Auditory Mechanisms: Proceedings of the Ninth International Symposium Held at Portland, Oregon, USA 23 - 28 July 2005

Auditory Mechanisms Processes and Models (with CD-Rom)

Alfred L. Nuttall Tianying Ren Peter Gillespie Karl Grosh Egbert de Boer editors

Auditory Mechanisms Processes and Models

Auditory Mechanisms Processes a n d Models Proceedings of the Ninth International Symposium held at Portland, Oregon, USA

23 - 28 July 2005

Editor

Alfred L. Nuttall Oregon Health & Science University, USA Associate Editors

Tianying Ren Peter Gillespie Oregon Health & Science University, USA

Karl Grosh University of Michigan, USA

Egbert de Boer Academic Medical Center, The Netherlands

\fc

World Scientific

NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI

Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

AUDITORY MECHANISMS: PROCESSES AND MODELS (with CD-ROM) Proceedings of the Ninth International Symposium Copyright © 2006 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 981-256-824-7

Printed by Mainland Press Pte Ltd

PREFACE Dysfunction of the cochlea is the most common of all human forms of sensory loss. The World Health Organization estimates that 250 million people have a significant level hearing loss. In the United States, 1 of every 1000 newborns has a severe to profound hearing loss. With age, about 60% of those over 70 years old will have a serious loss of auditory capability. More than 40 genes have been associated with cochlear sensory impairment. Critical to the prevention of hearing loss as a serious global health problem is the detailed knowledge of cochlear function. The Workshop on Auditory Mechanisms: Processes and Models was the ninth in a series that has also come to be known as the "Mechanics of Hearing Workshops." Inner ear mechanics is a special area of study that explores the details of function relevant to understanding normal hearing and hearing loss. It is easy to recognize the relevance of cochlear mechanics study to both basic and applied auditory science. The otoacoustic emission is one such topic. Otoacoustic emissions potentially provide a view into the cochlea to observe the micro-mechanics. However, interpretation of changes in the emissions requires a greater understanding of their origin and wave propagation. During the past 20 years since the start of the Workshops, research into the mechanics of hearing has undergone numerous major developments. Particularly important are the experimental procedures have been developed for manipulating and viewing the micromechanical responses of the inner ear, even down to the sub-cellular level. The Workshop brought together an interdisciplinary group of scientists including the leading researchers working on the cochlea from the level of the whole system through the structural protein level. One character of the meeting that differs from the typical auditory neuroscience gatherings is the strong representation of mathematical modeling. This combination of experimentalists and modelers enables a deeper presentation and discussion of theoretical issues. Indeed, much time was available for formal discussion of two major scientific controversies: 1) On the role of outer hair cell stereocilia in "powering" cochlear amplification and 2) On the amount of reverse propagation of energy from the cochlea by fluid acoustic compression waves. The book organization begins with papers on the function of the organ of Corti as a system in the chapter titled "Whole-Organ Mechanics." "Hair Cells" follows concerning the soma of outer hair cells. Hair cell transduction is addressed in the chapter "Stereocilia" and otoacoustic emissions make up the chapter titled "Emissions." Finally, modeling of cochlear function is treated in the chapter "Cochlear Models." Each chapter has a paper from one or more plenary speakers. Of particular note is that this Workshop honored Prof. Egbert de Boer as a founder of the Mechanics Workshop series of meetings. His paper derives from a plenary lecture. Questions and answer responses are included at the end of the papers and there is a separate "Discussion" chapter that presents the content of a lively evening session of the Workshop.

v

vi

The Workshop was supported and made possible by generous funding support from public and private sources. An NIH conference grant was provided by the National Institute on Deafness and Other Communication Disorders. Instrument manufacturers Polytec Inc., Tucker-Davis Technologies and Etymotic Research Inc. provided support. Of particular relevance, the Workshop received generous support from hearing aid manufacturers, The Oticon Foundation, Starkey Hearing Research Center, and a cochlear implant manufacturer, Advanced Bionics. The Workshop also established a new model for scientific conferences, as there was a linked but financially separate, public science outreach/training event. Held at the Oregon Museum of Science and Industry in Portland, Drs. James A. Hudspeth and Billy Martin delivered an interactive lecture to a group of high school students. The Workshop attendees were also present. A reception followed, allowing the personal interaction of the students and the scientists. This event was generously funded by the Burroughs Wellcome Foundation. The editors would like to thank the International Organizing Committee for their role in the planning of the Workshop and for efforts on finding financial support. We are grateful to the Plenary Lecturers for their stimulating presentations, to the session chairs and discussion moderators in helping run the meeting, and to all the participants for maintaining the tradition of a high quality meeting. We are indebted to many others for the success of the Workshop and for this book. The Department of Otolaryngology at the Oregon Health & Science University is the home of the Oregon Hearing Research Center (OHRC) and responsible for creating the rich basic and clinical research environment that enables meetings such as this Workshop. The faculty and students of OHRC deserve praise for their assistance. We have deep gratitude for the core group of OHRC staff that contributed so much of their time and energy, Linda Howarth, Jill Lilly, Scott Matthews, Theresa Nims and Edward Porsov, without whose help the Workshop would have been ordinary at best, instead of extraordinary as it was. Finally I wish to thank my scientist colleagues, many of whom are close friends, for creating such an exciting and fruitful scientific environment as the Mechanics of Hearing Workshop, and for the honor and pleasure of hosting this ninth Workshop.

A.L. Nuttall Oregon Health & Science University Portland, Oregon April 2006

The International Organizing Committee J. Allen - Illinois, USA W. E. Brownell - Texas, USA N. P. Cooper - Keele, United Kingdom P. Dallos - Michigan, USA A. Gummer - Tubingen, Germany S. Puria - California, USA C. Shera - Massachusetts, USA R. Withnell- Indiana, USA The Local Organizing Committee: A. L. Nuttall - Oregon, USA E. de Boer - Amsterdam, The Netherlands P.G. Gillespie - Oregon, USA K. Grosh - Michigan, USA T. Ren - Oregon, USA R. Walker - Oregon, USA Plenary Lecturers W. E. Brownell, Texas, USA E. de Boer - Amsterdam, The Netherlands R. Fettiplace, Wisconsin, USA J. Guinan, Massachusetts, USA J. A. Hudspeth, New York, USA P. Nairns, California, USA

DATA DIPS AND PEAKS (WITH APOLOGIES TO ELLA FITZGERALD) Heaven, I'm in heaven And my heart beats so that I can hardly speak. 'Cause I finally found the funding that I seek. Now I'm measuring those data dips and peaks. Heaven, I'm in heaven And the cares that hung around me 50 weeks Finally vanished like a gambler's lucky streak With acquiring all those data dips and peaks. Now I love to go to meetings. And to hear or give a speech But I don't enjoy them half as much As data dips and peaks. I love to read and write a paper. And a physics course to teach But they don't thrill me half as much Basilar membrane velocity al the 17 kH? As data dips and peaks best frequency location evoked by 100 microA current applied to tho cochlea

Oh points on my screen I want to analyze you Just one effect new Will carry me through to

•

Heaven, I'm in heaven And my heart beats so that I can hardly speak. 'Cause I finally found the funding that I seek. Now I'm measuring those data dips and peaks.

Laura Greene, professor of physics at the University of Illinois at UrbanaChampaign, wrote this song in 2001. The melody is that of "Cheek to Cheek. " Says Greene, "Maybe the apologies should have been to Irving Berlin, who wrote the original song, but I copied the words and style from the Ella Fitzgerald/Louis Armstrong rendition, trying to follow Ella's phrasing as much as possible. I am also a great fan of Ella in general." Attendees of the Mechanics of Hearing Banquet at Mount Hood's Timberline lodge will, perhaps painfully, remember the role this song played in the evening's entertainment. Inset graphic: Cochlear mechanics dips and peaks with thanks to Drs. Alfred Nuttall, Karl Grosh, and Jiefu Zheng. Reprinted with permission from Physics Today, July 2005, page 58. Copyright 2005, American Institute of Physics.

vm

PREVIOUS PUBLICATIONS FROM THIS SERIES OF WORKSHOPS: Mechanics of Hearing. Edited by E. de Boer and M.A. Viergever. Nijhoff, the Hague/Delft University Press, 1983. Peripheral Auditory Mechanisms. Edited by J.A. Allen, J.L. Hall, A. Hubbard, S.T. Neely, and A. Tubis. Springer, Berlin, 1986. Cochlear Mechanisms: Structure Function and Models. Edited by J.P. Wilson and D.T. Kemp. Plenum, New York. 1989. The Mechanics and Biophysics of Hearing. Edited by P. Dallos, CD. Geisler, J.W. Matthews, M.A. Ruggero, and C.R. Steele. Springer, Berlin, 1990. Biophysics of Hair Cell Sensory Systems. Edited by H. Duifhuis, J.W. Horset, P. van Dijk, and S.M. van Netten. World Scientific, Singapore, 1993. Diversity in Auditory Mechanics. Edited by E.R. Lewis, G.R. Long, R.F. Lyon, P.M. Narins, C.R. Steele, and E. Hecht-Poinar. World Scientific, Singapore, 1996. Recent Developments in Auditory Mechanics. Edited by H.Wada, T. Takasaka, K. Ideda, K. Ohyama, and T. Koike. World Scientific, Singapore, 2000. Biophysics of the Cochlea: From Molecules to Models. Edited by A.W. Gummer, E. Dalhoff, M. Nowotny, and M.P. Scherer. World Scientific, Singapore, 2002.

IX

This conference was supported by a generous grant from the National Institutes of Health National Institute on Deafness and Other Communication Disorders. It is also supported by the following organizations: Advanced Bionics Etymotic Research, Inc. The Oticon Foundation Phonak Hearing Systems Polytec, Inc. Starkey Hearing Research Center, Berkeley Tucker Davis Technologies

XI

'.->.:

:>

-± *

XII

s_
10

11

12

13

14

10

c

• O — ••-— V10

12

13

14

» Xx o

i-

11

D

r te^:-*-,. !"

Before cochleostomies After cochleostomies 340mOsm 300 mOsm washoul ___ V

Before cochleosfomies After coctileostomles 260mOsm 300 mOsm washoul

11

12

13

Frequency {kHz)

14

« 30

\ ^ - ^ • O —^ —V— 10

V

V

Before cacftrea$lomi«S O After cochleostomles,^ 340mOsm ^ * 300 mOsm washoul 11

12

13

14

Frequency (kHz)

Figure 2. Perilymph osmolarity modulates CAP and DPOAE thresholds. In one animal, CAP (A) and DPOAE (C) thresholds decreased with hypoosmotic perilymphatic perfusion and recovered with washout. In a different animal, the thresholds reversibly increased with hyperosmotic perilymphatic perfusion (B&D).

Frequency (kHz)

Figure 3. Mean changes in CAP (A) and DPOAE (B) thresholds measured after perfusion with hypoosmotic and hyperosmotic perilymph relative to 300 mOsm. Each data point is the average of measurements from five animals. The error bars represent the SEM.

Our mathematical model predicted a 4 dB increase in basilar membrane velocity with hypoosmotic perilymph and a 18 dB decrease in basilar membrane velocity with hyperosmotic perilymph (Fig. 5). The changes in basilar membrane velocity were concentrated at the characteristic frequency, as would be expected if the cochlear amplifier were predominantly affected. There was little change in the phase of basilar membrane velocity. These results are consistent with the shifts in CAP thresholds at the same resonant frequency (10-12 kHz).

46

4 Discussion Hyperosmotic perilymph inhibits and hypoosmotic perilymph potentiates cochlear function. These data support our hypothesis that perilymph osmolarity modulates the gain of the cochlear amplifier through changes in OHC electromotility. Importantly, these effects are qualitatively consistent with what would be expected based on experiments in isolated OHCs. By incorporating these data from isolated OHCs into our cochlear model, we found that our modeling and experimental results were quantitatively quite similar.

Figure 4. Example of the effect of perilymph osmolarity on the F2-F1 quadratic distortion product cochlear microphonic (CM). The CM within the shaded areas declines because of perfusion artifact and is meaningless. However, the CM immediately following the perfusion (arrows) demonstrates the change due to osmotic challenge. (A) Hypoosmotic perilymph increases the CM. (B) Hyperosmotic perilymph decreases the CM. Both normalize within 100-200 sec as the osmolarity normalizes.

•1'

12

/^V.

0.1 8 10 12 14 16x10 2f1-f2 frequency (Hz)

D 251 u s -

10 12 14 16x10" 2f1-f2 frequency (Hz)

12 16 Frequency (Hz)

Figure 2. Magnitude (A) and phase (B) of stapes vibration at frequency of fl (squares) and 2fl-f2 (triangles), the roundtrip delay of the emission (C), and the relationship between the roundtrip and forward delays (D). Slopes of the phase curves (B) show a delay time of 366 u,s for 2fl-f2 and 210 us for fl. The slope of the phase curve in Panel C shows 156 us roundtrip delay of the emission in the cochlea. The forward delay at 17 kHz (251 us) is significantly greater than the round trip delay (156 um).

20x10

4 Discussion The backward-traveling-wave theory was developed by Kemp in 1986 [5] mainly based on the fact that the cochlea-generated sound can be measured in the ear canal [1] and a mathematical demonstration that the cochlear travelling wave can travel in

83

both directions [6]. This theory has been overwhelmingly accepted and extensively studied Since 1986 [3, 8-10]. Cochlear fluid compression-wave theory was developed from a sensory outerhair-cell swelling model described by Wilson [11], in which hair cell volume changes displace the stapes footplate and result in the emission. The cochlear fluid compression theory was further developed by Narayan, et al. and Avan et al. [12, 13] by measuring BM vibration and the pressure in the cochlea. In a recent study, Ren [14] measured spatial patterns of the BM vibration at emission frequency and found a normal forward travelling wave and no sign of a backward travelling wave. This finding indicates that the cochlea emits sounds through its fluid as compression wave. The cochlear fluid compression theory was systematically reviewed by Ruggero recently [15]. f2/f1 ratio 1.4

1.6

A

^ 8

B6 £4

30

(radians)

Apical site — ~ ~ J J

m/s)

f2/f1 ratio

1.2

^

Basal site

Apical site —-"^sw^fe 0

4 8 12 16x10 2f1-f2 frequency (Hz)

1.2

%B ^^fen^

| .

2

1.4

O

1.6

14

^*^£**±J3£

Figure 3. Magnitude (A) and phase (B) of BM vibration at frequency 2flf2 at two longitudinal locations basal to the f2 site. The phase-decrease rate for the apical site is greater than that for the basal site. The slope of the phase difference indicates a delay of 31 us.

4 8 12 16x10 2f1-f2 frequency (Hz)

However, the cochlear-fluid compression-wave mechanism cannot account for reports that the roundtrip delay of the emission is approximately two times as great as the forward delay. Since this finding is based on the acoustical measurement in the ear canal, the external- and middle-ear delays have unavoidably contaminated the roundtrip delay measurement. Thus, the group delays of the cubic DPOAE was measured in the ear canal, at the stapes, and on the BM at £2 location in this study. It was found that the emission delay measured in the external ear canal (Fig. IB) is significantly greater than the forward propagation delay (Fig. 2 D), which somewhat agrees with the previous findings that the roundtrip delay of the emission is approximately twice as great as the forward delay. Significantly, the cochlear roundtrip delay of the emission measured at the stapes (Fig. 2 C) is smaller than the forward delay (Fig. 2 D). This result indicates that the emission is likely generated at a cochlear location basal to f2 site, and the backward propagation delay is extremely small. This result supports the cochlear-fluid-compression-wave model and not the backward-travelling-wave theory. Phase data of BM vibration at two different longitudinal locations (Fig. 3 B) demonstrate that the vibration at emission frequency arrives at the basal location earlier than the apical location, indicating a forward travelling wave.

84

Acknowledgments We thank E.V. Porsov for writing software, and S. Matthews for technical and editorial help. Supported by the NIH-NIDCD, and the National Center for Rehabilitative Auditory Research (NCRAR), Portland Veteran's Administration Medical Center. References 1. Kemp, D.T., 1978. Stimulated acoustic emissions from within the human auditory system. J Acoust Soc Am. 64(5): 1386-91. 2. Kimberley, B.P., Brown, D.K., Eggermont, J.J., 1993. Measuring human cochlear traveling wave delay using distortion product emission phase responses. J Acoust Soc Am. 94(3 Pt 1): 1343-50. 3. Schoonhoven, R., Prijs, V.F., Schneider, S., 2001. DPOAE group delays versus electrophysiological measures of cochlear delay in normal human ears. J Acoust Soc Am. 109(4): 1503-12. 4. Ren, T., 2002. Longitudinal pattern of basilar membrane vibration in the sensitive cochlea. Proc Natl Acad Sci U S A . 99(26): 17101-6. 5. Kemp, D.T., 1986. Otoacoustic emissions, travelling waves and cochlear mechanisms. Hear Res. 22: 95-104. 6. de Boer, E., 1983. Wave reflection in passive and active cochlear models. Mechanics of Hearing, ed. E. de Boer and M.A. Viergever. The Hague: Martinus Nijhoff. 135-142. 7. von Bekesy, G., 1960. Experiments in Hearing. New York: McGraw-Hill. 8. Shera, C.A., Guinan, J.J. Jr., 1999. Evoked otoacoustic emissions arise by two fundamentally different mechanisms: a taxonomy for mammalian OAEs. J Acoust Soc Am. 105(2 Pt 1): 782-98. 9. Bowman, D.M., et al., 1998. Estimating cochlear filter response properties from distortion product otoacoustic emission (DPOAE) phase delay measurements in normal hearing human adults. Hear Res. 119(1-2): 14-26. 10. Knight, R.D. Kemp, D.T., 2001. Wave and place fixed DPOAE maps of the human ear. J Acoust Soc Am. 109(4): 1513-25. 11. Wilson, J.P., 1980. Model for cochlear echoes and tinnitus based on an observed electrical correlate. Hear Res. 2(3-4): 527-32. 12. Narayan, S.S., Recio, A., Ruggero, M.A., 1998. Cubic distortion products at the basilar membrane and in the ear canal of chinchillas, in Twenty-first Midwinter Research Meeting of ARO. Abstract 723. St. Petersburg Beach, Florida.

85 13. Avan, P., et al, 1998. Direct evidence of cubic difference tone propagation by intracochlear acoustic pressure measurements in the guinea-pig. Eur J Neurosci. 10(5): 1764-70. 14. Ren, T., 2004. Reverse propagation of sound in the gerbil cochlea. Nat Neurosci. 7(4): 333-4. 15. Ruggero, M.A., 2004. Comparison of group delays of 2fl-f2 distortion product otoacoustic emissions and cochlear travel times. 5(4): 143-147. Comments and Discussion Withnell: In measuring the 2fl-f2 OAE delay, it appears that you calculated the phase gradient of the response. The phase gradient is confounded by a mixing of mechanisms. Can you clarify how your measure of group delay is a valid measure of cochlear travel time? I was also unclear about your correction for stimulus delay for the OAE (so that you could reference it to the stapes) - did you reference the stimulus delay to the place of measurement i.e., the microphone in the ear canal? If not, why not (and could you explain what you did)? Answer: Although the 2fl-f2 OAE delay was calculated based on the phase gradient in this study, it was not used to measure cochlear travel time because it is a mixture of the external-, middle-, and inner ear delays. The cochlear round-trip delay of the 2fl-f2 was obtained by subtracting the fl delay measured at the stapes from the 2flf2 delay at the same location. Because the cochlear delay of the OAE was measured based on stapes vibration, there was no need to reference the stimulus delay to the microphone in the ear canal.

MEDIAL OLIVOCOCHLEAR EFFERENT EFFECTS ON BASILAR MEMBRANE RESPONSES TO SOUND

N.P. COOPER 1 AND J.J. GUINAN JR.2. ' MacKay Institute of Communication and Neuroscience., Keele University, Keele, Staffordshire, ST5 5BG, England E-mail: [email protected] Eaton Peabody Laboratory, Mass. Eye & Ear Infirmary, Boston, USA. E-mail: jjg@epl. meei. harvard, edu Sound-evoked responses of the basilar membrane are shown to be influenced by electrical stimulation of the medial olivocochlear efferent system. Both fast (T~50ms) and slow (x~10s) effects can be observed in the basal turn of the cochlea. Differences between the fast and slow effects imply that outer hair cells can influence basilar membrane motion in at least two ways. Differences between the effects observed on the basilar membrane and in the auditory nerve (as assayed using compound action potential recordings in the same cochleae) imply that outer hair cells influence more than just basilar membrane motion.

1 Introduction Medial olivocochlear (MOC) efferent neurones modulate the acoustic sensitivity of the cochlea via synaptic contacts with outer hair cells (OHCs) (for review see [1]). MOC-evoked inhibition of auditory nerve (AN) responses is accompanied by mechanical inhibition at the level of the basilar membrane (BM) [2-6]. It is not known exactly how much of the neural inhibition is mediated mechanically, however. The present study seeks to investigate this issue further. Specifically, we seek to verify (i) whether both the fast and slow effects of MOC stimulation on AN responses [7] have mechanical bases (as shown in [6]), and (ii) whether the fast effects on BM motion are sufficient to explain the AN inhibition [8] which is seen at both low and high sound pressure levels (as shown in [5]). 2 Methods Sound-evoked vibrations of the BM were recorded using a laser interferometer in deeply anaesthetised guinea-pigs and chinchillas (see [9] for details). Electrical stimulation of the MOC efferents was paired with acoustic stimulation of the ear in such a way that the fast and slow effects of the efferent stimulation could be distinguished readily (cf. Fig. 2). Efferent stimuli (100-300 ms long trains of 300 us-wide current pulses at intervals of 3.3-5 ms, presented once every 330-1500 ms) were delivered to the floor of the fourth ventricle using a bipolar electrode (see [8] for details). Ossicular vibration measurements confirmed that the

86

87 efferent shocks

300

Time (ms)

Figure 1. Efferent inhibition of BM responses to low-level CF tones. Experiment K3096 (GP, CF=18kHz, 30dBSPL CF tones presented for 600 ms every second. Responses averaged 450x and bandpass filtered from 14-22 kHz. Response phases analyzed over 2 ms windows).

effects of the electrical stimuli originated in the cochlea, as opposed to the middleear. Compound action potential (CAP) recordings were used to assess the the cochlea's acoustic sensitivity both with and without MOC efferent stimulation. 3 Results 3.1 Efferent stimulation has both fast and slow effects on basilar membrane responses to sound BM responses to characteristic frequency (CF) tones were inhibited over two distinct time-scales by efferent stimulation. Each burst of efferent shocks produced a fast effect that began within 5-10 ms of the first shock-pulse, as shown in Figure 1. The fast inhibition developed towards a steady-state with an intensity-dependent time constant of -30-100 ms. The BM recovered from the fast inhibition with a slightly shorter time constant (typically -30 ms), beginning within -10 ms of the last shock-pulse in each train (cf. Fig. 1). A second, slower form of inhibition became evident when intermittent efferent stimulation (shock-burst duty cycles of : The OCT system used a 1310nm (~95nm bandwidth) SLD from BWTEK (model BWC-SLD), coupled to a network of single-mode optical fibers. The chamber was vibrated at 16kHz and by ±1 nm 3 Models and Results 3.1 OCT Image of organ of Corti

Figure 1. The OCT image of organ of Corti. The white arrows show the locations where the vibration measurements, plotted in Figure 2, were made. The picture on the right shows the intensity profile along the z-direction slice where the vibration measurements were made. 3.2

The normalized vibration signal at 16 kHz. ,

| 1,. J ,,.

o

3, locally developed computer programs for image segmentation and 3-D surface triangulation. The software is available for free downloading [3]. For the

115

116 histological images, slide-to-slide alignment was done manually. For both data sets, structures of interest were outlined either manually or semi-automatically. The configuration and material properties for the new finite-element model are the same as those of our previous model for the cat [1]. The dimensions of the model were estimated from the new human 3-D reconstruction. 3 Models and Results Figs. 1 and 2 show 3-D reconstructions of the cat and human lenticular processes, respectively. Fig. 3 shows a preliminary simulation result for the simplified model of the human lenticular process. More bending is apparent in the pedicle than in the joint, similar to our previous finding for the cat.

Fig. 1. Cat reconstruction

Fig. 2. Human reconstruction

Fig. 3. Human simulation results

4 Discussion Because the bony pedicle is very much thinner in one direction than in the other, it may provide hinge-like incudostapedial flexibility, thus controlling the degree of rocking of the stapes and affecting the nature of the input to the cochlea. Acknowledgements This work was supported by the Canadian Institutes of Health Research, the Natural Sciences and Engineering Research Council (Canada), and the Fonds de recherche en sante du Quebec. References 1. Funnell W.R.J., Siah T.H., McKee M.D., Daniel S.J., Decraemer W.F., 2005. On the coupling between the incus and the stapes in the cat. JARO 6, 9-18. 2. Alsabah B., Liu H., Funnell W.R.J., Daniel S.J., Zeitouni A.J., Rappaport, J.M., 2005. Secrets of the lenticular process and incudostapedial joint. Ann. Mtg. Can. Soc. of Otolaryngol. Head & Neck Surgery, St. John's, Newfoundland. 3. Funnell, W.R.J., 2005: AudiLab software. http://audilab.bmed.mcgill.ca/~funnell/AudiLab/sw/

NOVEL OTOACOUSTIC BASELINE MEASUREMENT OF TWO-TONE SUPPRESSION BEHAVIOUR FROM HUMAN EAR-CANAL PRESSURE

E. L. LE PAGE AND N. M. MURRAY OAEricle Laboratory, P.O. Box 6025, Narraweena, NSW2099 Australia E-mail: ericlepage@oaericle. com. au J. D. SEYMOUR National Acoustic Laboratories, 126 Greville Street, Chatswood, 2067 Australia E-mail: John, [email protected]. au We describe extension of otoacoustic emission technique intended to directly register change in cochlear mechanical baseline. A two tone probe/masker experiment is described in human subjects. Instead of just calculating distortion products from the averaged responses, low frequency variation in ear canal pressure is obtained and the pattern of positive and negative summating / adaptive behaviour versus frequency and level of the masker is reminiscent of two-tone suppression contours. The technique largely eliminates middle ear considerations.

1 Introduction Previous work has shown mechanical behaviour in the baseline position of the basilar membrane in guinea pig preparations analogous to, and measured simultaneously with summating potential behaviour measured at the round window, with similar polarity variations with frequencies above and below the best frequency of the place. Mechanical measurements by Flock more recently have observed substantial dc-shifts in the motion of the Hensen cells. Not all measureable position shifts are interpreted as OHC motile behaviour. Transient development of hydrops is now invoked to explain them. The question of whether dc-shifts occur in relation to outer hair cell homeostasis remains. Quadratic distortion products undergo baseline shifts and these have been interpreted as operating point shifts in OHC potentials by Salt and colleagues. Evoked otoacoustic emissions are an important window into cochlear mechanical behaviour and their human characteristics have been explored extensively in terms of distortion products, transient responses and stimulus frequency emissions. Mostly, emissions contain considerable noise, particularly at low frequencies. The working hypothesis here is that much of this measurement noise is indeed due to adaptive OHC response, hydropic response, or both. Significant external noise exists as cardiac pressure pulse in the ear canal. We have investigated whether cochlear summating responses are salvageable by using signal averaging of the ear canal pressure and looking for differential changes and computing linear regressions on each of the segments defined by onsets and offsets.

117

118

2 Methods and results A standard DPOAE probe is sealed in the ear canal. A two-tone masking paradigm is used, e.g. a contant 25 ms probe tone of 3 kHz at 70 dB SPL is repeated at 50ms intervals. A masker tone of 7ms duration is added 9ms after the start of the probe tone. Both bursts employ 1ms rise/fall times. The masker is varied in frequency and level (Fig.l). Each digitally-generated two-tone pair is repeated phase reversed, and the sum and difference computed. The whole sequence is repeated ten times, taking 2 minutes, and the 10 responses averaged to eliminate external noise. Baseline pressure changes are here determined from the rate of the the difference component (Pa/s). For sound levels above the probe tone level, and for an increasingly wide frequency range with higher level, masker onset produces condensation adaptive response; offset produces rarefaction. This is reproducible within each subject, but varies across subjects.

Transition: MASKER ONSET

i 2= 1 0.25 Masker frequency (octaves from probe)

Figure 1. Level and frequency dependence of ear canal baseline pressure with two-tone masking experiment in one human subject. Probe is fixed (centre) while the masker is varied above and below probe by H oct in 1 /12 oct steps. The z-axis dimension is positive or negative rates of summation (baseline dc-shift Pa/s). Mid-gray is baseline invariance i.e. constant mean pressure. Light regions (see masker onset) indicate condensation, dark regions (particularly with offset) is rarefaction shift.

3 Discussion The technique benefits from various measures for noise reduction, particularly the differencing between the pairs which are unlikely to differentially cause stapedius reflex. These responses are not emissions in the audio-frequency sense, but suggest electro-mechanical adaptation in the cochlea at low frequencies likely for a long length of spatial integration. These results add support to previous demonstration "dc-shifts" in direct mechanical measurements. Most intriguing is the suggestion that the contours may indicate a dc-bias origin for two-tone masking effects. References and poster download: www.oaericle.com.au

IS THE SCALA VESTIBULI PRESSURE INFLUENCED BY NON-PISTON LIKE STAPES MOTION COMPONENTS? AN EXPERIMENTAL APPROACH W.F. DECRAEMER University ofantwerp,171Groenenborgerlaan, B-2020 Antwerpen, E-mail: wim. decraemer@. ua. ac. be

.Belgium

S.M. KHANNA, O. DE LA ROCHEFOUCAULD, W. DONG, E.S. OLSON Columbia University, 650 West 168th Street, NY 10032 ,New York, USA E-mail: [email protected] The mode of vibration of the stapes is predommantly piston-like but at higher frequencies, rotations about the long and short footplate axis are also observed. An experiment was performed to verify whether the non-piston components influence the pressure produced in the cochlea. First the pressure in the scala vestibuli behind the footplate was measured using a micro-pressure sensor while a microphone recorded the pressure produced by the sound source in the ear canal. Then the motion of the stapes was measured under different angles and all 3D stapes motion components were calculated. Piston motion and tilt of the footplate could thus be correlated with vestibular pressure in the same ear. With the present experimental data we can also directly calculate individual cochlear input impedances and find the width of the transmission band and the time delay in the middle ear.

1 Introduction We have shown (e.g. Decraemer and Khanna 2003a) that the mode of vibration of the stapes is predominantly piston-like but that at higher frequencies rotations about the long and short footplate axis are also observed. Because the footplate motion produces the pressure wave in the cochlea, we can ask whether the non-piston components influence the pressure produced in the cochlea. To answer this we have measured the 3-D vibration velocity of the stapes along with the scala vestibuli pressure and ear canal pressure in the adult gerbil. 2 Methods and Results Young gerbils with healthy ears were used for this study. The animals were anaesthetized, the external ear canal was cut short and a small plastic tube was cemented in place to affix the sound source. The middle ear cavity was opened and the pressure in the scala vestibuli at a point closely behind the footplate was measured using a micro-pressure sensor (Olson, 1998) while a probe tube microphone simultaneously recorded the pressure produced by the sound source in the earcanal. The motion of the stapes was measured under different viewing angles with a heterodyne interferometer. Assuming rigid body behaviour the 3-D components were calculated (Decraemer and Khanna, 2003a). Using a 3-D model

119

120

of the stapes (based on a microCT scan of the experimental ear (Decraemer et al, 2003b)) the coordinate transform that puts the stapes in an intrinsic reference system was determined so that the piston-like motion and the tilt of the footplate are obtained as the velocity component along the y-axis and rotations about the x and zaxes (Fig.l). The motion components can now be correlated with the fine structure of the scala vestibuli pressure in the same animal.

— omega (10 rad/sperPa) -omega (102 rad/s per Pa)

Fig. 1 shows the SV re EC pressure gain and the 3 motion components that can produce diplacement along the piston axis of the stapes (these 3 curves also normalized to EC pressure). In some frequency regions the pressure gain is smoother than the piston motion component; in other regions they are both smooth, and similar.

phase omega -1000

0.5

1.5 2 2.5 frequency in Hz

3.5

4 x10 4

References 1. Decraemer, W.F., Dirckx, J.J.J., Funnell, W.R.J., 2003, Three-dimensional modeling of the middle-ear ossicular chain using a commercial high-resolution xray CT scanner, J. Assoc. Res. Otolaryngology, 4,250-263. 2. Decraemer, W.F., Khanna, S.M., 2003, Measurement, visualization and quantitative analysis of complete three-dimensional kinematical data sets of human and cat middle ear, Proceedings of the Middle ear mechanics in research and otology, Matsuyama, Japan, 3-10. 3. Olson, E. S., 1998, Observing middle and inner ear mechanics with novel intracochlear pressure sensors, J. Acoust. Soc. Am. 103 (6), 3445-3463.

BIOMECHANICS OF DOLPHIN HEARING: A COMPARISON OF MIDDLE AND INNER EAR STIFFNESS WITH OTHER MAMMALIAN SPECIES B. S. MILLER, S. 0 . NEWBURG, A. ZOSULS, AND D. C. MOUNTAIN Boston University Hearing Research Ctr, 44 Cummington Strt, Boston, MA 02215, USA E-mail: [email protected] D. R. KETTEN Woods Hole Oceangographic Institution, Mailstop 36, Woods Hole, MA 02543, E-mail: [email protected] The purpose of this study was to measure both middle ear stiffness and basilar membrane stiffness for the bottlenose dolphin (Tursiops truncatus) and compare these results with similar measures in other mammalian species. It was found that the point stiffness of the bottlenose dolphin basilar membrane has a gradient from 20 N/m near the base to 1.5 N/m near the apex and the middle ear has a stiffness of 1.37 x 106 N/m. These values are considerably higher than those reported for most terrestrial mammals, yet consistent with species specialized for high-frequency hearing.

1 Introduction Hearing is arguably a principal sense for odontocetes, or toothed whales, and because it takes place underwater, it is reasonable to assume that the odontocete auditory system is highly derived [1]. Understanding the specialized odontocete auditory system could provide insights into hearing in general and may be useful for comparative studies of hearing in other species. A common approach in modeling the auditory periphery is to start with an acoustic power flow model in which the external ear, middle ear, and cochlea are treated as a series of connected acoustical and mechanical systems. Outputs from each system provide inputs for the next. Key parameters in the power flow model are middle ear stiffness, which dominates the middle ear impedance at low frequencies, and basilar membrane volume compliance, which dominates cochlear impedance [2]. 2 Methods Detailed ear preparation and measurement methods for the middle ear stiffness are outlined in Miller et al. [3], Basilar membrane stiffness measurements were similar to those made by Olson and Mountain [4]. All measurements reported here were made using excised tympano-periotic bones of Tursiops truncatus. Samples were

121

122 obtained post-mortem from stranded animals in cooperation with normal stranding response procedures and under letters of agreement and research permits issued to Harvard University, Woods Hole Oceanographic Institution, and D.R. Ketten. Figure I

3 Results and Discussion In terrestrial mammals, correlation between middle ear acoustic stiffness and low frequency cutoff of hearing threshold can be expressed according to the function: / c = 1 . 0 2 x 10"6 k°-5i

(1)

• • • Mouse j7]

o. i

"i

'

To * "

Too

Characteristic Frequency (KHz)

where/, is the -20 dB cutoff frequency and k is the acoustic stiffness of the middle ear [3]. The acoustic stiffness of the bottlenose dolphin middle ear was measured to be 1.04xl017 Pa/m3. Using this value in Eq. 1 yields/I of approximately 7.56 KHz, which is close to value of 8 KHz obtained from inspection of the behavioral audiogram. Stiffness gradients along length of basilar membrane in bottlenose dolphin were measured for three ears from three different animals. Point stiffness was converted to volume compliance, following Naidu [5], using basilar membrane dimensions from Wever et al [6]. Fig. 1, a plot of volume compliance vs. characteristic frequency, shows bottlenose dolphin volume compliance to be similar to that of the mouse [7], a terrestrial species capable of high frequency hearing. Estimates of bottlenose dolphin characteristic frequency were based on the behavioral audiogram and cochlear anatomy [6] [8]. References 1. Ketten, D.R., 2000. Cetacean Ears. In: Au, W., Popper, A.S., Fay, R., (Eds.), Hearing by Whales and Dolphins. Springer-Verlag, New York. 2.

Rosowski, J.J., 1994. Outer and Middle Ears. In: Fay, R.R., Popper, A.N., (Eds.), Comparative Hearing: Mammals. Springer-Verlag, New York.

3.

Miller, B.S., Zosuls, A.L., Ketten, D.R., Mountain, D.C., 2005. In press. Middle ear stiffness of the bottlenose dolphin Tursiops truncatus. IEEE J Oceanic Eng

4.

Olson, E.S., Mountain, D.C., 1991. In vivo measurement of basilar membrane stiffness. J Acoust Soc Am 89, 1262-75.

5.

Naidu, R.C., 2001. Mechanical properties of the organ of corti and their significance in cochlear mechanics, Boston University.

123

6.

Wever, E.G., McCormick, J.G., Palin, J., Ridgway, S.H., 1971. Cochlea of the dolphin, Tursiops truncatus: the basilar membrane. Proc Natl Acad Sci U S A 68, 2708-11.

7.

Von Bekesy, G., 1960. Experiments in hearing McGraw-Hill, New York.

8.

Johnson, C.S., 1967. Sound detection thresholds in marine mammals. In: Tavolga, W., (Ed.), Marine Bioacoustics. Pergamon, New York. pp. 247260.

II. Hair Cells

AN EXPERIMENTAL PREPARATION OF THE MAMMALIAN COCHLEA THAT DISPLAYS COMPRESSIVE NONLINEARITY IN VITRO A. J. HUDSPETH AND DYLAN K. CHAN Laboratory of Sensory Neuroscience and Howard Hughes Medical Institute, The Rockefeller University, 1230 York Avenue, New York, NY 10021, USA E-mail: [email protected] To delineate the cellular mechanisms underlying the cochlear active process, we have developed an active in vitro preparation of the cochlea from the clawed jird. The amplitude and phase of the active mechanical and electrical responses of this preparation accord with those obtained in vivo. Analysis of the resonant properties of the exposed cochlear segment discloses two principal modes of oscillation: a second-order mode whose resonant frequency is set by the bulk volumetric stiffness of the segment and the fluid mass loading it, and a less prominent traveling-wave mode whose resonant frequency more closely matches the best frequency in vivo.

1 Introduction An active process plays a dominant role in shaping the responsiveness of the mammalian cochlea, especially for low-amplitude stimuli near the characteristic frequency for a particular cochlear location. Throughout the tetrapod vertebrates, this active process is characterized by four features: amplification of inputs, frequency selectivity, compressive nonlinearity, and spontaneous otoacoustic emission [1]. Two mechanisms have been advanced as candidates to explain the active process. Membrane-based electromotility is an attractive possibility, especially in light of its extraordinary frequency responsiveness [2]. Nonetheless, three arguments weigh against this mechanism at present. First, despite several ingenious proposals [3, 4], it remains possible that the operation of electromotility at high frequencies is limited by the hair cell's membrane time constant. Second, whereas the active process is ubiquitous in the ears of tetrapods, electromotility based on the protein prestin [5] appears to be confined to the outer hair cells of mammals. Even if electromotility underlies the mammalian active process, it follows another mechanism must be at work in non-mammalian tetrapods. Finally, despite the wealth of valuable results on the mechanism of electromotility, the process has not been demonstrated to account quantitatively for any of the four hallmark features of the active process. The second candidate for the active process is active hair-bundle motility. This phenomenon has been shown to demonstrate each of the four key features of the active process [6, 7]. The cellular mechanisms thought to underlie active hairbundle motility, Ca2+-dependent reclosure of transduction channels and myosinbased adaptation, occur in mammals [8, 9] as well as in the amphibians and reptiles

127

128 in which the phenomena were initially characterized. However, whether hair-bundle motility can operate at the high frequencies characteristic of mammalian audition, up to many tens of kilohertz, remains uncertain. To determine which of the candidate mechanisms underlies the active process in the mammalian cochlea, researchers require an experimental preparation that both displays the macroscopic signatures of the active process and is amenable to interventions that test the roles of electromotility and hair-bundle motility. The present publication describes such a preparation and provides additional features of its operation not included in the initial description [10]. 2 Methods The common or clawed jird, Meriones unguiculatus, is a burrowing rodent found in desert and steppe habitats in Mongolia and adjacent portions of China and Russia. As a member of the murine Subfamily Gerbillinae, this animal is sometimes termed a "gerbil." The anatomical accessibility of the jird's cochlea, which is partially exposed in a large bulla, commends the species for investigations such as ours. Segments of the jird's cochlear partition were isolated and prepared as described [10]. The acoustic properties of the experimental chamber were calibrated with a pressure transducer (8507C-1, Endevco), and cochlear microphonic responses were recorded with extracellular silver-silver chloride electrodes. The mechanical responses of the in 100 vitro preparation were measured by laser Doppler velocimetry E c (501 OFV, Polytec) to detect vertical movement of the E tectorial membrane and by a photodiode projection system to I 10 a. assess radial hair-bundle v> movement of inner hair cells. T3 "5

3 Results The radial hair-bundle movement of an inner hair cell typically exhibits a compressive nonlinearity in response to lowlevel acoustic stimulation (Fig. 1), so the in vitro preparation retains the cochlear active process. To compare the hair-bundle responses to the

1 0 {AnDty [11] where Mis the number of mols, NA the Avogadro's number and D the diffusion constant (um2 s"1). The Monte Carlo algorithm can be exploited to approximate the Brownian motion of the individual molecules (random vjalk) with arbitrary boundary conditions. In the limit of N=l, the function NAC(x,y,z,At) can be interpret as the occurrence probability, after a time At, of a displacement of a single molecule from the origin to the point of coordinates (x,y,z), i.e. the product of the three independent probabilities Px, Py, Pz of a displacement along the axes x, y, z. These probability distributions are normalized Gaussians with variance a = yJ2Dkt. In our algorithm, molecular motion is not followed at the level of the actual Brownian motion, rather it is described at a much coarser level using N of the order of 10s particles and a time step At of the order of 10"5 s. Figure 1. Cell boundary construction (plasma membrane and nucleus). We assumed generalized cylindrical symmetry for the hair cells, whereby the symmetry axis is a smooth curve belonging to the focal plane. Starting from an image of the hair cell (A) we intended to simulate, we designed the contour of the plasma membrane in the focal plane and constructed a 3D model (B and C) of the membrane from the interpolated 2D contour (A). The interaction between the simulated particles and the cell boundaries was assumed to obey the solution of the unidimensional diffusion equation for a instantaneous point source in a infinite cylinder of infinitesimal thickness [11].

140 2.2

Chemical

reactions

2+

Ca binding reactions are a fundamental mechanism to maintain intracellular Ca 2+ concentration ([Ca 2+ ] ; ) at sub-uM levels. The reactions involving Ca 2+ , a pool of endogenous buffers (B) as well as one exogenous buffer (F, typically, a fluorescent dye), and the mass conservation law were simulated by the following two sets of partial differential equations:

^ ^ - O C a n m - O C a B ] dt (Eq.l) cfCaF] = C[Ca 2 + ],[F]-^ F F [CaF] dt

3[Ca2 dt

5[CaB] 5[CaF]_ dt dt 3[CaB]_ 9[B] dt dt d[CaF] _ 5[F] dt

(Eq.2)

dt

where k^ , k^ and k^ , k^ are, respectively, the binding and unbinding rate constants of Ca 2+ to B and F. Molar concentrations were mapped to number of particles by the use of a mapping factor $ = CVii/«v,i for each species i, which defines the relationship between the number »v,i of simulated particles of the z'-th specie counted within a given volume J 7 and the corresponding concentration Cv>; . Chemical reaction computations (Eqs. 1 and 2) were performed by subdividing the 3-D diffusion space in cubic voxels of side / (comprised between 200 nm and 500 nm) and using a time step Ax = 5-10"7 s. 2.3

Calcium influx

Under whole-cell voltage clamp conditions, hair cells of the frog semicircular canal, stimulated by depolarization, revealed Ca 2+ entry at selected sites (hotspot) located mostly in the lower (synaptic) half of the cell body [12 and 13]. Their mean estimated diameter dn01 is about 276 nm [14], which is very close to the spatial resolution, /, of our simulations. For this reason, we assumed the hotspots to be point sources whose time dependence is dictated by that of the underlying Ca 2+ current. To determine Ca 2+ influx, we fitted [15] experimental current traces to obtain, using the mapping factor %, the mean number «Ca2* (?) of Ca 2+ ions entered through a single hotspot at time t, nc^(t)=

round\

^

V ^FcX

, where Qc^{t) '

"HOT

is

J

the total charge carried by Ca 2+ into the cell, Fc = 9.6485x10 4 C mol"1 is the Faraday constant and « H OT the number of active hotspots present in the cell. The function roundQ was used throughout to approximate the result to the nearest integer number of particles.

141 2.4 Calcium extrusion and storage During the course of a typical Ca2+ transient, various pumps and exchangers remove Ca2+ from the cytoplasm. In hair cells, the hair bundles rely on mobile Ca2+ buffers, the plasma membrane Ca2+-ATPases (PMCAs) and the SERCA pumps of the endoplasmic reticulum to regulate Ca2+ levels [16]. Uptake of Ca2+ due to pumps can be modeled as an instantaneous function of the [Ca2+];, Ca2+

4

l

dt

,,

'

!>*],-

[Ca 2+ ]; + tf M "

[9, 10, 16 and 17]. The parameter y depends to the number of pumps and their maximal turnover rate, KM is their Michaelis constant and the exponent m equals one, for the PMCA pumps, and two for the SERCAs. 2.5 Converting particle counts to simulatedfluorescence signals An estimate of the [Ca2+]( change can be obtained by fluorescence experiments using single wavelength indicators [12, 13] such as Fluo3, Oregon Green 488 BAPTA-1 and many others. At a given wavelength of emission, the measured fluorescence signal F can be expressed by F=Sbnb+S/if (Eq.3), where nb is the number of molecules of dye buffered to Ca2+ and n/ is the number of free dye molecules [3]. In general, Sb and Sf depend of many parameters of the experimental setup. Suppose the dye to be in equilibrium with Ca2+, we can obtain the free Ca2+ concentration change by A[~Ca2+j = AF/F0=(F-F0)/F0

(Eq.4), where F0 is the

2+

mean basal fluorescence signal before Ca enters the cell [3]. Nevertheless, the equilibrium hypothesis underlying Eq.4 breaks down near active zones during Ca2+ influx. In order to compare simulation results to experimental data we defined a = SbISf to obtain, using Eq.3, the relationships: F = Sf(anb + tij-), F0 = Sj-(anbo + rij-0) (Eqs.5 and 6), where nM and np are, respectively, the number of dye molecules bound to Ca2+ and the initial number of free molecules at equilibrium (before Ca2+ enters the cell). In our simulations involving Oregon Green 488 BAPTA-1, we set a=5 (measured on our imaging setups). Defining A as the constant of proportionality between the number n of real molecules and the one N of simulated particles, we obtain, from Eqs.5 and 6, F = Sj-A(aNb + Nf) and F = SfA.(aNb0+Nf0). Leading to the final expression: ArCa 2+ l sAF/FQ= [aNb +Nf- aNb0 -jV/0]/(aj\r60

+ Nf0).

To include in the model the error on AF/F0 due to the poor axial resolution of wide field microscopy, we considered the relationship between the fluorescence intensity, Fz, in the image plane due to a point source and the source distance, z, from the focal plane (z = 0) . In particular, we estimated the ratio a>(z) = F/FZ=Q , by fitting the data of Hiraoka et al. [18] for the case of a 90 urn diameter illumination field.

142

To simulate the operating conditions of the CCD camera used to acquire the fluorescence images, wc integrated numerically the computed fluorescence signal over time intervals of 4.03 ms, corresponding to the actual CCD exposure time. Consecutive integration periods were separated by a delay of 0.1 ms to account for data transfer from the CCD image area to its storage area [19]. 3 Results and Discussion Figure 2. Setting initial conditions for the simulations. The hair cell examined in the following was 25 urn long. The location and the number of the active hotspots were estimated: I) from the experimental Ca"' current entering the cell, considering that each hotspot generated aboul a 45pA current [10 and 13] and, 2) from the pseudo-color movie of the ratio AF/F0 obtained by processing the fluorescence images captured during the experiment with a mean period of 4.03 ms (including 0.1 ms of data transfer), during 50 ms cell depolarization. The simulated Ca2* current (shown as smooth line) was derived by fitting the patch-clamp data and equally distributing Ca2" influx between the ten active hotspots.

Ca2-current fit

0 „. Ml

>

,„

4M

200 220 240 260

280 300

320

340

360 380

400

Time (ms)

For these experiments we used hair cells of the semicircular canals of the frog (crista ampullar is). We carried out several simulations involving different BAPTA total concentrations because we were interested in obtaining an estimate of the basal concentration of the endogenous native Ca2* buffers in hair cells. This is central to the comprehension of intracellular Ca2+ dynamics. The best agreement between experimental and simulated kinetics was obtained using 1.6 raM BAPTA as the equivalent (in the simulations) of the endogenous buffers. This value is the same obtained from experimental results in saccular hair cells [20]. Figure 3 shows how Monte Carlo (unlike PDE methods) correctly reproduces the intrinsic noise features of the AF/Fa signal. We also found that the overwhelming contribution to the speed of the recovery phase of the signal (over the one second time scale of these simulations) is due to the buffers, instead of to the calcium pumps in the plasma membrane and the ER. Note that the concentration of free calcium that reaches the apex of the cell is only about 70 nanomolar starting from a resting concentration of 50 nanomolar. In conclusion, this simulation code can be used as a versatile instrument. Several cellular phenomena involving diffusion, buffering, extrusion and release within cellular staictures can be accurately simulated with using our variant of the Monte Carlo algorithm with acceptable CPU time consumption.

143

Figure 3. Real and simulated hair cell Ca2* dynamics. We simulated about 150,000 particles reacting within voxels of side /=0.5 urn with computational steps of 0.5 us. (A) Fluorescence-ratio (AF/Ft,) pseudo-colour images of the simulated (left) and real cell (right) compared after about 100 ms from the onset of the Ca"' current (Figure 2) at the ten hotspots. The black circles superimposed on the two figures are the regions of interest (ROls) where AF/F0 was measured (panel B), placed approximately in zones corresponding to the location of two selected hotspots. (B) Comparison between virtual (black line) and experimental (red line) fluorescence-ratio AF/F0 from the ROls in A. (C) The mass action law. which predicts proportionality between the signal A/-"//'",, and the free calcium concentration change, brakes down because of the local non equilibrium of the system. To make the point we analyzed pseudo-line scan plots obtained by plotting the lime course of the relevant signal at each pixel along the line shown superimposed on the cell plotted with the white hotspots (Panel D).

Acknowledgements We thank C. D. Ciubotaru (Venetian Institute of Molecular Medicine, Padua, Italy) for help with computer programming and image processing and S. Bastianello (idem) for helpful comments.

144 References 1. Issa, N.P., Hudspeth, A.J., 1994. Clustering of Ca2+ channels and Ca2+activated K+ channels at fluorescently labeled presynaptic active zones of hair cells. Proc Natl Acad Sci U S A 91(16): 7578-82. 2. Tucker, T., Fettiplace, R., 1995. Confocal imaging of calcium microdomains and calcium extrusion in turtle hair cells. Neuron 15(6): 1323-35. 3. Grynkiewicz, G., Poenie, M., et al., 1985. A new generation of Ca2+ indicators with greatly improved fluorescence properties. J Biol Chem 260(6): 3440-50. 4. Saxton, M.J., 1994. Anomalous diffusion due to obstacles: a Monte Carlo study. Biophys J 66(2 Pt 1): 394-401. 5. Saxton, M.J., 1996. Anomalous diffusion due to binding: a Monte Carlo study. Biophys J 70(3): 1250-62. 6. Kruk, P.J., Korn, H., et al., 1997. The effects of geometrical parameters on synaptic transmission: a Monte Carlo simulation study. Biophys J 73(6): 2874-90. 7. Gil, A., Segura, J., et al., 2000. Monte carlo simulation of 3-D buffered Ca2+ diffusion in neuroendocrine cells. Biophys J 78(1): 13-33. 8. Bennett, M.R., Farnell, L., et al., 2000. The probability of quantal secretion near a single calcium channel of an active zone. Biophys J 78(5): 2201-21. 9. Lumpkin, E.A., Hudspeth, A.J., 1998. Regulation of free Ca2+ concentration in hair-cell stereocilia. JNeurosci 18(16): 6300-18. 10. Wu, Y.C., Tucker, T., et al., 1996. A theoretical study of calcium microdomains in turtle hair cells. Biophys J 71(5): 2256-75. 11. Crank, J., (1975). The Mathematics of Diffusion. London, Oxford University ' Press. 12. Lelli, A., Perin, P., et al., 2003. Presynaptic calcium stores modulate afferent release in vestibular hair cells. J Neurosci 23(17): 6894-903. 13. Rispoli, G., Martini, M., et al., 2001. Dynamics of intracellular calcium in hair cells isolated from the semicircular canal of the frog. Cell Calcium 30(2): 131-40. 14. Roberts, W.M., Jacobs, R.A. , et al., 1990. Colocalization of ion channels involved in frequency selectivity and synaptic transmission at presynaptic active zones of hair cells. J Neurosci 10(11): 3664-84. 15. Rispoli, G., Martini, M., et al., 2000. Ca2+-dependent kinetics of hair cell Ca2+ currents resolved with the use of cesium BAPTA. Neuroreport 11(12): 2769-74. 16. Dumont, R.A., Lins, U., et al., 2001. Plasma membrane Ca2+-ATPase isoform 2a is the PMCA of hair bundles. J Neurosci 21(14): 5066-78. 17. Goldbeter, A., Dupont, G., et al., 1990. Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation. Proc Natl Acad Sci U S A 87(4): 1461-5.

145 18. Hiraoka, Y., Sedat, J.W., et al., 1990. Determination of three-dimensional imaging properties of a light microscope system. Partial confocal behavior in epifluorescence microscopy. Biophys J 57(2): 325-33. 19. Mammano, F, Canepari, M, Capello, G, Ijaduola, RB, Cunei, A, Ying, L, Fratnik, F, Colavita, A, 1999. An optical recording system based on a fast CCD sensor for biological imaging. Cell Calcium, 25(2): 115-123. 20. Roberts, W.M., 1993. Spatial calcium buffering in saccular hair cells. Nature 363(6424): 74-6.

E L E C T R O - M E C H A N I C A L W A V E S IN ISOLATED OUTER HAIR CELL

S. CLIFFORD, W.E. BROWNELL* AND R.D. RABBITT Dept. ofBioengineering, Univ. Utah, Salt Lake City, UT, USA E-mail: [email protected] *Bobby R. Alford Department Otorhinolaryngology and Communicative Sciences, Baylor College of Medicine, Houston, TX, USA E-mail: [email protected] Recent in vitro and in vivo data have drawn attention to the presence of high-frequency electro-mechanical resonances in the electrically evoked response of the cochlear partition and analogous resonances in isolated cochlear outer hair cells (OHCs). Resonances in isolated OHCs are similar to those present in damped piezoelectric structures and therefore it has been suggested that the behavior may result from the interplay of electro-mechanical potential energy and mechanical kinetic energy. In OHCs, the total potential energy includes both mechanical and electrical terms associated with the lateral wall while the kinetic energy accounts for the inertia of the moving fluids and tissues entrained by the moving plasma membrane. We applied first principles of physics to derive a model of OHC electromechanics consisting of an electrical cable equation directly coupled to a mechanical wave equation. The model accounts for the voltage-dependent capacitance observed in OHCs by means of a nonlinear piezoelectric coefficient. The model predicts the presence of electromechanical traveling waves that transmit power along the axis of the cell and underlie highfrequency resonance. Findings suggest that the subsurface cisterna (SCC) directs current from the transduction channels to the lateral wall and slows the phase velocity of the traveling wave. Results argue against the common assumption of space-clamp in OHCs under physiological or patch clamp conditions. We supplemented the traveling wave model with an empirical description of transduction current adaptation. Results indicate that the so-called RC paradox isn't paradoxical at all; rather the capacitance of the OHC may work in concert with transduction current adaptation and electro-mechanical wave propagation to achieve a relatively flat frequency response.

1 Introduction Current theories concerned with the sensitivity and frequency selectivity of mammalian hearing involve OHCs functioning as active amplifiers [1], boosting mechanical input to the inner hair cells. Both active hair bundle motion [2] and somatic electromotility [3, 1] are involved The mechanism somatic force production, while not completely understood, is not directly dependent upon ATP [4] and is in part, due to the outer hair cells (OHCs) highly specialized trilaminate lateral wall. It has been speculated that OHC somatic force production requires the cells to maintain cycle-by-cycle membrane potential modulations up very high frequencies well above the whole-cell membrane time constant [5]. One would expect the OHC membrane capacitance to short circuit the cell at high frequencies and prevent voltage driven displacement from occurring—this is known as the RC paradox [6]. Piezoelectric models of the OHC lateral wall are among the numerous attempts that have been made to address the RC paradox [7-14]. Piezoelectric models predict

146

147 experimental results such as whole-cell piezoelectric resonance exhibited by OHC [15] at high frequencies [16-20]. In addition, recent piezoelectric models agree with the relatively flat frequency response generated by cells upon low frequency stimulation in the pipette micro-chamber configuration [21]. OHC electromechanical behavior is consistent with thermodynamic Maxwell reciprocity required of piezoelectric materials [22, 23]. It is also useful to note that this remarkable piezoelectric behavior of OHCs is closely linked to the expression of the membrane-bound protein prestin [24-26]. It has been shown that isolated OHCs exhibit high-frequency electrical resonances as predicted by the piezoelectric models [20]. Resonances in piezoelectric materials arise due to the interaction between mechanical potential and electrical potential energy as well as kinetic energy. These piezoelectric resonances have standing modes of vibration that are established by constructive interference of waves traveling in one direction with waves traveling in the opposite direction [27, 28]. This connection between resonance, wave propagation and the presence of piezoelectric-like resonances in OHCs led us to develop the piezoelectric traveling wave theory of OHC somatic motility. Results suggest three factors that may be essential OHC somatic motility for high-frequency hair bundle motion: 1) an effective RC corner that shifts up with increasing frequency, 2) trasduction current adaptation that increases current with frequency and, 3) electro-mechancial wave propagation along the lateral wall. 2 Methods 2.1 OHC Traveling wave equations An axisymmetric model of the OHC was derived from first principles by treating the lateral wall as a piezoelectric material with constitutive behavior described by Tiersten [27]. A conductance tensor was added to the standard piezoelectric theory to account for membane conductance, and a Boltzmann function to account for strain-dependent saturation of the piezoelectric coefficient and the assocaited OHC voltage dependent capacitance [9, 29, 30]. Under the assumption of axisymmetric deformations, homogeneity, locally constant intracellular volume (for each dx slice of the cell conservation of linear momentum along the axis of the hair cell gives d2u j d2u dV du ni —2T = c —2r - a y— ' *- > dt dx dx dt where x is the axial position along the cell, t is time, u(x,t) is the local axial displacement, and c is the mechanical speed (in the absence of an electric field) along the axis of the cell . The parameter a is proportional to the piezoelectric coefficient, and y is the effective damping coefficient resulting from interaction with both the fluid inside outside the cell. Based on large OHCs from the apical turn of the guinea pig, we estimate c~2.9 m/s, a~88 m2/v-s2, and /-4.5e3 s"1 (at 1

148 kHz). Note if the voltage V is constant or the piezoelectric coefficient a is zero, then Eq. 1 reduces to the classical wave equation. Spatial variation of the membrane potential Fwas modeled using a distributed approach similar to Halter et al. [31]. In this model, it is assumed that current flows from the apical end of the cell along the narrow annular space between the subsurface cisterna (SSC) and the plasma membrane. This assumption has not been validated experimentally but, interestingly, results in an electro-mechanical wave speed consistent with resonance frequencies observed experimentally [19] and reproduces the relatively flat whole cell and force and displacement observed experimentally [21]. Part of the current entering the cell at the cilia is shunted to ground through the piezoelectric element in the lateral wall, while the remaining fraction reaches the base of the cell. From Kirchoff s current and voltage laws, the cable equation governing the membrane potential for the piezoelectric case is A.2—--T

V-/3

= -TJI >

(2)

dx dt dxdt where V(x,t) is the perturbation in the membrane potential, I(x,t) is the injected current (per unit length), A is the classical space constant appearing in the cable equation, x is the classical membrane time constant associated with the zero-strain condition , and 1/ 77 is the membrane conductance per unit length that appears in the cable equation [32]. The above equation reduces to the standard cable equation in the absence of strain (du/dx = 0 ), or when the piezoelectric coefficient is zero p=Q. For the highly resistive lateral wall of large OHCs from the apical turn of the guinea pig cochlea we estimate X = 1.8e-3 m, T = 2 s, /?= 0.28 V-s, and rj=2.65e6 Q. To model the relationship between hair-bundle motion and the transduction current, we used a very simple first-order model that accounts for some of the major properties of transduction current adaptation

*L + ±Ii = G*.

(3)

dt r, dt where / is the transduction current, T is the transduction current adaptation time constant, G, is the transduction current gain and x is the bundle displacement. For 1 kHz, we estimate T ~ 49e-6 s and G, ~ 0.012 Amp/m [33]. For sinusoidal stimuli below 1/z,, adaptation causes the transduction current to increase as the frequency of hair bundle motion is increased. For bundle frequencies higher than (1/T,) this simple model predicts relatively flat current gain and phase. 3 Results and Discussion There are three key features of the piezoelectric traveling wave equations that may have direct relevance to OHC function—particularly at high auditory frequencies where single-compartment models may fail. The first feature (cable equation) leads

149 us to question the concept of space-clamp and frequency-independent RC input properties of OHCs. An infinitely long cable, even in the absence of piezoelectricity (JJ=0), has a frequency dependent input capacitance, and a corner frequency that moves up with increasing frequency. Fig. 1 shows the voltage at x=0 of an infinite cable to an impulse of current injection at (applied at t=0, x=0 for P=0). Notice in the left panel that the voltage decays with multiple relaxation times showing that a single RC model is not appropriate to capture the frequency dependent input impedance. For the cable equation, the input capacitance and conductance both decrease with increasing frequency above (1/T) due to the fact that the length of membrane clamped by the injected current becomes shorter as the frequency is increased. Hence, it is never possible in a simple cable to exceed the corner frequency using current injection at a point (e.g. solid curve in Fig. IB is always above the dotted curve). We hypothesize that OHCs behave in a similar way and that the variation in OHC length along the cochlea optimizes the frequency dependent length constant of the cell with respect to the best place in the cochlea. 100-

B

S

^

10-

_^*^

1 0.1 0.01 - !"•"""'• 0.5

1.0

1.5

Time < t > %,}

"

"

T

S

n

»•'•»'''"'" 1

^

>™T-r-rrmr—T-r-rrc m)

o.i i w Input Frequency ( O) T M)

Fig. 1. Response of an infinite cable to impulse current injection at x=0. Left panel (A) shows nonexponential decay of the voltage at x=0 illustrating multiple relaxation times. Panel B illustrates the apparent corner frequency (1/TM) of the cable as a function of input frequency. Below the cable corner frequency, the cable is "space-clamped" for a finite length corresponding to the DC length constant. Above the cable corner frequency, loss through the membrane reduces the length of the clamped segment and thereby decreases the input capacitance. As a result the corner is never reached. Instead, relative to the input stimulus, the cable appears to become shorter as the frequency is increased.

Results in Fig. 1 indicate that the "effective" size of the cell felt at the transducer may decrease with frequency thus bypassing part of the problem of capacitive shunt by the membrane. The second feature (transduction current adaptation) further builds on this effect. Since the transduction current adapts (Fig. 2A) for maintained hair bundle displacements, the current magnitude will increase with bundle frequency (at least below 1/T,) and that this will also counteract membrane capacitance (Fig. 2B). This is illustrated in Fig. 2 for a simple first-order linear model of transduction current adaptation.

150

1 A

T

-I

0

1 2 Time (n»)

3

-

l

i

l

l

0.1

i

10

100

Frequency 0d\7)

Fig. 2. Panel A shows adaptation of a model outer hair cell transduction current (lower) in response to a step bundle displacement (above). This form of adaptation is a high-pass filter in the frequency domain (B, solid curves) that would be expected to counteract the roll-off in hair-cell receptor potential caused by membrane capacitance (B, dashed curves).

The third key feature of the model is the fact that the piezoelectricity introduces slow electro-mechanical traveling waves. This occurs because piezoelectricity couples mechanical inertia and stiffness to the electrical cable properties. Waves are predicted support cycle-by-cycle function of OHCs somatic electromotility at high auditory frequencies and quantitatively predict high frequency electro-mechanical resonances of isolated cells [19]. Fig. 3 shows voltage and displacement predicted by this model for three cases: A) sinusoidal voltage stimuli (mV) using a pipette microchamber B) sinusoidal current injection (pA) using a patch pipette attached to the base of the cell and C) sinusoidal hair bundle displacement (urn) to induce a modulated transduction current. It is important to note the significant differences in voltage and displacement patterns between these three stimulus types.

151 A. Pipette Microchamber-0.1 kHz

_ Qispiacenwni Ai for T = 0, it would be reasonable to assume t h a t AJJ > Ai still holds for T > 0 even if the compliance of the state I is greater than the state II. We will come back to this issue later. The probability Pu that the motor is in state II is given by,

_

exp[-/3AG] 1 + exp[—pAGJ

where f3 = 1 / ( A : B T ) , fcs being Boltzmann's constant and T is the temperature. The elastic modulus K of the lateral membrane depends on the state of the motor because the motor undergoes changes in its compliance. Let the elastic modulus be K / when PJJ = 0 and K// when Pu = 1. A simple dependence of the elastic moduli on the motor state Pu would be a linear combination, K = KI(1-PII)

+ KIIPII,

(5)

which is assumed in the calculation given below. To solve our equations, a number of additional assumptions are required. One such assumptions is volume constant constraint. Another is a relationship between motor stiffness and membrane stiffness. The former is ei + 2e2 = v, where the volume strain v is a constant, which is related to turgor pressure of the cell, t\ is axial strain, and £2 is circumferential strain. The latter condition can be. C7 = K71

(6)

Cn = K-\

(7)

158

3

E x a m p l e : U n i f o r m Stiffness-Changes

Here the simplest possible model for stiffness changes is examined for illustration. Let us assume that the membrane stiffness changes uniformly, keeping the ratios of stiffness in the two states are constant, i.e. K,

7K77.

(8)

W i t h this assumption the observed stiffness changes correspond to 7 \

0.3 (Fig.

! ) •

Another experimental observation to satisfy is that the voltage-dependence of cell displacement has a linear relationship with applied pressure [17]. However, the "uniform change" model predicts nonlinear shift even if the difference in the stiffness in the two motor states is smaller t h a n the difference required for the voltage dependence of the axial stiffness (Fig. 2). stiff ness(nN/m)

B displacement^ nm)

microchamberpotentialV)

2

-0.2

—

-0.1 0 0.1 0.2 microchamberpotentiaiy)

Figure 1. Effect of reducing stiffness of the compact state on voltage dependences of cell length (A) and the axial stiffness (B). From the top, the values for the stiffness parameter 7 is 1, 0.8, 0.6, 0.4, and 0.3. With decreasing 7, changes of both length and compliance take place at more negative potential. For larger 7, the stiffness is has a minimum, which is due to gating compliance. Load-free condition. Data points are adopted from [14] obtained with a configuration in which the basal end is sucked into a micro-chamber. The membrane potential is more negative than the micro-chamber potential by about 50 mV and changes less steep. Thus the value for q is adjusted to 0.7 e to fit the data. The elastic moduli used are 80% of the values in Table 1 in ref [11]. Other parameter values are not changed.

4

Size Reversal: T h e P a r a d o x

As we have seen earlier that the compact state must be significantly more compliant than the extended state to be able to explain the experimentally observed voltage-dependence of the axial stiffness. For relatively large membrane tension,

159 amplitude axialstrainbypressure 0.06 %05* 0.04 0.03

-0.06

-0.04

-0.02

axial pressure strain

Figure 2. Effect of turgor pressure on the amplitude and voltage-dependence of length changes by electromotility. Axial strain at —75 mV is used for an indicator for turgor pressure. The data points are taken from Fig. 5A in[17]. Volume strain 0.2 gives rise to axial strain —0.08, which approximately corresponds to 0.5 kPa. Values of parameters are in Table 1 except for the volume strain v. A: The amplitude. The prediction of the model (solid line) is not affected by the stiffness ratio 7. B: Voltage dependence of the motor. The membrane potential at which the cell has half-amplitude displacement (mid-point potential) is plotted against axial strain at the reference voltage. The values for 7 is from the top, 1, 0.825, 0.65, 0.475, and 0.3. The data points are taken from Fig. 5A in [17]. Shaded area indicates the range of membrane tension that may correspond to [14]

such a condition could make the membrane area of the compact state larger t h a n that of the extended state. In the following we examine if such a reversal takes place under our experimental conditions. For numerical evaluation, we assumed that the dimension of the motor is 100 nm 2 , corresponding to 10 nm particles, and that the elastic moduli of state II is given in Table 1 in ref [11]. At P = 0 . 5 kPa, the maximum turgor pressure in the experiment shown in Fig. 2, membrane tension stretches the area of state II by 1.8 nm 2 . For 7 = 0 . 3 , the increased area of state I by stretching is 6 nm 2 . Because the membrane area of state II is larger than state I by 3.7 nm 2 at null membrane tension, the state / becomes larger t h a n the state II when P = 0 . 5 kPa. Is such a reversal of the membrane area of the two states due to increased membrane tension physically reasonable? Consider a physical entity such as a protein which has two conformational states, compact and extended. It appears reasonable that the compact state is more compliant because the extended state would be harder to stretch further. However, how can a compact state become larger by being stretched and still remains more compliant? It would be reasonable to assume t h a t increased area strain leads to increased stiffness so that such reversal in size does not happen.

160 In the region where the model encounters a paradox due to applied pressure, it is not surprising that the model is unable to explain the result of pressure experiments [16,17]. The axial stress-strain experiments [14], however, do not impose such large membrane stress and does not lead to size reversal. 5

Discussion

The argument presented above is based on an assumption that changes in motor stiffness is uniform. Instead of assuming a simple relationship Eq. (8), it might be possible to seek stiffness changes that satisfy pressure experiments and axial stiffness experiments as constraints. However, it turns out that models that assumes orthotropic elasticity cannot satisfy all these constraints. This examination therefore indicates that the problem associated with "size paradox" is representative of the problem. Size reversal can be avoided by assuming t h a t the compact state / is softer only for small stress below, say Tc. The stiffness of the compact state must rise quickly with increased membrane tension to prevent size reversal. To be consistent with the pressure experiments, the difference in stiffness of the two motor states can be appreciable only for turgor pressure less than 0.1 kPa (Fig. 2), which is somewhat lower than reported values in vitro. Pressure changes due to membrane potential changes is up to 1 Pa and keeps membrane tension well below Tc. Then the axial stiffness could be a monotonic function of the membrane potential. It should also be noted that voltage-dependent cell motility at turgor pressure less t h a n 0.1 kPa is dominated by area changes. Stiffness changes, if large, cannot be significant in the free energy because membrane tension is low. Thus observed length changes and force generation of outer hair cells cannot be epiphenomena. There is yet another problem. Recall here that area difference has been determined by the motor's dependence on membrane tension over a relatively wide range above Tc. The area difference below Tc must be larger. However, there is no ways of determining the area difference of the motor states because the effect of membrane tension on the motor cannot be used to determine it. References 1. W. Brownell, C. Bader, D. Bertrand, and Y. Ribaupierre. Evoked mechanical responses of isolated outer hair cells. Science, 227:194-196, 1985. 2. B. Kachar, W. E. Brownell, R. Altschuler, and J. Fex. Electrokinetic shape changes of cochlear outer hair cells. Nature, 322:365-368, 1986. 3. J. F . Ashmore. A fast motile response in guinea-pig outer hair cells: the

161

4.

5.

6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16.

17. 18.

molecular basis of the cochlear amplifier. J. Physiol. (Lond.), 388:323-347, 1987. M. C. Liberman, J. Gao, D. Z. He, X. Wu, S. Jia, and J. Zuo. Prestin is required for electromotility of the outer hair cell and for the cochlear amplifier. Nature, 419:300-304, 2002. J. Zheng, W. Shen, D. Z.-Z. He, K. B. Long, L. D. Madison, and P. Dallos. Prestin is the motor protein of cochlear outer hair cells. Nature, 405:149155, 2000. J. F. Ashmore. Forward and reverse transduction in guinea-pig outer hair cells: the cellular basis of the cochlear amplifier. Neurosci. Res. Suppl., 12:S39-S50, 1990. J. Santos-Sacchi. Reversible inhibition of voltage-dependent outer hair cell motility and capacitance. J. Neurophysioi, 11:3096-3110, 1991. K. H. Iwasa. Effect of stress on the membrane capacitance of the auditory outer hair cell. Biophys. J., 65:492-498, 1993. X. X. Dong, M. Ospeck, and K. H. Iwasa. Piezoelectric reciprocal relationship of the membrane motor in the cochlear outer hair cell. Biophys. J., 82:1254-1259, 2002. K. H. Iwasa. A membrane model for the fast motility of the outer hair cell. J. Acoust. Soc. Am., 96:2216-2224, 1994. K. H. Iwasa. A two-state piezoelectric model for outer hair cell motility. Biophys. J., 81:2495-2506, 2001. J. Howard and A. J. Hudspeth. Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell. Neuron, 1:189-199, 1988. D. Z. Z. He and P. Dallos. Somatic stiffness of cochlear outer hair cells is voltage-dependent. Proc. Natl. Acad. Sci. USA, 96:8223-8228, 1999. D. Z. Z. He and P. Dallos. Properties of voltage-dependent somatic stiffness of cochlear outer hair cells. J. Assoc. Res. Otolaryngol., 1:64-81, 2000. K. H. Iwasa. Mechanisms for the fast motility of the outer hair cell from the cochlea. In E. R. Lewis, G. R. Long, R. F . Lyon, P. M. Narins, C. R. Steele, and E. Hecht-Poinar, editors, Diversity in Auditory Mechanics, pages 580-586. World Scientific, Singapore, 1997. M. Adachi and K. H. Iwasa. Electrically driven motor in the outer hair cell: Effect of a mechanical constraint. Proc. Natl. Acad. Sci. USA, 96:7244-7249, 1999. M. Adachi, M. Sugawara, and K. H. Iwasa. Effect of turgor pressure on outer hair cell motility. J. Acoust. Soc. Am., 108:2299-2306, 2000. N. Deo and K. Grosh. Two state model for outer hair cell stiffness and motility. Biophys. J., 86:3519-3528, 2004.

CHLORIDE AND THE OHC LATERAL MEMBRANE MOTOR

J. SANTOS-SACCHI, L. SONG, J.P. BAI, D. NAVARATNAM Otolaryngology, Neurobiology and Neurology, Yale University School of Medicine, 333 Cedar St, New Haven Ct. 06510, USA E-mail: [email protected] The OHC motor, likely comprised of prestin and other associated proteins intrinsic to the cell's lateral membrane, presents sensitivity to chloride ions. We have been studying the effects of intra and extracellular chloride on many of the biophysical traits of the OHC motor through evaluations of the cell's nonlinear capacitance. Here we review some of our recent observations, including interactions between the motor's tension dependence and CI flux through the lateral membrane. Additionally, we report on our efforts to estimate intracellular CI in intact OHCs, and on our estimates of the motor's chloride sensitivity in intact OHCs. These data are helping us to understand how the cochlea amplifier is managed in vivo. Finally, we illustrate how prestin can be used to identify the presence of the environmental toxin tributyltin that can leach from toxin-treated marine structures, including sonar domes.

1 Introduction Nonlinear amplification in the mammalian organ of Corti relies on anionic interactions with the outer hair cell (OHC) lateral membrane motor, a key component being the integral membrane protein, prestin [1-4]. This anion modulation has been shown for prestin directly, in transfected cells, as well as in native OHCs. Chloride, the most abundant physiological anion, probably plays the major role, though we have shown in the intact OHC that sulfate can also support motor activity as evidenced by robust nonlinear capacitance (NLC)[5], the electrical signature of prestin's voltage-dependence [6;7]. Here we report on the potential effects of intracellular and extracellular CI on OHC motor activity, and show that interactions of the motor and chloride, while substantial, cannot fully account for many of the motor's biophysical traits. 2 Methods OHCs were freshly isolated from the adult guinea pig organ of Corti by sequential enzymatic (dispase 0.5 mg/ml) and mechanical treatment in Ca-free medium. Currents from voltage-clamped cells were recorded using an Axon 200B amplifier, Digidata 1321A (Axon Inst., CA, USA) and the software program jClamp (Scisoft, CT). Solutions (see Figure legends for composition of pipette and extracellular solutions) were delivered to individual cells by Y-tube, during continuous whole bath perfusion with control extracellular solution consisting of NaCl (140mM), CaS0 4 (2 mM), MgS0 4 (1.2 mM) and Hepes (10 mM), pH 7.2, 300 mOsm. Nonlinear membrane capacitance was evaluated using a continuous high-resolution

162

163

(2.56 ms sampling) two-sine voltage stimulus protocol (10 mV peak at both 390.6 and 781.2 Hz), with subsequent FFT-based admittance analysis as fully described previously [8;9]. These high-frequency sinusoids were superimposed on voltage ramps. C-V data were fit with the first derivative of a two-state Boltzmann function and a constant representing the linear capacitance [10], ze

b = exp

•zeyVm-Vpkcm)

(1) kT kT(l + b) V kT J where Qmax is the maximum nonlinear charge moved, Vpkcm is voltage at peak capacitance or half maximal nonlinear charge transfer, Vm is membrane potential, Ciin is linear capacitance, z is apparent valence, e is electron charge, k is Boltzmann's constant, and T is absolute temperature. Cm = Q.

: + C«

3 Results 3.1 One-third ofOHC motor charge movement is insensitive to intracellular CI In order to study the effects of intracellular chloride on OHC motor function, we used the chloride ionophore, tributyltin (TBT) to assure absolute control of chloride on the inner aspect of the lateral membrane. Fig. 1 shows the dosei *, T (8)

E o.

3-

a

(5)

0.06

B > £

100 80 60 -

(12)

*!

*

e>

(6)

" ¥ " "T"

'-*-,,

20

I

Figure 1. OHC motor-Cl dose-response relationship in presence of TBT. Nonlinear charge density, Qsp (A) and Vpkcnl (B) as a function of intracellular sub-plasmalemmal CI concentrations are fitted with logistic Hill function (filled triangles, malate as substitute anion). Each point represents the average (+/se; numbers in parentheses) from recordings with TBT (1 (JVI) present. Qsp and VpkCm were measured after pipette washout reached steady state. Open triangles represent values from 5 mM CI intracellular/extracellular with gluconate as substitute anion.

°

"g. -20 > -40 -

[CI] i n / 0 U ,(mM)/wTBT

response function for chloride ion effects on motor charge movement and Vpkcm. While chloride has continuous, though saturating, effects on Vpkcm, effects of CI

164

E O

Vm ( mV)

Figure 2. Competing effects of Y-tube perfusion pressure and CI flux on NLC. Whole cell recording with 1 mM CI in pipette (malate substitute anion), 140 mM CI outside. Conditions: a, 140 mM perfusion pipette off and away from cell; b, perfusion turned on. Note slight shift of NLC to right; c, tip moved close to ^5o cell. Note increase in NLC but shift to right; d, switch to 1 mM CI perfusion. Note expected shift to right; e, switch back to 140 mM perfusion. Note shift back to left. All traces depict steady state conditions.

on Qsp are absent below about 1 mM CI. After substantiating with TBT that setting equal intra and extracellular levels of chloride affords absolute control of CI activity at the motor's inner aspect, we determined that the Cl-NLC IQ is about 7 mM [4], 3.2 Tension and chloride affects on the motor are independent The motor's nonlinear charge movement and VpicCm are sensitive to tension applied to the membrane that houses prestin [11-16]. An increase in membrane tension typically causes a shift in Vpkcm to the right and a decrease in peak NLC in wholecell voltage clamped OHCs [14], while an increase in CI causes a shift to the left and an increase in NLC [3]. The effects of tension are not driven by CI flux across the lateral membrane even though tension can gate GmetL [3]. Fig. 2 shows that the tension induced by single cell Y-tube perfusion (fluid flow) can overpower the effects of induced CI influx. That is, a rightward shift in Vpkcm occurs when a pipette perfusing 140 mM CI is placed close to the cell (condition c), even though the

0.0 -

-0.2 -

Vm ( mV )

Figure 3. Prestin transfection in CHO cells does not induce Gmc10 generations). 2.2 Electrophysiology Recording and stimulation of mouse utricle hair cells in intact epithelia were carried out using methods similar to those previously described [3]. Sensory epithelia were excised from P0-P7 mice in MEM (Invitrogen, Carlsbad, CA) supplemented with 10 mM HEPES, pH 7.4 (Sigma, St. Louis, MO). To remove the otolithic membrane, the tissue was bathed for 20 min in 0.1 mg/ml protease XXIV (Sigma) dissolved in MEM plus 10 mM HEPES pH 7.4. The tissue was mounted onto a glass coverslip and held flat by two glass fibers; the coverslip was mounted in an experimental chamber on a fixed-stage upright microscope (Axioskop FS; Zeiss, Oberkochen, Germany) and viewed with a 63x water-immersion objective with differential interference contrast optics.

171

B

2000

2000 1500

1500

cz 1000

1000

500

500

100

200

Time (ms)

10

20

Time (ms)

Figure 1. Transduction currents and time-dependent adaptive shift in C57BL/6 (control) and Y61GMyolc hair cells. A,B: transduction currents in response to mechanical displacements of -1000 to +2000 nm (increments of 200 nm) for C57BL/6 (A) or Y61G (B) mouse hair cells. Each current trace is averaged from 8 (C57BL/6; 210± 15 pA) or 13 (Y61G; 199 ± 19 pA) traces. C, D: inferred-shift analysis of positive adaptive shifts calculated from average traces in A and B. C and D are identical except for abscissa scale. C57BL/6 (black) shifts are slower than Y61G (gray) shifts.

Electrophysiological recordings were performed in an artificial perilymph solution that contained (in mM): 137 NaCl, 5.8 KC1, 10 HEPES, 0.7 NaH 2 P0 4 , 1.3 CaCl2, 0.9 MgCl2, and 5.6 D-glucose, vitamins and amino acids as in MEM (Invitrogen), pH 7.4 and 311 mOsm/kg. Recording electrodes were filled with (in mM): 135 KC1, 5 EGTA-KOH, 5 HEPES, 2.5 Na2ATP, 2.5 MgCl2, and 0.1 CaCl2; this solution was pH 7.4 and 284 mOsm/kg. Hair cells were stimulated by drawing the

172 kinocilium into a pipette filled with extracellular solution [3]; transduction currents were recorded as described [8]. Current records were averaged using Clampfit 8.2 (Axon Instruments) and analyzed using a Mathematica 5.1 program as described [8]. Total extent

2000

0

1000 2000 Displacement (nm)

300

Slow extent

Fast extent

Slow t

Fastt

Slow rate

Fast rate

I200 "§ 100 Of

0 1000 2000 z Z'~ DiiCtiiC^Srfrfi'^ 0 1000 2000 0 1000 2000 Displacement (nm) Displacement (nm) Figure 2. Dissection of properties of fast and slow adaptation in C57BL/6 (black points andfits)and Y61G (gray points and fits) hair cells using inferred-shift analysis. A-C: total (A), slow (B), and fast (C) extent of adaptation extrapolated to infinite time. D-E: time constants for slow (D) and fast (E) adaptation. Note stimulus-dependent increase in fast adaptation rate. F-G: rates of slow (F) and fast (G) adaptation. Note faster slow and fast adaptation in Y61G hair cells.

173 3 Results 3.1 Average transduction currents and inferred-shift analysis To better compare adaptation kinetics, we averaged transduction-current records from C57BL/6 or Y61G hair cells (Fig. 1A,B). By eye, Y61G currents appeared to adapt slightly faster, although the difference was relatively subtle. To both extract the adaptive shift quantitatively and to separate fast and slow adaptation, we subjected traces in A or B in response to positive bundle deflections to inferred-shift analysis [8, 9]. By deconvolving the current records with the highly nonlinear displacement-response relation, inferred-shift analysis allowed extraction of the shift of this relation with time. After this analysis, the faster adaptation seen in Y61G hair cells was much more apparent, particularly for large displacements at short times (Fig. 1C,D). 3.2 Separation of fast and slow slipping adaptation To measure the contributions of fast and slow adaptation to the inferred-shift traces of Fig. 1C, we fit the time-extent relations with double-exponential functions [8, 10]. This analysis yielded fast and slow extents and time constants (T); the extent divided by the extent yields the initial rate. These parameters are illustrated in Fig. 2. The data were fit as previously described [8]. 4 Discussion Averaging current records as we did here allows for a slightly different biasing of the control and Y61G datasets. In our previous work [8], we carried out the inferred-shift analysis on data from individual cells, then averaged the shift-time records. This latter approach weights all cells identically, as the resulting extenttime relations are independent of the size of the transduction current. In the present analysis, we selected for cells of large current amplitudes. Moreover, the averages will be weighted towards the cells with the largest transduction currents. Because these cells often have the fastest adaptation as well, they may indeed be more representative of endogenous hair cells than are cells with small transduction currents, which may have suffered physical and enzymatic trauma from the dissection. Thus the present analysis allows a different view of the properties of fast and slow adaptation from our previous work, although the fundamental conclusions remain the same [8]. These results revealed that Y61G mice have shortened time constants for both fast and slow adaptation, with little change in the extent of adaptation. The consequence of these changes was to increase the rates of both fast and slow adaptation, albeit over different displacement ranges. Accelerated slow adaptation in Y61G mice was prominent in intermediate displacement ranges (500-

174 1500 nm), while the rate of fast adaptation was larger for displacements above 1500 nm. The time constant for fast adaptation (ifast) in C57BL/6 cells remained at 10-12 ms for all displacements, while it decreased from ~12 ms to 10 centimorgans (potentially containing a significant number of genes) with a very large variance between animals. In addition, dominant 129 alleles unlinked to Myolc could also contribute. This consideration raises three points. First, even with backcrossing, proper controls for these experiments would be not only C57BL/6 mice, but also 129 mice. Although the C57BL/6 contribution is much larger, 129 genes easily could affect properties we are studying. Second, a better strategy for gene targeting is to maintain the mutation in a single strain, e.g., if the mutation is generated in 129 ES cells, cross the mutant chimera to 129 mice and maintain the mutation on that strain. Finally, the background strain issue is avoided altogether with a strategy like that used for our Y61G experiment where the phenotypic effect is generated within a single cell, such as happens when NMB-ADP inhibits Y61G Myolc. Each cell serves as its own control.

175 Acknowledgments This work was supported by grants R01 DC003279 to J.A. Mercer (P.G. Gillespie. and J.R. Holt, subcontract Pis) and ROl DC002368 to P.G. Gillespie. References 1. Eatock, R.A., 2000. Adaptation in hair cells. Annu. Rev. Neurosci. 23:285314. 2. Gillespie, P.G., Gillespie, S.K., Mercer, J.A., Shah, K., Shokat, K.M., 1999. Engineering of the myosin-ip nucleotide-binding pocket to create selective sensitivity to N(6)-modified ADP analogs. J. Biol. Chem. 274:31373-31381. 3. Holt, J.R., Gillespie, S.K., Provance, D.W., Shah, K., Shokat, K.M., Corey, D.P., Mercer, J.A., Gillespie, P.G., 2002. A chemical-genetic strategy implicates myosin-lc in adaptation by hair cells. Cell. 108:371-381. 4. Cheung, E.L., Corey, D.P., 2005. Ca2+ changes the force sensitivity of the hair-cell transduction channel. Biophys. J. in press. 5. Bozovic, D., Hudspeth, A.J., 2003. Hair-bundle movements elicited by transepithelial electrical stimulation of hair cells in the sacculus of the bullfrog. Proc. Natl. Acad. Sci. USA. 100:958-963. 6. Martin, P., Bozovic, D., Choe, Y., Hudspeth, A.J., 2003. Spontaneous oscillation by hair bundles of the bullfrog's sacculus. J. Neurosci. 23:45334548. 7. Kennedy, H.J., Evans, M.G., Crawford, A.C., Fettiplace, R. 2003. Fast adaptation of mechanoelectrical transducer channels in mammalian cochlear hair cells. Nat. Neurosci. 6:832-836. 8. Stauffer, E.A., Scarborough, J.D., Hirono, M., Miller, E.D., Shah, K., Mercer, J.A., Holt, J.R., Gillespie P.G., 2005. Fast adaptation in vestibular hair cells requires myosin-lc activity. Neuron. 47:541-553. 9. Shepherd, G.M.G., Corey, D.P., 1994. The extent of adaptation in bullfrog saccular hair cells. J. Neurosci. 14:6217-6229. 10. Hirono, M., Denis, C.S., Richardson, G.P., Gillespie, P.G., 2004. Hair cells require phosphatidylinositol 4,5-bisphosphate for mechanical transduction and adaptation. Neuron. 44:309-320. 11. Batters, C , Arthur, C.P., Lin, A., Porte,r J., Geeves, M.A., Milligan, R.A., Molloy, J.E., Coluccio, L.M., 2004. Myolc is designed for the adaptation response in the inner ear. EMBO J. 23:1433-1440. 12. Clark, R., Ansari, M.A., Dash, S., Geeves M.A., Coluccio, L.M., 2005. Loop 1 of transducer region in mammalian class I myosin, Myolb, modulates actin affinity, ATPase activity, and nucleotide access. J Biol Chem. 280:3093530942.

THE PIEZOELECTRIC OUTER HAIR CELL: BIDIRECTIONAL ENERGY CONVERSION IN MEMBRANES W.E. BROWNELL Baylor College of Medicine, Houston, TX 77030., USA E-mail: [email protected] Membranes show bidirectional energy conversion in that their mechanical strain and electrical polarization are coupled. Changes in transmembrane potential generate mechanical force and membrane deformation results in charge movement. The coefficients for the electromechanical transduction and the mechano-electrical transduction have the same magnitude, satisfying Maxwell reciprocity and suggesting a piezoelectric-like mechanism. Outer hair cell models that include its piezoelectric behavior indicate that charge movement occurs at frequencies that span the mammalian hearing range. Experiments have confirmed the modeling results, including the presence of resonances at high frequencies. Another set of experiments have measured electrically evoked pN forces in long (>10 um) cylinders of cellular membrane having radii 10 ms) and the other with shorter ( 3 6 9 12 18 ff y 3 tal P ost -Ns Da

3 Results Fig 1 shows the average specific compliance (error bar 1 s.e.m.) of isolated OHCs as a function of developmental age. Specific compliance increased by more than a factor of 2 (from 0.032 to 0.067 km/N/um of length) up to P9. Specific compliance then decreased between P9 and P12 (around the onset on hearing) to close to the P3 value (0.030 km/N/um). The average value of specific compliance did not change significantly in later development. For comparison, the specific compliance of adult guinea pig OHCs is also shown in Fig. 1 (data from [19]). Adult guinea pig OHCs are about 5 times stiffer than mature gerbil OHCs. We examined the potential contributions of the major components of the OHC lateral wall to the changes in specific compliance during development. Fluorescence intensity profiles were obtained from isolated gerbil OHCs. To reduce the effects of bleaching, we used fade-resistant fluorescent labels (Alexa 488 and Alexa 568) and a procedure in which cells were exposed to laser illumination only once and were otherwise kept away from ambient and ultraviolet light. At birth (P0), phalloidin labeled F-actin was particularly strong throughout the OHC LW (Fig. 2B), including the entire basolateral cellular membrane. The intensity of the label in the OHC LW decreased progressively during development such that in late development the intensity was on average about one-third of that observed at P0 (p < 0.001). In contrast, label for spectrin was observed mainly in the cuticular plate (CP) at P0. Label appeared to extend basalward during development such that the entire lateral wall was labeled by P9. The average intensity of the label was constant up to and including P9 (Fig. 2C). The intensity of the label increased substantially between P9 and P12, which suggested that a new round of sysnthesis of spectrin or incorporation into the LW had occurred. The intensity of spectrin label in the LW declined only slightly in the later stages of development. In contrast, label for prestin in the LW was observed in significant quantities only after P6 and reached a nearly-mature level at P12 (Fig. 2D). However, a small but significant increase in the intensity of prestin label was observed after PI2, which

190 suggests that some incorporation of new prestin occurs even in the late stages of development. A)

2©Q - i ^ * ^ 1502 z> 100 SO-

1" C)

200-

Hi

150

5fl

QDQ

f f T T

0 3 i

S « IS 1821 24

°* im-,Pm"a

250-1

fiS

0-

200 180

•"

I £• 100-

100-

so0 3 6 8 12151*2124

Post-Nafal Day

T'T'T'M' 0 3 6 9 12 IS 18 21 24

Post-Natal Day

Figure 2. Changes in synthesis of proteins in gerbil OHC lateral wall during post-natal development. A) Isolated OHC labeled for F-aetin showing the fluorescence intensity profile obtained at 50% of cell length. B) Average (+1 s.e.m.) peak fluorescence intensity of F-actin in the lateral wall at 50% of cell length as a function of post-natal day (** = different from P0, p < 0.01) C) Average (+1 s.e.m.) peak fluorescence intensity of spectrin as a function of post-natal day (** = different from P9, p < 0.01) (average of 25%, 50% and 75% of length) D) Average (+1 s.e.m.) peak fluorescence intensity of prestin at 50% of cell length as a function of postnatal day (** = different from P12, p < 0.01).

4 Discussion

If the CL is important for determining OHC mechanical properties, a detectable change in OHC mechanics should occur during CL formation. The striking increase in OHC specific compliance observed between P3 and P9 corresponds closely in time to the elaboration of spectrin in the OHC lateral wall (Fig. 3). It might have been expected that OHC stiffness would increase at the onset of hearing. However OHC deformability increased substantially. The function of this increase is not clear, but our anatomical studies offer an explanation. The incorporation of spectrin in the LW appears to have a significant impact on OHC mechanical properties. This is not surprising as spectrin filaments are thought to be significantly more compliant than F-actin [20]. The CL is the only cytoskeletal structure capable of modifying OHC mechanics during development. We did not observe any other actin or spectrin structures that underwent substantial changes during this time period. Likewise, although

191 microtubules develop during this period [21, 22], they are not connected in such a way as to confer structural rigidity. Other LW structures are also unlikely to mediate the observed changes in OHC mechanics. Weaver and Schweitzer [23] have described a steady increase in cisternae content after the onset of hearing. This increase would be expected to contribute extra stiffness to the LW at that time. The extent and development of the cisternae in earlier development are unknown. Prestin in the LW is also hypothesized to contribute stiffness to the OHC [13]. There is a rapid amplification of prestin expression in the OHC from P6 to P12. The insertion of prestin into the LW corresponds closely to the dramatic decrease in OHC specific compliance from P9 to PI2. This suggests that the large density of prestin in the lateral wall membrane significantly changes the stiffness of the membrane. In contrast, there is also a significant increase in the spectrin content of the CL between P9 and PI2. However, if our inferences from the early stages of development are correct, the further incorporation of spectrin would be expected to increase, not decrease, specific compliance. For effective transmission of force to the organ of Corti, the OHC must have sufficient axial stiffness to work against the load applied by the organ of Corti. A previous report showed that demembranated OHCs, consisting mainly of the CL, are readily deformable and have about one hundredth of the stiffness of intact OHCs [24]. The OHC LW therefore appears to act as a composite material with properties distinct from that of any of its individual components. Our data suggest that both prestin and the OHC CL significantly modify the mechanical properties of intact OHCs.

II

Figure 3. Comparison of developmental progression of specific compliance and the lateral wall proteins actin, spectrin, and prestin.

1* Developmental Age 0) results in an increase in Vz (i.e., 5VZ > 0), corresponding to a shortening of the cell. 2.3

Physics of the piezoelectric

effect

Warren Mason was the first to show t h a t as a piezoelectric crystal is compressed, the material's bound charge q moves proportionally to the length change 51, namely q ex. 61 [2]. In the same publication Mason provids a summary of his experimental results in terms of an electrical equivalent circuit. If one assumes that the OHC is piezoelectric, then the OHC model may be implemented as shown in Fig. 1, via two transformers. The two volume velocities Vz and Vr give rise to the two currents (charge flows) qz and qr which are integrated by the membrane capacitance Cm, resulting in to voltage vm(t) across the capacitor. Likewise, a change in voltage across the membrane causes a force on the embedded charge, giving rise to two independent strains in the membrane, resulting in a net pressure change (i.e., pr and pz). The transformer relations t h a t relate these efforts (p, v) and flows (q, V) are pz = (j)zVz,

pr = <j)rVr

<jz = (j)zVz,

qr =

(6)

(j)rVr.

Define compliances cz, cr and c shown in Fig. 1 as capacitors, as the reciprocal of stiffnesses (c = 1/fc), kz = 1/cz = (2e* - e)/RV kc = 1/cr EE (ec/2 - e)/RV k = 1/c = -e/RV.

(7)

Having defined the transformers in (6), one may proceed to write down the elastic circuit equations from the circuit diagram 'Vz-Vt' Vt qm

=

kz — k k 0.

(17)

e,ec

Vz=0

Also (2Gr + Gz)sV = 0.191 x 10" 3 sV.

yv =

(18)

vz=o Given (4) and (15), Vp = (2Gr - Gz)sVVt

= 0.329 x

l0^3sVVt,

(19)

where Vt is in Pascals, resulting in yp = 0.329 x 10^ 3 sV.

(20)

The product of Vp and Vt represents the Poisson coupled elastic energy. Define 7 = Gr/Gz. From Fig. 1 of [1], 7 = - 1 / 0 . 4 3 = - 2 . 3 2 6 , while from Fig. 2 of [1], 7 = Gr/Gz = —1.884. These two estimates come from different experiments and 6 different cells. An average of these two estimates gives 7 = —2.1. The parameter 7 may be interpreted as the reciprocal of the Poisson ratio of some presumed circumferential tubes around the the cell (like barrel hoops). If 7 is exactly 2, it would imply that the membrane enveloping the OHC conserves volume. (This might represent fluid and other structures trapped between the cisternae and the cell plasma membrane, for example.) The case of incompressible tubes, 7 = —2, is close to the average value of Iwasa and Chadwick (1992) data. Thus (jfr

7 = — « - 2 ± 40%. GZ From this point on we shall assume that 7 = —2.

(21)

200

From (15) — = -27 :

(22)

vz

For the conditions of the Iwasa and Chadwick (1992) experiment, combining (4) with (21) gives Vp = 5VZ. while (3) and (22) give V = 3VZ. 2.5 The in vivo cell At acoustic frequencies, or in the in vivo case when the cell is sealed, V = 0. From (3) Vr = Vz, leading to Vp = 2VZ. Assuming no axial load (Vz = 0), and a constant applied voltage (qm = 0), the ratio of Vr to Vz may be found from (5) 2e, e c /2-

Vz

(23) Kc

Combining (22) and (23) gives kz ~ —4:kc, or equivalently cz « — cr/A. Since both — Gz and Gr were found to be greater that zero (see (16) and (17)) it follows that ezec > e2 and that e > e c /2. Thus from (7), kc < 0. From (23), this is the same as saying that as the turgor pressure in increased, the cell becomes fatter and shorter.

rxr-

-9m(*)

qr~ qz

C™

um(i)

•

Vr ( * ) . +

n

Vr

^z

+ N2

M •+ Vr Cr(V~m)

-W,

Vz Vp,

+

cz{Vm)

(

)Vz(t)

c(Vm)

±J

-T>t

Figure 2. Final circuit diagram with turger pressure as the source. Since the net volume at acoustic frequencies must be zero, Vz = V r , and Vp = 2V z .

Figure 2 shows the configuration of the final curcuit with the membrane compliances shown as voltage dependent, the volume velocity constrained to be

201 zero, as required at acoustic frequencies, with the turger pressure shown as a battery, the acoustic power source of the cell. Since Vz = Vr, and Vp = 2VZ, using the circuit of Fig. 2 one may easily find the turgor pressure and evaluate the axial acoustic impedance of the cell and relate the nonlinear capacitance to the axial loading on the cell. From Eq. 9 p

kc

<prkz — r

4>Z+4>T

kz+kr

kz+kr

I Grr

Vz Vm

(24)

This leads to a very simple result. For the OHC to be nonlinear, either kz and or kr must be voltage dependent. Furthermore, this leads to a direct prediction about the voltage dependent nonlinear capacitance, and its relationship to the voltage dependent stiffness and displacement. 3

Conclusion

We have reformulated the OHC constitutive equations in terms of acoustic variables and summarized the electromechanical properties of the OHC with a piezoelectric circuit following Mason's classic model [2]. Future steps will to incorporate OHC NL capacitance along with voltage controlled stiffness results into this scheme. As these data are nonlinear our circuit will necessarily acquire nonlinear voltage-controlled circuit elements. It is our hope that the incorporation of voltage dependent values for ez(Vm), e c (V m ) and e(Vm) will be sufficient to represent all of the nonlinear response of the OHC. We would like to thank Robert Haber for discussions on the form of (1) and on the physical intrepretation of the axial to radial coupling. References 1. Iwasa, K. and Chadwick, R., 1992. Elasticity and active force generation of cochlear outer hair cells orientation. J. Acoust. Soc. Am 92, 3169-3173. 2. Mason, W.P., 1939. A dynamic measurement of the elastic, electric and piezoelectric constants of rochelle salt. Phys. Rev. 52, 775-789. 3. Spector,A., Brownell, W., and Popel, A., 2003. Effect of outer hair cell piezoelectricity on high-frequency receptor potentials. J. Acoust. Soc. Am. 90, 453-461.

A MODEL OF HIGH-FREQUENCY FORCE GENERATION IN THE CONSTRAINED COCHLEAR OUTER HAIR CELL ZHIJIE LIAO AND ALEKSANDER S. POPEL Johns Hopkins University, Baltimore, Maryland 21205 USA Email: zliao(a),bme. ihu. edu and apopel(a),bme. ihu. edu WILLIAM E. BROWNELL Baylor College of Medicine, Houston, Texas 77030 USA Email: brownell(a),bcm. tmc. edu ALEXANDER A. SPECTOR Johns Hopkins University, Baltimore, Maryland 21205 USA Email: aspector(a).bme.ihu.edu The cochlear outer hair cell (OHC) has a unique property of electromotility, which is critically important for the sensitivity and frequency selectivity during the mammalian hearing process. The underlying mechanism could be better understood by examining the force generated by the OHC as a feedback to vibration of the basilar membrane. In this study, we propose a model to analyze the effect of the constraints imposed on OHC on the cell's high-frequency active force generated in vitro and in vivo. The OHC is modeled as a viscoelastic and piezoelectric cylindrical shell coupled with viscous intracellular and extracellular fluids, and the constraint is represented by a spring with adjustable stiffness. We found that constrained OHC can achieve a much higher corner frequency than free OHC, depending on the stiffness of the constraint. We also analyzed cases in which the stiffness of the constraint was similar to that of the basilar membrane, reticular lamina, and tectorial membrane and found that the force per unit transmembrane potential generated by the OHC can be constant up to several tens of kHz.

1 Introduction The cochlear outer hair cell (OHC) plays a key role in the amplification and frequency discrimination during the mammalian hearing process. Through the mechanism termed electromotility [1], the OHC is capable of changing its length in response to changes in the cell's transmembrane potential. Because the OHC is constrained in the cochlear structure, such a change in somatic length generates a force that is fed back to the vibrating basilar membrane (BM). As a consequence, the movement of the BM is adjusted to enhance sensitivity and frequency selectivity. The force generated by OHCs is of critical importance and has already been studied in both experiments and models. A number of studies have been developed for low-frequency conditions. Hallworth [2] has used a suction pipette to hold the basal end of the OHC and measured the force that was generated by the cell and

202

203

applied to a glass fiber against the OHC apical end. Iwasa and Adachi [3] chose the whole-cell voltage-clamp technique to examine force generation. Hallworth [2], Iwasa and Adachi [3], and Spector et al. [4] had developed models to analyze the OHC active force. Frank et al. [5] have applied the microchamber setup [6] and, for the first time, measured the OHC high-frequency active force generation. They also demonstrated that the force generated by OHC could be constant up to tens of kHz. Tolomeo and Steele [7] have developed a dynamic model of OHC vibrating under the action of mechanical and electrical stimuli and interacting with the intracellular and extracellular viscous fluids. Ratnanather et al. [8] had considered both the viscosity of the fluids and that of the cell wall. In this study, we have modeled the constrained OHC as a circular cylinder held by a micropipette (microchamber) and attached to a spring at the other end. The viscous intracellular and extracellular fluids and the viscoelastic and piezoelectric cell's lateral wall are coupled. By choosing to make the stiffness of the spring equal to that of the glass fiber or to that of the cochlear components, we were able, respectively, to model experimental conditions or make predictions regarding the OHC active force production in vivo. We found that a constrained OHC could achieve a much higher corner frequency than a free OHC, and that the force per unit transmembrane potential in vivo could be constant up to a few tens of kHz. Our model can provide the effective inertial and viscous properties of the cell-and-fluids system for dynamic models of OHC with lumped parameters. Also, this model describing OHC as a local amplifier can be incorporated into a global cochlear model that considers the cochlear hydrodynamics and frequency modulation of the receptor potential. Finally, the proposed approach can lead to a better understanding of the mechanics underlying OHC high-frequency electromotility.

2 Model As shown in Fig. 1, the total traction exerted on the cell wall surface is determined by the intracellular and extracellular fluids: "cell

= 5

ext

_

"int

'

W

where gcell is the total traction exerted on the cell wall surface, and o ext and 6 int are, respectively, the tractions due to the cell's wall interaction with the extracellular and intracellular fluids. The constitutive equations for the cell wall that include the orthotropic elastic, viscous and piezoelectric components [7, 8] take the form, \N

n

uv

_

dux dx + ur r

c

~92"/

n -v dxdt -rj

dur

yjt _

204

Here Nx and Ng and are the components of the stress resultant (i.e., the product of the stress and cell wall thickness) generated in the cell wall; the subscripts r, x and 9 indicate the radial, axial and circumferential directions, respectively; Cs are the stiffness moduli; ux and ug are two components of the displacement; 77 is the cell wall viscosity; / is time; V is the transmembrane potential change; and ex and eg are two coefficients that determine the production of the local active stress resultant per unit transmembrane potential [9, 10].

Figure 1. In vivo the outer hair cell (OHC) is sandwiched between tectorial membrane and basilar membrane (a). Such system can be modeled as a cylindrical shell, interacting with surrounding viscous fluids and constrained by two springs (b). In vitro the microchamber is used to measure high-frequency OHC force generation by attaching a fiber to the cell end (c). For simplicity, only the excluded part of cell is considered, and the cell holding point at the orifice of the microchamber can be treated as the fixed boundary condition (d).

The movement of intracellular and extracellular fluids is governed by linearized Navier-Stokes equations [7]. The closed end of the cylindrical cell is treated as an oscillating rigid plate immersed in the fluid that will add extra hydrodynamic resistance to the cell wall; also, additional terms associated with the effect of the constraint (spring) are factored into the equation. The stress (resultant) and displacement can be expressed as the Fourier series in the cell's wall and fluid domains. Then, the Fourier series are substituted into the governing equations for the corresponding domains, and the respective boundary conditions are taken into account. As a result of these derivations, the solution in terms of the Fourier coefficients of the cell wall displacement is obtained as follows: u ecu = L' c cel i+k fluid +k elld +k spring J (—opiez) > (3) were fl u and g are, respectively, the vectors of the Fourier coefficients of the cell wall displacement and the stress due to electrical stimulation of the cell. Also, kceii, kfiuid, kend and kspring are the matrices that determine the stiffness associated with the cell wall, fluids, closed end, and constraint, respectively. Finally, the cell end displacement wend can be calculated from the displacement coefficients vector n , and the force acting on the constraint is obtained as "cell' * end

° ^constr ^end

t

\^)

205 where kmnstr is the stiffness of the cell constraint, represented by a spring attached at the cell's end. The force .Fend is equal to the active force generated by the cell as a result of its electrical stimulation. We compute this force and present our results in terms of force per unit transmembrane potential. The use of active force per unit transmembrane potential allows us to analyze the effect of the constraints in vivo separately from the effect of high-frequency changes in the receptor potential. The elastic moduli and coefficients of the electromotile response for the cell wall are chosen as Cn = 0.096 N/m, Cu = 0.16 N/m, C22 = 0.3 N/m, and ex = 0.0029 N/Vm, e9 = 0.0018 N/Vm [4, 9, 10]. We also choose 1 x 10-7 Ns/m for the cell wall (surface) viscosity and 6 x 10"3 Ns/m2 and 1 x 10~3 Ns/m2 for the intracellular and extracellular (volume) fluid viscosity, respectively. 3 Results and Discussion Our model results agreed well with and were validated by the low-frequency force measured by Hallworth [2] and Iwasa and Adachi [3]. Fig. 2 shows the force magnitude, displacement, and phase shift for various levels of stiffness of the constraint (spring). To simulate both experimental and physiological conditions, we included sets of four curves in which the dashed lines correspond to the stiffness of the fiber in the experiment by Frank et al. [4], and the solid, dotted, and dashed-dotted lines correspond to the stiffness of the cochlear membranes constraining the OHC in vivo. The fiber stiffness in the experiment by Frank et al. [4] was equal to 0.17 N/m. In vivo, OHCs are constrained by the underlying BM and the overlying tectorial membrane ™ and reticular lamina (RL). Thus, we have estimated the effects of these three components of the cochlea. The stiffness of the BM in the basal turn of the cochlea was estimated as 1.25 N/m [11], and this case is illustrated by the solid lines in Fig.2. Zwislocki et al. [12] had estimated the stiffness of the TM as 0.05 N/m. Recently, Scherer and Gummer [13] have probed the organ of Corti along the RL (the TM was removed). The upper and lower limits of the obtained stiffness were equal, respectively, to 0.2 N/m and 0.05 N/m. Assuming that the stiffness of the OHCs underlying the RL in Scherer and Gummer's [13] experiment was much smaller than that of the RL, we attribute the stiffness they measured to the RL. Thus, the dotted and dashed-dotted lines in Fig. 2 correspond, respectively, to the upper and lower limits of the stiffness of the RL. The dashed-dotted lines also represent the case in which the stiffness of the constraint is equal to that of the TM.

206

(A) :

(B)

V v. v V. v.

\ £ = 0.20N/m fc = 0.17N/m £ = 0.05N/m

\

^ \ \ : \ V:

k: loading stiffness Cell length = 30 urn

£ = 1.25 N/m k = 0.20 N/m * - 0 . 1 7 N/m fc = 0.05 N/m t = 0 N/m

A: loading stifthess Cell length = 30 fim

10'

Frequency (Hz)

Frequency (Hz)

(C)

\

k = 1.25 N/m k = 0.20 N/m k -0.17 N/m k = 0.05 N/m k = 0 N/m

k: loading stiffness Cell length = 30 urn

Figure 2. Modeling the high-frequency force generation. (A) force (per unit transmembrane potential); (B) displacement; (C) phase. 1.25 N/m is the stiffness of the basilar membrane in the basal turn [11], while 0.20 and 0.05 N/m are the upper and lower limits of stiffness of the reticular lamina located at the positions of OHCs [13]. 0.05 N/m is also the stiffness of tectorial membrane [12]. The loading stiffness used in the experiment of Frank et al. [4] is 0.17 N/m. The near-isometric force can be constant at -60 pN/mV up to 100 kHz, if the BM stiffness is chosen.

Frequency (Hz)

The results presented in Fig. 2 demonstrate the importance of the effect of the imposed constraints on the active force produced by the OHC. A more constrained cell had a longer range of constant active force: the ranges of constant active forces reached 30 kHz when the constraint stiffness is 0.17 N/m as used in the experiment by Frank et al. [4], and the force reaches 100kHz when the constraint stiffness was equal to that of the BM (1.25 N/m). In terms of estimating the active force production by the OHC in vivo, we can reasonably predict that the physiological case lies somewhere between the cases corresponding to the stiffness of the BM and that of the RL. Therefore, our results indicate that the active force produced by the OHC under physiological conditions is, probably, constant up to a few tens of kHz. An accurate prediction of the active force production in vivo will require a more complete model of the constraints imposed on OHC in which the characteristic stiffness of all three components (the BM, TM, and RL) is explicitly considered. Nevertheless, our finding that the constrained OHC has a greater (up to tens of kHz) range of a constant active force is consistent with the cochlear frequency map. Indeed, the basal (high-frequency) area

207

of the cochlea associated the cochlear amplifier has a much greater stiffness in the BM that imposes constraints on OHCs in this area. Several factors could have contributed to the longer active force plateau under conditions of higher stiffness of the constraint. One of them is that the higher the stiffness of the constraint, the smaller the movement of the cell (Fig. 2B). Thus, the losses associated with the interaction with the two surrounding fluids and with the relative motion of the components of the cell composite wall become reduced for highly constrained cells. This condition results in a greater roll-off frequency for the force. Another factor is related to the increase in the total stiffness of the system (cell + spring) that also results in an increase in the roll-off frequency. As we have already mentioned, we computed the active force per unit the cell transmembrane potential, and the total force will be equal to the product of the obtained force per unit transmembrane potential and the receptor potential. Thus, the frequency dependence of the total active force generated by the OHC in vivo will be determined by a combination of mechanical factors, which are associated with cell vibration, and the electrical (piezoelectric) properties of the cell membrane shaping the receptor potential. 4 Conclusions A model of the OHC active force generation under high-frequency conditions is proposed. It is shown that OHC is capable of generating a constant force per unit transmembrane potential of up to tens of kHz, depending on the constraint stiffness. The greater the stiffness of the constraint, the broader the frequency range of the constant active force produced by the cell. The proposed approach can be used to provide the effective dynamic properties of the cell+fluid system explicitly relating them to the viscosity and mass of the fluid involved in cell vibration as well as to the viscosity on the cell wall. The developed model can serve as an OHC-associated module in global models of the cochlea. Acknowledgments This work was supported by research grants DC02775 and DC00354 from the National Institute of Deafness and Other Communication Disorders (NIH). References 1. Brownell, W.E., Bader, CD., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science. 224, 194196.

208

2. Hallworth, R., 1995. Passive compliance and active force generation in the guinea pig outer hair cell. J. Neurophysiol. 74, 2319-2328. 3. Iwasa, K.H., Adachi, M., 1997. Force generation in the outer hair cell of the cochlea. Biophys. J. 73, 546-555. 4. Spector, A.A., Brownell, W.E., Popel, A.S., 1999. Nonlinear active force generation by cochlear outer hair cell. J. Acoust. Soc. Am. 105, 2414-2420. 5. Frank, G., Hemmert, W., Gummer, A.W., 1999. Limiting dynamics of highfrequency electromechanical transduction of outer hair cells. Proc. Natl. Acad. Sci. USA. 96,4420-4425. 6. Dallos, P., Hallworth, R., Evans, B.N., 1993. Theory of electrically driven shape changes of cochlear outer hair cells. J. Neurophysiol. 70, 299-323. 7. Tolomeo, J.A., Steele, CD., 1998. A dynamic model of outer hair cell motility including intracellular and extracellular viscosity. J. Acoust. Soc. Am. 103, 524-534. 8. Ratnanather, J.T., Spector, A.A., Popel, A.S., Brownell, W.E., 1997. Is the outer hair cell wall viscoelastic? In: Lewis, E.R., Long, G.R., Lyon, R.F., Narins, P.M., Steele, C.R., Hecht-Poinar, E. (Eds.), Diversity in Auditory Mechanics. World Scientific, Singapore, pp. 601-607. 9. Spector, A.A., Brownell, W.E., Popel, A.S., 1998. Estimation of elastic moduli and bending stiffness of the anisotropic outer hair cell wall. J. Acoust. Soc. Am. 103, 1007-1011. 10. Spector, A.A., Jean, R.P., 2003. Elastic moduli of the piezoelectric cochlear outer hair cell membrane. Experimental Mechanics 43, 355-360. 11. Gummer, A.W., Johnstone, B.M., Armstrong, N.J., 1981. Direct measurement of basilar membrane stiffness in the guinea pig. J. Acoust. Soc. Am. 70, 1298-1309. 12. Zwislocki, J.J., Cefaratti, J.K., 1989. Tectorial membrane II: Stiffness measurements in vivo. Hearing Res. 42, 211-227. 13. Scherer, M.M., Gummer, A.W., 2004. Impedance analysis of the organ of Corti with magnetically actuated probes. Biophys. J. 87, 1378-1391. Comments and Discussion Chadwick: How do you reconcile your result of increasing the plateau region of the hair cell response with increasing stiffness of the hair cell constraint, with those of Mammano who suggests the softness of Deiters' cells help to increase the plateau region? Answer: It seems that the question stemmed from a misinterpretation of Mammano's statement that was not about Deiters' cell softness but rather about the viscosity of that cell. The estimates of Deiters' cell stiffness by Tolomeo, Steele, and Holley show that Deiters' cells are very stiff with the point stiffness about 20 times greater than that of the basilar membrane. These data on Deiters' cell stiffness

209 were used in our modeling to predict the active force plateau region under physiological conditions. We appreciate the stimulating question. Gummer: Thank you for bringing to our attention that the bandwidth of the electromotile response is increased by elastic loading of the cell. However, there is a major difference between your model results and our experimental results (Frank et al, 1999); namely, for "unloaded" cells, we found bandwidths about a decade larger than your model values (for a 30-um cell, 35 kHz instead of your value of 5 kHz in Fig. 2B). Also, the measured asymptotic high-frequency slope was -12 dB/oct, instead of the -6 dB/oct reported here. What could be the sources of these discrepancies? Answer: Our estimate of the frequency slope of the electromotility curve in Fig. 2A in Frank et al. (1999) is about -8 dB/octave, which is similar to our data in Fig. 2 of our paper published in this proceedings. However, the estimate of the corner frequency of electromotility in our model result is indeed smaller than that in Frank et. al. (1999). Several factors, such as the holding potential and viscosities of cell wall and internal fluids, could contribute to this difference. To fully understand the observed discrepancy, an additional analysis is required. Thank you for your thorough analysis of our modeling results and for the stimulating questions.

THEORETICAL ANALYSIS OF MEMBRANE TETHER FORMATION FROM OUTER HAIR CELLS

E. GLASSINGER AND R. M. RAPHAEL Rice University, MS-142, PO Box 1892, Houston, TX, 77251-1892, E-mail: [email protected]

USA

The mechanical properties of cellular membranes can be studied by forming a long, thin, bilayer tube (a tether) from the membrane surface. Recent experiments on human embryonic kidney and outer hair cells (OHCs) have demonstrated that the force needed to maintain a tether at a given length depends upon the transmembrane potential. Since the OHC tether force is highly sensitive to the holding potential, these results suggest that the unique electromechanical properties of the OHC membrane contribute to the voltage response of the tether. Here we develop a theoretical framework to analyze how two proposed mechanisms of OHC electromotility, piezoelectricity and flexoelectricity, affect tether conformation. While both forms of coupling are predicted to lead to experimentaly observable changes in tether force, piezoelectric coupling is predicted to cause an increase in tether force with depolarization while flexoelectric coupling is predicted to lead to a decrease in force. The results of this analysis indicate tether experiments can provide insight into electromechanical behavior of the OHC membrane.

1 Introduction Since membranes are fundamental components of many basic cellular processes, understanding how they respond to changes in mechanical, chemical and electrical environments is an essential and crucial step towards characterizing the cellular basis of both normal and disease states. One method to study the properties of cellular membranes is to extract a thin bilayer tube, termed a tether, from the membrane surface. This tube can be formed by using an optical or magnetic force transducer to pull an attached bead away from the membrane surface. Analyses of tether experiments have provided measurements of the local bending stiffness of both synthetic and cellular membranes [1, 2]. In addition, analyses have helped to correlate changes in cellular function with changes in tension and membranecytoskeletal adhesion energy [3]. Recent tether experiments on voltage-clamped outer hair cells have demonstrated that the force required to maintain a tether formed from both outer hair cells (OHCs) and human embryonic kidney cells (HEKs) is sensitive to the transmembrane potential [4, 5]. The greater force gains measured for tethers formed from OHCs suggest that the unique electromechanical properties of the membranes of these cells contribute to the voltage sensitivity of the tether force. The normal electromechanical response of the OHC membrane is believed necessary for the remarkable frequency discrimination and sensitivity of mammalian hearing [6]. These cells amplify the fluid vibrations of the cochlea by transducing electrical energy into mechanical energy. In mammals, this response

210

211

depends upon the expression of the integral membrane protein prestin [7]. Determining how prestin transduces electrical into mechanical energy will provide fundamental insights into the underlying mechanism of the cochlear amplifier. A number of theories suggest prestin functions as a piezoelectric type motor in which its conformational changes lead to changes in membrane tension and/ or strain [8, 9]. Macroscale analysis of the whole cell deformation provides a linear piezoelectric coupling coefficient on the order of 10"12 C/m [9]. Another model proposes that instead of expanding membrane area, prestin changes the membrane curvature [10]. The theory is based upon flexoelectricity, a form of electromechanical coupling observed in both synthetic and native membranes [11]. In this analysis, we consider theoretically how these modes of electromechanical coupling affect the conformations of tethers formed from cellular membranes. This work extends current thermodynamic models of tether formation to account for energies of both active area and curvature changes and provides a theoretical framework upon which the proposed mechanisms of electromotility can be evaluated. 2 Models and Results 2.1 Thermodynamic analysis of membrane electromechanics Equilibrium tether conformations can be predicted by determining the stability points of the extended energy variational, 9 0 = 8G-dW [12]. For isothermal deformations, G is the electric Gibbs energy and W accounts for the external mechanical and electrical loads applied to the tether. The electric Gibbs energy is obtained by integrating the electric Gibbs energy density G over the membrane area. Equilibrium membrane conformations satisfy: dG - dW = 0 . When required, solutions are obtained numerically using a variant of the Newton-Raphson method in which the step size is adjusted by bisection to ensure the error is reduced for each iteration [13]. 2.2 Thermodynamic analysis of tether equilibrium The thermodynamic analysis of tether conformation is extended from a model developed by Hochmuth et al. to interpret the behavior of tethers formed from cellular membranes [2]. In this section, an overview of this model is provided. Since most cells have a complex geometry, the cellular membrane is approximated as a flat, semi-infinite disc of radius rd,o [2]. The tether shape is parameterized as a cylinder of length Lt and radius Rt. Under the assumption that tether formation does not cause area dilation, the decrease in area of the membrane disc (-AAd) equals the change in tether area [2].

212 The work to form a tether is done by the tether force F and the far-field tension T of the membrane disk: W=FLt + TAAd. The energy density (J/m2) of the tether is the sum of the local bending energy and the membrane-cytoskeletal adhesion energy density y: G=

-kcc2+y.

R,

(1)

iz

=»-~F

Figure 1: Schematic of tether formation from a semi-infinite disc. For this model, the change in area of the disc (jtTd2OTd!02) equals the tether

Here kc is the local area 2-ER,L,. bending stiffness of the membrane and c is the sum of the two principal curvatures of the membrane. For the geometry of this model, the curvature is the inverse of the tether radius, 1/R,. For a tether of area 2nR,Lh the energy is: nKL

'- + 2nR,Lty. R.

(2)

Equilibrium tether conformations can be predicted by minimizing the following expression with respect to R, and Lt: nk L H

o 0.75

Voltage [V]

Voltage [V]

Frequency [Hz]

Voltage [V]

Figure 2. A. Measured (dotted line) and calculated (solid line) Cm, where lines represent values determined at different frequencies. Lines represent in decreasing magnitude 0.25f, 0.5f, l.Of, 2.0f, 4.0f and 8.0f Hz where f: 195.625 Hz. B. Comparing phase of Y for OHC at peak C, (solid triangles) and at 0.1 V (solid squares), with that obtained for model circuits with similar capacitors (open diamonds 51 pF and open circles 30 pF), where Rm: 200 MQ and series resistance, Rs : 4 Mfi. Open triangles: gain of OHC capacitance. C. Real (Y) of OHC. Lines represent frequencies outlined in A in increasing order from bottom to top of plot. Inset compares Re(Y) (solid lines) with G determined at DC (circles). Rs for OHC recording, was 4.3 MQ

Measured capacitance, Im(Y)/(27if) (Im(Y): imaginary part of Y) approaches the calculated capacitance, Cm [1] at frequencies < l/(27tRmCm), about 6-50 Hz for the cell shown in Figure 2A. The gain of the calculated Cm decreases from 1.2 at 0.5f Hz to 0.9 at 8.0f Hz (f=195.625 Hz), because of the roll-off induced by Rs (Figure 2B). The maximum phase of Y occurs between 0.25f and 0.5f for peak Cm, and at l.Of for minimum OHC Cm. The optimum frequency to measure Cm of OHC is at a frequency when gain is maximum and noise is minimum, and is around 200 Hz where f = l/(2nV(RmRs)Cm) and phase(Y) is maximum for lowest Cm (Figure 2A and B). Acknowledgments Supported by NIDCD research grants R01 DC 02775 and DC00354. References 1.

Santos-Sacchi J., Kakehata S., Takahashi S., 1998. Effects of membrane potential on the voltage dependence of motility-related charge in outer hair cells of the guinea-pig. J. Physiol. 510: 225-35.

MODELING OUTER HAIR CELL HIGH-FREQUENCY ELECTROMOTILITY IN MICROCHAMBER EXPERIMENT ZHIJIE LIAO AND ALEKSANDER S. POPEL Johns Hopkins University, Baltimore, Maryland 21205 USA Email: [email protected] and [email protected] WILLIAM E. BROWNELL Baylor College of Medicine, Houston, Texas 77030 USA Email: [email protected] ALEXANDER A. SPECTOR Johns Hopkins University, Baltimore, Maryland 21205 USA Email: [email protected] 1 Introduction and Methods Cochlear outer hair cells (OHC) are critically important for the amplification and sharp frequency selectivity of the mammalian ear [1]. The microchamber experiment has been an effective tool to analyze the OHC high-frequency performance [2-4]. In this study, we simulate the OHC electromotility in the microchamber. Our model considers the inertial and viscous properties of fluids inside and outside the cell as well as the viscoelastic and piezoelectric properties of the cell composite membrane [5]. The final solution to calculate OHC motile response was obtained in terms of Fourier series [6]. 2 Results and Discussion Fig. 1 displays the OHC electromotility in two extreme conditions: no-slip condition (OHC can not at all move in and out of the microchamber orifice) or full-slip condition (OHC can move freely through the microchamber orifice without any imposed friction). For low frequencies, the no-slip condition results in an electromotile response twice as great as that in the full-slip condition, but this difference reduces at high frequencies. Dallos et al. [2, 3] reported electromotility range 0.92 ~ 4.74 nm/mV for the 55 ~ 72 um cells. These experimental results are in good agreement with our model predictions (1.3 ~ 2.7 nm/mV) for the 60 um cell. Frank et al. [4] obtained smaller cell length changes (0.25 nm/mV), and the reason for that may come from the fact that the set point is not at the steepest part of OHC electromechanical transduction curve. Fig. 2 shows that indeed by shifting setpoint potential to more hyperpolarization our model results can be made closer to Frank's results [4]. By assuming the coefficients (ex and eg) that determine the production of the local active stress resultant per unit transmembrane potential is

233

234

proportional to the slope of the electromechanical transduction curve, we found that, if the set-point potential shifts 100 mV toward higher polarization, the predicted cell displacement amplitude reduces to 0.25 - 0.5 nm/mV depending on the chosen boundary condition at the cell-pipette interface. q = 0.5 Applied voltage : 1 mV Cell length : 60 mm Cell wall viscosity: 1 x 10" Ns/m External fluid viscosity : 1 x 10" Ns/m2

200 •

0

Internal fluid viscosity : 6x10" Ns/m2 -200 -

No-slip -400 -

\*^'

Full-slip -600 -

-800

Frequency (Hz)

Fig. 1. Modeling OHC at the microchamber experiment under the full-slip and no-slip conditions. The cell length is 60 um, and it is half included and half excluded.

J-

^

1 ' \ I1 11 \ \ 1 1 \ 1 ' \ 1 1 \ 1 I ^— ... 1 . . . . 1 Applied voltage (mV)

Fig. 2. Estimation of set-point in Frank's et al. experiment [4], The electromechanical transduction function curve comes from Dallos et. al. [2]. Two points are selected to calculate electromechanical responses.

3 Conclusions We propose a model of high-frequency electromotility of outer hair cell generated in the microchamber experiment. The model can both reconcile the existing results of different groups and better understand the high-frequency performance of the cell. References

6.

Brownell, W.E., Bader, CD., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science. 224, 194196. Dallos, P., Hallworth, R., Evans, B.N., 1993. Theory of electrically driven shape changes of cochlear outer hair cells. J. Neurophysiol. 70, 299-323. Dallos, P., Evans, B. N., 1995. High frequency motility of outer hair cells and the cochlear amplifier. Science. 267, 2006-2009. Frank, G., Hemmert, W., Gummer, A.W., 1999. Limiting dynamics of highfrequency electromechanical transduction of outer hair cells. Proc. Natl. Acad. Sci. USA. 96, 4420^1425. Spector, A.A., Brownell, W.E., Popel, A.S., 1999. Nonlinear active force generation by cochlear outer hair cell. J. Acoust. Soc. Am. 105, 2414-2420. Tolomeo, J.A., Steele, CD., 1998. A dynamic model of outer hair cell motility including intracellular and extracellular viscosity. J. Acoust. Soc. Am. 103, 524-534.

CHLORPROMAZINE AND FORCE RELAXATION IN THE COCHLEAR OUTER HAIR CELL PLASMA MEMBRANE - AN OPTICAL TWEEZERS STUDY D.R. MURDOCK, S. ERMILOV, AND B. ANVARI Rice University, Department

of Bioengineering, 6100 Main Street, Houston TX 77005, USA E-mail: [email protected]

A.A. SPECTOR AND A.S. POPEL Johns Hopkins University, Department of Biomedical Engineering, Street, Baltimore MD 21218, USA

3400 North

Charles

W.E. BROWNELL Baylor College of Medicine, Bobby R. Alford Department of Otorhinolaryngology Communicative Sciences, One Baylor Plaza, Houston TX 77030, USA

and

The cationic amphipath chlorpromazine (CPZ) is postulated to selectively partition into the inner leaflet of the plasma membranes and modulate the electromotile behavior of cochlear outer hair cells (OHCs). We used an optical tweezers system to characterize the mechanical properties of OHCs plasma membrane (PM) through the formation and analysis of membrane tethers in the presence and absence of CPZ. We observed characteristic force relaxation when the tethers were formed and maintained at a constant length for extended periods. This relaxation process was modeled using a 2nd order Kelvin body that provided stiffness, membrane viscosity-related measurements, and relaxation time constants, which collectively indicated an overall biphasic nature of relaxation. Our results with CPZ strengthen the hypothesis linking the drug's effect to reducing the mechanical interaction between PM and cytoskeleton.

1 Introduction The mammalian outer hair cell (OHC) is a cylindrical epithelial cell that is essential for normal hearing [1]. Chlorpromazine (CPZ) is a cationic amphipath that is postulated to preferentially partition into the inner leaflet of the OHC phospholipid bilayer and shifts the electromotile response curve in OHCs [2]. We formed and then analyzed OHC membrane tethers using a viscoelastic model in order to better understand the mechanism by which CPZ affects cochlear function. 2 Methods Optical tweezers provide an advanced technique for precise micromanipulation and force measurements. A microsphere manipulated with the optical trap was moved away from the cell forming a thin strand (tether) of membrane material. Membrane tethers exhibited force relaxation with time when held at a constant length (Fig.

235

236

1A). A 2nd Order Generalized Kelvin model (Fig. IB) was selected to model this behavior in order to obtain salient information related to mechanical properties of the membrane tether. Calculated parameters included stiffness values (/i), coefficients of friction (77), force relaxation times ( r ) , and equilibrum force (Feq). 90 I

A

•

Force Data

—

Kelvin Model Fit

B

M2

n2

.. 70

Mi

; 60

www

" 50

1

"ui""" '

40 1

in

1

1

100

150 Time (s)

"7""" Mo

AAAAA_ Un

Figure 1. A: Force relaxation in OHC membrane tether. B: 2nd order generalized Kelvin body used to model tethering force data.

3 Results and Discussion Upon 0.1 mM CPZ application, the first relaxation time remained virtually unchanged from the NES values while the second relaxation time decreased by -50% (p 0 is ~0.5 (ref. 15). Fits of eqn. (1) to the results deviated from the gating-spring model in that the constant A increased as adaptation progressed. A further difference is that A was much larger than expected from the gating spring model. In that model, A is the product of the number of MET channels and the single-channel gating force, less than 30 pN for OHC's [14], whereas values 20 to 100-fold larger were needed for the fits in Fig. 3C. Nevertheless, the results are still consistent with force production being linked to the probability of opening of the MET channels. In some OHCs the force-displacement relationship possessed a negative slope region but in five cells more extreme behavior was observed: for a range of stimuli, the displacement of the end of the flexible fiber attached to the hair bundle exceeded that of the end cemented to the piezoelectric device thus, the forcedisplacement relationship became negative as adaptation progressed, indicating that the hair bundle is doing work on the fibre. Maximum force generation, estimated as the difference between steady state and instantaneous force-displacement plots at fixed displacement, was 517 ± 96 pN.

250

200

400

Displacement (roil)

Figure 3. Mechanical properties of OHC hair bundle. A. Average MET currents (top) in a PI 1 rat OHC in response to stimulation with a flexible fiber, stiffness Movements of end of fiber attached to piezo (middle) and of the hair bundle (bottom). B. Peak MET current (7) scaled to its maximum value (Imax, 0.37 nA) plotted against displacement at peak of current. C. Force-displacement plots at different times (t) after the peak of the current: t = 0 (filled circles), 0.07ms, 0.27 ms, 0.47 ms, 0.67 ms, 3.9 ms, 8 ms (filled triangles). Smooth curves are fits to eqn. 1 using p 0 (X) relation from B. and Ks = 3 mN/m.

3.3 Calcium dependence of bundle mechnanics If force generation by the bundle reflects gating and adaptation of the MET channel, it should be susceptible to altering extracellular Ca2+. Lowering Ca2+ reversibly reduced the hair bundle mechanical non-linearity and slowed its onset. To determine the time course of force production, the change in force between the instantaneous relation (t = 0, measured at the peak current) and the plots at subsequent times were measured at a fixed displacement corresponding to the point at which the compliance was maximal. This analysis in four cells indicated that bundle force develops with the same time course as fast adaptation. For example, in one cell force production occurred with time constants of 0.3 ms (1.5 mM Ca2+) and 0.6 ms (0.02 mM Ca2+) which were similar to those of fast adaptation under the same conditions: 0.28 ms (1.5 mM Ca2+) and 0.68 ms (0.02 mM Ca2+). (The adaptation time constants measured with the flexible fiber were slower than those reported above probably because the stimulus onset was slower due to the voltage command to the piezoelectric device being filtered at a lower corner frequency, 1.5 kHz compared to at least 5 kHz with the stiff probe). These observations provide evidence that OHC hair bundles can generate force of substantial magnitude (> 500 pN) on a sub-millisecond time scale similar to that of fast adaptation. It is presently unclear what process might underlie force production of such speed and magnitude. A mechanism attributable to the MET channels implies either ten times more channels per stereocilium or intrinsic properties different from those in sub-

251 mammalian vertebrates. Alternative sites for force generation include the stereociliary rootlets or the apical surface of the cell, though either site would require signal transmission from the MET channels at the tips of the stereocilia. 4 Discussion We have measured the properties of outer hair cell MET channels in isolated preparations derived from immature rats and exposed to conditions different from those in the intact cochlea. Our limited evidence on the lack of variation in maximum current and adaptation time constant with age suggests that our results may approximate those in animals with fully developed hearing [6]. However several corrections are needed to extrapolate to in vivo conditions. These include the presence of an endolymph with K+ as the major cation, an endolymphatic potential of 80 mV, and a higher temperature. Each of these factors will increase the amplitude of the transducer current and the rate of adaptation. Our previous extrapolations [6] indicate that the current amplitudes will be about 4-fold larger, 6 - 9 nA, and that the adaptation time constants will be 8-fold faster. Other things being equal, correcting the measured values in 0.02 mM Ca2+ (Fig. 2) imply adaptation time constants, xA, in vivo of 30 us at the low-frequency position and 11 (is at the high-frequency position. These time constants are equivalent to a halfpower frequency (l/2TtxA) of the high-pass filter of 5.3 kHz and 14.5 kHz at the two cochlear locations, which are very similar to the estimated CFs of 4 kHz and 14 kHz respectively. These corrections are necessarily approximate but suggest a correspondence of the adaptation time constants to the hair cell CF. If active force generation by the hair bundles has a parallel time course to fast adaptation, then it too will have kinetics that are matched to the CF. However, it is not yet possible to make force measurements on hair bundles at the microsecond speed needed to rigorously test this assertion. Nevertheless, the predicted speed of fast adaptation suggests that the hair bundle motor may provide positive mechanical feedback at stimulation frequencies of tens of kilohertz. The hair bundle motor could therefore supplement force generation by the somatic motor at high frequencies, or may even constitute the major mechanism of cochlear amplification [15, 16]. Acknowledgments This work was supported by grant ROl DC 01362 to RF from the NIDCD. References 1. Dallos, P., 1992. The active cochlea. J. Neurosci. 12,4575-4585.

252

2. Brownell, W.E., Bader, C.R., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science 227, 194196. 3. Kennedy H.J., Crawford A.C., Fettiplace, R., 2005. Force generation by mammalian hair bundles supports a role in cochlear amplification.Nature 433:880-3. 4. Kros, C.J., 1996. Physiology of mammalian cochlear hair cells. In: Dallos, P., Popper, A.N., Fay, R.R. (Eds.) The Cochlea. Springer, New York, pp 318-385. 5. He, D.Z.Z., Jia, S., Dallos, P., 2004. Mechanoelectrical transduction of adult outer hair cells studied in a gerbil cochlea. Nature 429, 766-770. 6. Kennedy, H.J., Evans, M.G., Crawford, A.C., Fettiplace, R., 2003. Fast adaptation of mechanoelectrical transducer channels in mammalian cochlear hair cells. Nat. Neurosci. 6, 832-836. 7. van Netten S.M., Dinklo, T., Marcotti, W., Kros, C.J., 2003. Channel gating forces govern accuracy of mechano-electrical transduction in hair cells. Proc. Natl. Acad. Sci. USA 100, 15510-15515. 8. Muller, M., 1991. Frequency representation in the rat cochlea. Hear. Res. 51, 247-254. 9. Bosher, S.K., Warren, R.L., 1978. Very low calcium content of cochlear endolymph, an extracellular fluid. Nature 273, 377-378. 10. Ricci, A.J., Crawford, A.C., Fettiplace, R., 2003. Tonotopic variation in the conductance of the hair cell mechanotransducer channel. Neuron 40, 983-90. 11. Crawford, A.C., Fettiplace, R., 1985. The mechanical properties of ciliary bundles of turtle cochlear hair cells. J. Physiol. 364, 359-379. 12. Howard, J., Hudspeth, A.J., 1988. Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell. Neuron 1, 189-199. 13. Russell, I.J., Kossl, M., Richardson, G.P., 1992. Nonlinear mechanical responses of mouse cochlear hair bundles. Proc. R. Soc. Lond. B. 250, 217227. 14. van Netten, S.M., Kros C.J., 2000. Gating energies and forces of the mammalian hair cell transducer channel and related hair bundle mechanics. Proc. R. Soc. Lond. B. 267, 1915-1923. 15. Fettiplace, R., Ricci, A.J., Hackney, CM., 2001. Clues to the cochlear amplifier from the turtle ear. Trends Neurosci. 24, 169-175. 16. Chan, D.K., Hudspeth, A.J., 2005. Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro .Nat Neurosci. 8, 149-55.

253 Comments and Discussion Gummer: According to your force-displacement curves, displacements of several hundred nanometers are required before the hair-bundle is able to exert force on the stimulus fiber. Although you explained that the very fast adaptation process possibly causes "smearing" of measured 10- functions, the required displacement amplitudes are up to two orders of magnitude greater than cochlea-amplified basilar-membrane amplitudes (typically, 0.3 nm at 0 dB SPL). That is, could the active hair-bundle mechanics reported here be simply a high-intensity phenomenon, and therefore, largely irrelevant for cochlear amplification? Answer: Force generation in Fig. 3 of our chapter occurs for hair bundle displacements covering the gating range of the mechanotransducer channels as is expected for the active process. However, the current-displacement (I-x) relationships measured with a flexible fiber are broader than determined with a rigid probe, probably due to the unavoidably slow onset of the stimulus, slower even than the fast adaptation time constant - less than 0.1 ms. During bundle stimulation with a flexible fiber, the mechanotransducer channels will become adapted during the stimulus onset, and the I-x curve will be shifted positive. The measured I-x curve will then be the sum of unshifted and shifted curves, the net effect being to broaden the I-x relationship. To both overcome this problem and measure the true speed of force generation will require developing an even faster method of delivering force steps to the hair bundle.

STEREOCILIARY VIBRATION IN THE GUINEA PIG C O C H L E A

A. FRIDBERGER, I. TOMO, M. ULFENDAHL AND J. BOUTET DE MONVEL Center for Hearing and Communication Research, Department of Clinical Neuroscience, KarolinskaInstitutet, M1.00-ONH, Karolinska Universitetssjukhuset, 17176Stockholm E-mail: anders.fridberger@cfh. ki.se Using a novel technique for rapid time-resolved confocal microscopy, we acquired image sequences showing the sound-evoked motion of inner and outer hair cell stereocilia bundles in the apical, low-frequency regions of the guinea pig cochlea. Motion of structures of interest was analyzed by optical flow computation. Sound stimulation at 80 - 100 dB SPL and 200 Hz led to deflection of both inner and outer hair cell stereocilia. The deflection was linearly related to the displacement of the reticular lamina. However, deflection was smaller for inner hair cell stereocilia. Phase differences were also found: deflection of inner hair cell stereocilia led that of the outer hair cell by 44 degrees on average. It was previously shown that apical inner hair cells have 10 - 16 dB larger AC receptor potentials than outer hair cells (Russell & Sellick, 1983; Dallos, 1985). Our results suggest that inner hair cells are equipped with transducer channels of higher conductance or higher density than are the outer hair cells. In view of the tiny deflection that inner hair cells are supposed to detect, it might also be that active processes acting at the level of their stereocilia are necessary near threshold.

1 Introduction Outer hair cell (OHC) stereocilia are firmly embedded into the gelatinous tectorial membrane. This connection causes OHC stereocilia to deflect in response to the organ's vibrations. Inner hair cell (IHC) stereocilia do not appear to be attached to the tectorial membrane, and the mechanism by which they deflect is therefore less obvious. Electrophysiological recordings suggested that IHC stereocilia motion is driven by fluid interaction in the tiny space between the tectorial membrane and the reticular lamina [1]. This would imply that IHC bundle deflection is proportional to the velocity of the organ of Corti, while in OHCs deflection is proportional to the organ's displacement. Here we present a detailed account of stereocilia motion in the apical region of the guinea pig cochlea in excised temporal bone preparations. Images were acquired by a modified confocal microscope and analyzed using optical flow analysis. 2 Methods 2.1 Preparation and Sound Stimulation Pigmented guinea pigs were decapitated and the temporal bone attached to a holder, with the external auditory meatus facing a loudspeaker. An important difference from our previous studies [2-4] was that the preparation was immersed in an endolymph-like solution. Reissner's membrane was ruptured using a fine needle.

254

255 Thereafter, the dye RH795 was added to the perfusion medium (12.5 ug/ml; Molecular Probes). Due to the opening in Reissner's membrane, this dye stained stereocilia on both inner and outer hair cells. Because the preparation was immersed in an endolymph-like solution and perfused with normal medium, the hair cell's natural ionic environment was preserved. The preparation was mounted on a laser scanning confocal microscope and visualized at a pixel size of 110 nm. Sound stimulation was applied at 200 Hz, close to the expected best frequency for this cochlear region. Stimulus levels ranged between 88 and 110 dB re 20 uPa. Due to the immersion of the preparation and opening of the apical turn, the stimulus level is reduced. Under these experimental conditions, organ of Corti vibrations are generally thought to be unaffected by OHC motility. Passive mechanical processes are crucial for organ function, being predominant in the living animal at these sound intensities. 2.2 Time-resolved confocal imaging The phase relation between each image pixel and the sound stimulus was tracked by sampling the voltage waveform driving the loudspeaker. Pixels having similar phases were collected, forming an image of the preparation at a given phase of the stimulus. 2.3 Analysis of hair bundle motion Stereocilia displacements during a full cycle of motion were analyzed by a wavelet differential optical flow algorithm [4]. The optical flow of the resampled and smoothed image sequence was computed. A significant increase in accuracy was obtained compared to our previous studies [2-4], displacements on the order of a few nanometers being estimated with a magnitude error less than 10%. 3 Results 3.1 Stereocilia motion Figure 1A shows two OHCs imaged during sound stimulation. The reticular lamina and the hair bundles rotated in phase with the stimulus, making the cilia to deflect, showing a pivoting motion from base to tip. Figure IB displays the trajectories of these two points. The main axis of motion at the base of the hair bundles matched the long axis of the cilia. A small radial motion component gave the trajectory the shape of an elongated ellipse. The trajectory of the tip of the bundle was also an elongated ellipse, but its orientation was different from that of the base. This difference led to a deflection of the hair bundle directly in phase with the displacement of the reticular lamina. This deflection was computed by simply subtracting the tip and base trajectories. As the cells moved downward, the OHC bundle deflected 28 nm to the left, for a total base displacement of 95 nm. Thus, displacement of the organ of Corti toward scala tympani resulted in deflection in the

256 inhibitory direction. The pattern of OHC bundle trajectories remained very similar at higher sound intensities. Notably the trajectories' orientations were almost the same at all intensities. We also measured the bundles' angular deflection, defined as the angle formed between the two extreme positions of the stereocilia. For stimulus levels between 92 and 110 dB SPL, OHC deflection angles were between 0.130.88°. Figure 1C shows an IHC in the same preparation and at the same location as the OHCs seen in Figure 1 A. The displacements of the IHC bundle tip and base were about 30% smaller than those of the OHCs at equal stimulus level (maximum displacement at the base of 66 nm). The deflection amplitude of the IHC bundle was 14 nm, about half that of the OHC. As a result, the angular deflection of the IHC bundle were in the range 0.08-0.54°, about 40% smaller than the values found for the OHCs. Angular deflections of 25 pairs of IHCs and OHCs were measured from 4 preparations. Each pair referred to an IHC and an OHC at the same location in the cochlea. In all cases, the OHCs showed larger stereocilia deflections than IHCs. The mean angular deflections for the applied range of sound intensities was 0.49° ± 0.30° and 0.97° + 0.60° for IHCs and OHCs, respectively. This difference was significant when assessed according to Student's t-test for paired variables Defle&tan

Base 0

20

40

60

X Displacement (nm)

Deflection

Figure 1. A) Confocal image showing two OHCs during sound stimulation at 200 Hz and 98 dB SPL. Scale bar, 3 um. B) Motion at the base and the tip of the hair bundle. Deflection was computed as the vector difference between the trajectories. C) Confocal image of an IHC at the same location as the cells in panel A. D) Motion at the tip, base and the computed deflection of the hair bundle.

X Displacement (nm)

(pO.00001). The standard deviations reflect variation caused by different vibration amplitudes in different IHC-OHC pairs, rather than measurement errors. The slopes

257 of the regression lines (stereocilia angular deflection versus reticular lamina displacement) were not significantly different for IHCs and OHCs (0.35° / 100 nm for OHCs and 0.41° /100 nm for IHCs). 3.2 Phase relations OHC bundle deflection was in phase with the reticular lamina displacement, as the minima (and maxima) of both recordings occurred at the same instants. Using Fourier transformation, we found that IHC cilia deflection led reticular lamina displacement by 44° on average. 3.3 Apparent pivot axes of the stereocilia We analyzed the apparent pivot axes of the tips and bases of the stereocilia by the least-squares method described in [2, 3]. Results are illustrated in Figure 2. The bundle bases of the IHC and of the first row OHC rotated around similar axes located in the region of the IHC base or lower. The pivot axis of the second row OHC bundle base was found closer to the reticular lamina, near the head of the pillar cells. Although the pivot axes of the tip and base of the IHC bundle were significantly different, both were found below the reticular lamina in the same directions (the corresponding trajectories being nearly parallel). Both parts of the IHC bundle thus moved in similar ways, following the rotation of the reticular lamina. By contrast, the trajectories of the OHC stereocilia had different orientations from tip to base. The pivot axes of the OHC bundle tips were found in a direction nearly parallel to the reticular lamina, somewhere above the head of the pillar cells. 4 Discussion Figure 2. Pivot analysis of hair cell stereocilia motion. Sound intensity in this case was 104 dB SPL. Estimated pivot axes are positioned in a schematic drawing of the organ of Corti. Circles: OHC bundle bases (rows 1 and 2). Crosses: OHC bundle tips. Diamond: IHC bundle base. Star: IHC bundle tip. The lines show the directions perpendicular to the trajectories of the corresponding cilia bases or tips.

258 4.1 Pattern of cilia deflection for outer hair cells The observed trajectories of the OHC cilia bases and tips are consistent with a model of OHC bundle deflection driven by the opposing rotations of the reticular lamina and the tectorial membrane. An important difference with classical models [5] is that the motion of the organ of Corti is far from being rigid, which was seen even at the level of a single hair bundle. The apparent center of rotation of the tips was closer from the hair cells than naively expected from the point of attachment of the tectorial membrane. This pattern was observed consistently in many experiments. If significant, the observed difference might have several origins. The most natural one would be the presence of deformations in the tectorial membrane, but it could also reflect a relative shallowness in the coupling between the OHC cilia and the tectorial membrane. 4.2 Pattern of stereocilia deflection for inner hair cells Our data provide direct evidence that deflection of IHC stereocilia occurs by a different mechanism than the one at work in OHCs. Our results are consistent with a model of IHC cilia deflection driven by fluid interactions, as expected from their lack of attachment with the tectorial membrane. IHC stereocilia deflection was found to lead the displacement of the reticular lamina by 44°, a figure representative of most our experiments, and close to previous estimates obtained from electrophysiological studies (65 - 80° measured by Dallos [6]; and -50°, observed at 86 dB SPL by Dallos and Cheatham [7]). A model of IHC bundle deflection driven purely by fluid velocity, as frequently assumed, would correspond to a phase lead of 90°. Our smaller phase lead estimate rather suggests that the IHC bundles responded to a combination of velocity and displacement. This feature is not unexpected in realistic models of hair bundle deflection driven by hydrodynamic forces [8]. It seems also likely that interaction with the Hensen stripe could affect the fluid flow around IHC cilia [9]. 4.3 Small amplitude of IHC bundle deflection In typical experiments, the deflection of OHC stereocilia had an amplitude about twice that of IHC stereocilia (when observed at the same location in the cochlea). At least two natural explanations for this may be mentioned. Clearly, attachment of stereocilia to the tectorial membrane should help stimulate the OHC bundles, resulting in a more effective deflection. In addition, OHCs show larger amplitudes of vibration in response to sound than do the IHCs, the latter being located closer to the overall pivot axis of the organ of Corti [2,3 and figure 2], In this view, the fact that reticular lamina displacement and angular cilia deflection were near proportional with similar slopes for IHCs and OHCs is of interest. This creates an issue when considering the induced receptor currents. Electrophysiological

259 measurements indicate that receptor potentials in IHCs are about 4 times larger than in OHCs [6,10]. Taking account of the hair cells' impedances (estimated in Dallos' recordings [6]), receptor currents are found to be about twice larger in IHCs than in OHCs, in vivo. Comparing with our results, this means that IHCs are about 4 times more effective to convert deflection into a receptor current than are the OHCs. If the hair bundles of IHCs and OHCs have similar mechanical properties, this would seem to imply a difference in the transduction channels themselves (e.g. higher conductance, larger number, or higher opening sensitivity of IHC transduction channels). References 1.

2.

3. 4.

5.

6. 7. 8. 9. 10.

Dallos P., Billone M.C., Durrant J.D., Wang C.-Y., Raynor S., 1972. Cochlear inner and outer hair cells: Functional differences. Science 177:356 -358. Fridberger A., Boutet de Monvel J., Ulfendahl M., 2002 Internal shearing within the hearing organ evoked by basilar membrane motion. J Neurosci 22:9850-57. Fridberger A., Boutet de Monvel J., 2003. Sound-induced differential motion within the hearing organ. Nature Neurosci 6:446-48. Fridberger A., Widengren J., Boutet de Monvel J., 2004. Measuring hearing organ vibration patterns with confocal microscopy and optical flow. Biophys. J. 86, 535-43. Rhode W.S., Geisler CD., 1967. Model of the displacement between opposing points on the tectorial membrane and reticular lamina. J Acoust Soc Am. 42: 185-190. Dallos P., 1985. Response characteristics of mammalian cochlear hair cells. J Neurosci 5:1591-1608. Cheatham M.A., Dallos P. 1998. The level dependence of response phase: Observations from cochlear hair cells. J Acoust Soc Am 104: 356 - 69. Freeman M., Weiss T., 1990. Hydrodynamic forces on hair bundles at low frequencies. Hear Res 48:17-30. Steele C.R., Puria S., 2005. Forces on inner hair cell cilia, in press. Russell I.J., Sellick P.M., 1983. Low-frequency characteristics of intracellularly recorded receptor potentials in guinea-pig cochlear hair cells. J Physiol. 338:179-206.

Comments and Discussion Gummer: I am happy to see that you are also proposing fluid amplification in the subtectorial space as a possible mechanism for stimulating IHC stereocilia (see Gummer et al., this volume). Since this mechanism requires an intact tectorial

260

membrane (TM), which could be compromised by opening Reissner's membrane, please state whether: i) the TM is intact, ii) the OHC stereocilia are embedded in the TM, and iii) the proximity of Hensen's stripe to the IHC stereocilia. Answer: Tectorial membrane integrity was assessed after completion of the measurements by staining it with ConA/Alexa488. The tectorial membrane retained its normal size, position and relation to both outer and inner hair cell stereocilia. Hensen's stripe was located close to the hair bundle but I do not have a measurement of the distance right now. The image showed during the talk is representative of our experiments and indicates that Hensen's stripe is very close to the stereocilia. Aranyosi: Your measurements show that the reticular lamina undergoes elliptical motion. We also saw elliptical trajectories of motion in the alligator lizard cochlea, and showed that (1) such motion could be explained by a rigid body model, and (2) this model exhibited two modes of motion — a translation in the transverse direction, and a rotation centered near the neural side of the basilar membrane. Can your elliptical trajectories be explained by rigid body motion, and if so, do you see evidence of multiple modes of motion of the organ of Corti? Answer: I did not have time to mention this during the talk, but the data, which is shown in the manuscript submitted to this meeting, indicates that the motion is far from being rigid. Different structures within the organ have different centers of rotation (see also Fridberger et al., J Neuroscience (2002); Fridberger and Boutet de Monvel, Nature Neuroscience (2003); Fridberger et al., Biophysical J (2004)). Guinan: I noticed that in your plot of IHC stereocilia phase, the two points with the lowest amplitudes had much different phases than the other points. This is reminiscent of the level-dependent phase jumps seen in auditory nerve firing by many people. Is the level difference you see in IHC stereocilia phase significant? And, if so, do you know of a methodological reason for it, or is it telling us that there is a change with sound level in the vibrational mode of the organ of Corti so that IHC stereocilia are driven with a different phase at different levels? Answer: We have seen reversals of the phase in some preparations, but we have not explored the phenomenon in a systematic way. The parallel to the auditory nerve recordings is interesting and I hope that we will be able to say more about this in the future.

THE COCHLEAR AMPLIFIER: IS IT HAIR BUNDLE MOTION OF OUTER HAIR CELLS? 'SHUPING JIA, 2JIAN ZUO, 3PETER DALLOS, '*DAVID Z.Z. HE 'Department of Biomedical Sciences, Creighton University, Omaha, NE 681752St. Jude Children Research Hospital, Memphis, TN 381053Auditory Physiology Laboratory, Northwestern University, Evanston, IL 60208 Cochlear outer hair cells (OHCs) are involved in a mechanical feedback loop in which the fast somatic motility of OHCs is required for cochlear amplification. Alternatively, amplification is thought to arise from active hair bundle movements similar to that in non-mammalian hair cells. We measured the voltage-evoked hair bundle motions in the gerbil cochlea to determine if such movements are also present in mammalian OHCs. The OHCs displayed a large hair bundle movement that was not based on mechanotransducer channels but originated in somatic motility. Significantly, bundle movements were able to generate radial motion of the tectorial membrane in situ. This result implies that the motility-associated hair bundle motion may be part of the cochlear amplifier.

1 Introduction It is generally believed that mechanical amplification by hair cells is necessary to enhance the sensitivity and frequency selectivity of hearing. In the mammalian cochlea OHCs function as the key elements in a mechanical feedback loop that most likely involves OHCs, organ of Corti micromechanics and the tectorial membrane (TM), with inner hair cells (IHCs) responding to the output of the feedback loop (7,2). OHCs exhibit a voltage-dependent length change termed electromotility (3). This somatic motility is thought to underlie cochlear amplification in mammals (/4). The alternative view is that the amplification arises from active hair bundle motion, a phenomenon that has been observed in non-mammalian hair cells (5,6). In order to further study if hair bundle movements are responsible for amplification in mammalian OHCs, we evaluated voltage-evoked hair bundle activity in the cochlea of gerbils and prestin knockout mice (4). 2 Results Sensory epithelia were dissected from the cochleae of adult gerbils and prestin knockout mice. The resulting coil preparation was bathed in artificial perilymph and mounted on the stage of a Leica upright microscope with a 63x water-immersion objective. Under bright-field illumination at high magnification, the hair bundles behaved as light pipes (7) and appeared as bright V-shaped lines (Fig. 1A). To measure bundle motion, the magnified (l,260x) image of the edge of the hair bundle was projected onto a photodiode through a rectangular slit. The photodiode-based

261

262

system, mounted on the photo-port of the Leica microscope, had a 3-dB cutoff frequency of 1,100 Hz and was capable of measuring motion down to ~5 nm with moderate averaging and low-pass filtering. Before the voltage-evoked bundle motion was measured, we recorded mechanotransducer currents to verify that the mechanotransducer apparatus in the stereocilia was not damaged. Fig. IB shows an example of such recording from an apical turn gerbil OHC. The hair bundle was deflected by a fluid jet (with pipette tip diameter of 10 urn) positioned 20-30 um away from the bundle. Transducer currents were recorded at the holding potential of-70 mV in the voltage-clamp mode. Large transducer current was observed (Fig. IB). The size of the current is comparable to previous studies in mammalian OHCs (8-10). To determine bundle motions, sinusoidal voltage bursts (102 Hz) were applied to the OHCs through the patch electrode. The voltage command varied the membrane potential from -100 to -40 mV from a holding potential of -70 mV. Examples of the voltage-evoked hair bundle movements are shown in Fig. 1C. Bundle motion is asymmetrical with depolarization evoking larger bundle motions in the direction toward the tallest stereocilia than hyperpolarization does in the opposite direction. The direction of bundle motion during membrane potential change is consistent with that seen in turtle hair cells (7,11), but is of opposite polarity to that seen in bullfrog saccular hair cells (12,13). Fig. 1. A. Hair bundles of OHCs under high magnification (63x water-immersion objective) with bright field illumination. Double-headed arrow indicates the direction of bundle motion. Scale bar represents 10 um. B. Mechanotransducer currents recorded from an apical turn gerbil OHC from the coil preparation. The bundle was deflected by an oscillating stream from a fluid jet positioned -20-30 um away from the bundle. The response shown is the average of 3 trials. The voltage command (102 Hz) to drive the water jet is presented at the bottom of the panel. Inward current is plotted downward. C. Voltage-evoked bundle motions of a gerbil OHC at two different Jims Iflisj Time<msj extracellular calcium concentrations. The 102 Hz voltage command varied the membrane potential from 100 to ~W) mV around the holding potential of -70 mV. Positive bundle motion (toward tall cilia) is plotted upward in this and all subsequent figures. D. Bundle motion before and after 100 uM streptomycin was perfused to the OHC stereociliary region. The responses in C and D were the averages of 100 trials. The scale bar in C also applies to the responses in D.

Hair cells of several non-mammalian species display an active hair bundle motion in response to changes in membrane potential (7, 11-13). The active motion, intimately associated with mechanotransducer channels, is secondary to alteration of calcium influx in the stereocilia and is, therefore, dependent on the extracellular calcium concentration (7,11). We sought to determine whether the bundle motion observed in OHCs also operates on a similar basis. Bundle motion was examined

263

when the extracellular calcium concentration was altered. Fig. IC shows an example when the extracellular calcium was reduced to 5 uM. Robust voltageevoked bundle motion was still observed. Streptomycin is known to block mechanotransducer channels (8) and eliminate active and spontaneous bundle motion (7,13). We perfused 100 uM streptomycin to the ciliary area to see whether it blocked the voltage-evoked bundle motion in OHCs. As shown in Fig. ID, the bundle motion was not affected by streptomycin. Collectively, these results suggest that the observed bundle motion in OHCs is different from the voltage-evoked bundle motion seen in non-mammalian hair cells. As an alternative to motility derived from mechanotransducer processes, it is possible that bundle motion arises as some consequence of somatic motility. To demonstrate that the observed hair bundle motion is associated with somatic motility, we examined the voltage-evoked bundle motion in neonatal gerbils. Studies have shown that the onset of OHC motility occurs around 6-8 days after birth (14) while mechanotransducer channels are known to be mature at birth (8,9). Voltage-evoked bundle motions of apical turn OHCs were measured from developing gerbils at 4, 8, and 12 days after birth (DAB). Fig. 2A shows some examples of the responses measured from those preparations. At 4 DAB when electromotility had not yet developed, no voltage-evoked bundle motion was detected (n=10), although large transducer currents could be measured (data not shown). At 8 DAB, we observed small bundle motion in 1 of 8 cells examined. At 12 DAB when all OHCs exhibit electromotility (14), voltage-evoked bundle motion was detected in all 7 cells studied, with a magnitude of approximately 72% of that of the adult OHCs with the same voltage stimulation. The fact the development of bundle movements correlates with the development of somatic motility suggests that the voltage-evoked bundle motion is related to somatic motility. We examined the voltage-evoked bundle motion in prestin (75) knockout mice (4). Such measurements are important to determine whether there is any small transducer channel-based bundle motion that is overshadowed by the dominant motility-associated bundle motion. These mice have normal morphology of the hair bundles and normal mechanotransducer functions (4,16) with no OHC somatic motility. We measured transducer currents first to confirm that their mechanotransducer channels are functional. Fig. 2B shows an example of the transducer current recorded from an apical turn OHC of the prestin knockout mouse. As shown, large asymmetrical transducer current was observed. We measured the voltage-evoked bundle motion from the OHCs of prestin-null mice. No voltage-evoked bundle motion was seen in any of the 11 cells examined (Fig. 2C). In contrast, when the voltage-evoked bundle motion was measured from OHCs of wild-type mice, large bundle motions were seen for all cells studied. We also measured the voltage-evoked bundle motion with the ciliary area perfused with endolymph-like solution to mimic the in vivo chemical condition in 5 additional prestin-null OHCs. No voltage-evoked bundle motions were observed in any of the

264

5 cells examined. This confirms that the voltage-evoked bundle motion is indeed associated with somatic motility. Fig. 2. A. Voltage-evoked bundle motions measured from 4-, 8-, and 12-day-old gerbil OHCs. The stimulus waveform and voltage command is the same as shown in Fig. 1C. B. Mechanotransducer currents recorded BCWB from an apical turn OHC of prestin knockout mouse. C. Lack of voltage-evoked bundle motion from the prestin knockout mouse OHC. D. Bundle motions of an apical turn gerbil OHC as a function of voltage levels (from a holding potential of -70 mV). Steadystate response from D was fitted with a second-order Boltzmann function (solid line) and plotted in the bottom panel. Slope function (dashed line) was obtained as the derivative of the Boltzmann function. The series resistance was 75% compensated. Because membrane conductances were blocked, the uncompensated voltage error (not corrected in the plot) was less than 4 mV at the largest voltage levels. '""vuHg* t£v)" f£jo»ty{Hij """ E. Motility-associated bundle motions evoked by a series of voltage bursts with different frequencies (frequency is shown on the top of the response waveforms). The peak-to-peak response was measured and plotted as a function of frequency in the bottom panel. 4 DAS

Subsequently, we examined bundle motion as a function of membrane potential (input-output function). Fig. 2D shows an example of the response measured from an apical turn gerbil OHC when the membrane potential was stepped from the holding potential of -70 mV. The responses were asymmetrical and nonlinear with saturation in both directions, similar to that seen in OHC somatic motility (77). We fitted the response with a second-order Boltzmann function, and the maximum sensitivity calculated from the derivative of this function was ~5 nm/mV (Fig. 2D). The maximum peak-to-peak response observed in the example was 567 nm. The largest peak-to-peak response observed among 6 cells examined was 832 nm. We also examined the frequency response of the voltage-evoked bundle motion between 50 and 1,000 Hz using sinusoidal voltage bursts. An example is shown in Fig. 2E. Apparently, large bundle motions were still present at 1,000 Hz. The frequency response of the bundle motion was similar to that of OHC somatic motility measured under whole-cell voltage-clamp condition (18). The TM is an important element of the mechanical feedback loop and its role in mechanoelectrical transduction, frequency tuning, and cochlear amplification has been demonstrated (19-21). The most direct path for OHC bundle motion to influence input to IHCs is through the TM. We questioned whether hair bundle motion could generate a radial TM motion. For this purpose, the gerbil hemicochlea (22) was used to examine TM radial motion driven by OHC bundle motion. Hemicochleae (Fig. 3A) were prepared from 25 to 30 day old gerbils. Whole-cell recordings were made from the upper basal turn where OHC mechanotransducer currents were previously recorded (70). The cells were current-clamped to a level

265

that would result in a membrane potential of approximately -70 mV. Current (100 Hz sinusoid, 100 to 300 uA) bursts generated by a modified battery-powered stimulator (Isostim A320, WPI) created a diverging electrical field between the stimulating pipette (tip diameter of 4 um) positioned 50-60 urn away from the OHCs and the indifferent earth in the bath. This focal electrical stimulation depolarizes and hyperpolarizes OHCs near the electrode (23). Fig. 3C shows an example of simultaneous recordings of radial motion of the TM and the membranevoltage response of an OHC. As shown, the focal electrical stimuli resulted in a net membrane potential change of 18 mV (peak-to-peak) and produced a radial TM motion of ~10 nm (peak-to-peak). Depolarization (hyperpolarization) resulted in TM motion toward the spiral ligament (modiolus). While the voltage response of the OHC was nearly symmetrical, TM motion was asymmetrical, with both ac and dc components. This asymmetry resembles that of the bundle motion considered above and may originate from the asymmetry of OHC somatic motility (77). To confirm that the TM motion was the result of bundle motion, we measured TM motion in preparations where the TM was detached from the hair bundles of OHCs. As expected, no TM motion was detected (Fig. 3D) in any of 15 such preparations examined. We also observed radial TM motion when 100 mV sinusoidal voltage was applied to one OHC under the whole-cell voltage-clamp condition (data not shown) This again confirms that the TM motion was the result of bundle motion. Fig. 3. A. Hemicochlea from a 30-day-old gerbil. The square represents the area where the TM motion was measured using a photodiode-based technique. The white double-headed arrows indicate directions of the TM motion measured. Small black arrow indicates the Hensen's stripe on the underside of the TM. B. Hensen's stripe and IHC bundle at high magnification. Bars in A and B represent 10 urn. C. Simultaneous recordings of TM radial motion and membrane potential changes of an OHC from the upper basal turn of a 28-day-old gerbil hemicochlea. Current f S f — < ^ — — — ^] fmttftmm vsftage response (100 Hz sinusoid, bottom trace in B) was •ss3 (%m*Kinjected c« -^" injected through another pipette positioned ~50 um away from the cell under recording to depolarize and hyperpolarize it. Upward deflection in the trace represents the movement of the TM toward the spiral ligament. D. TM motion and membrane voltage response measured from another hemicochlea when the TM was detached from the hair bundles No TM motion was observed. The responses are the averages of 200 trials. 'VfflSMh.

3 Discussion This work demonstrates significant ciliary rotation evoked by OHC electromotility. Yet, in the absence of electromotility, ciliary rotation, presumably related to the

266

mechanotransducer channels, is below the resolution limit of our system. The motility-associated bundle motion is large (over 800 nm), approximately ten times (20 dB) larger than the transducer-channel based bundle motions observed in nonmammalian hair cells (7,12,13). Voltage-evoked bundle motion of IHCs was reported in a recent study (24) using a two-chamber preparation. The motilityassociated response possibly overshadows transducer channel-based mechanisms in OHCs. It is not fully established how OHC length changes result in bundle motion. However, tilting of the cuticular plate during motility has been reported to occur at high frequencies (up to 15 kHz) in coil preparations (25). Rotation of the reticular lamina as a result of OHC motility was also seen in situ (23). It is, therefore, likely that rotation of the reticular lamina along its fulcrum at the pillar heads and possibly tilting of the cuticular plate within the reticular lamina during OHC length change can produce bundle motions. OHC somatic motility has been proposed to be responsible for cochlear amplification in mammals. However, it is yet to be fully determined how active somatic movements of OHCs excite IHCs. Obviously, coupling OHC motility to basilar membrane and reticular lamina movements in an appropriate phase would boost their displacements. In addition, the bundle motion associated with OHC somatic motility provides a possibility for OHC motility to boost the input to IHCs. Because movement of the bundle is able to produce radial motion of the TM, this motion could amplify mechanical input to the IHC by increasing fluid motion in the TM-reticular lamina gap. It is such fluid flow that stimulates the freestanding IHC cilia (27). It is conceivable that fluid-pumping by Hensen's stripe (see Fig. 3B) onto the closely apposed IHC cilia is the excitatory mechanism. The ' V or ' W shaped staircase structure of the OHC stereocilia is well suited for promoting mechanical coupling between the TM and reticular lamina, which can transfer the motilitydriven hair bundle motion into the radial motion of the TM. It is, therefore, conceivable that the motility-associated hair bundle motion may be part of cochlear amplification in mammals. Under this scheme, OHC somatic motility not only boosts basilar membrane vibration but also drives the hair bundle motion, which is able to produce the radial motion of TM. The force produced by OHC hair bundles can further enhance the radial motion of the TM. Since the bundle and TM motions are both associated with somatic motility of OHCs, this scheme is in line with studies using prestin-knockout mice (4,16), which support motility-based amplification as the dominant mechanism in the mammalian cochlea. The principal argument against somatic motility as the amplifier is that the lowpass filter characteristics of OHC membrane attenuate receptor potentials at high frequencies. However, it has been proposed that extracellular potential changes within the organ of Corti could drive OHC motility at high frequencies (28). Recent measurements of basilar membrane vibration and extracellular potentials provide evidence that those extracellular potentials can indeed drive OHC motors at high frequencies (29). Furthermore, theoretical modeling also indicates that the

267

piezoelectric property of OHCs can significantly increase the frequency response of OHCs (30). References 1. Dallos, P., Fakler, B., 2002. Prestin, a new type of motor protein. Nat. Rev. Mol. Cell Biol. 3, 104 2. Santos-Sacchi, J., 2003. New tunes from Corti's organ: the outer hair cell boogie rules. Curr. Opin. Neurobiol. 13,459 3. Brownell, W.E., Bader, C.R., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses in isolated cochlear outer hair cells. Science 227, 194 4. Liberman, M.C., et al., 2002. Prestin is required for outer hair cell electromotility and the cochlear amplifier. Nature 419, 300 5. Hudspeth, A.J., 1997. Mechanical amplification of stimuli by hair cells.Curr. Opin. Neurobiol. 7,480 6. Fettiplace, R., Ricci, A.J., Hackney, CM., 2001. Clues to the cochlear amplifier from the turtle ear. Trends Neurosci. 24, 169 7. Ricci, A.J., Crawford, A.C., Fettiplace, R., 2000. Active hair bundle motion linked to fast transducer adaptation in auditory hair cells. J. Neurosci. 20, 7131 8. Kros, C.J., Rusch, A., Richardson, G.P., 1992. Mechano-electrical transducer currents in hair cells of the cultured neonatal mouse cochlea. Proc. R. Soc. Lond. B. Biol. Sci. 249, 185 9. Kennedy, H.J., Evans, M.G., Crawford, A.C, Fettiplace, R., 2003. Fast adaptation of mechanoelectrical transducer channels in mammalian cochlear hair cells. Nature Neurosci. 6, 832 10. He, D.Z.Z., Jia, S.P., Dallos, P., 2004. Mechanoelectrical transduction of outer hair cells studied in a gerbil hemicochlea. Nature 429, 766 11. Crawford, A.C, Fettiplace, R. 1985. The mechanical properties of ciliary bundles of turtle cochlear hair cells. J. Physiol. 364, 359 12. Assad, J.A., Hacohen, N., Corey, D.P., 1989. Voltage dependence of adaptation and active bundle movement in bullfrog saccular hair cells. Proc. Natl. Acad. Sci. USA. 86, 2918 13. Bozovic, D., Hudspeth, A.J., 2003. Hair-bundle movements elicited by transepithelial electrical stimulation of hair cells in the sacculus of the bullfrog. Proc. Natl. Acad. Sci. USA 100, 958 14. He, D.Z.Z., Evans, B.N., Dallos, P., 1994. First appearance and development of electromotility in neonatal gerbil outer hair cells. Hear. Res. 78, 77 15. J. Zheng et al., 2000, Prestin is the motor protein of cochlear outer hair cells. Nature 405,149 16. Cheatham, M.A., Huynh, K.H., Gao, J., Zuo, J., Dallos, P., 2004. Cochlear function in prestin knockout mice. J. Physiol. 560, 821 17. Santos-Sacchi, J., 1989. Asymmetry in voltage-dependent movements of isolated outer hair cells from the organ of Corti. J. Neurosci. 9, 2954

268 18. Santos-Sacchi, J., 1992. On the frequency limit and phase of outer hair cell motility: effects of the membrane filter. J. Neurosci. 12, 1906 19. Legan, P.K., et al., 2000. A targeted deletion in alpha-tectorin reveals that the tectorial membrane is required for the gain and timing of cochlear feedback. Neuron 28, 273 20. Lukashkin, A.N., et al., 2004. Role of the tectorial membrane revealed by otoacoustic emissions recorded from wild-type and transgenic Tecta (deltaENT/deltaENT) mice. J. Neurophysiol. 91, 163 21. Gummer, A.W., Hemmert, W., Zenner, H.P., 1996. Resonant tectorial membrane motion in the inner ear: its crucial role in frequency tuning. Proc. Natl. Acad. Sci. USA 93, 8727 22. Hu, X.T., Evans, B.N., Dallos, P., 1999. Direct visualization of organ of Corti kinematics in a hemicochlea. J. Neurophysiol. 82, 2798 23. Mammano, F., Ashmore, J.F., 1994. Reverse transduction measured in the isolated cochlea by laser Michelson interferometry. Nature 365, 838 24. Chan, D.K., Hudspeth, A.J., 2005. Ca(2+) current-driven nonlinear amplification by the mammalian cochlea in vitro. Nat. Neurosci. 8,149 25. Reuter, G., Gitter, A.H., Thurm, U., Zenner, H.P., 1992. High frequency radial movements of the reticular lamina induced by outer hair cell motility. Hear. Res. 60, 236 26. Dallos, P., Billone, M.C., Durrant, J.D, Wang, C.-y., Raynor, S., 1972. Cochlear inner and outer hair cells: functional differences. Science 177, 356358 27. Kennedy, H.J., Crawford, A.C., Fettiplace, R., 2005. Force generation by mammalian hair bundles supports a role in cochlear amplification. Nature 433, 880 28. Dallos, P., Evans, B.N., 1995. High-frequency motility of outer hair cells and the cochlear amplifier. Science 267,2006 29. Fridberger, A., et al., 2004. Organ of Corti potentials and the motion of the basilar membrane. J. Neurosci. 24, 10057 30. Spector, A.A., Brownell, W.E., Popel, A.S., 2003. Effect of outer hair cell piezoelectricity on high-frequency receptor potentials. J. Acoust. Soc. Am. 113,453 Comments and Discussion Chan: Very nice work. My question relates to the discrepant results regarding voltage-evoked movement of hair bundles- whereas both Fettiplace and myself have observed voltage-evoked bundle movement that is sensitive to transduction-channel block (by streptomycin or amiloride), you do not find such a streptomycin-sensitive. Is it possible that this discrepancy is related to the bias of the transducer channel? Your transducer-current traces suggest a resting open probability of only a few percent, whereas Fettiplace's results place the transducer closer to 10-20%, and my

269

microphonic recordings place the transducer near 50%, which is typically observed in vivo in OHCs at high frequencies. Answer: I could not explain the discrepancy between my data and those of Fettiplace. In our preparation, only 5% of transducer channels were open. The preparation is essentially the same as that used by Fettiplace et al. I would assume that more channels are open in vivo (as you have showed) with the tectorial membrane attached. It is not clear whether more channels operating at rest would contribute to bundle motion. The V-shaped structure of the stereocilia certainly is not very well suited for the ciliary rotation. The direction of tip-links is also not unidirectional. Anyway, we are using an isolated cochlear preparation and hopefully, this preparation will provide some answers.

PRESTIN-LACKING MEMBRANES ARE CAPABLE OF HIGH FREQUENCY ELECTRO-MECHANICAL TRANSDUCTION

B. ANVARI AND F. QIAN Department

of Bioengineering, 6100 Main St., MS-142, Rice University, Houston TX 77005, USA E-mail: anvari(a),rice.edu, E-mail: fensqian(a),rice.edu F. A. PEREIRA

Hufflngton Center on Aging, Department of Otorhinolaryngology & Communicative Science, Department of Molecular and Cellular Biology, One Baylor Plaza, Houston TX 77030, USA E-mail: foereira(a),bcm. tmc. edu W. E. BROWNELL Department

of Otorhinolaryngology & Communicative Sciences, One Baylor Plaza, TX 77030, USA E-mail: brownell(a),bcm. tmc.edu

Houston

Using a novel experimental technique that combines optical trapping with patch-clamp and fluorescence photometry, we provide preliminary evidence that native biological membranes are capable of electrically-induced piconewton level force generation in the absence of specialized transmembrane proteins such as prestin. Force generation is dependent on membrane tension and the transmembrane electrical potential. Salicylate diminishes and prestin enhances force generation.

1 Introduction Mammalian outer hair cells (OHCs) within the organ of Corti are specialized sensory cells with force generating capabilities [1]. Recently, an OHC transmembrane protein, prestin, has been discovered [2]. When prestin is expressed in non-auditory mammalian cells it endows the transfected cells with electromotility [2], and voltage-dependent non-linear capacitance (NLC) [3], which serves as a reliable "signature" of electromotility [3]. Atomic force microscopy experiments have demonstrated that upon electrical stimulation of rat prestin-transfected human embryonic kidney (HEK) cells in a microchamber configuration, forces up to a stimulus frequency of 20 kHz are generated [4], Conversely, mechanical stimulation of the cells shifted the voltage-dependence of the NLC. The preponderance of these experimental results clearly establishes that prestin enhances native motility and imparts NLC to cells, and suggest that prestin contributes to the mechanism responsible for OHC electromotility. In this paper, we report measurements of electrically-induced forces by prestin-lacking membranes and outer hair cells.

270

271 2 Methods We have designed and constructed a system that combines optical tweezers with patch-clamp and fluorescence photometry techniques [5]. With this system, optical tweezers are used to form a plasma membrane tether from a patch-clamped cell while fluorescence photometry is used to measure electrically-induced forces by membranes. We form membrane tethers by trapping a fluorescent sulfate-derivatized polystyrene microsphere (typically 4.0 um in diameter) and bringing it in contact with the cell. The cell is subsequently moved away from the trapped microsphere using a piezoelectric translator (PZT) to form a membrane tether linking the trapped microsphere to the cell. Patch pipettes with typical resistances of 2-4 MQ are pulled from borosilicate capillary tubes, and placed near an optically-trapped microsphere. After a seal with resistance of >1GQ is formed, a voltage pulse or gentle suction is applied to break the membrane patch in order to enter the whole cell patch configuration. The light from a Xenon source is used for fluorescence excitation of the trapped microsphere. The fluorescent emission from the microsphere is focused onto a quadrant photodetector (QPD). Light from a halogen source is used for visualization of the cells by a CCD camera. We use the dynamic displacement of the trapped fluorescent microsphere from the trapping center in response to force application as a technique to obtain timeresolved force measurements. Specifically, as the tether is elongated by movement of the PZT, the trapped microsphere is displaced from its trapping center to cause a change in the fluorescence intensity projected onto the QPD surface, generating a continuous voltage signal on each quadrant. Calibration of the transverse microsphere displacement is performed using the displacement of a coverslip-adherent microsphere, positioned at the same focal plane as a trapped particle, to known transverse distances with the PZT, and recording the change in QPD differential voltage signal, as described in our previous work [6]. To calibrate for the transverse trapping force, a solution is flown (by moving the PZT) through a trapped particle within the chamber at a known velocity, and the drag force acting on the spherical microsphere is calculated from Stokes' law [6]. Outer hair cells were obtained from the cochlea of Albino guinea pigs within four hours of the animal sacrifice. Both cochlea were dissected from temporal bones, and placed into the normal extracellular solution (NES). After 5 min of incubation, OHCs were harvested using a microsyringe and placed in a poly-Dlysine coated sample chamber with 1.5 ml of NES.

272

(a)

Human embryonic kidney (HEK) cells were used as models to investigate force generation in the absence of prestin. Cultured HEK cells were incubated into the sample chamber for 2 hours. After the cells became adherent to the bottom of the sample chamber, the culture medium was substituted with 1.5 ml of an NES solution.

(b)

3 Results Examples of tethering force measurements from a giant unilamellar lipid vesicle (GULV), a wildtype HEK cell, and an OHC under nonvoltage clamped conditions are shown in Figure 1. The magnitude of the peak value, (c) which represents the tether formation force, was the least (=40pN) for the GULV, and greatest (=120pN) for the OHC, with an intermediate value (=70pN) for the HEK cell. The larger value of the force required to pull tethers from the OHC reflects the influence of the underlying cortical lattice, which is absent Figure 1. Tethering force profiles for: (a) GULV, (b) wildtype HEK, and in the GULV and HEK cells. The steady state (c) OHC without voltage-clamping. force values showed a similar trend with the lowest value (=20pN) for the GULV, an intermediate value (~25pN) for the HEK cell, and the greatest value (=50pN) for the OHC, an indication of increased membrane tension with a progression in membrane-cytoskeleton complexity. We carried out experiments aimed at investigating the membrane mechanical response to high frequency sinusoidal electrical excitation (Figure 2). Using Fourier analysis of the temporal force measurements, we observed that both OHC and wildtype HEK cell membranes were capable of producing a force in response to lOOmV peak-to-peak electrical excitation at 3.1kHz. Note that the attenuations caused by the low-pass filtering of patch-clamp amplifier leave the possibility that membranes may respond to much higher electrical excitation frequencies. These results confirm the ability of membranes to generate mechanical force in response to changes in high frequency transmembrane potential even in the absence of specialized membrane proteins such as prestin, while the presence of prestin in the OHC enhances the amplitude of the generated force.

273

When carrying out the experiments at various holding potentials, we discovered that the amplitude of force generation was voltage-dependent at both low and high frequency electrical excitations (Figure 3). Results (normalized to the response at zero holding potential) from membrane tethers formed from HEK cells (w=7) demonstrate a reduction by an approximate UBU f i l l

^

I I

i OHC

1.0

2.0

3.0

L

L

factor of three in electrically-induced force generation as the membrane becomes increasingly depolarized at 1kHz sinusoidal excitation frequency (±20mV peak-to-peak). Results from membrane tethers formed from two OHCs show a similar trend at lower excitation frequency of 6Hz (±20mV peak-topeak). We also carried out experiments using wildtype HEK cells where membrane tethers were pulled to various lengths to effectively induce changes in the membrane tension, and measured the electrically-induced force generation in response to 1kHz sinusoidal

4.0

S.0

6.0

FrftQuefley £kHz) Figure 2. Electrically-induced force generation from wildtype HEK and OHC membrane tethers in response to 3.1kHz sinusoidal excitation.

excitation (±100mV) at holding potential of -40mV. Results demonstrate that force generation increases with changes in membrane tension as the tether length is increased (Figure 4).

Holding potential |mV) OHC

Holding potential (mV)

Figure 3. Electrically-induced force generation for membrane tethers formed from wildtype HEK cells and OHCs at various holding potentials.

274 HEK cull 0.14

%""""""" i"a"""

21

si — g -

"^j

T«8iar length (urn)

Figure 4. Electrically-induced force generation for membrane tethers formed from wildtype HEK cells at various tether lengths.

Early experiments have suggested that salicylate (Sal) induces extra negative surface potential to membranes [7], presumably by partitioning its benzene ring into the lipids. We observed a nearly two-fold decrease in the amplitude of the electrically-induced force generation by membrane tethers formed from wildtype HEK cells in the presence of lOmM extracellular Sal (Figure 5) when compared with the results in the absence of Sal (Figure 2).

Figure 5. Electrically-induced force generation from wildtype HEK membrane tethers in presence of lOmM Sal.

«

ZS

3 . 0 4 . 0

S.O

6,0

4 Discussion Although the exact mechanism for our observed electrically-induced force generation by membranes is not known (let alone its enhancement by prestin), the process may be viewed as generation of mechanical stresses that result from changes in membrane surface area (piezoelectric phenomenon) [8,9], or curvature (flexoelectric phenomenon) [10-12]. Flexoelectricity may be attributed to changes in the lipid surface charge equilibrium associated with the charged head groups of phospholipids: curving the membrane causes an effective displacement of electric charges across the whole membrane (e.g., excess of negative charges over the expanded outer surface and deficiency over the compressed inner surface), which results in a large electric dipole (or more generally, multipoles) [13]. Converse flexoelectric effect may be attributed to the Lippman equation [14] that equates the surface charge to the negative derivative of the interfacial tension with respect to the electrostatic potential. The mobile charges within the lipid membranes are attracted to the charges supplied by an external voltage source. These mobile charges repel each other laterally, creating a local pressure and changing the net interfacial

275

tension. In a membrane bilayer, it is this differential tension between the two interfaces that can induce curvature changes [15]. Therefore, membrane surface charge and membrane tension are two key physical properties whose effects on force generation need to be understood. The fact that our previous results [16] have not indicated a significant difference in the mechanical (as opposed to electromechanical) characteristics of membranes, and yet, we observe a decrease in force generation in presence of Sal in wildtype HEK cells, which lack prestin, tends to suggest that a motor-like mechanism may exist within the membrane itself whose origin may be traced to charge properties of the lipids. Our preliminary results with Sal are not only consistent with the hypothesis of Sal-induced inhibition of electromotility with Sal acting as a chloride competitor [17], but also provide the additional information that membranes themselves may possess a motor-like ability that is impaired by Sal. Recently, other investigators have reported that hair bundles of mammalian hair cells are capable of force production [18,19]. Our observation of electricallyinduced force generation by prestin-lacking membranes is consistent with these studies. We are motivated by our preliminary studies, which suggest an enhancement of a native membrane-based motor mechanism by prestin, to explore which particular structural features of prestin as well as its interaction with the membrane may contribute to the overall electrically-induced force generation. While it is reasonable to expect that presence of specific proteins within the membrane will alter the intrinsic membrane electrical polarization resulting from the charged lipid head groups, it remains unknown as to what prestin domains will induce the greatest effect. To address these issues, we plan to use prestin-transfected HEK cells, mutated prestins, and other protein members of the SLC26A family to which prestin belongs in our future studies. Acknowledgements This study was supported in part by a grant (R01-DC02775) from the National Institute of Deafness and Other Communication Disorder at the National Institutes of Health. References 1. Brownell, W.E., Bader, C.R., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science 227, 1946. 2. Zheng, J., Shen, W., He, D.Z., Long, K.B., Madison, L.D., Dallos, P., 2000. Prestin is the motor protein of cochlear outer hair cells. Nature 405, 149-55. 3. Santos-Sacchi, J., Dilger, J.P., 1988. Whole cell currents and mechanical responses of isolated outer hair cells. Hear Res 35, 143-50.

276

4. Ludwig, J., Oliver, D., Frank, G., Kleocker, N., Gummer, A.W., Fakler, B., 2001. Reciprocal electromechanical properties of rat prestin: the motor molecule from rat outer hair cells. Proc Natl Acad Sci U S A 98, 4178-83. 5. Qian, F., Ermilov, S., Murdock, D., Brownell, W.E., Anvari, B., 2004. Combining optical tweezers and patch clamp for studies of cell membrane electromechanics. Rev Sci Instrum 75, 2937-2942. 6. Ermilov, S., Anvari, B., 2004. Dynamic measurements of transverse optical trapping force in biological applications. Ann Biomed Eng 32, 1016-26. 7. McLaughlin, S., 1973. Salicylate and phospholipid bilayer membranes. Nature 243, 234-236. 8. Dong, X.X., Ospeck, M., Iwasa, K.H., 2002. Piezoelectric reciprocal relationship of the membrane motor in the cochlear outer hair cell. Biophys J 82, 1254-9. 9. Spector, A.A., Jean, R.P., 2004. Modes and balance of energy in the piezoelectric cochlear outer hair cell wall. J Biomech Eng 126, 17-25. 10. Petrov, A.G., 2002. Flexoelectricity of model and living membranes. Biochim Biophys Acta 1561, 1-25. 11. Raphael, R.M., Popel, A.S., Brownell, W.E., 2000. A membrane bending model of outer hair cell electromotility. Biophys J 78, 2844-62. 12. Glassinger, E., Raphael, R. M., 2005. Theoretical analysis of membrane tether formation from outer hair cells. In: Nuttall, A.L. (Ed.), Auditory Mechanisms: Processes and Models. World Scientific, London. 13. Todorov, A.T., Petrov, A.G., Fendler, J.H., 1994. Flexoelectricity of charged and dipolar lipid membranes studies by stroboscopic interferometry. Langmuir 10, 2344-2350. 14. Brett, C.M.A., Brett, A.M.O., 1993. Electrochemistry principles, methods, and applications. Oxford Scientific Publications, Oxford. 15. Zhang, P.C, Akeleshian, A.K., Sachs, F., 2001. Voltage induced membrane movement. Nature 413, 428-432. 16. Ermilov, S., Brownell, W.E., Anvari, B., 2004. Effect of salicylate on outer hair cell plasma membrane viscoelasticity: studies using optical tweezers. In: Cartwright, A.N., (Ed.), Nanophotonics and Biomedical Applications, SPIE International Symposium on Biomedical Optics. SPIE, San Jose, CA. 5331, 136-142. 17. Oliver, D., He, D.Z., Kleocker, N., Ludwig, J., Schulte, U., Waldegger, S., Ruppersberg, J.P., Dallos, P., Fakler, B., 2001. Intracellular anions as the voltage sensor of prestin, the outer hair cell motor protein. Science 292, 2340-3. 18. Kennedy, H.J., Crawford, A.C., Fettiplace, R., 2005. Force generation by mammalian hair bundles supports a role in cochlear amplification. Nature 433, 880-883. 19. Chan, D.K., Hudspeth, A.J., 2005. Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro. Nat Neurosci 8, 149-155.

Ca z+ CHANGES THE FORCE SENSITIVITY OF THE HAIR-CELL TRANSDUCTION CHANNEL1 E. L. M. CHEUNG 2 AND D. P. COREY Howard Hughes Medical Institute and Department of Neurobiology, Harvard Medical School, Boston, MA 02115, USA E-mail: [email protected] The mechanically gated transduction channels of vertebrate hair cells tend to close in ~1 ms following their activation by hair bundle deflection. This fast adaptation is correlated with a quick negative movement of the bundle (a "twitch"), which can exert force and may mediate an active mechanical amplification of sound stimuli in hearing organs. We used an optical trap to deflect bullfrog hair bundles and to measure bundle movement while controlling Ca2+ entry with voltage clamp. The twitch elicited by repolarization of the cell varied with force applied to the bundle, going to zero where channels were all open or closed. The force dependence is quantitatively consistent with a model in which a Ca2+-bound channel requires ~3 pN more force to open, and rules out other models for the site of Ca2+ action.

1 Introduction The extraordinarily high sensitivity and sharp frequency tuning of vertebrate hearing require the presence of an active mechanical amplification, a process that apparently resides within the mechanosensitive hair cells themselves [1,2]. By selectively increasing the vibration of the basilar membrane on which hair cells ride, this "cochlear amplifier" contributes up to 50 dB of gain to the acoustic signal [3]. Two different mechanisms have been proposed to underlie the cochlear amplifier: a shortening of cochlear outer hair cells driven by depolarization ("electromotility") [4,5], and a quick negative movement of the hair cells' mechanosensitive stereocilia caused by Ca2+ entry through transduction channels ("fast adaptation") [6,7,8]. In fast adaptation, Ca2+ entering through transduction channels at the tips of stereocilia is thought to bind directly to the channels or to associated components of the transduction apparatus, thereby promoting channel closure and rapidly reducing the receptor current. When they close, the channels exert a small force on the filamentous linkages between stereocilia and move the bundle of stereocilia by a few nanometers (the "twitch") [6]. Bundles pushing back against the overlying tectorial membrane, if in phase with the stimulus, might then amplify the mechanical stimulus [9,10]. Since fast adaptation has been observed in a variety of species and hair cell organs, the hair bundle-based mechanism is attractive for non-mammalian hearing organs, which lack electromotility but have cochlear amplification qualitatively similar to that found in mammals [11]. This mechanism is also attractive for the mammalian cochlea: because fast adaptation is

2

This chapter is excerpted from a paper to be published in the Biophysical Journal Present address: Depts. of Biological Sciences and Applied Physics, Stanford University

277

278 associated with ion entry through transduction channels rather than with the subsequent receptor potential, it might operate at higher speeds. Several Ca2+-dependent mechanisms for fast adaptation have been proposed: First, Ca2+ could bind directly to the transduction channel to stabilize the closed state and thereby shift the P0(F) relation [6,8]. Second, Ca2+ could bind to an intracellular elastic "reclosure element" in series with the channel, reducing its spring constant, and the reduced tension would allow channels to close [12]. Third, Ca2+ could bind to a "release element" in series with the channel so as to lengthen it by a fixed distance, releasing tension in an elastic element and again allowing closure [13]. To distinguish among these three potential mechanisms, we made simultaneous electrical and mechanical measurements of fast adaptation in single bullfrog hair cells. Receptor currents were recorded and Ca2+ entry was controlled using wholecell patch clamp techniques, while a gradient force optical trap was used to apply forces to hair bundles and to measure force- and Ca2+-dependent bundle movements. We found that fast adaptation is only consistent with a model in which Ca2+ directly promotes channel closure, and in which channels altered by Ca2+ binding require 3.4 + 0.8 pN more force to open. 2 Methods Physiology. Single hair cells were dissociated from the saccule of adult bullfrogs (Rana catesbeiana). The bath contained (in mM) 120 Na+, 2 K+, 5 Cs+, 4 Ca2+, 135 CI", 3 Dextrose, and 5 HEPES at pH= 7.27. In some experiments, external solution was exchanged with one containing 0.1 Ca2+, or with 0.1 Ca2+ and 0.2 mM gentamicin. Pipettes contained 105 Cs+, 3 Mg2+, 111 CI", 3 NaATP, 1 BAPTA, 5 HEPES, pH=7.25. Whole cell patch clamp recordings were made using conventional patch clamp techniques with acquisition and analysis programs written in Lab View 5.1. The acquisition program generated the voltage and twodimensional mechanical commands synchronously via two hardware-connected A/D boards. Optical trap. An optical trap was constructed using a Nd:YAG laser on an inverted microscope with a high-numerical-aperture microscope objective. The Nd:YAG beam was deflected with a two-dimensional acousto-optic deflection (AOD) system and bead movements were detected with a HeNe laser following the design of Visscher and Block [14]. Single latex beads (2.0 p.m) in external solution were trapped and calibrated, and then attached to the kinociliary bulb of a hair cell using the trap to press it against the bulb. The displacement of every bead was calibrated and recorded with step displacements of the trap prior to attaching it to the bundle. A gigaseal was then established. Care was taken to keep the pipette away from the detection beam path.

279

3 Results 3.1 Movement of a hair bundle in response to force steps We dissociated hair cells from bullfrog sacculi, and used the whole-cell patch clamp method to control transmembrane voltage and record receptor current. Force steps were generated by step displacements of the infrared beam; their rise time was about 15 us, so the bundle-deflection risetime (200-400 us) was limited only by the viscous drag on the bead and bundle. Positive force steps, which deflect a bundle towards its kinocilium, elicited rapidly activating transduction currents which saturated with 100-150 nm bundle deflection (Fig. 1A). The activation curve (Fig. IB) was comparable to those measured with fast stimulators in bullfrog and turtle [6,8,15]. We also observed a typical gating compliance [6]. From fits to the current and the compliance in 7 cells, we found an average of 23 ± 3 channels, a gating spring stiffness of 0.75 mN/m and a gate swing of 2.5 ± 0.5 nm (channels at each end of the tip link, mean ± SE). 3.2 Movement evoked by depolarization By changing Ca2+ influx through open transduction channels and thus changing the forces produced by the fast and slow adaptation processes, voltage alone can produce movement of a hair bundle [16,17,18,10]. In response to a depolarizing voltage step, we found that a freestanding hair bundle moved in three distinct phases. The slowest phase occurred in tens of milliseconds and was negative-going; it is thought to be the mechanical correlate of slow adaptation and is attributed to the myosin-lc motor complex climbing up the actin cores of stereocilia [18,19,8,20]. The middle phase was positive-going and took place in a few milliseconds, the same timescale as fast adaptation; it is thought to be a voltageinduced twitch corresponding to the relaxation in tip link tension when channels open after Ca2+ unbinds from some intracellular element [21,15,10]. The fastest phase was a negative movement with depolarization, which we term the "flick." This movement was previously observed in turtle hair cells, where it was described as being linearly voltage-dependent and occurring as fast as the voltage clamp could depolarize the cell [21] The "flick:" a fast, voltage-dependent movement. We found that the flick is nonlinear with voltage, saturating at large positive potentials (data not shown). It is apparently not a Ca2+-dependent process, nor does it require any ion influx through transduction channels. On the other hand, the flick seems to require both intact and taut tip links, suggesting a voltage-dependent conformational change of some component of the transduction apparatus. The flick is not altered by force-dependent channel gating, although it might still involve a voltage-dependent conformational change of the channel.

280

Figure 1. Mechanical and electrical responses to a family of force steps (A) Receptor current with two phases of adaptation. (B) Peak receptor current as a function of deflection. (C) Bundle movement with two phases of adaptation. The bundle movement corresponding to A showed a fast deflection followed by a slow relaxation for large deflections. For small positive deflections, an additional small and rapid negative movement occurred at the same timescale as the fast phase of adaptation (arrow). (D) Force vs. deflection; force measured at the peak of the receptor current. (E) Amplitudes of fast and slow adaptation with increasing deflection. The fast phase of I(X) shift (o) showed near-complete adaptation for small steps but declined for larger steps, whereas the slower phase (•) was negligible for small steps, and rose to -80% for larger steps. (F) Instantaneous stiffness of the bundle as a function of bundle deflection. The stiffness showed the characteristic dip near the center of the I(X) curve due to gating compliance.

100

nm

/S

*

//

50 Jrjj

0

AtmmmmmwM

1

nm 100 detection

° ' 0 nra lite"" deflection

The "twitch:" a mechanical correlate of fast adaptation. We found that fast adaptation of the mechanosensitive current was slowed either by reducing external Ca2+ or by depolarizing the cell to reduce Ca2+ influx. Depolarizing the cell to -60 or -40 mV, which reduces Ca2+ influx through transduction channels, also slowed the twitch commensurately. Our observations support the idea [12,21,15] that the twitch is a mechanical correlate of fast adaptation and that it follows from Ca2+ entry through transduction channels. Next, we wanted to determine where Ca2+ acts to mediate this twitch. To measure in detail the mechanical correlates of Ca2+ action, we again controlled Ca2+ entry by changing the membrane potential but focused on the second phase of bundle movement (the twitch). For a depolarization to +60 mV, a freestanding bundle exhibited a negative, sub-millisecond flick, and a slower positive twitch (Fig. 2A). A repolarizing step back to -80 mV produced flick and twitch in the reverse directions. We measured the amplitude of the twitch following the flick (arrows, Fig. 2A). The "off twitch for depolarization (in which Ca2+ is expected to unbind) had the same magnitude as the "on" twitch for repolarization (Fig. 2B), suggesting that the twitch involves a reversible binding reaction with a fixed mechanical correlate. When we reduced Ca2+ in the external solution, reducing

281 fast adaptation in the receptor current, we reduced the voltage-induced twitch in both directions—further evidence that the voltage-induced twitch is generated by the same mechanism as the deflection-induced twitch (data not shown). 3.3 Predicting the force dependence of repolarization twitch To understand the twitch quantitatively, we first asked how Ca2+ binding would affect the position-force relation of a hair bundle. We began with a simplified mechanical model which treats the bundle as a stereocilia pivot spring (stiffness ks) in parallel with the transduction complex. The transduction channel is in series with an elastic gating spring (stiffness kg) and in series with the myosin motor mediating slow adaptation. This simple model can account for the gating compliance illustrated in Fig. IF and for slow adaptation. Ca2+ might act on any of these •. ••„ -30 ^ >»# elements to cause a movement of the V bundle. First, Ca2+ V * might bind to the transduction channel to change the relationship between force and open probability. Second, Ca2+ might bind to an internal elastic element that is the Figure 2. Movement produced by repolarization to allow Ca2+ influx, gating spring or in varying force bias on a hair bundle. The negative movement was largest series with it, to over the range where force activates the channels, (see text) change its stiffness. Finally, Ca2+ could bind to an internal element that changes conformation to lengthen slightly. With certain parameters, in particular if the gating swing is large and the gating spring is stiff, all three models can produce qualitatively similar negative bundle movements over some range of force steps. If the gating swing is small or the gating spring soft, however, only the first model can produce a twitch. For any parameters, the three models can clearly be distinguished if the twitch upon Ca2+ entry is measured over a range of applied force.

282

3.4 Measuring the force dependence of the twitch We deflected bundles with a series of force steps while Ca2+ influx into the stereocilia was halted by a depolarization to +40 mV. After 6 ms, the cell was hyperpolarized to -120 mV to allow Ca2+ entry, and we measured the resulting movement (Fig. 2C). We measured bundle movement from the peak of the flick to the plateau of the twitch, but before much movement from slow adaptation had occurred (Fig. 2C, inset). These data were compared with predictions of the three different models. For each cell, the relevant parameters could be measured from data as in Fig. 1, leaving just one free parameter for fitting. In the third model (Axg), we could vary the change in gating spring setpoint upon Ca2+ binding. Fig. 2D shows the best fit, with Axg=-0.29 nm (a shortening with Ca2+), and fits with Axg at twice and half that value. In the second model (Akg), we varied the change in spring stiffness upon Ca2+ binding. Fig. 2E shows the best fit, with AKg=+35.1 uN/m (a stiffening with Ca2+) and twice and half that value. In the first (AP0), we could vary the shift of the P0(f) curve upon Ca2+ binding. Fig. 2F shows a fit with Af0=1.5 pN ( corresponding to lowered open probability with Ca2+). A similar fit to the voltage-dependent twitch was done for six other cells. In all seven cases the AP0 model fit the data well and the other two models did not. Finally, we can determine the effect of Ca2+ on channel sensitivity. The P0(F) curve shifted to the right due to Ca2+ binding, indicating that a single channel with Ca2+ bound requires 3.4 + 0.8 pN more force along the tip link axis to open. 4 Discussion It has long been recognized that Ca2+ entering through hair-cell transduction channels binds within nanometers to promote closure of the channel. Our measurements, tested by three models, strongly suggest how: that Ca2+ shifts the force dependence of activation such that 3-4 pN more force, equivalent to 1-2 kT, is needed to open a Ca2+-bound channel. It has been proposed that such a mechanism may mediate frequency tuning in auditory organs [6], and a model incorporating such a mechanism produces amplification of bundle movement for small stimuli of appropriate frequency [7]. Thus, understanding the site of Ca2+ action narrows the search for the cochlear amplifier in molecular terms. Because the amplifier exhibits tonotopic variation in frequency in most auditory organs, this also narrows the search for a variable element underlying tonotopy.

283

Acknowledgments We thank Steven M. Block for advice on construction of the optical trap and Lynda Stevens for administrative assistance. Supported by NIDCD grant DC00304 (to DPC). DPC is an Investigator of the Howard Hughes Medical Institute. References 1. Dallos, P., Harris, D., 1978. Properties of auditory nerve responses in absence of outer hair cells. J Neurophysiol 41:365-383. 2. Brown, M.C., Nuttall, A.L., Masta, R.I., 1983. Intracellular recordings from cochlear inner hair cells: effects of stimulation of the crossed olivocochlear efferents. Science 222:69-72. 3. Overstreet, E.H., 3 rd , Temchin, A.N., Ruggero, M.A., 2002. Basilar membrane vibrations near the round window of the gerbil cochlea. J Assoc Res Otolaryngol 3:351-361. 4. Brownell, W.E., Bader, C.R., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science 227:194196. 5. Dallos, P., Evans, B.N., 1995. High-frequency motility of outer hair cells and the cochlear amplifier. Science 267:2006-2009. 6. Howard, J., Hudspeth, A.J., 1988. Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell. Neuron 1:189-199. 7. Choe, Y., Magnasco, M.O., Hudspeth, A.J., 1998. A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectricaltransduction channels. Proc Natl Acad Sci U S A 95:15321-15326. 8. Wu, Y.C., Ricci, A.J., Fettiplace, R., 1999. Two components of transducer adaptation in auditory hair cells. J Neurophysiol 82:2171-2181. 9. Hudspeth, A.J., Choe, Y., Mehta, A.D., Martin, P., 2000. Putting ion channels to work: mechanoelectrical transduction, adaptation, and amplification by hair cells. Proc Natl Acad Sci U S A . 97:11765-11772. 10. Chan, D.K., Hudspeth, A.J., 2005. Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro. Nat Neurosci 8:149-155. 11. Manley, G.A,. 2001. Evidence for an active process and a cochlear amplifier in nonmammals. J Neurophysiol 86:541-549. 12. Bozovic, D., Hudspeth, A. J., 2003. Hair-bundle movements elicited by transepithelial electrical stimulation of hair cells in the sacculus of the bullfrog. Proc Natl Acad Sci U S A 100:958-963. 13. Gillespie, P.G., Corey, D.P., 1997. Myosin and adaptation by hair cells. Neuron 19:955-958. 14. Visscher, K., Block, S.M., 1998. Versatile optical traps with feedback control. Methods Enzymol. 298:460-489.

284

15. Ricci, A.J., Crawford, A.C., Fettiplace, R., 2002. Mechanisms of active hair bundle motion in auditory hair cells. J Neurosci 22:44-52. 16. Crawford, A.C., Evans, M.G., Fettiplace, R., 1989. Activation and adaptation of transducer currents in turtle hair cells. J Physiol (Lond) 419:405-434. 17. Assad, J.A., Hacohen, N., Corey, D.P., 1989. Voltage dependence of adaptation and active bundle movement in bullfrog saccular hair cells. Proc. Nat. Acad. Sci., USA 86:2918-2922. 18. Assad, J.A., Corey, D.P., 1992. An active motor model for adaptation by vertebrate hair cells. J. Neurosci. 12:3291-3309. 19. Gillespie, P.G., Wagner, M.C., Hudspeth, A. J., 1993. Identification of a 120 kd hair-bundle myosin located near stereociliary tips. Neuron 11:581-594. 20. Holt, J.R., Gillespie, S.K., Provance, D.W., Shah, K., Shokat, K.M., Corey, D.P., Mercer, J.A., Gillespie, P.G., 2002. A chemical-genetic strategy implicates myosin-lc in adaptation by hair cells. Cell 108:371-381. 21. Ricci, A.J., Crawford, A.C., Fettiplace, R., 2000. Active hair bundle motion linked to fast transducer adaptation in auditory hair cells. J Neurosci 20:7131-7142. 22. Benser, M.E., Marquis, R.E., Hudspeth, A.J., 1996. Rapid, active hair bundle movements in hair cells from the bullfrog's sacculus. J Neurosci 16:56295643. Comments and Discussion Brownell: I have two questions related to the fast, voltage dependent bundle "flick". 1) We have demonstrated at this meeting that membranes generate electromechanical force even in the absence of specialized proteins such as prestin (Anvari et al.). This force, like the flick, is greatest for hyperpolarizing potentials and becomes smaller as the holding potential is depolarized. We have not yet tested the calcium dependence of prestin free tethers but we know calcium is not required for outer hair cell electromotility. We have previously calculated that a change in membrane curvature can quantitatively account for the length changes observed outer hair cell electromotility with membrane depolarization resulting in a decrease in the radius of curvature (Raphael et al., 2000). If stereocilia membranes were to undergo comparable depolarization induced reductions in radius, the cumulative effect would be to move the bundle in the negative direction. Given the similarities, can you identify a compelling reason why electromechanical force generated by the stereocilia membrane might not contribute to the flick? 2) At the risk of answering my own question I wonder if you have looked at the effect of salicylate on the flick? If a membrane based electromechanical force were responsible we would expect to see a reduction in flick magnitude with increasing salicylate concentrations. Answer: An intriguing feature of the flick movement is that it requires taut tip links. The flick is abolished by cutting the tip links with BAPTA, or by negative

285 bundles deflections that would relax the tip links. Consequently, we should look for a mechanism that changes tip-link tension. In the membrane curvature model, depolarization increases curvature. If stereocilia have wavy membranes (and good rapid-freeze deep-etch images suggest they don't; Kachar et al., 2000), then depolarization might cause the membrane to tighten around the actin cores of stereocilia, pushing fluid into the cell body. If the actin cores cannot resist the tightening force, the stereocilia might shorten. However we might expect that stereocilia would shorten proportionally, so that at the level of a tip link the taller stereocilium of a pair would shorten by the same amount as the shorter of a pair, producing no change in tip-link tension. Thus it seems unlikely that membrane curvature could produce the flick movement. A way to test it would be to try salicylate, which we have not done.

HAIR BUNDLE MECHANICS AT HIGH FREQUENCIES: A TEST OF SERIES OR PARALLEL TRANSDUCTION K.D. KARAVITAKI AND D.P. COREY Department of Neurobiology and Howard Hughes Medical Institute, Harvard Medical School, Boston, Massachusetts 02115, US E-mail: [email protected] Propagation of stimuli across the stereocilia within a hair bundle affects the gating of transduction channels. Tip links and lateral links are the two most probable candidates in providing the mechanical connection between the stereocilia. To distinguish between the two we measured the movement of individual stereocilia when pulling on the tallest stereocilium of a bundle. Hair cells were isolated and their hair bundles were displaced using a glass pipette attached to the kinocilium and driven by a piezoelectric bimorph. The stimuli were sinusoids with frequencies at 20 Hz and 700 Hz. The motion of the bundle was visualized using stroboscopic video microscopy and was quantified using cross correlation methods. Our data suggest that the bundle moves as a unit and that adjacent stereocilia bend at their bases and touch at their tips. We argue that this motion is consistent with the lateral links being involved in the propagation of stimuli across the bundle and with transduction channels being mechanically in parallel.

1 Introduction When the tip of a hair bundle is deflected by the force of a sensory stimulus, the stereocilia move as a unit and produce a shearing displacement between adjacent tips (reviewed in [1]). The resulting stimulus could be applied to transduction channels in two different ways: First, if tip links provide the main connection between stereocilia, then the tallest stereocilium of a column pulls on the next, which pulls on the next. The transduction channels are mechanically in series, and the opening of one channel reduces the force on others of the series (negative cooperativity). Second, if stereocilia are primarily held together by lateral links, then transduction channels are mechanically in parallel. The opening of one channel increases force on other channels, making them more likely to open (positive cooperativity). How the opening and Ca2+ -dependent closing of transduction channels affects cochlear mechanics depends critically on which model, or how much of each model, dominates the mechanics. To distinguish beteween these models we measured the movement of individual stereocilia when pulling on the kinocillium of a bundle using low and high frequency stimuli. Preliminary data show that the hair bundle moves as a unit and that individual stereocilia do not bend or splay during stimulation. The implications from such findings are discussed.

286

287 2 Methods Isolated hair cells from the bullfrog sacculus were dissociated as described in Assad et al. [2]. Briefly, sacculi were surgically exposed and bathed for about 14-15 min (depending on the size of the frog) in oxygenated perilymph-like solution (120 mM NaCl, 2 mM KCl, 0.1 mM CaCl2, 3 mM Dextrose, 5 mM Hepes, pH -7.3) containing 1 mM EGTA and ImM MgCl2 used to lower the free Ca2+ concentration. Sacculi were subsequently removed from the frog and dissected to remove the otoconia from their apical surface. The otolithic membrane was removed after treating the sacculi with 50 \xglml protease XXIV(Sigma Chemicals) for 22 min. Hair cells were flicked out of the sacculus and allowed to settle onto a petri dish with a clean glass bottom containing the oxygenated perilymph-like solution. We used cells that had settled on their sides so that we could image their hair bundles along their excitation axis. The hair bundles were displaced using a glass pipette attached by suction to the kinocilium and driven by a piezoelectric bimorph. The stimuli were sinusoids with frequencies at 20 Hz and 700 Hz and peak amplitude ranging from 250-300 nm. Hair cells were visualized with a 63x water immersion objective with an additional 5x magnification and modified DIC optics. The resolution of the images was about 30nm/pixel. Illumination was via a high power light emmiting diode (LED) (Luxeon, 5-Watt Star, A.p ~ 505 nm) positioned onto the field diaphragm. A CCD camera (Hamamatsu, C2400) was mounted on the phototube of the microscope (Zeiss, Axioskop) and was connected to an image processor (Hamamatsu, Argus). Hair bundle motion was visualized by strobing the LED at eight equally spaced phases during the stimulus period. Acquisition programs were written in LabView 6.1 (National Instruments) and generated the voltages that controlled the bimorph and the current source driving the LED, via a National Instruments A/D board. Resulting images (Fig. 1A) were used to create animations of the observed motion. Images were interpolated and high passed filtered. Features of interest (like the edge of individual stereocilia) were selected (Fig. IB) and cross correlation metheods were used to quantify their motion. 3 Results 3.1 Stereocilia motion is sinusoidal and varies with height relative to the base In Figure 2 we plot the timecourse of displacement of the tallest stereocilium in the focal plane at different heights along its length for a 20 Hz stimulus frequency. The magnitude of the displacement increased with height relative to the insertion point of the stereocilium. This trend was the same for the 700 Hz stimulus. For each displacement we also show the resulting fitted sine waveform calculated using the magnitude of the primary frequency component at 20 Hz. We will subsequently use the magnitude of the fitted waveforms to understand the motion of the stereocilia.

288

Figure 1. (A) Hair bundle image showing the glass probe attached to the kinocilium. Scale bar: 2 urn (B) Same image as in (A), high pass filtered, showing the extractions of interest. Extractions bl-b9 were used to correct for drift and rocking of the bundle while stimulation. The dots at the base of each stereocilium indicate the estimated pivot points. Figure 2. Displacement of the tallest stereocilium at 20 Hz.. Symbols result from our correlation analysis while the corresponding lines result from fitting the data points with a sine wave. Different symbols correspond to extractions from different heights along the bundle as indicated in Figure 1.

3.2 Stereocilia displacement is proportional to their height To understand the displacement profile of each stereocilium we plotted the Time (msec) magnitude of motion at different heights relative to its insertion point (Fig. 3). At each point along the length of the stereocilium the displacement was proportional to the height and was fitted well with a straight line. Results were similar for different stereocilia within the hair bundle for both stimulus frequencies. Within experimental error, stereocilia move as rigid rods, pivoting at their bases, even at higher frequency.

289 S 6n

Figure 3. Peak displacement of individual stereocilia measured at different heights above their pivot points. Linear fits are shown for each set of data. Top row 20 Hz stimulus, bottom row 700 Hz stimulus. All data are from the bundle shown in Figure 1.

20 Hz

/ stereocilium 1 100

S 6

200

stereocilium 8

stereocilium 4 100

300

200

300

100

200

300

100

200

300

700 Hz

/ 100

200

300

0

100

200

300

Peak Displacement (nm)

3.3 Displacement of adjacent stereocilia, at the same height, is similar We plotted the displacement magnitude of adjacent stereocilia and observed that, each moved by the same amount when measured at the same height (Fig. 4). For both stimulus frequencies the displacement magnitude of short stereocilia had a maximum deviation of about 25nm relative to the tallest stereocilium measured along the same height.

20 Hz

T

700 Hz

4

2 -

£ 2-

/ 100

200

Peak Displacement (nm)

300

>

•

ZA

Ji

0

Figure 4. Data from Figure 3, overplotted in the same graph for each frequency.

6 -i

0

f : 100

200

1 4 8

300

Peak Displacement (nm)

We have used isolated hair cells from the bullfrog sacculus to understand the motion of the hair bundle in response to low and high frequency sinusoidal stimuli. We recorded from cells within 2.5 hours following animal decapitation. Cells that had any of the: swollen soma, broken stereocilia, missing kinocillia were not used. Although the stiffness of the hair bundles were not measured in these experiments,

290

other investigators have shown that similar enzymatic protocols preserved the stiffness of the bundle within 10% of its original value [3]. We also expect that due to our enzymatic treatment ankle links will be absent in our hair bundles [4, 5, 6]. Our preliminary data show that the magnitude of stereocilia displacement is proportional to their height for both low and high stimulus frequencies. The stereocilia appear to move as rigid rods that pivot at their insertion points (pivot points). Previous investigators have shown that hair bundle stiffness decreases as the inverse square of the distance relative to its pivot point [7, 8]. Such stiffness profile is consistent with the stereocilia moving as rigid rods that pivot at their insertion point. Similar results have been obtained by Corey et al. [9] using very low frequency stimuli. Recently, Cotton and Grant [10, 11, 12] suggested that different stereocilia within the same hair bundle move differently depending on their location relative to the kinociliary axis of symmetry. Our experiments so far have not shown such differences. Displacement of adjacent stereocilia is similar when measured at the same height, and there is no evidence that the bundle is splaying during our stimuli. Corey et al. [9] used a simple geometrical model of the hair bundle, and assuming that individual stereocilia bend only at their insertion point and that they touch at their tips found that the front and the back edge of the hair bundle move the same distance when measured at the same height. They also demonstrated the same result experimentally using low frequency stimuli. Similar modeling data have been obtained by Jacobs and Hudspeth [5]. Our experimental data combined with the above mentioned modeling studies appear to support the idea that the bundle moves as a unit and that adjacent stereocilia bend at their bases and touch at their tips. Our data suggest that when the hair bundle from the bullfrog saculus is deflected, all the stereocilia within the bundle receive the same stimulus. If tip links were to provide the main connection between stereocilia the shortest stereocilium would be deflected by a smaller amount due to the serial opening of the transduction channels. On the other hand lateral links connecting adjacent rows of stereocilia appear more likely to effectively propagate the stimulus forces across the hair bundle. The involvement of lateral links in the propagation of the stimulus within a bundle has been previously hypothesized [1, 5, 13, 14]. If that is the case then transduction channels appear to be mechanically in parallel resulting in positive cooperativity which might be required to explain negative hair bundle stiffness [15]. Acknowledgments This work was supported by the Howard Hughes Medical Institute (HHMI). D.P.C. is an investigator and K.D.K. is a research associate of the HHMI.

291 References 1. Howard, J., Roberts, W.M., Hudspeth, A.J., 1988. Mechanoelectrical transduction by hair cells. Ann. Rev. Biophys. Chem. 17, 99-124. 2. Assad, J.A., Shepherd, G.M.G., Corey, D.P., 1991. Tip-link integrity and mechanical transduction in vertebrate hair cells. Neuron 7, 985-994. 3. Bashtanov, M. E., Goodyear, R.J., Richardson, G.P., Russell, I.J., 2004. The mechanical properties of chick (Gallus domesticus) sensory hair bundles: relative contributions of structures sensitive to calcium chelation and subilisin treatment. J. Phyiol. 559, 287-299. 4. Hudspeth, A.J., Corey, D.P., 1977. Sensitivity, polarity, and conductance change in the response of vertebrate hair cells to controlled mechanical stimuli. Proc. Natl. Acad. Sci. USA. 74, 2407-2411. 5. Jacobs, R.A., Hudspeth, A.J., 1990. Ultrastructural correlates of mechanoelectrical transduction in hair cells of the bullfrog's internal ear. Cold Spring Harbor Symp. Quant. Biol. 55, 547-561. 6. Goodyear, R.J., Marcotti, W., Kros, C.J., Richardson, G.P., 2005. Development and properties of stereociliary link types in hair cells of the mouse cochlea. J. Comp. Neurol. 485, 75-85. 7. Crawford, A.C., Fettiplace, R., 1985. The mechanical properties of ciliary bundles of turtle cochlear hair cells. J. Physiol. 364, 359-379. 8. Howard, J., Ashmore, J.F.,1986. Stiffness of sensory hair bundles in the sacculus of the frog. Hear. Res. 23, 93-104. 9. Corey, D.P., Hacohen, N., Huang, P.L., Assad, A.J.,1989. Hair cell stereocilia bend at their bases and touch at their tips. Soc. Neurosci. Abstr. 15,208. 10. Cotton, J., Grant, W., 2004. Computational models of hair cell bundle mechanics: I. Single stereocilium. Hear. Res. 197, 96-104. 11. Cotton, J., Grant, W., 2004. Computational models of hair cell bundle mechanics: II. Simplified bundle models. Hear. Res. 197, 105-111. 12. Cotton, J., Grant, W., 2004. Computational models of hair cell bundle mechanics: III. 3-D utricular bundles. Hear. Res. 197, 112-130. 13. Pickles, J.O., Comis, S.D., Osborne, M.P., 1984. Cross-links between stereocilia in the guinea pig organ of Corti, and their possible relation to sensory transduction. Hear. Res. 15, 103-112. 14. Pickles, J. O., 1993. A model for the mechanics of the stereociliar bundle on acousticolateral hair cells. Hear. Res. 68, 159-172. 15. Iwasa, K.H., Ehrenstein, G., 2002. Cooperative interaction as the physical basis of the negative stiffness in hair cell stereocilia. J. Acoust. Soc. Am. I l l , 2208-2212. Also see Erratum on J. Acoust. Soc. Am. 112, 2193.

292

Comments and Discussion Aranyosi: You showed that disassociating the tip links with BAPTA had no effect on the lack of splay of hair bundles, implying that the side and/or ankle links hold the bundle together. Measurements from Hudspeth's group, among others, show that the tip links contribute significantly to the overall stiffness of the hair bundle, implying that bundle deflections are resisted primarily by the tip links. How do you reconcile these two observations? Answer: This question illuminates an interesting dichotomy between stiffness to bundle deflections and stiffness that holds the bundle together. We found that stereocilia don't separate by more than a few nanometers when deflected over the full activation range, suggesting that side links provide considerable stiffness to prevent stereocilia separation. At the same time, they allow relative shear of stereocilia tips over many nanometers (20 nm over the activation range and more than 200 nm for some of the largest deflections we gave). Thus the side links mediate a kind of sliding adhesion that prevents separation of stereocilia membranes but allows them to slide relative to one another. Side links therefore don't resist the deflection of stereocilia and don't contribute to deflection stiffness. Deflection stiffness in our measurements is contributed in roughly equal measure by the gating springs and the pivot stiffness of stereocilia. In chick hair cells (Bashtanov et al., 2004) the shaft connectors also contribute significantly to deflection stiffness.

HAIR CELL TRANSDUCER CHANNEL PROPERTIES AND ACCURACY OF COCHLEAR SIGNAL-PROCESSING C. J.W. MEULENBERG AND S. M. VAN NETTEN Department

of Neurobiophysics, University of Groningen, Nijenborgh 4, 9747 AG, Groningen, The Netherlands E-mail: c.j. w. meulenberg@rug. nl s.m. van. netten@rug. nl

Mechanically activated transducer channels in cochlear outer hair cells (OHC's) transduce sound encoded mechanical signals into electrical signals. Entry of extracellular Ca2+ through these channels modulates transduction by reducing their open probability, a phenomenon called adaptation [1]. Analysis of the mechanical and electrical characteristics of the transducer channels in OHC's has shown that the transducer channel's open probability can be adequately described by a differentially activating two-state model [2], Also a direct relationship was demonstrated between the gating spring stiffness (Ks) and the accuracy (amia = 2kT/[Ks-D~\ = 5.4 nm, where D is the distance between the engaging positions of the closed and open conformational state) with which hair bundle position can be detected as a result of intrinsic channel stochastics. In combination with an assumed Ca2+-dependent gating spring stiffness [e.g. 3], we predict on the basis of the two-state model that at endolymphatic Ca2+ concentrations (~ 20 uM) an improved accuracy (CT„,;„ ~ 3 nm) can be attained at the equilibrium position of the hair bundle.

Experimental data on mouse OHC's recorded in 1.3 mM extracellular Ca2+ (Figure 1, squares) were taken as reference and a differentially activating two-state model was used to generate fits (Figure 1, solid lines) [2]. Decreasing the energy gap, As, with 1.5 kT, shifts the current-displacement curve in the negative direction, which is associated with lowering the extracellular Ca2+ concentration (dashed lines A, B). It does not affect the operational range, nor the accuracy. With a As of 5 kT opposite effects are observed (dotted lines A, B). In rat OHC's, altering the extracellular Ca2+ concentration from 1.5 mM to the endolymphatic Ca2+ concentration (~ 20 uM) shifts the operational range about 20% in the negative direction (atpoptn = 0.5) and causes a doubling of the hair bundle's passive stiffness, which could possibly be due to an increased Ks [3]. Modelling an almost doubled Ks (12.9 uN/m; dashed line C, D) we observe a similar relative shift, a decrease of the (instantaneous) operational range and an improved accuracy, amin, to about 3 nm at the hair bundle's resting position (X= 0). Decreasing Ks to 5 uN/m (dotted lines C, D) shifts the current-displacement curve in the positive direction, broadens the operational range and degrades the accuracy. Under normal endolymph conditions a Ca2+-dependent Ks might therefore cause a hair cell to have an optimal accuracy at the hair bundle's resting position. The associated limited operational range may be effectively extended by the dynamical effects of Ca2+-dependent adaptation, so as to combine a suitable operational range with a high signal-to-noise ratio of cochlear signal processing.

293

294 Effect of \e

Effect of K

c

s

600-

/

% 400-

KV s / O 200-

-150

100,

-100

-50

0

50

100

-100

-50

0

50

100

150

-100

-50

0

50

100

150

If

tz

o

s

100

nu

E S

0-150

150

F p

i1 £p • .' 1 pp -'

c oE 10

10 A«4-

-150

-100

-50

0

Act

50

100

Hair bundle displacement (nm)

150

-150

Hair bundle displacement (nm)

Figure 1. Hair cell transducer current (A, C) and accuracy (B, D) as function of hair-bundle displacement (X), together with modelled effects of changing the (deactivated) state energy difference (Ae) and the gating spring stiffness (Ks). Fits of the two-state gating-spring model (solid lines) to measured data (squares) are taken from [2] with Ks = 7.2 (xN/m; As= 3.5 kT; Ncb = 66; X0 = -33 nm; D = 26 nm; so that Omin = 5.4 nm. A and B show the effects of changing As; dashed line As =2 kT, dotted line As= 5 kT. C and D show the effects of Ks; dashed line Ks~ 12.9 nN/m, dotted line Ks = 5 |iN/m.

References 1. Eatock, R.A., Corey, D.P., and Hudspeth, A.J., 1987. Adaptation of mechanoelectrical transduction in hair cells of the bullfrog's sacculus. J. Neurosci. 7,2821-2836. 2. van Netten, S.M., Dinklo, T., Marcotti, W., Kros, C.J., 2003. Channel gating forces govern accuracy of mechano-electrical transduction in hair cells. Proc. Natl. Acad. Sci. USA. 100, 15510-15515. 3. Kennedy, H.J., Crawford, A.C., Fertiplace, R., 2005. Force generation by mammalian hair bundles supports a role in cochlear amplification. Nature 433, 880-883.

Ca2+ PERMEABILITY OF THE HAIR BUNDLE OF THE MAMMALIAN COCHLEA C. HARASZTOSI, B. MTJLLER AND A. W. GUMMER Department Otolaryngology, University Tuebingen, Elfriede-Aulhorn-Strasse 5, 72076 Tuebingen, Germany, E-mail: csaba.harasztosi@ uni-tuebingen.de Although experimental and theoretical information about intracellular concentration of Ca2+ in the stereocilia of lower vertebrates is available, there is only few information about mammalian systems. The aim of the present experiments was to investigate the origin of mechanically evoked Ca2+ signals in the hair bundle of outer hair cells (OHC).

1 Methods OHCs were mechanically isolated from the adult guinea-pig cochlea. Ca2+ transients were evoked by deflection of the stereocilia using a fluid-jet stimulator. To facilitate Ca2+ entry into the hair bundle, Ca2+ concentration in the fluid-jet solution was 4 mM (extracellular 100 uM). Intracellular Ca2+ changes were monitored using the acetoxymethyl ester form of the fluo-3 dye and the fluorescence signals were detected by a confocal laser scanning microscope. 2 Results 2.1 Average Ca + signals in the hair bundle The time course of the onset of the average intracellular Ca2+ transient in the hair bundle was exponential; the average time constant (T) was 0.26±0.19 s. Application of the open transduction-channel blocker dihydrostreptomycin (DHSM, 100 \\M) caused the speed of the Ca2+ elevation to become significantly slower, x=2.14±1.36 s; this change was partially reversible (x=0.75±0.24 s) after washout. Application of DHSM did not influence the steady-state amplitude of the average Ca2+ transients. The decay of the intracellular Ca2+ signal after removal of the fluidjet stimulus was also exponential; the time constant was 3.15±1.31 s. 2.2 Local effect of DHSM The local effect of DHSM can be seen in Fig. 1 as a decreased slope of the onset of the signal. The first column demonstrates the average intracellular Ca2+ transient while the second indicates the local effect of DHSM. In the DHSM row, the time delay between the basal and apical signals was eliminated by the drug. This effect of DHSM showed reversibility, plotted in the third row, labeled "Washout".

295

296

AF/F

AF/F,

/"\ Control

AF/F„ DHSM

V AF/F,

f\

AF/F,

AF/F,

,m

,«8e^

"\

Washout

I Vs.... ' 10

Time [s]

20

Figure 1. In the schematic drawing of the stereocilia, the rectangles indicate the regions of interest (ROI), the area where the signal was collected for analysis. In the left column, ROI was chosen for the whole hair bundle, while in the right column the apical S»i» and basal signals were separated. In the DHSM row of the right column, the time delay between the basal and apical signals was eliminated by the ^ a S t y e a drug.

*a

8i8«go 10

20

Time [s]

3 Discussion An interpretation of the observed fluorescence pattern is that Ca2+ can enter stereocilia through the transduction channels and also through the membrane by a transduction channel independent pathway(s). The result of the DHSM experiment is that Ca2+ entry through transduction channels is faster than through other pathways. The observation that the fluorescence started to increase first at the tip region of the middle row of stereocilia implies that Ca2+ entered first through transduction channels, which are supposed to be in that location. The result that DHSM preferentially blocked Ca2+ entry in the middle of the hair bundle, also supports the hypothesis that transduction channels are located far from the tip of the tallest stereocilia. Acknowledgments We would like to thank Serena Preyer for helpful discussions and Anne Seeger for her technical support.

IV. Emissions

COMPARATIVE MECHANISMS OF AUDITORY FUNCTION: GROUND SOUND DETECTION BY GOLDEN MOLES P. M. NARINS Depts. of Physiological Science and Ecology & Evolutionary Biology, UCLA, Los Angeles CA 90095, USA E-mail: pnarins&Mcla. edu The Namib Desert golden mole, Eremitalpa granti namibensis, is a nocturnal, surfaceforaging mammal, possessing a massively hypertrophied malleus which presumably confers low-frequency, substrate-vibration sensitivity through inertial bone conduction. When foraging, E. g. namibensis typically moves between sand mounds topped with dune grass which contain most of the living biomass in the Namib Desert. We have observed that foraging trail segments between visited mounds appear remarkably straight, suggesting sensory-guided foraging behavior. Foraging trails are punctuated with characteristic sand disturbances in which the animal "head dips" under the sand. The function of this behavior is not known but it is thought that it may be used to obtain a seismic "fix" on the next mound to be visited. Geophone recordings on the mounds reveal spectral peaks centered at ca. 300 Hz ca. 15 dB greater in amplitude than those from the flats. Seismic playback experiments suggest that in the absence of olfactory cues, golden moles are able to locate food sources solely using vibrations generated by the wind blowing the dune grass on the mounds. Morever, the mallei of the golden moles in the genera Chrysochloris and Eremitalpa are massively hypertrophied. In fact, out of the 117 species for which data are available, these golden moles have the greatest ossicular mass relative to body size (Mason, 2001). Laser Doppler vibrometric measurements of the malleus head in response to seismic stimuli reveals peak sensitivity to frequencies below 300 Hz. Functionally, they appear to be low-frequency specialists, and it is likely that golden moles hear through substrate conduction (Supported by NIH Grant DC00222).

1 Introduction Golden moles are blind, noctural, surfacing-foraging mammals that live in subSaharan Africa south of a line from Uganda in the east to Cameroon in the west. Mitochondrial DNA analysis has recently placed the golden moles (family Chrysochloridae) in the Afrotheria clade, a group composed of seemingly disparate taxa that share a common evolutionary origin in Africa [1], although this view has been recently challenged [2]. Mason and others [3-6] have noted that some genera of golden moles possess extraordinarily hypertrophied mallei. Fielden and her colleagues discovered that these small, blind animals hunt at night for small insects, spiders and even lizards located in sand mounds or hummocks topped with dune grass [7]. Challenged to produce an adaptive explanation for their remarkable ossicles, we (a) initiated an investigation of the foraging behavior of these animals in the Namib Desert [8], (b) completed a seismic playback study in the field to determine the cues necessary to attract the moles [9], (c) are involved in a modeling effort to understand the

299

300

coupling of the ear to the skull [6, 10], and see Mason [11-13], and (d) are carrying out a functional study of the ossicular motion in response to seismic stimuli [10,16]. In this paper, I review the present state of our knowledge about the use of seismic cues by the golden mole in foraging, and relate this to the functional anatomy of its highly specialized middle ear. Models have been proposed that suggest that the golden mole middle ear may function as an inertial motion detector. Evidence for this view is presented as well as preliminary measurements of the modes of ossicular vibration in response to substrate-borne vibration. 2 Field Recordings 2.1 Seismic measurements Foraging trails of individual golden moles were examined over as long a distance as possible in the linear dune fields of the Namib Desert in Gobabeb, Namibia. Along the trails, the moles visit mounds or hummocks which are located at the base of the slip-face of the giant linear dunes. These mounds are topped with live dune grass; they have been shown to contain 99% of the living biomass in the Namib Desert [7], and represent rich food sources for the golden moles. Foraging trails consisted of a) footprints, b) small depressions indicating head-dipping behavior in which the animal stops forward motion and buries his head beneath the sand, and c) extended disturbances in the sand indicating sandswimming in which the animal moves just beneath the surface of the sand. All trail features were mapped including the locations of head-dipping and sandswimming events. We used calibrated geophones to measure substrate velocities of both mounds and the desert flats; from these, power spectra were calculated. To obtain relaible geophone readings, it was necessary to couple the geophones physically and firmly to the substrate; combining the output of an array of three orthogonally-oriented geophones provided the resulting velocity vector at the surface. 2.2 Results We found that encounters with food patches were statistically non-random, suggesting that foraging in this species is sensory-guided. Peak velocity amplitude of a typical hummock is -5 dB re 1 \ivnls at a frequency of ca. 300 Hz, whereas the peak velocity amplitudes of the desert flat measured far from any hummock are typically 15-20 dB lower than the hummocks, and at a frequency of ca. 120 Hz (Fig. 1). Peak hummock velocities were significantly above the noise floor at distances on the order of 20m, longer than any inter-hummock path segment we observed for any mole. This suggests their potential use by the moles as seismic beacons for localizing concentrated prey sources. Geophone measurements made directly on or near the mounds revealed seismic signals emanating from the movements of the prey items themselves, principally

301

dune termites. These signals are typically short-duration, click-like pulses exhibiting broadband power spectra with spectral peaks below 50 Hz. Thus, foraging by the Namib Desert golden mole involves a two-stage seismic detection system in which the first stage consists of localizing prey-containing mounds at relatively long distances (approaching 20 m), whereas the second stage involves detection of prey movements near the mound.

= 310 Hz

mound

10000 1 l " " " !

100

1000

1 ITT'T"

10000

Frequency (Hz) Figure 1. (a) Typical velocity amplitude spectra for geophone recordings made from the top of a medium-sized mound and from the flat sand, (b) Difference between two spectra shown in (a). (After Narins et al., 1997, Reprinted with permission.)

Distances between adjacent head-dips were significantly smaller within 0.5m of a mound than they were at >0.5m from a mound (p < 0.05, Mest, «=6) [8]. These results may be considered the spatial analog of the hunting bat's terminal buzz in which echolocation pulses are produced at very high rates as the bat closes in on its prey, presumably to increase temporal resolution in the last phases of prey capture.

302

3 Field Playback Studies 3.1 Setup To determine the cues that are used by golden moles to localize the hummocks, we hypothesized that the wind blowing the dune grass sets the hummocks into resonance, producing the tone-like vibrations that travel as surface waves detectable by our geophones. To test this directly, we made gcophone recordings at the base of a hummock of the substrate vibrations made by wind blowing the dune grass. We then buried eight seismic sources (Clarke Synthesis transducers, model TST 229 F4 ABS) in a circle of radius 5m, and activated three adjacent transducers with the geophone recordings. We placed one geophone at the center of the arena and adjusted the playback level of each source to be ca. 0.0001 cm/s (rms vertical velocity) at the geophone. In addition, we plotted the surface velocity values at 32 points to visualize the vibrational field within the arena (Fig. 2). Once the sources were activated, we placed a golden mole in the center of the arena, released it and observed its sandswimming trajectory as it moved toward the edge of the arena (»=9). Motion trajectories were mapped and the exit points for each mole tested were noted. Between trials, the sand in and around the arena was raked thoroughly and swept smooth to eliminate residual olfactory and tactile cues.

Figure 2. Schematic view of the circular test arena (radius: 5m) for seismic playback experiments in the Namib Desert. Three of the eight vibration transducers (2,3,4) are simultaneously activated with a seismic recording of wind blowing the dune grass (see text); the remaining five transducers arc silent. Individual mole trajectories are shown. The linear scale bar indicates velocities in multiples of 0.05 mm/s; the numbers in the arena indicate contour lines with the same units.

303

3.2 Results All nine sandswimming moles exited the hemi-arena containing the active sources (Fig. 2). Moreover, the two surface-walking moles were not attracted to the active seismic sources. These preliminary results support the hypothesis that in the absence of olfactory cues, these blind, nocturnal golden moles use seismic signals generated by the wind moving the dune grass-hummock complex to home in on the hummocks, and thus to locate food sources [9, 14]. 4 Modeling Efforts 4.1 Background When the log of the malleus plus incus mass is plotted against log body mass for 49 mammalian species, the ossicles that lie most significantly above the regression line through the data points are those of several golden mole species [5]. The hypertrophied mallei of the golden moles are extraordinary not only for their increased mass, but also for the displacement of the ossicular center of mass from the rotatory axis (Fig. 3a). This latter feature results in the malleus acting as an inertial motion sensor. 4.2 Model and Interpretation A simple mechanical model of the golden mole middle ear is shown in Fig. 3b. This model exhibits the first order properties of the Chrysochloris ossicles shown in Fig. 3a. The large mass of the ossicles, together with their relatively loose ligamentar suspension, is expected to bias the peak mechanical response of the malleus toward low frequencies [5], a prediction borne out by recent measurements [10]. It is of note that the model in Fig. 3b is also an excellent approximation of a mechanical analogy for a velocity sensor, i.e., a geophone. In this context, headdipping behavior may be viewed as a means of coupling the animal's skull to the substrate to ensure proper operation of its geophone-like middle ears.

304

Rotary axis

Figure 3. Inertial motion detection in the Cape Golden Mole, Chrysochloris asiatica. See text for explanation, (a) Ossicles of Chrysochloris (b) Mechanical analogy. (After [12], Reprinted with permission.)

5 Seismic Response of the Middle Ear Chrysochloris has a distinctly club-shaped malleus (Fig. 3a, 4a); this is likely an adaptation for sensing both airborne and substrate-borne stimuli [10,16]. 5.1 Methods The skull of Chrysochloris was attached to a metal plate with acrylic resin. The superior portion of the malleus head was exposed for either vertical or lateral measurements with the scanning laser Doppler vibrometer (SLDV/Polytec PSV300). For seismic stimulation the metal plate was driven either vertically (figure not shown) or laterally (Fig. 4b) by a vibration exciter (B&K 4809). The stimulus was a periodic chirp of vibration sweeping from 15-600 Hz with a calibrated amplitude of 100 (im/s (±20%) over this frequency range. The 20-40 points measured by the SLDV were restricted to the distal portion of the malleus head (Fig. 4a).

305 5.2 Results

Lateral Vibration GM#15

Laser Beam Setup

TJf

Motion Visualization

100

1000

Frequency [Hz]

Figure 4. (a) Schematic diagram of middle ear ossicles of C. asialica. The grid indicates the points scanned during the motion analysis. APM = anterior process of the malleus, LPI = lenticular process of the incus, SPI = short process of the incus, (b) head of C. asialica mounted on metal plate being driven laterally; motion visualization with SLDV showing z-axis translation, (c) LPI motion reconstruction using each component separately (e.g., Iz, tox, coy) or all components together (all).

Motion reconstruction was carried for the lenticular process of the incus (Fig. 4c). For lateral stimulation, the malleus showed a resonance peak between 100-200 Hz. Although the rotational motions were greatest around the x-axis, followed by the yaxis, the motion at the LPI is best approximated by the translational component, ft. 6 Discussion The results of this ongoing study are consistent with the hypothesis that golden moles use a two-stage seismic detection system to locate prey in the Namib Desert. In the first stage, the animal localizes the sand mounds topped with dune grass by sensing at a distance the vibrations generated by the wind-blown dune grass. In the second stage, the substrate vibrations generated by prey item movements are detected at close range. For both stages, the detection involves head-dipping behavior, which acts to couple the animal's skull firmly to the substrate, thus

306

enabling it to sense the propagated surface waves. Seismic playback experiments demonstrated that a pure vibrational stimulus generated by wind blowing the dune grass is attractive to the moles. Initial scanning laser Doppler measurements of the malleus motion in response to lateral seismic stimuli suggest that it does indeed act as an inertial motion sensor. Responses to vibrational stimuli in the vertical plane as well as to airborne sound are underway [16]. Acknowledgments G. Bronner, J.U.M. Jarvis, E.R. Lewis, M.J. Mason, and J. O'Riain collaborated on the field work in Namibia, U. Willi carried out the laser measurements of the middle ear ossicles, and S.W.F. Meenderink assisted with the preparation of Figure 2. Supported by NIH grant no. DC00222. References 1. Springer, M.S., Cleven, G.C., Madsen, O., de Jong, W.W., Waddell, V.G, Amrine, H.M., Stanhope, M.J., 1997. Endemic African mammals shake the phylogenetic tree. Nature 388, 61-64. 2. Zack, S.P., Penkrot, T.A., Bloch, J.I., Rose, K., 2005. Affinities of 'hyopsodontids' to elephant shrews and a Holarctic origin of Afrotheria. Nature 434,497-501. 3. Forster Cooper, C. 1928. On the ear region of certain of the Chrysochloridae. Philos. Trans. R. Soc. Lond. B 216, 265-283. 4. von Mayer, A., O'Brien, G., Sarmiento, E.E., 1995. Functional and systematic implications of the ear in golden moles. J. Zool. Lond. 236, 417430. 5. Mason, M.J., 2001. Middle ear structures in fossorial mammals: a comparison with non-fossorial species. J. Zool. Lond. 255, 467-486. 6. Mason, M.J., Narins, P.M., 2002. Seismic sensitivity in the Desert Golden Mole {Eremitalpa granti): A review. J. Comp. Pscychol. 116, 158-163. 7. Fielden, L.J., Perrin, M.R., Hickman, G.C., 1990. Feeding ecology and foraging behaviour of the Namib Desert golden mole, Eremitalpa granti namibensis (Chrysochloridae). J. Zool. Lond. 220, 367-389. 8. Narins, P.M., Lewis, E.R., Jarvis, J.U.M., O'Riain, J , 1997. The use of seismic signals by fossorial Southern African mammals: A neuroethological gold mine. Brain Res. Bulletin 44, 641-646. 9. Narins, P.M., Lewis, E.R., 2004. Ground sounds: seismic detection in the golden mole. Abstr. 147th meeting of the Acoustical Society of America, J. Acoust. Soc. Am. 115, 2555.

307

10. Willi, U., Bronner, G., Narins, P.M., 2005. The multimodal middle ear of the Cape Golden mole {Chrysochloris asiatica). Abstr. 28th ARO Res. Mtg. 320321. 11. Mason, M.J., 2003a. Morphology of the middle ear of golden moles (Chrysochloridae). J. Zool. Lond. 260, 391-403. 12. Mason, M.J., 2003b. Bone conduction and seismic sensitivity in golden moles (Chrysochloridae). J. Zool. Lond. 260, 405-413. 13. Mason, M.J., 2004. Functional morphology of the middle ear in Chlorotalpa golden moles (Mammalia, Chrysochloridae): Predictions from three models. J. Morphol. 261, 162-174. 14. Lewis, E.R., Narins, P.M., Jarvis, J.U.M., Bronner, G., Mason, M.J., 2005. Catch the whisper of the wind: possible uses of microseismic cues for navigation by the Namib golden mole. In preparation. 15. Mason, M.J., Narins, P.M., 2001. Seismic signal use by fossorial mammals. Amer. Zool. 41, 1171-1184. 16. Willi, U., Bronner, G., Narins, P.M., 2005. Ossicular differentiation of airborne and seismic stimuli in the Cape Golden mole {Chrysochloris asiatica). In preparation.

DPOAE MICRO- AND MACROSTRUCTURE: THEIR ORIGIN AND SIGNIFICANCE DAVID T. KEMP UCL Centre for Auditory Research, UCL EAR Institute, 332 Grays' Inn Road London WC1X 8EE, UK E-mail: emission(a),dircon. co. uk PAUL F. TOOMAN Institute of Laryngology and Otology, UCL EAR Institute. Now atAudiology Services Department, Milton Keynes General Hospital, Milton Keynes, UK. E-mail: Paul. Tooman&.mkeeneral. nhs. uk DPOAE amplitude variations with frequency can be due to interference between place and wave fixed components. When these components are separated other structure remains on a scale of one octave for wave-fixed DPOAE and on a scale of approx 1/5 octave or 400Hz at 3kHz in place-fixed DPOAE. Quasi-periodic peaks and valleys occur in both 2f,-f2 and 2f2-fi place-fixed emissions at specific DPOAE frequencies irrespective of the ratio of f2/fl and hence irrespective of the stimulus configuration on the basilar membrane. We present data and statistics on this structure from 12 human subjects and discuss its origin. Various hypotheses for the structure are discussed and assessed against the data including; a second DPOAE place fixed source, basal reflection standing waves, periodicity in cochlear refection and coherent reflection filtering. The experimental evidence best supports a coherent reflection filtering origin.

1 Introduction OAEs have the potential to inform us about the functional status of outer hair cells but this potential cannot be fully realized without a good understanding of the mechanisms of emission specifcally their inherent frequency dependance and their interactions. Interference between emissions from different mechanisms with different propagation times and also standing wave interference due to multiple internal reflection introduce great complexity into emission spectra. This presents a challenge to cochlear modelers and limits the practical interpretation of OAE data. Understanding of OAE complexity is steadily increasing. Kemp[l] identified place-fixed and wave-fixed DPOAE emission components on the basis of their different observed group delays observed with iso-f2/f 1 ratio sweeps, and associated these with irregularity based and nonlinear reflection based sources respectively. Zweig and Shera [2] described a coherent reflection mechanism for place-fixed emissions in which the waves within a broad and tall traveling wave peak filtered dense spatial cochlear irregularities resulting in a traveling wave reflector accounting well for place-fixed OAE group delay characteristics. Shera and Guinan [3] emphasized that the low latency wave-fixed DP component required only nonlinear mechanical interaction between the primaries to create a reverse DP

308

309

DP frequency (Hz)

DP frequency (Hz) .25-20B-2Q-15B-15-10B-10--5K-5-OB0-5SS5-10R10-15 *. .15-20

20-25

25-30

Figure 1 From [5]. Two human DPOAE intensity 'maps' for sidebands 2f,-f2 (upper half of each map) and 2f2-fi (lower half of each map) plotted for DP frequency against primary frequency ratio C/fl. The top map (a) shows total DP intensity, the bottom map (b) shows only the slow 'place fixed' DPOAE separated out by editing the inverse Fourier transform of iso-primary-ratio frequency sweeps. Total DP data (a) shows a horizontal band around £2/fl=1.2 which represents the condition of optimum emission of wave fixed 2frf2. No such condition exists for the emission of 2f2-f, which instead exhibits vertical (i.e. DP frequency dependant) banding in both maps. The placed fixed-only map (b) shows that vertical banding in 2f2-fi continues across the fl=f2 line into the 2f,-f2 structure. Primary levels were 70,70dBSPL

traveling wave whereas place-fixed emissions required only linear 'reflection' of an apical traveling DP or stimulus frequency wave at irregularities Recently Ren [4] has revived suggestions of a third DP emission mechanism viz. a direct pressure wave transmission from source to middle ear. Knight and Kemp [5] mapped human DPOAE intensity with primary frequency ratio against DP frequency and then separated the wave and place fixed components to observe their individual frequency structures (figure 1). The strong horizontal band of 2f,-f2 emission seen around £2/fl~1.2 in figure la is typical the wave-fixed DP component. It has a broad frequency structure on a scale of about an octave plus evidence of other structures on a scale of 100-200Hz probably due to interference with the underlying place fixed component. The 2f2-fi emission shows quasi-

310 periodic structure on a scale of 400Hz. This structure can also be traced in the placefixed only 2fi-f2map (lb) especially at low f2/fl ratios. Kemp and Knight [6] noted that wave-fixed DP emission occurs only for 2frf2 and other lower sidebands. This is because i) the traveling wave phase gradient of f2 is always steeper than that of fl if £2>f1 and ii) the two gradients have opposing influences on the phase of 2frf2, 3fi-2f2 etc. The lower frequency DP source's spatial phase (cp) gradient can therefore be less than that of fl and f2 and even change sign. At some f2/fl ratio the gradient will most closely match that of a true 2f]-f2 reverse traveling wave. DP traveling waves from the greatest number of DP source elements under the f2 envelope will then arrive coherently at the base leading to the strongest wave fixed DPOAE emission. At some smaller f2/fl the DP source phase gradient will become flat across an extended region and this might possibly couple more effectively to a pressure wave directly moving the oval and round windows with minimal delay, perhaps interfering with the wave-fixed traveling wave emission over a broad frequency scale. For even smaller f2/fl () = fcoe~ax — u2m, where UQ and a are real positive constants, the real solution of Eq.l, which is an hypergeometric function, was found either for x < xr or for x > xr [6]. The authors noted that the complex solution (traveling wave) for x < xr derived in [7] corresponds to the case of ")e

{ s

- > cos(m(t-u)+)

C1)

The components of the signal are described by the following parameters: frequency co, latency u, time-span s, amplitude K{y,(f) and phase <j). We have used a Gabor dictionary consisting of 106 atoms. It was shown in Jedrzejczak et al. [6] that Gabor functions approximate the signal of otoacoustic emissions very well. The idea of the method is illustrated in Fig.l. 2.2

Experimental procedures

Two data sets were analyzed. In both cases, otoacoustic emissions were recorded using the ILO 292 Echoport system designed by Otodynamics. Responses to 260 repetitions of stimuli were averaged with the "nonlinear" mode of stimulation. The acquisition window had a standard onset at 2.5 ms with a cosine rise/fall of 2.26 ms and flat top up to 20.5 ms.

348

10 time [ms| Figure 1. Illustration of the MP method. At the top the OAE signal; below its time-frequency representation (energy in shades of gray), found in the iterative MP decomposition into 66 atoms (99.5 % of energy). At the left: spectrum obtained by summation of the time-frequency distribution in time. At the bottom of the picture the 5 highest energy atoms found by the iterative procedure are shown. Their time-frequency representations and corresponding spectral peaks are connected by lines.

The first data set consisted of the OAE recordings from 12 young (20-25 years) adult men. In pure tone audiometry the hearing thresholds were 10-15 dB. For all these subjects, the responses to a click stimulus and a set of tone bursts stimuli of 5 frequencies (1000, 1414, 2000, 2828 and 4000 Hz) and of half-octave bands were measured. The tone-burst stimuli were constructed to cover the same frequency band (850 to 4750 Hz) as the click stimulus. The second experiment concerned the influence of noise on OAE. Two datasets of click evoked OAEs from 124 ears were recorded. The first dataset was measured from 62 ears of male personnel who serviced aircraft (aged 24-51), thus these individuals were regularly exposed to jet engine noises. The second set, used as the control group, consisted of 62 ears from age-matched males. These subjects were laryngologically healthy with hearing thresholds of 10-15 dB HL. The subjects exposed to aircraft noise had threshold levels that were in average 6.6 dB higher. The protocol of the experiments was approved by the board of human experimentation. 3 Results 3.1

Click and tone-burst evoked OAE

Tone and click evoked OAE were decomposed by means of the MP algorithm and the parameters of the components were found. In most cases the basic features of

349

the click evoked OAE are reproduced by the first 15 waveforms, which account for 95% of the energy of the signal. When the components of the signal are known, it is straightforward to construct the time-frequency distribution of the energy density (Figures 2 and 3). The time-frequency (t-f) representations of the tone evoked OAE are presented in Fig. 2. Usually the atom of the highest energy was closest to the frequency of the stimulation. It can be observed that the frequency of the tone stimulus is not exactly reproduced in OAE and the response depends on the individual features of the subject's cochlea. Namely for each subject there are some privileged frequencies, which appear to a higher or lower degree for different frequencies of the stimulus. E.g. in Fig. 2 a component of frequency of around 2 kHz appears at stimulation frequencies of 1414, 2000 and 2828 Hz. 1000 Hz

1414 Hz

2000 Hz

2828 Hz

4000 Hz

6 5 14 dSSk

cr 2 P

0

0 0 20 0 20 0 10 20 10 20 0 10 20 °0~ 10 10 time [ms] time [ms] time [ms] time [ms] time [ms]

Figure 2. Time-frequency distributions of energy for an OAE signal evoked by tone burst stimuli (from 1000 to 4000Hz) for one subject. Frequency of the stimulation is given above the maps.

In Fig. 3, showing energy distribution of click evoked OAE in t-f space, the centers of the atoms for click and tones evoked OAE are shown together. We can observe that the centers of tone evoked OAE tend to be shifted toward longer latencies. This could have been expected from the fact that the stimuli in the case of bursts were applied with some delay. We can conjecture that the click evoked response is the superposition of the tone responses, which indicates the linearity of the mechanisms for the applied level of stimuli.

350

4

8 12 time [ms]

16

20

Figure 3. Time-frequency distribution of energy obtained by means of the MP decomposition of click evoked OAE. White dots indicate t-f centers of the main atoms of click evoked OAE. Dark dots mark the positions of the strongest atoms of responses to tone bursts.

In Fig. 4 a histogram of time spans of resonant modes is shown. It has a bimodal character. It seems that there are some short-time resonant modes as well as long-time resonant modes. The second ones are connected with spontaneous OAE. A 30

B 6 5

,_,

20

>> g3 d-2 &

10

""1 0

0

2

4

6 8 10 12 14 16 18 t ime -sp an [ms]

0

(

10 time [ms]

Figure 4. A: Histogram of the time-spans (durations) of atoms that can be considered as resonant modes. Cases with long duration represent synchronized spontaneous activity (SSOAE). B: Example of energy distribution in t-f space of TEOAE with SSOAE activity (components of long duration).

3.2

Ears influenced by noise

In order to make statistical comparisons, atoms were grouped in half-octave frequency bands. Only the highest energy components for each subject in each band were selected for further analysis. Frequency-latency dependence as shown in Fig. 5A is logarithmic, which is a consequence of the cochlear structure. For the band up to 1414 Hz, there were no significant changes in the exposed group, but for higher frequencies, there was a significant shift towards longer latencies.

351 The time span parameter proved to be the least influenced by exposure of subjects to jet-engine noise. In Fig. 5B the trend can be observed that in all bands the duration of components of TEOAEs from ears exposed to noise was longer than in the non-exposed case. However, the difference between the two datasets was found to be statistically significant only for the 2000 Hz and 2379 quarter-octave band. B • -e• ^

X 3

•*-

6 5

exposed , norma!

4

•

• * -

'N*

-

exposed . normal

.

X 3

i e - ^a>» •e< •*• H3H

• O

•*.

mm
'\7 \V V I

'I

.

.

* • , ' , , • • ! , ,

• 1500

'•• 1750

',",

Frequency (Hz)

Figure 1. Left: DPOAE level as a function of Li level from 8s/octave sweeps for 5 different subjects.

has no spontaneous emissions, JL has one very small one, MH has a little larger one at low frequencies, the last two subjects MM and M W have several low level (below -5 dB SPL) SOAE. Custom programs for Mac computers (Mac OS X) controlled a Motu 828 D / A converter and wrote the data to disk for offline analysis. Two ER2 tube

357

1

•

•

'

:..!..!..-..'..:

'

.

- -360 1

-720

-1080 -1440

r

:

•

:

'...:...-mUM26.w.'.

:

.

.

:

"^v^i£=3U^--x--hiv ..'S^J^^JX^\_^ :

TVXNC"- s •

-1800

:

>-k

J "-S.VJ \ .

1

1

.

~\

"•>

•S^r>,

: ' 1

,

-.__ • : i

,

,

,

,

,

,

• • ,

,

1

1500 1750 Frequency (Hz)

Figure 2. Left: DPOAE phase as a function of Li level from 8s/octave sweeps. The phase at the lower levels for MW continues at the same rate at the higher frequencies.

phones were connected to an ER10 microphone which was inserted in the ear canal. Before being digitized using the Motu 828, the signal from the microphone •was preamplified by the Etymotic preamplifier and then amplified and filtered (300-10,000Hz) by a Stanford SR560 low noise amplifier under computer control. Sweeps with identical stimulus conditions (direction and duration) were av-

358 eraged to reduce the noise floor, or subtracted to estimate the noise floor. Sweeps with high noise levels were eliminated as long as a minimum of 8 sweeps could be averaged. Up and down sweeps were obtained to ensure that the rate of sweep did not effect the data and to provide an indication of the singal to noise ratio. In in interest of clarity we only present the upsweeps in this paper. At high levels the two curves are essentially identical. At lower D P O A E levels the sweeps vary somewhat a due to noise contamination. Sequential least-squares fit (LSF) analyses were used to extract the levels of the primaries and DPOAE. Overlapping Hann-windowed segments of data were LSF to in-phase and quadrature swept-tone components to obtain the amplitude and phase of the D P O A E .

3

Results

The fine structure obtained with the 8s/octave sweeps (2 octave taking 16s) differs greatly from subject to subject as can be seen in Figure 1. In all subjects the depth of the original fine structure decreases with increasing level, there are some small changes in the fine structure at lower levels but all showed major changes in the pattern at the highest level tested (L\ — Li = 75). A second wider fine structure appears this level at some frequencies in 2 subjects JL and MM. Examination of the phase from the same sweeps (Figure 2) reveals that the generator component is dominant at all levels for C W (the phase slope is always gradual. In all other subjects, the slope increases at low stimulus levels indicating that the reflection component becomes dominant at this level at some frequencies. Note that phase slope is reversed at the highest stimulus levels for JL. This coincides with the change to the wider fine structure in Figure 1, No fine structure is seen at higher primary levels when sweeping at 2s/octave (4s for 2 octaves) (Figure 3). At lower levels a wider fine structure similar to that seen for stimulus frequency OAEs is seen. It is is often associated with SOAEs. When the generator component was extracted from the 8s/octave sweeps using filtering in the time domain [5], the pattern was very similar to the 2s/octave sweeps. At higher primary levels the wider structure in JL is attenuated, but still visible. An Inverse Fourier Analysis of JL's d a t a reveals that their is an additional component with negative group delay. This component is there at all levels, but becomes equivalent in magnitude to the generator component near 70 dB SPL. In order to ensure that the effect did not stem from the sweeping primaries we established that the pattern of D P O A E fine structure was essentially identical when measured with more conventional procedures.

359

- Cjm05012l 4 s :

-20 -30-

1500 1750 Frequency (Hz)

Figure 3. Left: DPOAE level as a function of Li level from 2s/octave sweeps.

4

Discussion

The large individual differences in D P O A E fine structure with level can be better evaluated by the combination of the 8s/octave and 2s/octave sweeps. The 2s/octave sweeps provide a rapid tool for evaluating the generator component uncontaminated by the reflection component. The phase properties at the high-

360 est stimulus levels for JL were predicted for stimulus frequency OAE [2] when reflectance on the basilar membrane or the oval window is large. It is possible that the middle ear reflex is starting to impact the D P O A E fine structure at the higher levels by changing the amount reflected back into the inner ear at the oval window. Alternatively, the pattern seen is consistent with Mills [3] claim that there are two components one near the narrow traveling wave maximum and the other stemming from the more basal passive component. The negative group delay does not reflect negative travel time. Group delay gives an estimate of latency in a linear system, when a single filter is being tested. The cochlear is nonlinear and frequency dispersive (the filter changes with frequency). A nonlinear reflection would generate short group delays, but the travel time would still be twice the round trip travel time. The group delay would thus not represent travel time, but would reflect the underlying processes. Acknowledgments This research was supported in part by PSC CUNY and the National Institute on Disability and Rehabilitation Research, US D O E Rehabilitation Engineering Research Center - Hearing Enhancement. Changmo Jeung, Monica Wagner, and Marcin Wroblewski helped with the data collection and analysis. References 1. Mauermann, M., Kollmeier. B„ 2005. Distortion product otoacoustic emission (DPOAE) i n p u t / o u t p u t functions and the influence of the second D P O A E source.. J. Acoust. Soc. Am. 116, 2199-2212. 2. Talmadge, C.L., Tubis, A., Long, G.R., Tong, C , 2002. Multiple internal reflections in the cochlea and their effect on D P O A E fine structure. J. Acoust. Soc. Am 108, 2911-2932. 3. Mills, D,M., 1997. Interpretation of distortion product otoacoustic emission measurements. I. Two stimulus tones. J. Acoust. Soc. Am. 102, 413-429. 4. Long, G.R., Talmadge, C.L., Lee, J., 2004. Using sweeping tones to evaluate D P O A E fine structure.. ARO Abstr. 27, 102-102. 5. Dhar, S, Talmadge, C.L., Long, G.R., Tubis, A., 2002. Multiple internal reflections in the cochlea and their effect on D P O A E fine structure. J. Acoust. Soc. Am 112, 2882-2892.

THE BIOPHYSICAL ORIGIN OF OTOACOUSTIC EMISSIONS JONATHAN H. SIEGEL Northwestern University, Dept. of Communication Sciences and Disorders, 2240 Campus Drive, Evanston, II 60208, USA E-mail: i-siezel(a),northwestern. edu While studied extensively since their discovery by Kemp in the late seventies, the cellular basis of the phenomenon of otoacoustic emission remains unknown. Data from experiments in humans, chinchillas and Mongolian gerbils was used to test the hypothesis that otoacoustic emissions originate in the hair cell transduction apparatus. Specifically, a double Boltzmann model of the transducer predicts that emissions generated by a single tone (stimulus frequency otoacoustic emissions - SFOAE) should be measurable at stimulus levels 20 or more dB below neural threshold, but sufficient to modulate the activity of enough transduction channels to produce a macroscopically observable result. On the other hand, for a fixed lowlevel probe tone that evokes SFOAE, it should only be possible to demonstrate the presence of emission by using a suppressor tone large enough to drive the transducer into its nonlinear range, approximately where the suppressor level reaches neural threshold. This result should be independent of suppressor frequency. Both predictions were confirmed experimentally in all three species. The threshold suppressor level was consistently near the threshold of the compound neural response monitored with an extracochlear electrode, even for suppressors more than an octave higher than the frequency of a low-level (30 dB SPL) probe tone. Cochlear microphonic responses were always detected at the lowest levels demonstrating SFOAE. The hair cell transducer appears to be the site of interaction between the probe and suppressor tones for all suppressor frequencies, consistent with a single suppression mechanism. Nonlinear interactions demonstrated in SFOAE and CM between widely separated tones do not appear to have a correlate in the basilar membrane, suggesting that, at least under some conditions, pressure waves can be initiated directly from forces produced by the hair bundle.

1 Introduction Recent reports indicate that otoacoustic emissions originate in the hair cell transducer under conditions in which the cochlear amplifier is rendered inoperative [1-3]. Interest in the transducer is further heightened by the recent evidence that the cochlear amplifier resides in the hair bundle [4, 5]. It is not known to what extent the transducer contributes to otoacoustic emissions at low levels in normal ears. Stimulus-frequency otoacoustic emissions (SFOAE), which appear to be tones emitted by the ear in response to a tone, can be measured at levels near threshold [6]. To separate the SFOAE from the stimulus tone (probe) that evokes it, it is common to use a second moderately-intense (suppressor) tone to selectively remove the SFOAE. If the suppressor completely removes the SFOAE, then the residual, calculated as the vector change in the probe response when the suppressor is added to the stimulus [7,8], provides an accurate measure of the emission. If the suppression is less than total, then the residual does not accurately represent the

361

362

SFOAE. The part of the emission that is not suppressed may be erroneously considered part of the stimulus. Since the hair cell transducer has been implicated in the generation of otoacoustic emissions, it is of interest to explore the behavior of two-tone interactions in a computational model of the transducer and in experimental data. Experiments measured two-tone interactions in SFOAE and in the cochlear microphonic (CM) recorded from the round window. The CM is known to represent the summed receptor currents from hair cells [9], so similar two-tone behavior in SFOAE and CM would be expected if the transducer was the site of interaction of the stimuli for both phenomena. Measurements at near-threshold stimulus levels were used to simplify interpretations by restricting the cochlear region of interaction. 2 Methods These experiments were performed in anesthetized, tracheotomized chinchillas with body temperature maintained by a heating pad. The cartilaginous part of the ear canal and pinna and the lateral portion of the bony meatus are removed to allow optimal coupling of an Etymotic ER-10B+ otoacoustic emission probe. The bulla is opened to place a silver ball electrode on the round window to record CM and the compound action potential. Both middle ear muscles are severed from the ossicular chain. Animal procedures were approved by Northwestern Univeristy's IACUC. We measured stimulus frequency otoacoustic emissions using a variant of the commonly used suppression/vector subtraction method [7, 8, 10, 11]. The magnitude and phase of the residuals were expressed as the equivalent level and phase of a stimulus tone that would have produced the observed change in the ear canal pressure [10]. We simultaneously measured analogous suppression of the cochlear microphonic potentials in the same animals using the second A/D input of the sound card. Data were collected using Emav [12]. 3 Models and Results 3.1 Transducer model: Effect of bias The transducer model is a second-order Boltzmann fit to experimentallymeasured transducer functions [13, 14]:

g(0 = S«x/(l+fe(t)(l+*/(O) k,(t) = exp(0.065(24~x sel -x{t)) and k2(t) = exp(0.016(41 -xset-x(t))

(1) (2)

where g(t) is the conductance of the transducer, gmax is the maximum conductance, xse, is the offset from the normal operating point of the transducer function and x(t)) is the waveform of the input signal. Units of displacement are nanometers.

363

At the normal resting position (operating point) of the hair bundle (xset = 0), a small fraction of the transducer current is activated, due to transduction channels active at rest (Figure 1A). Deflections in the excitatory direction (positive) open more channels, while inhibitory deflections (negative) reduce the resting current by closing channels that were open at the resting position. The solid curve is the normal situation, while the dashed curve represents the addition of a static negative bias to the normal operating point. Figure IB depicts the output amplitude at the probe frequency for single tone excitation as a function of increasing input level. If the transducer set point is shifted to the right (xset= -50), the output amplitude is decreased significantly at low input levels, but grows rapidly to meet the response for the normal set point as the input amplitude is raised. The two curves exhibit relatively linear growth for input displacements below 15 nm. Figure 1. Basic character-istics of the hair cell trans-ducer. A: Displace-ment vs conductance plots for the normal set point and with the function displaced by 50 nm. B: Amplitude from the transducer of the response to a single tone for the two operating points depicted in A.

Transd cer Function (Kros, eta)., 1995)

/ /'

-

= 0 nm/ / xset = -50 nm

X set

-

^

// l

n i c n b r a m a n t /nm^

3.2

l Input Level (dB re 1 nm)

Residuals predicted by the transducer model

Figure 2 quantifies suppression of the probe tone in the transducer model for two paradigms. In the first, the suppressor tone is held at a relatively high fixed level and the response to the probe tone is depicted as a function of increasing level (thin solid curves). The measure of the output at the probe frequency is not the suppressed output itself, but the change from the unsuppressed response to the probe tone, directly analogous to the "residual" SFOAE at the probe frequency measured using a suppressor tone to separate the stimulus from the emission. The response to the probe in the absence of a suppressor is depicted as the thick solid line. For suppressors above about 50 dB re 1 nm, the amplitude of the residual is almost exactly the same as that of the response to the probe by itself, indicating essentially complete suppression of the probe. For fixed suppressor levels below 50 dB re 1 nm, the residual underestimates the actual probe response with an error that is constant (in dB) with decreasing probe level. In the same way, incomplete suppression of an SFOAE yields an inaccurate estimate of the emission.

364 true probe response

Figure 2. Dependence of the amplitude of the residual in the transducer model as a function of the level of either the probe (thin solid lines) or suppressor (dashed line) with the other tone fixed in level as indicated. The response of the probe when presented alone is indicated by the thick solid line. For a sufficiently strong fixed suppressor (Ls = 60 dB) the residual accurately measures the probe response. If the suppressor level is lowered (i.e., Ls = 40 dB) the residual underestimates the true probe response. 0

20 40 Probe or Suppressor Level (dB re 1 nm)

60

In the second paradigm, the probe tone is fixed in level and the suppressor level is varied (dashed curve). The transducer model predicts that the residual will always be detected at a lower level in the first paradigm than in the second. This behavior can be understood by considering that the sum of the two tones must drive the transducer out of its "quasi-linear" range for suppression to occur. As long as the fixed suppressor tone amplitude is large enough to do this on its own, residuals at the probe frequency can be detected at levels far below those at which the probe drives the transducer into nonlinearity by itself. A shift in operating point similar to that shown in Figure 1 reduces the difference in thresholds for the two paradigms. 3.3

Experimental verification of model predictions

The SFOAE and CM data both conformed to the major predictions of the transducer model. The SFOAE residual measured in response to a 4 kHz, 30 dB probe tone with a fixed 60 dB SPL suppressor and varied probe level was consis-tently detected at probe levels close to 20 dB lower than the threshold for suppres-sion for the fixed probe conditions (Figure 3). This was the case both for suppressor tones near the frequency of the probe or more than an octave higher (interaction region likely basal to that of the cochlear amplifier for the probe). The appearance of the residual above the noise floor was at similar stimulus levels for both paradigms and for both the SFOAE and CM. The threshold for suppression with fixed probes was not strongly dependent on probe level, as long as the residual was clearly detected above the noise floor for suppressors near 60 dB SPL (not shown). Unlike the SFOAE, the CM can be observed directly without using a suppressor to separate the stimulus from the response. The CM residual with fixed suppressor was displaced below the CM at the probe frequency for both the 3.9 kHz and 10 kHz suppressors, demonstrating that the CM was not completely suppressed even by the most intense suppressors used (70 dB SPL (not shown)). The two curves were closer for the 10 kHz suppressor, probably resulting from the spatial weighting of the round window electrode favoring nearby CM generators. Virtually identical results (not shown) confirm these predictions in Mongolian gerbils and humans.

365

0

20 40 60 Probe or Suppressor Sound Pressure Level (dB)

0

20 40 60 Probe or Suppressor Sound Pressure Level (dB)

Figure 3. Two-tone interactions measured in a chinchilla. A: SFOAE suppression conforms to the predictions of the transducer model with no shift in operating point. The residual is always seen at lower levels with the fixed suppressor paradigm (thick curves) than for the fixed probe paradigm (thin curves). This is true both for a suppressor near the probe frequency (3.9 kHz, solid curves) and for a suppressor more than an octave above the probe frequency (10 kHz, dashed curves). B: Similar behavior is seen in the suppression of the CM. The probe alone CM (Lp varied) is consistently larger than the CM residual, indicating incomplete suppression.

With a fixed 4 kHz, 30 dB SPL probe, the threshold for suppression for suppressors near or above the probe frequency was typically within 5 dB of CAP threshold at the suppressor frequency (data not shown). The CM at the suppressor frequency was consistently observed at levels typically 20 dB below the threshold for suppression. 4 Discussion A second-order Boltzmann model of the hair cell transducer accounts for several features of two-tone suppression measured in SFOAE and CM. The suppression data indicate that the transducers in the living intact cochlea operate at set points in which a significant fraction of the transducer conductance is active at the resting position of the hair bundle. Surprisingly small vibrations of the basilar membrane appear capable of exciting hair cells sufficiently to contribute to SFOAE. For example, for the chinchilla, a 4 kHz, 30 dB SPL tone produces an rms displacement of about 0.3 nm at the 9.5 kHz place (Ruggero, private communication). This same displacement would be reached in a sensitive cochlea at around -10 dB SPL for a tone at CF. The suppressor evokes a CM above the noise floor around this same SPL and begins to suppress the 4 kHz probe near 20 dB SPL, corresponding to a displacement of about 5 nm. Since the round window CM presumably underestimates the level at which hair cell transducer currents become significant, it therefore appears that the 4 kHz

366

probe tone evokes transducer activity at the place of the 10 kHz suppressor. We never demonstrated an SFOAE using a suppressor in which the probe tone would not have generated a CM "signal". It is reasonable to propose that the SFOAE is also a (suppressible) signal at even the lowest levels at which it is demonstrated. No suppression of the response to the 4 kHz tone should be evident in the basilar membrane vibrations at the 10 kHz place under these conditions [15], so hair bundle forces may create a pressure wave that contributes to SFOAE even near threshold. It has been proposed that the suppressor acts in two fundamentally different ways: it may remove SFOAE sources (signals) at the probe frequency that are actually present, or it may induce "...mechanical perturbations and/or sources of nonlinear distortion that would not otherwise be present..." [16]. However, in our measurements, it is plausible that the suppressor always removes a signal. Since CM suppression was not complete even at 70 dB suppressor levels, it appears likely that SFOAE suppression is also incomplete. If so, then it may be nearly impossible to completely suppress the SFOAE with suppressor tones that do not persistent and possibly pathological effects, even for probe tones as low as 30 dB SPL. It is difficult to know how much of the SFOAE goes undetected with suppressors commonly used to measure emissions. The range of stimulus levels over which the SFOAE can be considered a linear phenomenon appears to be confined to levels near and below CAP threshold. Nonlinear distortion is therefore likely to contribute significantly to SFOAE over most of their measurable range, not only at relatively high stimulus levels [17, 18]. Acknowledgments Supported by NIH grant DC-00419 and Northwestern University. References 1.

2.

3.

4.

Mom, T., Bonfils, P., Gilain, L., Avan, P., 2001. Origin of cubic difference tones generated by high-intensity stimuli: effect of ischemia and auditory fatigue on the gerbil cochlea. J. Acoust. Soc. Am. 110:1477-1488. Liberman, M.C., Zuo, J., Guinan, Jr., J.J., 2004. Otoacoustic emissions without somatic motility: Can stereocilia mechanics drive the mammalian cochlea? J. Acoust. Soc. Am. 116:1649-1655. Carvalho, S., Mom, T., Gilain, L., Avan, P., 2004. Frequency specificity of distortion-product otoacoustic emissions produced by high-level tones despite inefficient cochlear electromechanical feedback. J. Acoust. Soc. Am. 116:1639-1648. Chan, D.K., Hudspeth, A.J., 2005. Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro. Nature Neurosci. 8:149-155.

367

5. Kennedy, H.J., Crawford, A.C., Fettiplace, R., 2005. Force generation by mammalian hair bundles supports a role in cochlear amplification. Nature. 433: 880-883. 6. Schairer, K.S., Fitzpatrick, D., Keefe, D.H., 2003. Input-output functions for stimulus-frequency otoacoustic emissions in normal-hearing adult ears. J Acoust Soc Am. 114: 944-66. 7. Brass, D., Kemp, D.T., 1993. Suppression of stimulus frequency otoacoustic emissions J Acoust Soc Am 93:920-39. 8. Shera, C.A., Guinan Jr., J.J., 1999. Evoked otoacoustic emissions arise by two fundamentally different mechanisms: a taxonomy for mammalian OAEs. J Acoust Soc Am 105:782-98. 9. Dallos, P., 1973. The Auditory Periphery. Academic Press, New York. 10. Guinan, J.J., 1990. Changes in stimulus frequency otoacoustic emissions produced by two-tone suppression and efferent stimulation in cats. In: P. Dallos, CD. Geisler, J.W. Matthews, M.A. Ruggero and C.R. Steele (Eds.), The Mechanics and Biophysics of Hearing, Springer, Berlin, pp. 170-177. 11. Dreisbach, L.E., Chen, W., Siegel, J.H., 1998. Stimulus-frequency otoacoustic emissions measured at low- and high-frequencies in untrained human subjects. Assoc. Res. Otolaryngol Abs. 21:349. 12. Neely, S.T., Liu, Z., 1993. EMAV: Otoacoustic emission averager. Tech Memo No. 17 (Boys Town National Research Hospital, Omaha). 13. Kros, C.J., Lennan, G.W.T., Richardson, G.P., 1995. Voltage dependence of transducer currents in outer hair cells of neonatal mice. In: Active Hearing. A. Flock (Ed.) Elsevier Science, Oxford, pp. 113-125. 14. Lukashkin, A.N., Russell, I.J., 1998. A descriptive model of the receptor potential nonlinearities generated by the hair cell mechanoelectrical transducer. J. Acoust. Soc. Am. 103:973-980. 15. Rhode, W.S., Recio, A., 2001. Multicomponent stimulus interactions observed in basilar-membrane vibration in the basal region of the chinchilla cochlea. J. Acoust. Soc. Am. 110:3140-3154. 16. Shera, C.A., Tubis, A., Talmadge, C.L., Guinan Jr. J.J., 2004. The dual effect of "suppressor" tones on stimulus-frequency otoacoustic emissions. Assoc. Res. Otolaryngol Abs. 27:181. 17. Goodman, S.S.; Withnell, R.H., Shera, C.A., 2003. The origin of SFOAE microstructure in the guinea pig. Hear. Res. 183:7-17. 18. Talmadge, C.L., Tubis, A, Long, G.R., Tong, C , 2000. Modeling the combined effects of basilar membrane nonlinearity and roughness on stimulus frequency otoacoustic emission fine structure. J Acoust Soc Am 108:2911-2932.

368 Comments and Discussion Siegel: Jont Allen offers a valid reason to calibrate the source impedance of an otoacoustic emission probe to allow separation of the stimulus from the emission. I worry about the practicality of this approach. There is some finite error in estimating the source impedance (it is a quantity derived from pressure measurements). It is not known whether these errors are sufficiently large to give misleading results regarding otoacoustic emissions, whatever that might mean. The problem is knowing with confidence that a reliable measure has been made. I calibrate the pressure response of my otoacoustic emission probe carefully and have good reason to trust the levels it reports to within 1 dB over the frequency range of measurements. Since the quantity I measure is pressure, that is an appropriate calibration, regardless of the theoretical advantages in estimating emission power.

SPONTANEOUS OTOACOUSTIC EMISSIONS IN LIZARDS, AIR PRESSURE EFFECTS ON THEM AND THE QUESTION OF POINT SOURCES AND GLOBAL STANDING WAVES GEOFFREY A. MANLEY Lehrstuhlfur

Zoologie der Technischen Universitat Miinchen, Lichtenbergstrasse Garching, Germany. Email: geoffrey. manlev(3),wzw. turn, de

4, 85747

Shera [1] proposed that pressure effects on the middle ear provide a model for distinguishing between a point-source and a global standing-wave model of SOAE generation. A point source is supposed to be insensitive to changes in the boundary conditions for oscillation, whereas a standing wave would be influenced. Changing middle-ear pressure in humans alters both frequency and amplitude of SOAE, supporting Shera's assumption that mammalian SOAE originate through global standing waves. Lizards are highly reliable generators of SOAE, but their hearing organ differs from that of mammals in size, structure and micromechanics. Thus they provide a good system in which to continue to examine ideas about the generation of spontaneous emissions. In lizards, both negative and positive pressure changes were produced in the ear canal by adding or withdrawing air. Increases in pressure led to no or only small changes in frequency and amplitude, whereas pressure drops led to a fall or rise in SOAE frequency of up to several percent and to amplitude loss. These changes were observed over much smaller pressure ranges than those necessary in humans. The question is discussed as to whether such data permit a clear distinction of the nature of the emission source.

1 Introduction Unlike laboratory mammals, lizards are very reliable producers of spontaneous otoacoustic emissions (SOAE [2,3,4]). SOAE in non-mammalian papillae are generated by the transduction channels of the hair-cell stereovillar bundles [3] and new evidence points to the involvement of channels in mammalian active processes as well [5,6]. The patterns of lizard SOAE spectra correlate with the specific anatomy of the auditory papilla, especially with the presence or absence of a continuous tectorial structure. Papillae with continuous tectorial structures tend to be large with many hair cells and produce few, large-amplitude spectral peaks. In contrast, papillae without a tectorial membrane or with a salletal tectorial structure tend to produce a larger number of peaks of smaller amplitude [7,8]. These lizard data suggest that morphological features are important in the patterning of SOAE spectra. This is compatible with the idea that SOAE arise from point or localized sources in the hearing organ that, for some reason, emit more strongly than other regions, but also with the idea that impedance irregularities permit only particular standing-wave patterns. Humans, uniquely among mammals, have significant numbers of SOAE peaks and these are spaced at both regular and irregular frequency intervals [9]. One possible 'point-source' explanation for such spectral patterns, in which the local properties of the papilla determine the spectral

369

370

SOAE pattern, is morphological irregularity of the organ of Corti, especially apically, where the coiling is tighter [10]. Recent modeling work, however, suggests that the frequency patterning of SOAE spectra in humans is due to standing waves in the cochlea, set up between the active organ of Corti and reflection from the footplate of the stapes [1]. Such models assume that all hair cells of the cochlea are active and emit sound energy. Constructive interference of waves with particular path lengths to and from the middle ear would result in standing waves measurable as SOAE peaks, whereas destructive interference would obscure the presence of an active papilla at that frequency [1]. Irregular peak spacing in SOAE spectra is supposed to be due to impedance discontinuities. Although such models provide no explanation for the extreme rarity of SOAE in most laboratory mammals, they do model the common patterns of SOAE as reported by early workers (e.g., [11]). Since discussion of these distinctions has suffered from agreed definitions of the sources of SOAE, the following is offered: A point source is a localized group of hair cells that have sufficient spontaneous activity at a common frequency that part of the emitted energy is measurable in the ear canal. All the energy in point-source SOAE (PS-SOAE) derives from these local hair cells. The amplitude, however, will be sensitive to the impedance it sees - for example of the stapes footplate. In contrast, global standing-wave SOAE (GSW-SOAE) do not arise from a localized group of hair cells and even hair cells whose best response frequency is different may contribute energy to the signal. The SOAE signal derives from the funneling of energy by the particularities of standing-wave conditions in a given cochlear area: In the absence of a standing wave, no SOAE is observed. The relatively long path length leads to stable, narrow GSW-SOAE peaks. Experiments altering the properties of the middle-ear interface to the cochlea, such as changes in the relative air pressure across the tympanic membrane, are supposed by Shera [1] to provide a means of distinguishing between the pointsource and global standing-wave models of SOAE patterning. Whereas a point source should not be influenced by the properties of the middle-ear interface, global standing waves should be. Changes in middle-ear pressure have long been known to affect SOAE in humans [e.g., 9]. To provide a broader basis to continue the discussion of SOAE origins, this paper describes preliminary data on the effects of pressure changes on SOAE peak frequencies and amplitudes in two lizard species. 2 Methods The following two lizard species were used: Gerrhosaurus major (Gerrhosauridae, n=2) and Cordylus cordylus (Cordylidae, n=4). Both species have a salletal tectorial structure over the high-frequency region of the papilla and SOAE lie between 1 kHz and 5kHz. The length of their basilar papillae is about 600um in Cordylus and 1.4mm in Gerrhosaurus (estimated from [12]). Animals in a sound-attenuating chamber were anesthetized with isoflurane (Rhodia), placed on a thermal blanket to

371

control body temperature and their eardrums were checked for cleanliness. Their temperature was monitored by a tiny thermistor. A microphone (Etymotic ER-10B) in a coupler was sealed to the skin with Vaseline™. The coupler was attached by an air-tight joint to a tube with a 50ml airfilled syringe outside the acoustically-shielded chamber. Using the syringe, pressure changes were effected by adding or withdrawing air in 1 or 2mBar steps and measured using a hand-held pressure monitor (Greisinger GMH 3150) with a resolution of O.lmBar. Since larger positive pressures often led to leakage at the seal, measurements were begun using negative pressures. The microphone signal was amplified and either FFT analysed (Stanford SR760) or fed into a computer interface for analysis using Labview™ software. Up to 200 spectra were averaged (Harming window, frequency range up to 6 kHz). Pressure-induced changes were measured using narrowed frequency bandwidth and spectra were stored for each pressure step. Data files were later analysed using a spreadsheet program. Measurement sets were usually repeated up to three times. SOAE were identified in the zero-pressure-difference spectra and their frequency and amplitude determined at all pressure steps where they were still visible. Small pressure steps were necessary to reliably identify individual peaks. Changes in frequency were expressed in percent, amplitudes in dB relative to the values at zero pressure difference. Temperature also influences the SOAE frequencies [2,4], so measurements were only made when the body temperature was stable (±0.2°C). 3 Results In both species, small changes in air pressure led to frequency shifts and a drop in the amplitudes of SOAE peaks (Figs. 1, 2). After changes of maximally 10 to 15 mBar, the SOAE peaks were no longer visible. Pressure affected the SOAE in different ways: (a) In all cases, amplitudes were rarely increased and all decreased to the noise level during large frequency shifts. (b) Frequencies sometimes changed very little, they increased (from 1 to 3% in Gerrhosaurus, Fig. 2) or decreased (by maximally 5% in Cordylus). In general, the changes in frequency were larger for decreased than for increased air pressures. (c) In cases where several SOAE were observed in one ear, the air-pressure effects were larger for low-frequency SOAE and smaller for higher-frequency SOAE. (d) A relatively strong hysteresis was usually observed (e.g., Fig. 1). (e) Repeating the measurement series usually led to smaller values of shifts in later measurements, even if the repeat measurements were separated by several days.

372

With changes in air pressure, the two species showed, on average, frequency

2250

2750

3250 Frequency (Hz)

Figure 1: Spectra from the ear of Gerrhosaurus major measured during stepped changes in air pressure outside the eardrum from zero (top trace, through negative pressures down to -7 mBar, then back to zero and to positive pressures of maximally +8 mBar (bottom trace). Three to four SOAE peaks are visible.

shifts of opposite sign. The shifts were often small and even within the data from one species, cases of shifts of the opposite sign were observed. In all cases, larger frequency shifts were accompanied by a loss of SOAE amplitude (Fig. 2).

373

(Cordylus cordy U S 2R

Gerrosagrus major 1R;

/

t

/i
ext, arising from the sum of external sources, such as within the organ of Corti, from fluid pressure, or from applied forces, as well as a force, Frii0hc, that arises from the OHC force generator. In our model, forces are positive in the upwards direction by convention. Since a positive Fohc pulls down on the RL but pulls up on the BM, Frii0hc, can be described by two separate feedback loops, one resulting from the effect ofFohc at the RL and the other resulting from the effect of Fohc at the BM. The dotted feedback loop in Fig. 3 represents the former effect and the solid feedback loop represents the latter effect. Due to the other mechanical impedances in the system, only a fraction of the OHC force generator, Fohc, is transmitted back to the RL. A positive RL displacement leads to a positive Fohc, which causes the RL to be pulled down, which tends to decrease the positive RL displacement; therefore, the dotted feedback loop exhibits negative feedback. However, a positive Fohc also causes the BM to be pulled upwards, which tends to push the RL up and increase the positive RL displacement; therefore, the solid feedback loop exhibits positive feedback. Fn,,,«Xl

u rt

+/->. Ml

f*

z,

1 M-1,0 he

•

>

vm

K s-(ts+1}

I

''

F«jtw

^•nf^tm

z*

Haw

^D^OIK

^"MBJAMW,

K

Figure 4. Simplified version of the block diagram in Figure 3. Although Figure 3 shows both postive and negative feedback paths, combining both paths demonstrates that the overall feedback loop is always negative.

From Fig. 3, it appears that this system involves both positive and negative feedback since the effect of the OHC force at the RL and at the BM operates in

437

different directions. However, by combining the dotted feedback loop and solid negative feedback loop in Fig. 3, we can obtain a simplified block diagram that clearly demonstrates the negative feedback inherent in this topology (Fig. 4). The loop transmission is the multiplicative product around the loop in Fig. 4 [16]: _

KK *-bm S(TS +1) ZrlZbm +Z,Zohc + ZbmZohc

Since the parameters in the expression above are positive at D.C., the loop transmission or return ratio of the active OHC force generator is negative at D.C and there is negative feedback inherent in the system irrespective of parameter magnitude [16]. The loop gain (the absolute value of the loop transmission) is increased by the fact that the RL stiffness is less than that of the BM [13] so the intrinsic parameters of the cochlea tend to increase the negative feedback. We used parameters from the basal end of the cochlea (characteristic frequency, CF, = 43.6 kHz [19]) converted appropriately for volume velocities and pressures assuming an 18 um long by 30 um wide section with six OHCs [17,18]: Name K-bm

Mbm

Meaning BM stiffness (25 um probe) BM mass

Units N/m kg

Ref. [14]

N-s/m

—

N/m

[13]

kg

-

N-s/m

-

18 4

mN/m mV/nm

0.3

nN/mV

[201 [7,2122] [23]

0.305

ms

[211

Value 5.5 kbm

(2%-CFf Qbm Rbm

BM quality factor BM damping

6 {kbm-Mbni)

n

^bm

hi

RL stiffness (with 25 um probe)

Mrl

RLmass

Qrl Rri

RL quality factor RL damping

^bm

6 0-2W 6m 4

&k'-u'f ^ohc

K kf T

Single OHC stiffness Single OHC D.C. RLdisplacement-to-voltage ratio Single OHC D.C. voltage-toforce gain OHC membrane time constant

438

3 Results Simulations demonstrate that in analogy to the system in Fig. lc, higher OHC gains (ky) reduce mid-frequency roll-off of the OHC membrane potential (Fig. 5). The closed-loop pole due to the membrane time constant is increased from the open-loop 522 Hz to 4.7 kHz, which is a substantial speedup but is still a factor of 9.3 less than CF. However, the resonant gain at CF is increased with higher OHC gains, further compensating for the OHC time constant, and increasing the membrane potential at CF to almost the same level as it is at D.C. Decreasing the OHC gain by a factor of 10 (dotted line, green) in Fig. 5 results in a 2.5 dB drop in the resonant membrane potential at CF, raises the low-frequency asymptote, and changes the "tip-to-tail" ratio from -3.5 to -20 dB. The OHC force is actually 22.5 dB higher in the highgain case in Fig. 5 (solid line, blue) compared with the low-gain case since both the membrane voltage and ^are greater in the high-gain case. Figure 5. Bode magnitude plot of the transfer function from FrLext to the OHC membrane voltage, vm, based on the block diagram in Fig. 3. The high gain case (k/= 0.3 nN/mV) is shown in the solid blue line compared with the low gain case (k/ = 0.03 nN/mV), which is the dashed green line. fc, w 0.3 nwmv kl*Q.03nNtmV

it?

10*

4 Discussion We have shown that in engineered systems, slow motor time constants can be sped up with electrical amplification in a closed-loop negative feedback system. Analogously, the in situ micromechanical functional anatomy of the cochlea sets up a negative-feedback system that allows the slow OHC time constant to be compensated by the OHC gain. With negative feedback, OHC gain can be traded for bandwidth, allowing the OHC membrane potential to be extended without attenuation past the intrinsic membrane time constant. In addition, the resonant gain due to the resonant TM-RL and BM is increased by negative feedback, helping to further compensate for the OHC membrane time constant. Negative feedback around the BM was suggested by Mountain et al. [24] but in our model, it is negative feedback around the RL that is crucial for OHC speedup. To verify that our model is biologically realistic, we have also constructed a traveling-wave model of the cochlea with realistic parameters and compared the results to experimental data.

439 This model is beyond the scope of this paper but reveals that a good match to cochlear frequency-response curves with reasonable parameters is possible. Thus, the intrinsic architecture of the organ of Corti coupled with sufficient OHC gain and negative feedback is sufficient to extend the OHC bandwidth and generate adequate force at high frequencies. Therefore, no novel mechanisms are necessary. Nonetheless, our model is not mutually exclusive with other compensatory mechanisms that may act synergistically to allow high-frequency OHC somatic electromotility and amplification. Acknowledgments We are grateful for discussions with W. E. Brownell. T.K.L is a HHMI Predoctoral Fellow. This work is also supported in part by a CAREER award from the NSF, a Packard award, and an ONR Young Investigator award. References 1. Liberman, M.C., Gao, J., He, D.Z., Wu, X., Jia, S., Zuo, J., 2002. Prestin is required for electromotility of the outer hair cell and for the cochlear amplifier. Nature. 419, 300-304. 2. Cheatham, M.A., Huynh, K.H., Gao, J., Zuo, J., Dallos, P., 2004. Cochlear function in Prestin knockout mice. J. Physiol. 560, 821-830. 3. Santos-Sacchi, J., 2003. New tunes from Corti's organ: the outer hair cell boogie rules. Curr. Opin. Neurobiol. 13, 459-468. 4. Mountain, D.C., Hubbard, A.E., 1994. A piezoelectric model of outer hair cell function. J. Acoust. Soc. Am. 95, 350-354. 5. Dallos, P., Evans, B.N., 1995. High-frequency motility of outer hair cells and the cochlear amplifier. Science. 267, 2006-2009. 6. Nobili, R., Mammano, F., 1996. Biophysics of the cochlea. II: Stationary nonlinear phenomenology. J. Acoust. Soc. Am. 99, 2244-2255. 7. Ospeck, M., Dong, X.X., Iwasa, K.H., 2003. Limiting frequency of the cochlear amplifier based on electromotility of outer hair cells. Biophys. J. 84, 739-749. 8. Spector, A.A., Brownell, W.E., Popel, A.S. 2003. Effect of outer hair cell piezoelectricity on high-frequency receptor potentials. J. Acoust. Soc. Am. 113,453-461. 9. Weitzel, E.K., Tasker, R., Brownell, W.E., 2003. Outer hair cell piezoelectricity: frequency response enhancement and resonance behavior. J. Acoust. Soc. Am. 114, 1462-1466. 10. Zwislocki, J.J., Kletsky, E.J., 1979. Tectorial membrane: a possible effect on frequency analysis in the cochlear. Science. 204, 639-641.

440

11. Dong, X.X., Ospeck, M., Iwasa, K.H., 2002. Piezoelectric reciprocal relationship of the membrane motor in the cochlear outer hair cell. Biophys. J. 82, 1254-1259. 12. Allen, J.B., 1980. Cochlear micromechanics - a physical model of transduction. J. Acoust. Soc. Am. 68, 1660-1670. 13. Mammano, F., Ashmore, J.F., 1993. Reverse transduction measured in the isolated cochlea by laser Michelson interferometry. Nature. 365, 838-841. 14. Gummer, A.W., Hemmert, W., Zenner, H.P., 1996. Resonant tectorial membrane motion in the inner ear: its crucial role in frequency tuning. Proc. Natl. Acad. Sci. U.S.A. 93, 8727-8732. 15. Markin, V.S., Hudspeth, A.J., 1995. Modeling the active process of the cochlea: phase relations, amplification, and spontaneous oscillation. Biophys. J. 69, 138-174. 16. Bode, H.W., 1945. Network Analysis and Feedback Amplifier Design. D. van Nostrand, Princeton, NJ. 17. Fernandez, C , 1952. Dimensions of the Cochlea (Guinea Pig). J. Acoust. Soc. Am. 24, 519-523. 18. Nilsen, K.E., Russell, I. J., 2000. The spatial and temporal representation of a tone on the guinea pig basilar membrane. Proc. Natl. Acad. Sci. U.S.A. 97, 11751-11758. 19. Greenwood, D.D., 1990. A cochlear frequency-position function for several species~29 years later. J. Acoust. Soc. Am. 87,2592-2605. 20. He, D.Z., Dallos, P., 1999. Somatic stiffness of cochlear outer hair cells is voltage-dependent. Proc. Natl. Acad. Sci. U.S.A. 96, 8223-8228. 21. Housley, G.D., Ashmore, J.F., 1992. Ionic currents of outer hair cells isolated from the guinea-pig cochlea. J. Physiol. 448, 73-98. 22. Kros, C.J., 1996. Physiology of mammalian cochlear hair cells. In: Dallos, P., Popper, A.N., Fay, R.R. (Eds.), The Cochlea. Springer-Verlag, Berlin, pp. 328-330. 23. Scherer, M.P., Gummer, A.W., 2004. Vibration pattern of the organ of Corti up to 50 kHz: Evidence for resonant electromechanical force. Proc. Natl. Acad. Sci. U.S.A. 101, 17652-17657. 24. Mountain, D.C., Hubbard, A.E., McMullen, T.A., 1983. Electromechanical Processes in the Cochlea. In: deBoer, E., Viergever, M. (Eds.), Mechanics of Hearing. Delft Univ. Press, the Netherlands, pp. 119-126. Comments and Discussion Gummer: Your negative feedback model at the reticular lamina (RL) as a solution to the time-constant problem is very convincing. We know from the theoretical work of de Boer, Steele and others that the inertia of the basilar membrane (BM) is negligible, and from the experiments of Scherer and Gummer (Biophhys. J. 87, 1378-1391, 2004) that the inertia of the RL is also negligible. Does your model work if the inertial components of the BM and RL impedances are zero?

441 Answer: Yes, our model will still lead to speedup and increase in resonant gain with negative feedback if there is no inertial mass at the BM and RL. However, more OHC gain is needed to get the same speedup and the same increase in resonant gain. This is because, in the no-mass case, the open-loop singularities do not start off as complex singularities but instead reside on the real axis. So, more OHC gain is needed to move these singularities off the real axis into the complex plane. This possibility needs more investigation. However, a big increase in the required OHC gain is highly unlikely. As an aside, I also want to clarify that the RL mass in our model is meant to represent the mass of the TM-RL complex as a whole

THE COCHLEA BOX MODEL ONCE AGAIN: IMPROVEMENTS A N D N E W RESULTS R. NOBILI Department

of Physics

"G.Galilei", Via Marzolo 8, 35131 Padova, E-mail: [email protected]

ITALY

A. V E T E S N I K Universitats-Hals-Nasen-Ohrenklinik, Sektion Physiologische Kommunikation, Elfriede-Aulhorn Str. 5, 72076 Tubingen, E-mail: ales. vetesnik@uni-tuebingen. de

Akustik Und GERMANY

The hydrodynamic box model of the cochlea is revisited for the purpose of studying in detail the approximate scaling law that governs the tonotopic arrangement of its frequency-domain solutions. The law differs significantly from that derived by Sondhi in 1978, commonly known as "approximate shift-invariance", which suffers from an inaccuracy in the representation of the hydrodynamic coupling. Despite the absence of a similar scaling law in real mammalian cochleas, the results here presented may be significant in the perspective that a covariance law of a more general type should hold for real cochleas. To support this possibility, an argument related to the problem of cochlear amplifier-gain stabilization is advanced.

1

Introduction

It is assumed to be known t h a t the hydrodynamic box-model of the cochlea (Fig.lA) is governed by an equation of the form m£{x,t)

+ h(x)£{x,t)

+ k{x)£(x,t)

= -Gs(x)ti(t)-

/ G(x,x) £(x, t)dx , (1) Jo where £{x,t) is the displacement of a basilar membrane (BM) segment at BM position x and time t, dots standing for partial time derivatives; L is the length of the BM; m, h(x) and k(x) are respectively BM mass, BM viscosity and BM stiffness per unit BM length; cr{t) is the stapes displacement. Gs{x) and G(x,x) are the effective Green's functions accounting for the stapes-BM and the BMBM hydrodynamic couplings respectively. These depend uniquely on the fluid density p and the details of the cochlea geometry, i.e., in our case, L, the BM height H and the BM width W. Eq. (1) can be solved by numerical methods provided that m,k(x),h(x), p, L, H, W are known. We assume for these the standard values and profiles proposed by Allen in 1977 [1]: l . m = 0.05 g/cm,

442

443

2. k(x) = fco exp(—2ax), with fc0 = 109 g/(cm sec2), a = 1.7 cm" 1 . 3. /i(x) = ho exp(—ax), with ho = 300 g/(cm sec), 4. p = 1 g/cm 3 , L = 3.5 cm, if = 0.1 cm, W = 1 cm. The choice of an exponentially decreasing profile for k(x) is suggested by the fact that in most mammalian cochleas the BM responses to tones map tonotopically the interval of audible frequencies with an approximately exponentially decreasing profile. By contrast, there is no biologically plausible reason for assuming h(x) proportional to fc(x)1/2. But, as will be apparent in the next, this choice is crucial in order for the waveforms elicited by tones to vary regularly with frequency along the BM according to a well-approximated scaling law.

Figure 1. Cochlear box-model geometry. A: 3-dimensional model of the uncoiled cochlea showing a basilar membrane (BM) segment moving upwards. Horizontal arrows represent opposite displacements of oval and round windows. B : 2-dimensional representation showing stream lines as generated by a point-like source-sink pair. C: 2-dimensional model unfolded to a rectangle of length 1L and height H. The source-sink pair splits into a point-like source and a point-like sink symmetrically located with respect to x = 0.

Flattening the box model to a 2-dimensional [x, y] representation, as sketched in Fig.l, we find Gs(x) = 2p(L — x) and G(x + iy,x) as an analytic function defined on the upper complex semi-plane with logarithmic source and sink singularities at x + iy = L — x and x + iy = L + x respectively. Were this semi-plane unbounded, we would find G(x,x) = (P/TT) ln(|a; — x\/\x + x — 2L|). Actually, the mirroring effect of the rectangle boundaries forces the analytic function to be doubly periodic [3]. Thus we find instead ,_,, , p, isnfCfa; — L)|ml — snfC(x — L)|ml I G(a\x) = - l n —p—7 -~J— f~r,——~—(• , K ' 7T I sn[C(.x - L)\ m) + sn[C(x - L)\m]\

(2)

where sn(z\m) is the first Jacobi elliptic function of complex argument z and modulus m [4]. m is determined by the condition that the complete elliptic

,„.

444 integral of first kind K(m) = J"0 (1 —TOsin 2 B)~xl2 d0 satisfies the equality K{m)/K{\ - m) = L/H and C = K(m)/L. K(m) and K{1 - m) are indeed the quarter-periods of sn(z\m) along the real and the imaginary axis respectively. W i t h the assumed box-model parameters, m turns out to be very close to 1, namely m « 1 — 16exp(—TTL/H) = 1 —16exp(—357r). Correspondingly K(l — TO) is virtually equal to n/2 and C can be safely replaced by n/2H. 2

T h e b o x m o d e l in t h e h y p e r b o l i c a p p r o x i m a t i o n

Equation (1) can be rearranged and Fourier-transformed so as to read

I

L

G(x, x) rj(x, xo) dx + Z(x — x0) r](x, XO) = 2p(x — L) a(xo),

(3)

where r](x,XQ), &(xo) and XQ are respectively related to the Fourier transforms £„(x), Ou of £(;r, t), a(t) and t h e radian frequency LO by t h e equations rj(x, XQ) = £,u(x), O-(XQ) = &U and ^/fco/TOexp(—axo) = u>. We have then Z(x — XQ) = TO{1 — exp[2a(a;o — x)]

, exp[a(a;o — x)]} . (4) VTOfco Thus XQ becomes both a translational parameter for Z and the BM position where the real part of Z vanishes. Eq. (3) can be solved by numerical methods so as to obtain the repertoire of waveforms as elicited by tones of various frequencies. For XQ < L the waveform amplitudes fall down rapidly towards XQ and are virtually zero for x > XQ. Because of fluid incompressibility, these solutions, which will be called typical, satisfy the zero fluid-volume displacement equation I

rj(x,xo)dx=

Jo

/

r)(x,xo) dx = — H<J{XQ) .

(5)

Jo

Using the (undocumented) hyperbolic approximation sn(a;|TO) « tanh(:r) ta,nh(x — nL/2H), which holds for 0 < x < L with an error w 16exp(—357r), Eq. (2) becomes 1 G(x,x)

=G0(x,x)

G0(x, x) = j;[2L-{x

+ P(x-x) + x)-\x-

+ A(x + x) + B{x + x), x\], P{x -x)

where

(6)

= =¥ ln[l - e x p ( - ^ ) ] ,

1 In Sondhi's treatment [3] the approximation sn(x|m) ra tanh(x) was instead used, which led the author to overlook the term B in Eq. (6). Unfortunately, all mathematical manuals known to the Authors report this as an excellent approximation for m close to 1 without specifying that also the condition x < K(m) = L/2 must be satisfied. Actually, this approximation ignores the periodic structure of the elliptic function with quarter-period K(m) along the real axis. Consequently, the hyperbolic approximation of G(x, x) lacks the images of the source-sink pairs mirrored by the basal sides of the cochlear box.

445

A{x

3

+ x) = f ln[l - e x p ( - ^ 2 L - ^ + s ' ) ) ] , B{x + x) = =& ln[l -

e x

p(-^)].

T h e t h i n - c a n a l a p p r o x i m a t i o n satisfies a n e x a c t scaling law

For H —> 0, the singular terms A, B, P in Eq. (6) vanish and G(x, x) = GQ(X,X). The equalities dxG(x,x) = -2p6(x - x)/H, [ru(x)} w sul>(x)^UJi[ru,i(x))], where ru (x) is a local transformation of x depending upon u> but more general than a translation, and sUJ(x) is a complex coefficient possibly depending also on x. This formula correlates not only waveforms of different size and phase but also of different height/width ratio. The real cochlea geometry departs appreciably from that of the box model for at least one good reason: BM tapering and spiral canal tunneling allow the human cochlea t o cover the acoustic frequency range with a base-to-apex BM stiffness ratio one order of magnitude less t h a n that of the corresponding box model. If the geometry changes, the Green's functions also change in an approximately locally covariant way. But, in order for the entire cochlear equation to change the same way, the BM stiffness and viscosity profiles must change in particular ways. Whether this happens to some extent is not known presently, but a reason for suspecting this arises quite naturally from the problem of assuring a smooth cochlear amplifier gain (CAG) profile. Previous studies of the Authors [2] on a realistic model of the human cochlea with « 60 dB nonlinear gain over a wide frequency range showed that, due to long-range interactions, even the slightest local perturbation of a cochlear parameter caused severe instabilities. To restore gain uniformity without causing spontaneous oscillations, the CAG profile had to be suitably corrected over an appreciable neighborhood of the perturbation site. What natural supervising device might be able to perform this sort of distributed control in a bounded amount of time? Here we advance the hypothesis t h a t the local covariance of the waveforms favors the cochlear amplifier stabilization by means of locally feedback processes. References 1. Allen,J.B. (1977) Two-dimensional cochlear fluid model: New results J.Acoust.Soc.Am. 49:110-119. 2. Nobili, R., Vetesnik, A., Turicchia, L. and Mammano, F. (2003) Otoacoustic emissions from residual oscillations of the cochlear basilar membrane in a human ear model. J.Ass.Res. Otolaryngol. 4:478-494. 3. Sondhi,M.M. (1978) Method for computing motion in a two-dimensional cochlear model. J.Acoust.Soc.Am. 63:1468-1477. 4. Whittaker,E.T. and Watson,G.N. (1935) A Course of Modern Analysis, The University Press, Cambridge.

FOUR C O U N T E R - A R G U M E N T S FOR SLOW-WAVE OAEs CHRISTOPHER A. SHERA Eaton-Peabody Laboratory, Boston, MA 02114, USA email: shera@epl. meei. harvard, edu ARNOLD TUBIS Institute for Nonlinear Science, La Jolla, CA 92093, USA email: [email protected] CARRICK L. TALMADGE National Center for Physical Acoustics, University, MI 38677, USA email: [email protected]

1

Introduction

A recent paper [6] presents measurements of basilar-membrane (BM) motion to argue against the slow-wave model of OAEs, in which emissions propagate back to the stapes primarily via transverse pressure-difference waves (often simply called "reverse-traveling waves"). The experimental evidence adduced against slow-wave D P O A E s is two-fold: (1) group-delay measurements indicate that the stapes vibrates earlier than the BM at the distortion-product (DP) frequency and (2) longitudinal measurements of BM phase find no evidence for reversetraveling waves. These two experimental results, interpreted using the schematic illustrated in the bottom panel of Fig. 1, have been taken to confirm the suggestion [13,8] t h a t the reverse propagation of OAEs occurs via fast compressional (i.e., sound) waves [6]. The diagram posits that DP fast waves generated near X2 propagate nearly instantaneously t o the stapes, where the asymmetric movements of the oval and round windows create a slow (pressure-difference) wave t h a t propagates to Xdp, driving the transverse motion of the BM en route. Here, we present two pairs of counter-arguments against these claims [6]. The first pair critique the evidence against slows waves outlined above; the second pair argue t h a t the fast-wave model contradicts other well established facts of OAE phenomenology, thereby countering the conclusion t h a t compression waves play the dominant role in the production of otoacoustic emissions. 2

Counter-Argument

#1

The group-delay argument against slow waves fails when the DPs are generated near the point of measurement rather than remotely. The group-delay argument

449

450

nonlinear distortion and slow-wave generation

coherent reflection

nonlinear distortion and fast-wave generation fast-wave generation

Distance from stapes -

Figure 1. Schematic illustrating the generation of slow-wave (top) and fastwave (bottom) lower-sideband DPs. The panels show wave phase lag (increasing downward) vs cochlear location. In each case, slow waves (solid lines) at / i and /2 produce nonlinear distortion near X2, creating either slow or fast (dashed line) waves at f^p. Reverse waves travel to the stapes, where the fast wave creates a slow forward wave that then drives the BM at f^p. In the top panel, distortion near X2 also creates a forward wave that is partially reflected near £dp- In the bottom panel, the slow wave launched from the stapes creates a fast reverse wave near xa p . Empty boxes in the lower panel indicate unknown biophysical mechanisms. For simplicity, the diagram ignores multiple internal reflections. Adapted from [10,6].

against slow waves [6] follows from the contradiction between the group-delay data and the predictions of the schematic diagram shown in the top panel of Fig. 1. T h e argument hinges on a crucial feature of the diagram: Namely, t h a t the region of strong distortion that generates the / d p wave (denoted D in the diagram) is localized at some distance from the stapes. In other words, the argument assumes that the distortion measured in the motion of the stapes did not originate close to the stapes but has propagated to the point of measurement from a remote generation site located elsewhere in the cochlea. Although this assumption presumably holds under many experimental conditions, no evidence of its validity has been presented for the measurements in question [6]. On the contrary, given the relatively high levels of stimulation ( ~ 7 0 d B SPL) and the proximity of X2 to the base ( ~ 2 n n n ) , it seems likely that the DP generation "site" encompasses a considerable stretch of the basal turn of the cochlea. W h a t does the slow-wave framework predict when measurements are made inside the region of strong distortion, D ? Under such circumstances, the framework indicates that D P measurements are typically dominated not by propagated distortion, but by distortion generated close to the point of measurement. Group-delay data of the sort reported in [6] then reveal nothing about D P propagation delays or the relative time ordering of events at the D P frequency within the cochlea. Rather, group-delay measurements reflect changes in the output

451 of the local D P source, whose phase varies as the local phases of the primary tones change with frequency. When fi is fixed, as it was in the measurements [6], the framework predicts that the phase of a locally generated DP varies with the phase of the f\ wave at the site of generation. Measurements of BM transfer functions at two different points in the cochlea show that phase slopes at any given frequency below C F are shallower at the more basal location [7], and similar results presumably apply to intracochlear pressures that drive the stapes [3]. Viewed in this way, the finding that group delays controlled by the f\ wave are smaller at the stapes t h a n they are near x-i is thus entirely consistent with the predictions of the slow-wave framework. The observation t h a t the group-delay data can be explained within the slowwave framework obviates the need to postulate novel biophysical mechanisms to account for the results. Since the generation of compressional (sound) waves requires the vibration of a sound source (OHC somata? hair bundles?), the fastwave interpretation of the group-delay d a t a evidently requires t h a t the vibrating sound source be both (i) strongly coupled to the BM in one direction, since its vibration is presumed to be driven by forward-traveling BM waves at f\ and fi\ and (ii) weakly coupled to the BM in the other direction, since BM motion at /d p occurs significantly after stapes motion (i.e., only after the fast wave has generated a forward-traveling slow wave at the stapes). These two conflicting requirements appear difficult to reconcile with cochlear biophysics. Current understanding of the cochlear amplifier, for example, makes it hard to imagine synchronous volume changes in the hair cells, as proposed by Wilson [13], that are not also accompanied by forces t h a t couple strongly into the transverse motion of the BM. 1 3

Counter-Argument

#2

The longitudinal BM-phase argument against slow waves fails when the measured DPs are generated locally rather than remotely. At the DP frequency, the measured BM phase vs position data have negative slopes, as expected for forward- but not reverse-traveling waves. Curiously, three of the four longitudinal measurements presented as evidence against slow waves (see Fig. l a - c in [6]) were made at BM locations largely apical to X2, the presumed center of the 1 One theoretical possibility is that the cochlear amplifier (CA) operates not by generating forces that couple into BM motion locally near the OHC, but by generating compressional waves that couple into BM motion at the stapes via the impedance asymmetry between the cochlear windows. However, without considerable ad hoc manipulation this model for the CA cannot be made to amplify forward-traveling waves except at certain special locations in the cochlea determined by round-trip phase shifts, (de Boer [personal communication] has independently analyzed this model for the CA and uncovered other deficiencies.)

452 region of D P generation. Since both the slow- and fast-wave frameworks predict forward-traveling / d p waves in the region X2 < x < xap, the measurements cannot distinguish the two alternatives. The fourth measurement (Fig. Id) was made basal to #2, but its interpretation suffers from the same limitation as the group-delay data: The argument breaks down when applied inside the region D of strong distortion, where local rather than propagated distortion dominates the measurement. 2 The phase of the local distortion follows t h a t of the D P source, which has the form <j>src(x) = 2cpi(x) - (fa(x) + constant,

(1)

where <j>i(x) is the phase of the / i wave, etc. Since the measurements indicate t h a t STC(x) defined above has a negative slope, the experimental results again appear consistent with the predictions of the slow-wave framework. 4

Interlude

Counter-arguments # 1 and # 2 indicate that recent measurements claimed to refute the existence of slow-wave OAEs [6] fail to provide compelling tests of the slow-wave model. The failure of an argument, however, does not imply t h a t its conclusion is incorrect: It remains possible t h a t slow-wave OAEs really are negligible or non-existent and that fast-wave mechanisms dominate the production of otoacoustic emissions, as claimed. To address this possibility, counter-arguments # 3 and # 4 discuss two additional OAE measurements. Both measurements contradict simple predictions of the fast-wave model but have natural explanations in the slow-wave framework. 5

Counter-Argument

#3

The fast-wave model cannot account for the dramatically different phase-gradient delays manifest by lower- and upper-sideband DPOAEs. In the fast-wave model, DPs couple directly to the stapes via compressional waves whose propagation is unaffected by the properties of the BM. Once they couple into the fluids, fastwave DPs—unlike their slow-wave counterparts—undergo no BM-related filtering prior to their appearance in the ear canal. It therefore makes no difference whether fast-wave DPs are generated at cochlear locations whose CFs are above or below their own frequency. The fast-wave model thus indicates that both lower- and upper-sideband DPs are generated in the overlap region near X2 by identical "wave-fixed" mechanisms. As a consequence, the model predicts that 2 Even if the experiments [6] had established that the measurements were dominated by propagated rather than local distortion, interpretation of the data would still be enormously complicated by wave reflection from the stapes.

453 both D P O A E types should manifest nearly constant phase when measured using frequency-scaled stimuli (fixed fij f \ ) . This prediction of the fast-wave model is contradicted by experiment: Whereas the phase of lower-sideband DPOAEs (e.g., 2 / i — / 2 ) at near-optimal primary ratios remains almost constant (as predicted), the phase of upper-sideband DPOAEs (2/2 — /1) varies rapidly with frequency [4].3 The different phase gradients of lower- and upper-sideband DPOAEs can, however, be understood in the slow-wave framework. When DPs couple into BM pressure-difference waves they become subject to filtering by the BM. For lower-sideband DPs, the overlap region near x% is basal to the BM cutoff for / d p waves, and DPs generated in this region propagate freely. At near-optimal ratios, the multiple reverse-traveling D P wavelets created in the distortion region D combine coherently to produce a large reverse-traveling wave whose phase behavior is "wave-fixed." For upper-sideband DPs, however, the region near X2 is apical to the BM cutoff for / d p waves, and D P s generated in this region are strongly attenuated. As a result, place-fixed mechanisms at XdP become dominant [4], For example, upper-sideband DPs generated at x < x&p create slow waves propagating in both directions. Because of phase interactions among the wavelets arising from the distributed DP source, those wavelets initially traveling toward the stapes tend to cancel one another out, whereas those traveling toward XdP tend to reinforce one another. The result is a forward-traveling slow wave, which—as with any forward-traveling wave—undergoes partial coherent reflection near its characteristic place. Since the dominant reverse-traveling wave is generated by scattering off "place-fixed" perturbations, upper-sideband DPOAEs (like SFOAEs) have a rapidly rotating phase. 6

Counter-Argument

#4

The fast-wave model cannot account for the results of experiments performed using the Allen-Fahey paradigm. The Allen-Fahey paradigm [1] consists of measuring the ear-canal D P O A E as a function of r = / 2 / / 1 while the intracochlear DP response is held constant at Xdp (e.g., by monitoring the response of an auditory-nerve fiber tuned to /dp). Aside from possible suppressive effects, the predictions of the fast-wave model can be deduced immediately from the bottom panel of Fig. 1. Fixing the DP response at XdP is equivalent to fixing the fast wave at the stapes, which is equivalent to fixing the D P O A E in the ear canal. How does suppression modify this prediction? As r decreases towards 1, the primaries draw closer to XdP and their suppressive action reduces the response to 3

Although characteristic of mammalian DPOAEs, striking differences between the phasegradient delays of upper- and lower-sideband DPOAEs are not found in the frog [5].

454 the DP at x&p. To maintain the constant response mandated by the paradigm, the D P source output must be increased (e.g., by boosting the levels of the primary tones). When the source output is increased, the fast-wave pressure at the stapes and the D P O A E in the ear canal both increase correspondingly. For the Allen-Fahey paradigm, the fast-wave model therefore predicts t h a t the ear-canal DPOAE will increase at close ratios. This prediction, however, is contradicted by experiment: Studies performed using the Allen-Fahey paradigm all find t h a t the ratio of ear-canal to intracochlear DPs falls as r —> 1 [1,9,2]. The results of Allen-Fahey and related experiments can, however, be understood in the slow-wave framework, where they reflect changes in the effective directionality of the waves radiated from the distortion-source region [11]. Slowwave calculations explain the Allen-Fahey experiment by showing that at close ratios the distortion region D radiates much more strongly toward Xdp t h a n it does back toward the stapes. As a result, and despite the countervailing effects of suppression, fixing the response at x,ip causes the corresponding ear-canal D P O A E to fall as r —• 1. [Note t h a t in the top panel of Fig. 1 the forward- and reverse D P waves emanating from D need not maintain the same amplitude ratio at all values of r; contrast this with the bottom panel, where the ratio of reverse fast wave to forward slow wave is determined, independent of r, by impedance relationships at the stapes.] 7

Conclusion

The counter-arguments presented here indicate t h a t recent tests of the slowwave model [6] provide no convincing evidence against slow-wave OAEs. Furthermore, slow-wave OAEs appear necessary to account for varied aspects of OAE phenomenology well established in the literature. Although our counterarguments support the slow-wave model, they must not be construed to suggest t h a t fast-wave OAEs do not exist; absence of evidence is not evidence of absence. Indeed, we take the totalitarian view of physical law t h a t everything not forbidden is mandatory, and we therefore fully expect that both slow- and fastwave OAEs occur in the normal cochlea. The problem, then, becomes one of establishing the relative contributions of the two (or more?) emission modes and understanding their physical and physiological determinants. In principle, there need be no universal answer to these questions: The dominant OAE mode may vary with species and order (e.g., from amphibians to mammals), with cochlear location (e.g., from base to apex), and with stimulus or other experimental parameters. We have provided examples illustrating the importance of slow-wave contributions to the generation of mammalian OAEs; the role played by fast waves remains to be elucidated.

455 Acknowledgments Supported by grants from the NIDCD, National Institutes of Health. We thank Nigel Cooper, Paul Fahey, and Tianying Ren for helpful discussions. References 1. Allen, J.B. and Fahey, P.F., 1992. Using acoustic distortion products to measure the cochlear amplifier gain on the basilar membrane. J. Acoust. Soc. Am. 92, 178-188. 2. de Boer, E., Nuttall, A.L., Hu, N., Zou, Y., and Zheng, J., 2005. The Allen-Fahey experiment extended. J. Acoust. Soc. Am. 107, 1260-1266. 3. Dong, W. and Olson, E.S., 2005. Two-tone distortion in intracochlear pressure. J. Acoust. Soc. Am. 117, 2999-3015. 4. Knight, R.D. and Kemp, D.T., 2001. Wave and place fixed D P O A E maps of the human ear. J. Acoust. Soc. Am. 109, 1513-1525. 5. Meenderink, S.W.F., Narins, P.M., and van Dijk, P., 2005. Detailed / i , / 2 area study of distortion product otoacoustic emissions in the frog. J. Assoc. Res. Otolaryngol. 6, 28-36. 6. Ren, T., 2004. Reverse propagation of sound in the gerbil cochlea. Nat. Neurosci. 7, 333-334. 7. Rhode, W.S., 1978. Some observations on cochlear mechanics. J. Acoust. Soc. Am. 64, 158-176. 8. Ruggero, M.A., 2004. Comparison of group delays of 2 / i — / 2 distortion product otoacoustic emissions and cochlear travel times. Acoust. Res. Lett. Online 5, 143-147. 9. Shera, C.A. and Guinan, J.J., 1997. Measuring cochlear amplification and nonlinearity using distortion-product otoacoustic emissions as a calibrated intracochlear sound source. Assoc. Res. Otolaryngol. Abs. 20, 51. 10. Shera, C.A. and Guinan, J.J., 1999. Evoked otoacoustic emissions arise by two fundamentally different mechanisms: A taxonomy for mammalian OAEs. J. Acoust. Soc. Am. 105, 782-798. 11. Shera, C.A., 2003. Wave interference in the generation of reflection- and distortion-source emissions. In: Gummer, A.W. (Eds.), Biophysics of the Cochlea: From Molecules to Models, World Scientific, Singapore, pp. 439453. 12. Talmadge, C.L., Tubis, A., Long, G.R., and Piskorski, P., 1998. Modeling otoacoustic emission and hearing threshold fine structures. J. Acoust. Soc. Am. 104, 1517-1543. 13. Wilson, J.P., 1980. Model for cochlear echoes and tinnitus based on an observed electrical correlate. Hear. Res. 2, 527-532.

456

C o m m e n t s and Discussion T i a n y i n g R e n : The purpose of the following comments is not to defend the cochlear compression wave theory. Instead, they try to clarify a few points for helping our thinking of the D P O A E . Counter-Argument # 1 reads, in brief: The group-delay argument against slow waves fails when the DPs are generated near the point of the measurement rather than remotely. The longitudinal pattern of basilar membrane vibration measured at the same location as for the emission measurement in the gerbil shows a normal forward travel delay (Ren, 2002, PNAS, 99:17101-6). If the backward traveling wave is symmetrical to the forward wave it should show the same delay, which was not shown by the data. Counter-Argument # 2 reads: The longitudinal BM-phase argument against slow waves fails when the measured DPs are generated locally rather t h a n remotely. Since the measured region of the basilar membrane responses to tones goes from 8 to 24 kHz (Ren, 2002, PNAS, 99:17101-6), the phase curve near the basal end should have revealed the backward traveling wave, if it exists. In Fig. Id (Ren, 2004, Nat. Neurosci., 7:333-4) the observed location is clearly out of the D P generation site because the basilar membrane response to a 12 kHz tone is linear at the 17 kHz BM location. Most importantly, the 2 / i — fi phase calculated based on the j \ and $2 phases of BM vibration is different from the measured 2 / i — /2 phase, which demonstrates that the measured phase data are not dominated by the locally generated DP. Counter-Argument # 3 reads: The fast-wave model cannot account for the dramatically different phase-gradient delays manifest by lower- and uppersideband DPOAEs. T h e reverse propagation of the upper-sideband DPOAEs is different from t h a t of lower-sideband emissions. Although the slow-wave model can explain the fast phase change of the upper-sideband emission, the alternative interpretation based on the fast-wave model remains plausible, since the observed emission delay can be caused by the cochlear filter rather than by a backward traveling wave (Avan et al., 1998, Eur. J. Neurosci., 10:1764-70; Ruggero, 2004, ARLO, 5:143-7). R e p l y : Thank you for your thoughtful comments. 1. Model calculations indicate that relationships between the spatial patterns of BM phase produced by single tones (e.g., those reported in your PNAS paper) and the slopes of 2 / i — ji phase-vs-frequency functions (i.e., D P phase-gradient delays) measured on the BM, at the stapes, or in the ear canal are neither always straightforward nor intuitive. We therefore suggest caution when interpreting both experimental and numerical results, espe-

457 daily when the effective DP generation site is distributed over a relatively broad region of the cochlea a n d / o r reflection from the stapes occurs. 2. Measurements of distortion in single-tone responses are not the most sensitive indicators of the intermodulation distortion produced by two tones, especially when the total distortion is small compared to the primaries (the BM DPs in Fig. Id are 20 dB or more below the primary tones). When local distortion dominates the measured response slow-wave theory indicates that the 2 / i — fa DP phase is only approximately equal to 2<j>\{x) — 4>2(x); even though local distortion makes the controlling contribution, it is not the only component of the response. The main point of our first two counter-arguments is t h a t the slow-wave model can account for the salient features of the data t h a t have been used to argue against slow-wave mechanisms. 3. As pointed out elsewhere (e.g., Koshigoe and Tubis, 1982, JASA, 71:11941200; de Boer, 1997, JASA, 102:3810-3813; Shera et al., 2000, JASA, 108:2933-48), most of the so-called filter build-up cannot be separated from the travel time because the amplitude of the wave builds up while it is traveling. Tubis et al. (2000, JASA, 108:1772-85) demonstrated t h a t the cochlear filter—defined as the contribution to the BM mechanical transfer function arising from the "resonant denominator" in the W K B expression— gives only small contributions to the D P O A E phase derivatives in an active model. Even if it were possible to separate "travel time" from "filter buildup time" in some other meaningful way, it's not clear to what alternative interpretation you refer. Although slow-wave theory indicates t h a t the "reverse propagation of the upper-sideband D P O A E s is different from that of lower-sideband emissions," the same is not true in simple fast-wave models, in which fast-wave DPs propagate as compressional waves unaffected by the filtering (or other) properties of the BM (e.g., Wilson, 1980, Hear. Res., 2:527-32; Shera et al., 2005, ARO Abs., 28:657).

THE EVOLUTION OF MULTI-COMPARTMENT COCHLEAR MODELS

A.E. HUBBARD AND S. LU ECE Department

and Hearing Research Center, Boston University, Boston USA E-mail: [email protected] J. SPISAK AND D.C. MOUNTAIN

Biomedical Engineering

and Hearing Research Center, Boston University, Boston, USA

A major goal in cochlear modeling is to account for the functional mechanism of the cochlear amplifier (CA). Although numerous hypotheses have been presented, many are based on addons to the fundamental one-dimensional model, which assumes only the basilar membrane between two fluid-filled channels, scala vestibuli and scala tympani. Another class of models assumes more than two wave propagation channels (modes), and we call them multicompartmental models, a concept that originated with de Boer [1, 2, and 3]. Using a multicompartmental formulation, we put forward the hypothesis that the CA function is due to a combination of forces on the reticular lamina and the basilar membrane coming from both local hair cells and from a pressure wave that propagates in the fluid-filled spaces between the reticular lamina and the basilar membrane. A generic version of the model has been used to match data from various species. An improved model with parameters based on anatomical data from the gerbil can better match physiological data from the gerbil. A more advanced model that separates arcuate and pectinate regions of the basilar membrane shows the phase angle of the response of the arcuate region to low-frequency probe tones reverses at about midway down the cochlea. Overall, the models provide an explanation of how the CA might work.

1 Introduction How can cochlear outer hair cells (OHC) produce amplification if they have seemingly nothing to push against [1]? It was an enigma to the field of auditory science, a necessary riddle to be solved, since virtually all investigators believed OHCs underlay the cochlear amplifier. In one attempt to solve the riddle, de Boer assumed that the OHC stood between the reticular lamina (RL) and the basilar membrane (BM), pushing equally and oppositely on each, thus implying that if RL and BM could move differently, there could be fluid flow within the organ of Corti (OC). Unfortunately, simplifying assumptions would make a fait accompli the conclusion there was no way such a model could work in an energy-efficient, natural world, de Boer also explored a cylindrical version of the sandwich model and rejected it also [2]. A model in which waves propagated down the spiral sulcus, also failed to explain the cochlear amplifier [3], let alone matching experimental data. Quite to the contrary, matching experimental data was what a multicompartment model, called the traveling-wave amplifier model (TWAMP), did well [4]. It replicated the high and not narrow peaks, characteristic of the BM motion scaled by stapes motion found experimentally, as well as the corresponding phase

458

459 angle data. Although the TWAMP was a multicompartmental model, the model's additional compartment could not be unambiguously identified as an anatomical compartment in the cochlea. Chadwick et al [5] explored a model that had four fluid compartments, the fourth being the subtectorial fluid space. They could produce a gain of around 35 dB using forces on the order of 1 nN per OHC, but the peaks were not sharp enough to match physiological data. We built a multicompartmental model that assumed only somatic OHC motility [6] and found it could match highgain (low SPL) physiological data quite well using OHC force generation ~ 0.085 nN/nm RL deflection per OHC in the base down to -0.012 nNnm in the apex. In this paper, we elaborate two improved versions of that multicompartmental model. A third improvement on the model is in preliminary stages, and is reported in this book in a separate article. 2 Methods A hydromechanical drawing of the basic model is depicted in Figure 1. Over an incremental length along the cochlea, (one of 400 model sections) the biological cochlea has approximately ten OHCs embodied schematically as three OHCs in the cartoon. SV and ST are longitudinal compartments containing fluid. Between the RL and BM, which are modeled as resonant spring-mass-damper structures, is the fluid-filled space that we call the organ of Corti (OC) space. The OC compartment is the third compartment of the multicompartmental model. The RL resonance in all models to follow was on the order Figure 1. Inset: A stylized drawing of the cross-section of a three-compartment model The three compartments are SV, ST, and OC. OHCs push equally and oppositely against the RL and BM, which are resonant structures. Main figure: An electrical analog circuit for one section of the model. 400 sections with varying parameters comprise the entire model. OHC force, is represented as a pressure, since the force acts over an incremental area in the model. It is comprised of an active component that is proportional to the movement of the RL and a passive component. This assumes a rigid tectorial membrane and hair bundle deflection proportional to RL deflection. The "helper" circuit calculates passive opposition to OHC length change.

of a half-octave below the resonance of the BM. In all models explored, the impedance of the RL was on the order of l/10th to l/5th that of the BM. To assign the spring-mass-damper properties of the BM, we used a compliance map [7] and

460

chose the mass element to produce the tuned frequency required by the Greenwood function [8] for a gerbil. We embodied the cartoon shown in Figure 1 (inset) in an electrical impedance analog circuit. We calculated the circuit responses using either TSpice or a Cadence analog simulator, Spectre. We often checked the correspondence between the two simulators, especially in the case of unexpected outcomes. 3 Models and Results 3.1

The basic model with generic parameters

The basic model was able to replicate well the BM/Stapes ratio (magnitude and phase) for the chinchilla [9] using model parameters that were chosen, using a frequency-to-place map that was appropriate for the gerbil. Since the data were from a chinchilla, a model location was chosen so that the tuned frequencies of model and data matched. 3.2

The model using parameters more appropriate to the gerbil

The basic model was changed to incorporate the dimensions of the cochlear scalae as well as the approximate cross-section of the fluid-filled region between the RL and the BM. Both cochlear model fluid inertia and viscosity were estimated. Moreover, the point stiffness data taken from the gerbil were used to estimate the BM compliance values. We also switched the target data to be that obtained from the gerbil [10]. The model performance is co-plotted with the data in Figure 2. The model does a reasonable job in replicating the data. Although it is difficult to put a quantitative measure on goodness of fit, the model tuned to the gerbil does qualitatively somewhat worse than the generic compared to chinchilla data. 10

'

\ *—- experimental Data I I — Model 10'

!/ \

*J^ \

1 I 10*

I m

'> )'

Frequency (Hz)

10*

~"*"^\

'

V

r:

e 10 1

'""-"ess

>'

\ \\

—

Expeumental Dafa \ Model

Frequency (Hz(

. «*

Figure 2 Left panel: The velocity of the BM re. the stapes from the model alongside data from the gerbil obtained using 40 dB SPL probe tones. Right panel: Model and experimental phase angle.

461

3.3

The model improved adding an arcuate and pectinate BM regions

The BM was divided into arcuate (AZ) and pectinate (PZ) zones. Fluid was allowed to flow radially between AZ and PZ. We estimated the viscous passage between the Spaces of Neul, through the spaces between the pillars, into the tunnel of Corti. Thus, in addition to the longitudinal fluid compartment over the PZ region, another similar compartment was located over the AZ. The impedance of the AZ was made l/10th that of the PZ. This change greatly improved the phase angle comparison between the PZ phases of the model and the physiological data (see Figure 3), but the comparison between the PZ gains did not compare so well in the region beyond the best frequency. ©ain Pto* tor 30dB Input a t % J m m from ttw &as«

Area** OH ft** >

Figure 3 Magnitude (left panel) and phase (right panel) of BM/stapes ratio for the model with AZ and PZ explicitly represented are compared with experimental data [10].

- PicilnsteBMGalrt i - AreuawBMGaln * • gxptftmcrrta) Qaat |

frequency (tft)

"*

t»m» WW for 3M& Input a! ] . h i > from «M a

(>*«*)**« 8 M & * *

• — Areuat* 8 M fmn ' ..... experiments! OM*

Frequency (Hx)

However, another surprising result emerged from this exploration of the multicompartmental model with both AZ and PZ. The phase angle of the AZ pressure response to low-frequency tones reversed polarity about half-way down the cochlea. This could be significant, because it has for decades been known that the phase angle of the response to low-frequency tones (in the "tails" of the tuning curve) of neurons at various locations down the cochlea reverses, about half-way [11] down the cochlea. Figure 4 shows the phase of neural responses to lowfrequently probe tones, as a function of the best frequency (BF), which amounts to the spatial location down/up the cochlea alongside the model's AZ pressure phase angle.

462

M

m a

1 1

"i r100 HZ - N=»8

i

(

1

«« ,. , X 4, 5> » *

.*;

e £ -wo a.

i

-

SB -»•»

M I

i

'"* I

\

Figure 4. Single unit data [11] plotted versus the cochlear location at which BF occurs. The dashed line plots the AZ pressure as a function of distance down the cochlea. The experimental data show a 180 degree phase transition about half-way down the cochlea. Model data unwrap the opposite way.

"A t

f

1

1

.as

.s

1

2

\ i

4

8

IS

BF (KHZ)

4 Disc ussion How can a multicompartmental model in which the OHCs seemingly have nothing to push against work? Part of the answer is that the RL and BM are not in phase when the CA shows highest gain [6]. Thus RL and BM are essentially pushing off each other by way of the OHC connection. Since RL and BM are not in phase, there must be OC fluid flow. Thus, (Figure 5) there is also a traveling pressure wave in the OC, in addition to the pressure waves in SV, and ST. The real drive to the BM comes from the difference between the OC and ST pressure plus the force produced by the OHCs. This force is calculated as a pressure, because in each incremental piece of model there is an implied area of the BM. The various pressures drive the BM in different regions along the BM. The classical pressure difference [12, 13], P-, which is Psv - Pst, drives the BM in the more basal locations. However, as the waves approach the peak region of the velocity on the BM, the OHC forces become more significant than P-. This occurs about 1 mm basal to the peak. Up until this point, the OC to ST pressure difference has been negligible. However about Vi mm basal from the peak of the response on the BM, both the OHC forces and the OC pressure drive the BM comparably, and this action is continued on the apical side of the peak. Well past the peak and on the order of 30 dB down from the peak pressures, the P- wave, which contributed nothing to the BM velocity in the amplification region, is again dominant. Whatever phase lag was attained by the velocity response of the BM when the OC pressure and OHC forces were dominant, now will be wrapped to the nearest cycle of the phase of the velocity that results with P- driving the impedances of the BM and RL (see Fig. 1), thus creating a phase plateau many cycles down from the actual phase ofP-.

463

Figure 5. Left panel: Magnitudes of model pressure differences and OHC force calculated as a pressure. Right panel: Phase angle of the pressure and force responses.

Distance from the ftase (mm)

OHC —— P w - P s t ; .— Poc-Pst

X,

©stance (torn the Base (ram)

For an architecture that was once thought doomed to fail [1], the multicompartmental models actually show astonishing promise for explaining the CA, as well as fitting physiological data. It was surprising that the generic multicompartmental model fit chinchilla BM/Stapes ratio data so well. The model with "gerbil" parameters does a comparable job fitting gerbil magnitude data, although the phase angles are, arguably, not as good. To the contrary, the multicompartment model that includes the differentiation between AZ and PZ does well on phase, but the magnitude somewhat misses its mark. However BM motion data are in conflict with the AZ/PZ model's prediction that the AZ and PZ move out of phase [14]. The interesting reversal of the phase angle of the tunnel of Corti pressure that occurs about half-way down the cochlea found in the AZ/PZ model for low frequency probe tones has support from data from the auditory nerve. It leads one to speculate that the AZ pressure directly drives the inner hair cells at low frequency, a theory which we put forward in another article in this book. Acknowledgments We acknowledge the support of NIDCD.

1. de Boer, E., 1990. Wave-propagation modes and boundary conditions for the Ulfendahl-Flock-Khanna preparation. In: Mechanics and Biophysics of Hearing, ed. by P. Dallos, CD. Geisler, J.W. Matthews, M. Ruggero and C.R. Steele, Springer-Verlag, New York, 333-339. 2. de Boer, E., 1990. Can shape deformations of organ of Corti influence the traveling wave in the cochlea? Hear Res 44: 83-92. 3. de Boer, E., 1993. The sulcus connection. On a mode of participation of outer hair cells in cochlear mechanics. J. Acoust Soc Am 93:2845-2859. 4. Hubbard, A.E,. 1993. A traveling wave amplifier model of cochlear. Science, vol. 259, 68-71. 5. Chadwick, R.S., Dimitriadis, E.K. and Iwasa, K., 1996. Active control of waves in a cochlear model with subpartitions. PNAS 93(6): 2564-2569. 6. Hubbard, A.E., Yang, Z., Shatz, L., Mountain, D.C., 2000. Multi-mode cochlear models. In Recent developments in Auditory Mechanics, ed. by H. Wada, T. Takasaka, K. Ikeda, K. Ohyama and T.Koike, World Scientific, Singapore, 167-173. 7. Naidu, R.C., 2001. Mechanical properties of the organ of Corti and their significance in cochlear mechanics, PHD thesis of Boston University. 8. Muller, M., 1996. The cochlear place-frequency map of the adult and developing Mongolian gerbil. Hear Res. 94:148-56. 9. Ruggero, M. A., Rich, N.C., Robles, L., and Shivapuja, B.G., 1990. Middle ear response in the chinchilla and its relationship to mechanics at the base of the cochlea. J Acoust Soc Am 89: 1612-1629. 10. Ren, T. and Nuttall, A., 2001. Basilar membrane vibration in the basal turn of the sensitive gerbil cochlea. Hear Res 151:48-60. 11. Ruggero, M. and Rich, N., 1983. Chinchilla auditory-nerve response to lowfrequency tones. J Acoust Soc Am 73:2096-2108. 12. Peterson, B.P. and Bogert, L.C., 1950. A dynamic theory of cochlea. J Acoust Soc Am 22:369-381. 13. Zwislocki, J.J., 1950. Theory of the acoustical action of the cochlea. J Acoust Soc Am 22:778-784. 14. Cooper, N.P., 2000. Radial variation in the vibrations of the cochlear partition. In Recent developments in Auditory Mechanics, ed. by H. Wada, T. Takasaka, K. Ikeda, K. Ohyama and T.Koike, World Scientific, Singapore, 109-115.

465

Comments and Discussion Gummer: What are the dominant components of the impedances of the reticular lamina (RL) and organ of Corti (OC); for example, mainly viscoleastic for the RL, inertial for the OC? Olson: You show pressure predictions. How does your predicted ST pressure close to the BM compare with measurements of ST pressure close to the BM, e.g., Olson, Nature, 1999? Answer: The model we showed in the meeting was one-dimensional. Therefore, we cannot mimic Dr. Olsen's data as a function of distance from the basilar membrane. The model result, as viewed in the spatial domain and assuming frequency maps into distance along the basilar membrane, is similar to Dr. Olsen's result obtained farthest away from the basilar membrane in scala tympani. The pressure increases from near the oval window, peaks slightly around best place, drops a few dB andremains fixed to the end of the cochlea. There are some "wiggles" just apicalfrom the best place, which might correspond to dips in the actual pressure measurements, which were made at a fixed place, sweeping frequency.

W H A T STIMULATES THE INNER HAIR CELLS?

D. C. MOUNTAIN AND A. E. HUBBARD Boston University Hearing Research Center 44 Cummington St., Boston, MA, 02215, USA E-mail: [email protected], [email protected] We have recently proposed that the cochlear amplifier is a fluid pump driven by outer hair cell (OHC) somatic motility [1,2]. According to this hypothesis, the OHCs pump fluid into the tunnel of Corti (TOC) creating a second type of traveling wave that we call the organ of Corti (OC) wave. It is the OC-wave and not the classical traveling wave that is amplified by the OHCs according to the fluid-pump hypothesis. The question remains, however, how does the motion of the OC-wave get coupled to the inner hair cell (IHC) stereocilia? We hypothesize that the organ of Corti pressure distends the tissue in the IHC region leading to deflection of the IHC hair bundle. This hypothesis is supported by the observation that low-frequency IHC receptor potentials can be quite distorted and that the onset of distortion correlates with saturation of the OHC receptor current. We present a model based on the fluid pump hypothesis that replicates many features of the experimentally observed distortion in the IHC receptor potential.

1 Introduction Inner hair cell and auditory nerve responses to low-frequency tones can exhibit large phase shifts and complex response waveforms with increasing stimulus level [3-8]. These complex responses are also present in the IHC membrane conductance change, suggesting that they are also present in the mechanical stimulus to the IHCs, even when the stimulus frequency is well below the characteristic frequency of the measurement location. In contrast, the comparable basilar membrane (BM) responses are much less complex, exhibiting sinusoidal waveforms and only small phase shifts [9,10]. Figure 1 summarizes the low-frequency IHC transmembrane waveform measured by Cody and Mountain [8, 11] in the basal turn of the guinea pig cochlea. The positive peaks of the responses are much narrower and pointed than would be expected if the stimulus to the IHC was a sinusoid. To reconcile the discrepancy between the IHC and BM responses, Mountain and Cody [11] proposed that the OHCs stimulated the IHCs directly via somatic motility. This hypothesis was supported by the fact that the distortion in the IHC receptor potential correlated with saturation of the OHC receptor current as measured using the cochlear microphonic. Using this hypothesis, they developed a phenomenological model that could reproduce the IHC waveform distortion by assuming that the mechanical stimulus to the IHCs resembled a high-pass filtered version of the OHC receptor potential. The question remains, however, what is the mechanism by which OHC somatic motility could stimulate IHC mechano-transduction? To address this question, we

466

467 125 Hz

S28HZ

260 Hz

WAyVAWA'AW.'vVt¥,W "e

w

,'

.go

i

10

»

!

as

»

f

m

40

so

t* W

•

|

i

>

I

«

1

yvVVWsJ 0

to

20

30

0

10

20

39 " 40 "

60

0

10

20

»

40

SO

10

20

30

40

80

0

10

20

»

40

60

10

20

30

40

60


) is a complex coefficient with real part A' and imaginary part A". For a critical oscillator, it vanishes at the characteristic frequency, A(u>r) = 0. Thus, at this particular frequency, the response becomes essentially nonlinear for small amplitudes. The shape of the resonance, for nearby frequencies, is described by A(u) ~ a(u> — ur) close to the characteristic frequency tur, where a is a complex number. Furthermore, by its definition as a linear response function, A obeys A(u>) = A*(—u>). As a consequence, A'(0) = K is the passive stiffness of the system and A"(G) = 0. The real and imaginary parts of A(w) thus have the general form as displayed in Fig. 1.

Figure 1. Schematic representation of the real and imaginary parts of the linear response function A(co) = A' + iA" of a critical oscillator with frequency uir.

4

A c t i v e nonlinear traveling waves

We describe the basilar membrane by Eq. (1) using Eq. (2) for the local mechanical response properties. Motivated by the observed variation of the characteristic frequency along the BM, we assume t h a t the position dependence of characteristic frequencies is given by ujr(x) = u>oe~x^d.We thus obtain a nonlinear wave equation for the BM deformation. In frequency representation, it reads [19] -2pbuj2h

- iuT]h = dx \bldx (A{x,uj)h

+ B\h\2h\]

.

(3)

The complex solutions of this equation h{x) = H(x)et^x^ describe the amplitude H and the phase 0 of the BM displacement elicited by a periodic stimulus with incoming sound pressure p(x = 0,t) = p(0)e l w t . For simplicity, we take the coefficient B, describing the nonlinearity close to resonance, to be a purely

486

imaginary constant, B = i/3. This simple choice ensures that Eq. (2) has no spontaneously oscillating solution for p = 0. Examples for solutions to the wave equation are displayed in Fig. 2 The wave equation Eq. (3) describes traveling waves which are linear for small vibration amplitudes h at locations far from the resonance point xr where u> = ujr(xr). As the wave enters at x = 0, it encounters oscillators which locally have a high characteristic frequency as compared to the wave frequency to < u>r. Consequently, the imaginary part A"{LO) < 0 and energy is pumped into the wave by the active process (see Fig. 1). This pumping of the wave can cancel or even overcome the effects of viscous friction and thus enhance wave propagation and energy flow, but is not related to any unstable behavior of the wave.

Figure 2. Nonlinear active traveling waves for three different stimulus frequencies ( / = 370 Hz, 1.3 kHz and 4.6 kHz) and two different sound pressure levels (40 dB and 80 dB). Note that the waveform depends on stimulus intensity.

As the wave propagates towards the apex, its wavelength diminishes and its amplitude builds up, until it approaches the place of resonance. In the immediate vicinity of the characteristic place, \A\ becomes small while h increases. Thus the cubic term in Eq. (3) rapidly becomes more important than the linear term. This leads to a strongly nonlinear BM response. The wave peaks at x = xp < xr, where the response displays the characteristic nonlinearity of critical oscillators, h(xp) ~ p(xp) 1 / 3 . However, the vibration amplitude as a function of sound pressure level at a fixed position can exhibit responses which are not simple power laws. At positions beyond the characteristic place, x > xr, A' becomes negative and consequently the wave number q ~ uj/yA' becomes imaginary, indicating the breakdown of wave propagation. The wave is thus reflected from the characteristic place and the BM displacement decays very sharply for x > xr.

487 5

Discussion

Critical oscillators provide a general framework for the description of active amplification of sounds by cellular processes. While this description does not provide insights into the specific active processes which underly mechanical amplification on the cellular and molecular levels, it captures the general features in a simple and physically consistent way. The nonlinear wave equation which we present here provides a simple theoretical description of the nonlinear and active nature of the cochlear amplifier [19]. This framework can be extended to describe the BM motion elicited by stimuli containing multiple frequencies, by considering the generic nonlinear coupling of frequency components by critical oscillators [14]. The suppression of the response to one tone by the presence of a second tone, and the generation and wave-like propagation of distortion products, are natural consequences of this description. Furthermore, the flow of energy in the wave, as well as the pumping of the wave by active processes, can be clearly defined in this framework, taking into account nonlinear effects and energy supply by the active systems. The nonlinear wave described here has similarities to a laser cavity [23]; wave reflections along the basilar membrane and especially at the characteristic place lead to interesting and nonlinear reflection phenomena which will be discussed elsewhere. It has been suggested t h a t oto-acoustic emissions are related to modes in the cochlea which result from constructive interference of forward and backward traveling waves. Such modes also occur naturally in our nonlinear active wave description. Therefore, the framework of critical oscillators coupled hydrodynamically on the basilar membrane is consistent with the interpretation of oto-acoustic emissions as active wave resonances in the cochlea discussed in Ref. [23]. References 1. G. von Bekesy, Experiments in Hearing (McGraw Hill, New York 1960). 2. P. Dallos, A.N. Popper & R.R. Fay (Eds.), The Cochlea (Springer, New York 1996). 3. J. Zwislocki, Theorie der Schneckenmechanik: qualitative und quantitative Analyse, Acta Otolaryngol, suppl. 72 (1948). 4. G. Zweig, Basliar membrane motion, Cold Spring Harbor Symp. Quant. Biol. 40, 619-633 (1976). 5. E. de Boer, Auditory physics. Physical principles in hearing theory: I, Phys. Rep. 62, 87-174 (1980). 6. J. Lighthill, Energy flow in the cochlea, J. Fluid. Mech. 106, 149-213 (1981).

488 7. G. Zweig, Finding the impedance of the organ of Corti, J. Acoust. Soc. Am. 89, 1229-1254 (1991). 8. T. Gold, Hearing II. T h e physical basis of the action of the cochlea, Proc. Roy. Soc. B 135, 492-498 (1948). 9. D.T. Kemp, Evidence of mechanical nonlinearity and frequency selective wave amplification in the cochlea, J. Arch. Otorhinolaryngol. 224, 37-45 (1979). 10. W.S. Rhode, Observations of the vibration of the basliar membrane in squirrel monkeys using the Mossbauer technique. J. Acoust. Soc. Am. 4 9 , 1218+ (1971). 11. M.A. Ruggero et al, Basilar-membrane responses to tones at the base of the chinchilla cochlea, J. Acoust. Soc. Am. 101, 2151-2163 (1997). 12. I.J. Russel & K.E. Nilsen, The location of the cochlear amplifier: Spatial representation of a single tone on the guinea pig basilar membrane, Proc. Natl. Acad. Sci. USA 94, 2660-2664 (1997). 13. L. Robles & M.A. Ruggero, Mechanics of the mammalian cochlea, Physiol. Rev. 8 1 , 1305-1352 (2001). 14. Physical basis of two-tone interference in hearing, F. Julicher, D. Andor & T. Duke, Proc. Natl. Acad. Sci. USA 98, 9080-9085 (2001). 15. H. Duifuis et. al., in Peripheral Auditory Mechanisms, edited by J.B. Allen et. al. (Springer, Berlin 1985). 16. W h a t type of force does the cochlear amplifier produce? P.J. Kolston, E. de Boer, M.A. Viergever & G.F. Smoorenburg J. Acoust. Soc. Am. 88, 1794-1801 (1990). 17. E. de Boer, chap. 5 in Ref. 1 & references therein. 18. M.O. Magnasco, A wave traveling over a hopf Instability shapes the cochlear tuning curve, Phys. Rev. Lett. 90, 058101, (2003). 19. T. Duke and F. Julicher, Active traveling wave in the cochlea, Phys. Rev. Lett. 90, 158101 (2003). 20. S. Camalet, T. Duke, F. Julicher & J. Prost, Auditory sensitivity provided by self-tuned critical oscillations of hair cells, Proc. Natl. Acad. Sci. (USA) 97, 3183-3188 (2000). 21. V.M. Eguiluz et. al., Essential nonlinearities in hearing, Phys. Rev. Lett. 84, 5232-5235 (2000). 22. Y. Choe, M.O. Magnasco & A.J. Hudspeth, A model for amplification of hair-bundle motion by cyclical binding of C a 2 + to mechanoelectricaltransduction channels, Proc. Natl. Acad. Sci. USA 9 5 , 15321-15326 (1998). 23. C.A. Shera, Mammalian spontaneous otoacoustic emissions are amplitudestabilized cochlear standing waves, J. Acoust. Soc. Am. 114, 244-262 (2003).

M E C H A N I C A L E N E R G Y CONTRIBUTED BY MOTILE N E U R O N S IN T H E DROSOPHILA EAR

M. C. GOPFERT AND J. T. ALBERT Volkswagen-Foundation

Research Group, Institute of Zoology, University of Cologne, Weyertal 119, 50923 Cologne, Germany E-mail: [email protected], [email protected]

In the fruit fly Drosophila melanogaster, hearing is based on dedicated mechanosensory neurons transducing vibrations of the distal part of the antenna. Examination of this receiver's vibrations in wild-type flies and mechanosensory mutants had shown that the auditory mechanosensory neurons are motile and give rise to key characteristics that define the cochlear amplifier of vertebrates, including nonlinear compression and self-sustained oscillations, the mechanical equivalent of spontaneous otoacoustic emissions. Violations of the equipartition theorem now have confirmed that the neurons exhibit power gain, lifting the fluctuations of the receiver above thermal noise. By opposing damping, this neural energy contribution boosts the sensitivity and frequency-selectivity of the fly's antennal ear.

1 Introduction Spontaneous otoacoustic emissions, nonlinear compression, amplification, and frequency selectivity are the four essential characteristics that define the cochlear amplifier of vertebrates [1-4]. At least two of these criteria are met by the ear of the fly. In Drosophila, the distal part of the antenna serves as a sound receiver, vibrations of which are transduced by the chordotonal sensory neurons of Johnston's organ in the antenna's base (Fig. 1) [5,6]. As shown by laser Doppler vibrometric measurements, this antennal receiver nonlinearly alters its tuning with the intensity of sound, twitches spontaneously, and occasionally performs largeamplitude self-sustained oscillations [6-8]. These oscillations, which are the presumptive mechanical analogue of spontaneous otoacoustic emissions, reliably occur when the physiological condition of the animal deteriorates, e.g. after thoracic injection of dimethyl-sulphoxide (DMSO) [7,8]. Mutant analyses revealed that these oscillations as well as the receiver's twitches and nonlinearity are introduced by the sensory neurons of Johnston's organ: mechanosensory mutations such a tilB2, btv5PI, and nompA2, which specifically affect the mechanosensory neurons, linearize the receiver's response and abolish its twitches and oscillations [7,8]. Demonstrating the neurons' ability to mechanically drive the antennal receiver, these findings suggest that the fly's neurons -analogous to the motile hair cells of vertebratesprovide active mechanical amplification to boost the sensitivity of the ear. The benchmark of active amplification is power gain; more energy comes out of an amplifier than is initially fed in. Hence, establishing active amplification requires the demonstration of power gain, which, in strict terms, must be based on violations of fundamental principles of thermodynamics, the equipartition or the

489

490 fluctuation-dissipation theorem. Violations of the fluctuation-dissipation theorem have demonstrated power gain for isolated vertebrate hair cells [9]. Violations of the equipartition theorem, in turn, have documented the ability of the fly's auditory neurons to exhibit power gain inside the ear [10]. This latter work, the identification of neural energy contributions in the Drosophila auditory mechanics, is the topic of this chapter.

Figure 1. Confocal images of the fly's antennal ear. Pseudo-brighl-ficld image (left) dcpicling the three antcnnal segments (1-3) and the arista and corresponding confocal section (right) showing the mechanosensory and olfactory sensory neurons in the 2"'1 and 3"1 antennal segments, respectively. Neurons are labeled by the targeted expression of UAS-mCD8-GFP using the driver line Cha-GAL4. Arrows highlight the mechanosensory neurons of Johnston's organ, which mediate hearing.

2 Methods 2.1 Flies Oregon R was used as WT strain. The nompA2, btv5PI, and MB2 mechanosensory mutants were kindly provided by Maurice Kernan and Dan Eberl. The respective genetic backgrounds, en bw (for nompA2), w; FRT,0A FRf'3 (for btv5PI) and y w (for MB2) were used as controls. 2.2 Measurements and data analysis All mechanical measurements were performed in the absence of external stimulation. Using a Polytec PSV-400 scanning laser Doppler vibrometer, we measured the amplitude of the receiver's vibration velocity, XI, near the tip of the

491

arista (Fig. 1). After Fourier transformation, the spectral velocities, X(&>) , were converted into spectral displacements, \X(a>)\ with X(&>) = X(ft/)/#>, and subsequently squared, yielding the power spectral density, X (cd)\, of the receiver's displacement (Fig.2). Power spectra were fitted with the function of a forceddamped harmonic oscillator (Fig. 2), 2

/I m 2

2

2

FQ

2

X (co) 2

(«0 -« )

+

(-^)

(1) 2

where F 0 is the force acting on the oscillator, m the oscillator's apparent mass, (OQ the natural angular frequency, and Q the quality factor, with Q = ma>01 y and / denoting the damping constant. By integrating the fit function between zero and infinity, we obtained the fluctuation power, i.e. the mean square amplitude, X2 )of the receiver's displacement. The analysis presented is based on the receiver fluctuations in 20 animals per strain. 3 Results At thermal equilibrium, the fluctuations of a passive oscillator will obey the equipartition theorem, 1/2K( X2 \ = \l2kBT

with K = KS, where K is the

effective stiffness, K$ is the spring constant, kB is the Boltzmann constant, and T the absolute temperature. We used the equipartion theorem to deduce K from the receiver's fluctuation power, K = kBT I X2

Notably, the effective stiffness

obtained by this calibration equals the spring constant provided the system is passive. I the system is active, however, the effective stiffness will be smaller than the spring constant, reflecting the increase in fluctuation power (and energy) caused by the action of the additional force. In either case, the mean total energy of the system, E, can be written as E = (KS/K)-kBT, yielding an energy gain, AE, of AE = ((KS IK) — X) • kBT. Hence, provided that both K and Kg are known, active energy contributions can be separated from thermal fluctuations. For a simple harmonic oscillator, Ks can be deduced from the natural frequency, Ks = mco . We calibrated this relation using dead WT flies, the receivers of which can be expected to solely display thermal noise. Given a natural

492

frequency of 798 Hz, a fluctuation power of 0.3x10"16 m2, and Ks = K = 132 uN/m, we obtain a mass of 5.2 ng. Hence, provided the mass is constant, the receiver's spring constant is given as Ks = 5.2 • 10" a>0 . We used this relation to derive Ks from the natural frequency.

100

300 /(Hz)

100

1000

300 /(Hz)

1000

10-14-

I

u 10-ieJ X -% 10-18 10-22 100 C

1000

10-16

^\ll

WT SO NWI

>< 300 /(Hz)

JVI

10-20-

m-22100

\

N

300

1000

/(Hz)

100

300

1000

/(Hz)

Figure 2. Power spectra of the receiver's fluctuations. Example data showing the measured spectrum (thin trace) and the fitted harmonic oscillator model (thick trance) for one animal per strain.

To test the impact of non-neural energy contributions such as the activity of muscles, we examined the receiver's fluctuations in live mutants with defective mechanosensory neurons. Three different mutants with distinct natural frequencies of the receiver were examined (tilB2, btv5P1, nompA2, Fig. 2, 3). For all three mutants, we found K = KS, E = \kBT, and A £ = 0 . These results confirm that (i) the relation is valid, that (ii) the receivers of live flies with defective neurons are passive, that (iii) non-neural energy sources do not contribute to the receiver's

493

fluctuations and (iv) that the mass is constant; even the disconnection of the neurons from the receiver, as found in nompA2 mutants [12], does not affect the receiver's apparent mass. dead WT

100

live mutants

300

f„< Hz )

live WT & controls

1000

100

300

1000

f„(Hz) . WT SO

300 /"(Hz)

1000

Figure 3. Effective stiffness of the receiver as a function of the natural frequency. The straight line depicts the spring constant as deduced from the data of dead WT flies (Ks= 5.2- l(T9
UilJ7~T" . • • • / .

&mp R s a t t i v * tm SfeSs * 2

j88dk^d«o«i*»bite»ttj

t

1a

'• '

t

•t

MS n

ww(Mt l©r*»KweSK>2 «*«w> *^ftfiodfe

* / '

• ^.

tat

. •

i *WK'"."Wff"!'™ff^

•

™«wnrtrowWw».