181, 182 variables, 103, 104, 108, 113, 160 variation, 14, 57, 65, 142, 161, 167, 168, 179, 183 vascular bundle, 3, 16 vasoactive intestinal peptide, 141 vector, 30, 169, 179 velocity, ix, 2, 6, 7, 8, 9, 10, 14, 30, 52, 64, 65, 97, 107, 113, 114, 126, 162, 166, 167, 169, 174, 175, 177, 179, 180 Venus, 6, 64 vertebrates, ix, 132, 152 vesicle, 133, 154 vision, 117 vulnerability, 158, 174, 175, 183 W Wales, 27

Index wavelet, 164, 170, 172, 173, 174, 185 weakness, 43, 44 web, 120 wetting, 10 wheat, 14 white matter, 59 wind, 64 winning, vii, 1, 5 workers, 142

207 X

xylem, 9, 14, 16 Y yield, 75, 77, 78, 80, 83, 86, 89, 93

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