Biophysics Of The Cochlea: From Molecules To Models - Proceedings Of The International Symposium: From Molecules to Models 9789812704931, 9789812383044

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BIOPHYSICS BIOPHYSICS BIOPHYSICS BIOPHYSICS BIOPHYSICS

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BIOPHYSICS BIOPHYSICS BIOPHYSICS BIOPHYSICS BIOPHYSICS BIOPHYSICS Proceedings of the International Symposium held a t Titisee, Germany, 27 July - 1 August 2002

Editor

A.W. Gummer Assistant Editors

E. Dalhoff, M. Nowotny & M. F? Scherer Eberhard Karls University Tubingen Tubingen Hearing Research Centre Tubingen, Germany

yp y r l d Scientific .

ew Jersey London Singapore Hong Kong

Published by

World Scientific Publishing Co. Re. Ltd. 5 Toh Tuck Link, Singapore 596224

USA ofice: Suite 202,1060 Main Street, River Edge, NJ 07661

UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

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

BIOPHYSICS OF THE COCHLEA Copyright 0 2003 by World Scientific Publishing Co. Re. 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 981-238-304-2

Printed by FuIsland Offset Printing (S) Pte Ltd, Singapore

Preface At least 85% of hearing-impaired people - 160 million in Europe alone - suffer hearing problems attributable to their cochlea, for the most of whom a causal therapy is either not available or economically impossible. The cochlea transforms sound-induced vibrations of the middle ear into electrical signals in the auditory nerve. But to do this, the cochlea must meet specifications not yet achieved by any human-engineered system: i) sensitivity to hgstrom displacements, ii) response time in microseconds, iii) operation over an intensity range of 120 dB SPL (a million-fold), iv) frequency range of 100 Hz to 20 kHz, v) detection of intensity changes of 1 dB and frequency changes of 0.1%, and vi) extraction of signals in noisy environments (signal-to-noise ratios of -20 dB). This performance must be achieved by living, self-maintaining structures that are resistant to excessive displacements, are viscous and are inherently slow. The formidable technical specifications of the cochlea are realized by a so-called “cochlear amplifier”, an entity whose mode of operation somehow depends on the sound-induced motile response of specialized cells called “outer hair cells”. The cochlear amplifier must involve a complex biophysical interplay between molecular, cellular and hydrodynamic processes that, in spite of remarkably rapid progress in hearing research, is still not understood. This book represents the proceedings of a conference designed to advance our understanding of the biophysical basis of the cochlea. The conference brought together a multidisciplinary group of leading researchers working at the molecular, cellular and cochlear levels and using biological, theoretical and clinical techniques. The form of the conference was based on a series of seven held at intervals of about three years. They are commonly known as the “Mechanics of Hearing” conferences, after the name of the inaugural and exceedingly successful conference organized by E. de Boer in 1983. The conferences are designed to promote the integration of innovative theoretical and experimental aspects of basic and applied auditory research. There is no learned society, no international scientific committee, no institute or funding body that continuously supports or sponsors these conferences. Their success is driven by participants’ wish to meet regularly to: i) synthesize results from this rapidly progressing, multidisciplinary research area, ii) target new research goals and generate cutting-edge collaborative projects, and iii) disseminate the information to other researchers. Where previous conferences in this series included contributions dealing with the mechanics of the input to the cochlea - the middle ear - and with neural encoding at the output of the cochlea - in the auditory nerve -, this conference focused on cochlear processes only. This was necessitated by the recent,

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remarkably rapid experimental progress at the genetic, molecular, cellular and whole-organ levels of cochlear processing. The conference explored mechanisms associated with the non-linear, frequency selectivity of the cochlea produced by electromechanical forces from the outer hair cells. Since the motor molecule responsible for creating electromechanical force in the cell wall has been recently cloned, experiments are now being conducted to understand how these forces arise: how are changes in membrane potential sensed by the motor-complex, and how is the action of this complex harnessed to generate mechanical force by the whole cell. Entwined with these questions is the so-called “time-constant” problem: the time constant of the basolateral cell membrane is so large that, at high frequencies, the membrane potential - the drive for somatic electromechanics - could be attenuated by as much as two orders of magnitude and its phase delayed by 90”. Consequently, an alternate hypothesis - electromechanical action by the stereocilia themselves - has been postulated as the relevant “amplifying” mechanism at high frequencies. Accordingly, the first set of chapters deals with transduction mechanisms in stereocilia (Z. Stereocilia) and a second set with transduction mechanisms in the soma of outer hair cells (11.Hair cells). Experimental and theoretical aspects of the stereociliary and somatic hypotheses of electromechanics formed the basis of three of the plenary lectures (P. Dallos, P. Martin and G. Zweig). How electromechanical forces produced by the outer hair cells are coupled into the cochlear partition formed the basis of the thud set of chapters (ZZZ. Whole-organ mechanics), where a central aspect was measurement of the three-dimensional mechanics of the organ of Corti. The bridge between experiment and theory is the model. Therefore, models form an essential component of each set of chapters; there is also a set of chapters devoted to models of cochlear mechanics (ZK Cochlear models). A by-product of electromechanical transduction is otoacoustic emissions - a pressure change measured in the outer-ear canal which originates from the cochlea. Clinically, the emissions are of paramount importance because they give an objective diagnosis of the condition of the “cochlear amplifier”. Such a diagnosis is particularly important for pre-lingual children. Although otoacoustic emissions have become a routine diagnostic tool, poor understanding of the link between emissions and mechanical events in the cochlea has meant that the information gleaned from the emission data remains rudimentary, limiting their full clinical potential. The fifth set of chapters elucidates theoretical and clinical aspects of emissions (V. Emissions);the topic is introduced by a plenary lecture (C.A. Shera) that reviews this extensive field. The final set of chapters is an edited transcript of a recording of the discussion session held on the last evening of the conference (VZ. Discussion session). Arguably, the most valuable aspect of the book, this section documents current

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opinions on outstanding topics of cochlear biophysics and provides directions for future research. At the end of each manuscript, under “Comments and Discussion”, is given (where desired by the participants) a record of the questions that were asked and the answers given after each oral presentation. Since hearing-impairment can mean severe impairment of the quality of life, it was most appropriate that this conference was made possible by a substantial grant from the European Commission under their programme “Quality of Life and Management of Living Resources” (Proposal No. QLAM-2001-00159; Acronym: BIOCOCHLEA). The international community of hearing scientists is extremely grateful for this far-sighted support. We are also indebted to the financial assistance of the following companies: Adler Werbegeschenke GmbH & Co. KG, Saarbriicken; Attempto Service GmbH, Tubingen; Carl Zeiss, Jena and Oberkochen; Industrial Acoustics Company GmbH, Niederkriichten; Dr. Koch Computertechnik AG, Tubingen; Polytec GmbH, Waldbronn. The editors would like to thank members of the International Organizing Committee for their useful suggestions, particularly in the planning phases, and Chairpersons of Sessions for ensuring constructive and stimulating discussion. We have been enriched by the insightful reviews of the Plenary Lecturers, and we record our gratitude to them here. We are indebted to all participants for making the conference “work”. Finally, we are grateful to H.-P. Zenner, Director of the Department of Otorhinolaryngology, and to the Faculty of Medicine of the Eberhard-KarlsUniversity Tubingen in general, for creating and allowing a fruitfhl environment for hearing research in Tubingen to florish. We greatly appreciate the dedicated assistance of our research group: N. Bayer, T. Kaneko, D. Klassen, R. Lauf, S. Preyer, B. Pritschow, L. Schubert and C. Zinn, who contributed so much to the smooth running of the conference. Special thanks are extended to A. Seeger for her untiring administrative and secretarial assistance, without whom the conference would have been far less successful. We dedicate this book to the memories of our recently deceased colleagues and friends: Desmond L. Kirk, Alfons Rusch, Norma B. Slepecky and Graeme K. Yates, who contributed in different ways to our understanding of the biophysics of the cochlea.

A.W. Gummer Eberhard-Karls-University Tubingen September, 2002

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International Organizing Committee J.B. Allen, New Jersey, USA J.F. Ashmore, London, United Kingdom W.E. Brownell, Houston, USA P. Dallos, Evanston, USA A.W. Gummer, Tubingen, Germany I.J. Russell, Sussex, United Kingdom C.R. Steele, Stanford,USA Local Organizing Committee E. Dalhoff A.W. Gummer M. Nowotny M.P. Scherer A. Seeger Session Chairpersons J.B. Allen, New Jersey, USA E. de Boer, Amsterdam, The Netherlands W.E. Brownell, Houston, USA R. Fettiplace, Wisconsin, USA D.M. Freeman, Boston, USA J.J. Guinan Jr., Boston, USA R. Hallworth, Omaha, USA J. Howard, Dresden, Germany A.E. Hubbard, Boston, USA C. Kros, Sussex, United Kingdom D.C. Mountain, Boston, USA S.T. Neely, Omaha, USA R. Nobili, Padua, Italy E.S. Olson, New York, USA R.B. Patuzzi, Nedlands, Australia W.S. Rhode, Wisconsin, USA M.A. Ruggero, Evanston, USA J. Santos-Sacchi, New Haven, USA C.R. Steele, Stanford, USA Plenary Lecturers P. Dallos, Evanston, USA P. Martin, Paris, France M.A. Ruggero, Evanston, USA C.A. Shera, Boston, USA G. Zweig, Cambridge, USA

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Previous publications from this series of conferences Mechanics of Hearing. Edited by E. de Boer and M.A. Viergever. Nijhoff, The Hague/Delfi University Press, 1983. Peripheral Auditory Mechanisms. Edited by J.B. 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, C.D. Geisler, J.W. Matthews, M.A. Ruggero and C.R. Steele. Springer, Berlin, 1990. Biophysics of Hair Cell Sensory Systems. Edited by H. Duiluis, J.W. Horst, 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. Ikeda, K. Ohyama and T. Koike. World Scientific, Singapore, 2000.

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Photolegend 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.

Zinn, C. Kalluri, R. Patuzzi, R.B. van Netten, S.M. Tinevez, J.-Y. Martin, P. Kalinec, F. Santos-Sacchi, J. Gummer, A.W. Shera, C.A. h i a , S. Grosh, K. Hemmert, W. Aranyosi, A.J. Nuttall, A.L. Masaki, K. Karavitaki, K.D. Freeman, D.M. Anvari, B. Kaneko, T. Deo, N. Gildemeister, 0. Vilfan, A. Duke, T.A.J. Gopfert, M.C. Robert, D. Nobili, R. VeteSnik, A. Kros, C.J. Neely, S.T. Guinan, J.J. Jr. Steele, C.R. Hubbard, A.E. Sarpeshkar, R. Iwasa, K.H. Brownell, W.E. Dallos, P. Ruggero, M.A. Hackney, C.M. Fettiplace, R.

41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80.

Lukashkin, A.N. Klassen, D. Pritschow, B. Ren, T.Y. Khanna, S.M. de Boer, E. Zweig, G. Oswald, J. Nowotny, M. Smurzynski, J. Novoselova, S.M. Koch, D.B. Chadwick, R.S. Ulfendahl, M. Beisel, K.W. Wada, H. He, D.Z.-Z. Sen, D. Bell, A. Dimitriadis, E.K. Huber, A. Mountain, D.C. Howard, M. Stenfelt, S. Shaffer, L.A. Cheatham, M.A. Sugawara, M. Andoh, M. Schubert, L. Cooper, N.P. Janssen, T. Olson, E.S. Kim, D.O. Oliver, D. Hallworth, R. Duifhuis, H. Long, G.R. Miiller, R. Lonsbury-Martin, B.L. Martin, G.K.

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8 1 . Richter, C.-P. 82. Harasztosi, C. 83. Gacsi, E. 84. Tubis, A. 85. Popel, A.S. 86. Allen, J.B. 87. Spector, A.A. 88. Morioka, I. 89. Lukashkina, V. 90. Raphael, R.M. 91. Kachar, B. 92. Dalhoff, E. 93. McMahon, C. 94. Dinklo, T. 95. Rhode, W.S. 96. LeGoff, L. 97. OBeirne, G.A. 98. Howard, J. 99. Landolfa, M.A. 100. Butsch, K.-D. 101. Langer, M.G. 102. Koitschev, A. 103. Fink, S. 104. Withnell, R.H. 105. Dhar,S. 106. Lim, K.M. 107. Koppl, C. 108. Manley, G.A. 109. LePage, E.L. 1 10. Miller, A.J. 1 11. Taiji, H.

absent: Julicher, F. Preyer, S. Probst, R. Talmadge, C.L. Winn, D. Wolfe, F.

Conference Participants (numbers after surnames identi@persons on the photo) Allen, J.B. (86) 386 Forest Hill Way, Mountainside, NJ 07092, USA. [email protected] Andoh, M. (68) Tohoku University, Faculty of Engineering, Department of Mechanical Engineering, Wada Labolatory, Aoba-yama 0 1, Sendai, 980-8579, JAPAN. [email protected] Anvari, B. (19) Rice University, Bioengineering, MS 152, P.O. Box 1892, Houston, TX 77251 1892, USA. [email protected] Aranyosi, A.J. (14) Massachusetts Institute of Technology, 77 MassachusettsAve., Room 36-873, Cambridge, MA 02139, USA. [email protected] Beisel, K.W. (55) Boys Town National Research Hospital, Department of Genetics, 555 North 30th Street, Omaha, NE 68 131, USA. [email protected] Bell, A. (59) Research School of Biological Sciences, Australian National University, P.O. Box 475, Canberra, ACT 2601, AUSTRALIA. [email protected] Brownell, W.E. (36) Baylor College of Medicine, Department of Otorhinolaryngologyand Communicative Sciences, Houston, TX 77030, USA. [email protected] Butsch, K.-D. (100) Bernafon AG, Morgenstrde 131,30 18 Bern, SWITZERLAND. kdbobernafon.ch Chadwick, RS. (53) 5420 Alta Vista Rd., Bethesda, MD 208 14, USA. cha&ick@helix. nih.gov Cheatham, M.A. (66) Northwestern University, 2-240 Frances Searle Building, 2299 North Campus Drive, Evanston, IL 60208-3550, USA. [email protected]

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Cooper, N.P. (70) Bristol University, Physiology Dept., Bristol BS8 ITD, UK. [email protected] Dalhoff, E. (92) Universitiits-Hals-Nasen-Ohrenklinik,Sektion Physiologische Akustik und Kommunikation, Elfi-iede-Aulhorn-Str. 5,72076 Tubingen, GERMANY. ernst.dalhomuni-tuebingen.de Dallos, P. (37) Northwestern University, Neuroscience, Auditory Research Laboratory, 2299 North Campus Drive, Evanston, IL 60208-3550, USA. p-dallos@northestern. edu de Boer, E. (46) Academic Medical Centre, KNO Room D2-226, Meibergdreef 9, 1105 AZ Amsterdam, THE NETHERLANDS. [email protected] Deo,N. (21) 1863 Lake Lila Dr. #6C, Ann Arbor, MI 48 105, USA. [email protected] Dhar, S. (105) Indiana University, Department of Speech & Hearing Sciences, 200 South Jordan Avenue, Bloomington, IN 47405-7002, USA. sumitoindiana.edu Dimitriadis, E.K. (60) DBEPS/NIH, Bldg. 13/3N17, Bethesda, MD 20892, USA. [email protected] Dinklo, T. (94) Nijenborgh 4,9747 AG Groningen, THE NETHERLANDS. [email protected] Duifiuis, H. (76) University of Groningen, Fac. Math. & Natural Sciences, Dept. Biomedical Engineering, 9747 AG, Groningen, THE NETHERLANDS. [email protected] Duke, T.A.J. (24) Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, UK. [email protected],uk Fettiplace, R. (40) Department of Physiology, 185 Medical Sciences Building, 1300 University Avenue, Madison, WI 53706, USA. [email protected]. edu

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Fink, S. (103)

Universitatts-Hals-Nasen-Ohren-Klinik, Sektion Sensorische Biophysik, Elffiede-Aulhorn-Str. 5,72076 Tubingen, GERMANY. [email protected] Freeman, D.M. (18) MIT, 77 Massachusets Ave., Room 36-889, Cambridge, MA 02 139, USA. [email protected] Gildemeister, 0. (22) Chemin des Merles, CH-1213 Onex, SWITZERLAND. ogildemeister@eesur$ch Gbpfert, M.C. (25) University of Bristol, School of Biological Sciences, Woodland Road, Bristol BS8 IUG, UK. [email protected] Grosh, K. (12) Dept. of Mechanical Eng., University of Michigan, 3 124 GG Brown Bldg., 2350 Hayward Ave, Ann Arbor, MI 48109-2125, USA. [email protected] Guinan, J.J., Jr. (31) Eaton Peabody Lab, 243 Charles St., Boston, MA 021 14-3002, USA. jjg@epl. meei.haward.edu Gummer, A.W. (9) Universit&-Hals-Nasen-OhrenkIinik, Sektion Physiologische Akustik und Kommunikation, Elfi-iede-Aulhorn-Str. 5,72076 Tubingen, GERMANY. [email protected] Hackney, C.M. (39) Keele University, MacKay Institute of Communication and Neuroscience, School of Life Sciences, Staffordshire ST5 5BG, UK. [email protected] Hallworth, R. (75) Creighton University, Department of Biomedical Sciences, 2500 California Plaza, Omaha, NE 68178, USA. [email protected] Harasztosi, C. (82) University of Debrecen, Department of Physiology, Nagyerdei Krt.98, Pf. 22, 40 12 Debrecen, HUNGARY. [email protected],hu He, D.Z.-Z. (57) Boys Town National Research Hospital, Hair Cell Biophysics Laboratory, 555 North 30th Street, Omaha, N E 68131, USA. [email protected]

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Hemmert, W. (13) Poppelstr. 10,81541 Miinchen, GERMANY. Werner.hemmert@inJneon. com Howard, J. (98) Max-Planck-Institute of Molecular Cell Biology and Genetics, Pfotenhauerstralje 108,O1309 Dresden, GERMANY. howard@mpi-cbg. de Howard, M. (63) Dept. OTO (B205), University of Colorado, Health Sciences Center, Denver, CO 80262, USA. MacKenzie.Howard@UCHSC. edu Hubbard, A.E. (33) Boston University, Electrical and Computer Systems Engineering and Biomedical Engineering, 8 St. Mary's Street, Boston, MA 022 15, USA. aeh@bu. edu Huber, A. (61) Klinik fiir Ohren-, Nasen-, Hals- und Gesichtschirurgie,Frauenklinikstrde 24, CH-8091 Ziirich, SWITZERLAND. [email protected] Iwasa, K.H. (35) Biophysics Section, NIDCD, NIH, 9 Center Dr MSC 0922 (9A E 120), Bethesda, MD 20892-0922, USA. [email protected] Janssen, T. (71) Technical University of Munich, ENT-Department, Ismaninger Stralje 22, 8 1675 Miinchen, GERMANY. T.Janssen@lrz. tu-muenchen.de Jiilicher, F. Max-Planck-Institut fiir Physik komplexer Systeme, Nothnitzer Str. 38 0 1187 Dresden, GERMANY. julicher@mpipks-dresden. mpg.de Kachar, B. (91) National Institutes of Health, Section on Structural Cell Biology, NIDCD, Bldg. 50, Rm. 4249, Bethesda, MD 20892-8027, USA. kacharb@nidcd. nih.gov Kalinec, F. (7) House Ear Institute, Department of Cell and Molecular Biology, 2 100 West Third Street, Los Angeles, CA 90057, USA. [email protected]

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Kalluri, R. (2) Eaton Peabody Laboratory, Massachusetts Eye and Ear Infirmary, 243 Charles St., Boston, MA 021 14, USA. [email protected]; [email protected] Kaneko, T. (20) Universitats-Hals-Nasen-Ohren-Klinik, Sektion Physiologische Akustik und Kommunikation, Elfiiede-Aulhorn-Str. 5,72076 Tubingen, GERMANY. [email protected] Karavitaki, K.D. (17) Massachusetts Institute of Technology, Boston University Hearing Research Center, 44 Cummington Street, Room 420, Boston, MA 022 15, USA. [email protected] Khanna, S.M. (45) College of Physicians and Surgeons of Columbia University, Department of Otolaryngology / Head and Neck Surgery, 630 West 168th Street, New York, NY 10032, USA. [email protected] Kim, D.O. (73) University of Connecticut Health Center, Dept. Neuroscience, Farmington, CT 06030-3401, USA. [email protected] Koch, D.B. (52) Northwestern University, Auditory Physiology Laboratory, 2299 N. Campus Dr., Evanston, IL 6020 1, USA. [email protected] Koitschev, A. (102) Universiats-Hals-Nasen-Ohren-Klinik, Elfi-iede-Aulhorn-Str.5, 72076 Tubingen, GERMANY. [email protected] Kiippl, C. (107) Technische Universitat Miinchen, Zoologie, Lichtenbergstr.4, 85747 Garching, GERMANY. [email protected] Kros, C.J. (29) University of Sussex, School of Biological Sciences, Falmer, Brighton BN 1 9QG, UK. [email protected] Landolfa, M.A. (99) Max-Planck-Institute of Molecular Cell Biology and Genetics, PfotenhauerstraBe 108,01309 Dresden, GERMANY. landolfa@mpi-cbg. de

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Langer, M.G. (101)

Universittits-Hals-Nasen-Ohren-Klinik, Sektion Sensorische Biophysik, EIfiiedeAulhorn-Str. 5,72076 Tubingen, GERMANY. [email protected] Le Goff, L. (96) Section de Recherche, Institut Curie, UMR 168 CNRS "Physico-chimie Curie" 11 rue P. et M. Curie, 7523 1 Paris Cedex 05, FRANCE. Loic.Legomcurie.$ LePage, E.L. (109) Australian Hearing / NAL, 126 Greville Street, Chatswood, NSW 2067, AUSTRALIA. [email protected]. au Lim, K.M. (106) National University of Singapore, Mechanical Engineering Department, 9 Engineering Drive 1,117576 Singapore, SINGAPORE. [email protected] Long, G.R. (77) Speech and Hearing Sciences, CUNY Graduate Center, 365 Fifth Avenue, New York, NY 10016-4309,USA. glon@gc. cuny.edu Lonsbury-Martin, B.L. (79) Department of Otolaryngology (B205), University of Colorado, Health Sciences Center, 4200 E Ninth Ave., Denver, CO 80262-0001, USA. [email protected] Lukashkin, A.N. (41) University of Sussex, School of Biological Sciences, Falmer, Brighton BN1 9QG, UK. [email protected] Manley, G.A. (108) Lehrstuhl fiir Zoologie, Technische Universittit Miinchen, Lichtenbergstr. 4, 85747 Garching, GERMANY. [email protected] Martin, G.K. (80) Department of Otolaryngology (B205), University of Colorado Health Sciences Center, 4200 E Ninth Ave., Denver, CO 80262-0001, USA. [email protected] Martin,P. (6) Institut Curie, Section de Recherche, Laboratoire P.C.C. (UMR 168), 26, rue d'Ulm, 75005 Paris cedex 05, FRANCE. [email protected]

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Masaki,K. (16) Massachusetts Institute of Technology, 77 Massachusets Ave., Room 36-8 13, Cambridge, MA 02139, USA [email protected] McMahon, C. (93) University of Western Australia, Physiology Department, 35 Stirling Highway, Nedlands 6009, AUSTRALIA. [email protected] Miller, A.J. (110) 1039 Massachusetts Avenue, #202, Cambridge, MA 02138, USA. [email protected] Morioka, I. (88) Nursing College of Wakayama Medical University, Mikazura 580, Wakayama 64 1-001 1, JAPAN. moriokaiawakayama-nc.ac.jp Mountain, D.C. (62) Boston University, Biomedical Engineering, 44 Cummington St., Boston, MA 02215, USA. dcmabu. edu Miiller, R (78) BundeswehrkrankenhausUlm, Dept. of Otorhinolaryngology, Head and Neck Surgery, Oberer Eselsberg 40, 89081 Ulm, GERMANY. prmueller@altavista. de Neely, S.T. (30) Boys Town National Research Hospital, 555 North 30th Street, Omaha, NE 68 131, USA. [email protected] Nobili, R. (27) via Brigata Padova 17, Padova 35 100, ITALY. [email protected]@ it Novoselova, S.M. (51) V.A. Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191011, RUSSIA. [email protected] Nowotny, M. (49) Universiats-Hals-Nasen-Ohrenklinik, Sektion Physiologische Akustik und Kommunikation, Elfiiede-Aulhorn-Str. 5,72076 Tubingen, GERMANY. [email protected] Nuttall, A.L. (15) Oregon Health & Science University, Oregon Hearing Research Centre, 3 181 S.W. Sam Jackson Park Road, NRC04, Portland, OR 97201-3098, USA. [email protected]

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O’Beirne, G.A. (97) University of Western Australia, Physiology Department, 35 Stirling Highway, Nedlands 6009, AUSTRALIA. gobeirne@cyllene. m a .edu.au Oliver, D. (74) Universitiit Freiburg, Physiologisches Institut 11, Hermann-Herder-Str. 7, 79104 Freiburg, GERMANY. dominik.oliver@physiologie. uni-fieiburg.de Olson, E.S. (72) College of Physicians and Surgeons of Columbia University, Department of Otolaryngology / Head and Neck Surgery, 630 West 168th Street, New York, NY 10032, USA. eao2004@columbia,edu Oswald, J. (48) HNO-Klinik, Klhikum Rechts der Isar, Experimentelle Audiologie, TU Miinchen, Trogerstr. 32,81675 Miinchen, GERMANY. ham. [email protected] Patuzzi, R.B. (3) University of Western Australia, Physiology Department, 35 Stirling Highway, Nedlands 6009, AUSTRALIA. [email protected] Popel, A.S. (85) Johns Hopkins University, School of Medicine, Department of Biomedical Engineering, 720 Rutland Avenue, Baltimore, MD 21205, USA. apopelahu. edu Preyer, S. Universitats-Hals-Nasen-Ohrenklinik, Sektion Physiologische Akustik und Kommunikation, Elfiede-Aulhorn-Str. 5,72076 Tubingen, GERMANY. [email protected] Pritschow, B. (43) Universit2ts-Hals-Nasen-Ohrenklinik, Sektion Physiologische Akustik und Kommunikation, Elfkiede-Aulhorn-Str.5,72076 Tubingen, GERMANY. [email protected] Probst, R. University of Basel, HNO-Klinik, Kantonsspital, CH-403 1 Basel, SWITZERLAND. [email protected] Puria, S. (1 1) Stanford University, Mechanics and Computation Division and California Ear Institute at Stanford, Durand Bld., Room 262, Stanford, CA 94305, USA. puria@stanford. edu

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Raphael, R.M. (90) Department of Bioengineering, MS 142, Rice University, PO Box 1892, Houston, TX 7725 1-1892, USA. rraphael@rice. edu Ren, T.Y. (44) Oregon Hearing Research Center, 3 181 SW Sam Jackson Park Road (NRC 04), Portland, OR 9720 1-3098, USA. [email protected] Rhode, W.S. (95) University of Wisconsin, Dept. of Physiology, 1300 University Avenue, Madison, WI 53706, USA. [email protected] Richter, C.-P. (81) Northwestern University, 2299 North Campus Drive, Evanston, IL 60208, USA. [email protected] Robert, D. (26) University of Bristol, School of Biological Sciences, Woodland Road, Bristol BS8 lUG, UK. [email protected] Ruggero, M.A. (38) Northwestern University, Department of Communication, Sciences and Disorders, 2299 North Campus Drive, Evanston, IL 60208 3550, USA. [email protected] Santos-Sacchi, J. (8) Yale University, Dept. of Surgery (Otolaryngology) and Neurobiology, School of Medicine, BML 244,333 Cedar St., New Haven, CT 06510, USA. joseph.santos-sacehi@yale. edu Sarpeshkar, R. (34) Massachusetts Institute of Technology, Room 38-294,50 Vassar St., Cambridge, MA 02139, USA. [email protected] Schubert, L. (69) Mittlere Str. 5,70597 Stuttgart, GERMANY. lutz.schubert@stu&ew. uni-stuttgart.de Sen, D. (58) 20 Independence Blvd., Warren, NJ 07059, USA. dsen@ieee. org Shaffer, L.A. (65) Indiana University, Department of Speech & Hearing Sciences, 200 South Jordan Avenue, Bloomington, IN 47405-7002, USA. [email protected]

XXlV

Shera, C.A. (10) Eaton-Peabody Laboratory, Massachusetts Eye and Ear Infmary, 243 Charles St., Boston, MA 021 14, USA. [email protected] edu Smurzynski, J. (50) University Hospital, Department of Otorhinolaryngology (HNO), CH-403 1 Basel, SWITZERLAND. [email protected] Spector, A.A. (87) Johns Hopkins University, Department of Biomedical Engineering, 720 Rutland Avenue, Baltimore, MD 21205-2109, USA. [email protected] Steele, C.R. (32) Stanford University, Medical Engineering Department, Mechanics & Computation Division, Durand Building, Room 262, Palo Alto, CA 94305, USA. chasst@lelandStanford. EDU Stenfelt, S. (64) Chalmers University of Technology, Department of Signals and System, Gbteborg 41296, SWEDEN. [email protected] Sugawara, M. (67) Tokyo Institute of Technology, Department of Mechanical and Environmental Informatics, 2-12-1 0-okayama, Meguro-ku, Tokyo 152-8552, JAPAN. [email protected] Taiji, H. (111) National Tokyo Medical Center, Dept. of Otolaryngology, 2-5-1 Higashigaoka, Meguro-ku, Tokyo 152-8902, JAPAN. [email protected] Talmadge, C.L. University of Mississippi, National Center for Physical Acoustics, Oxford, MS 38677, USA. clt@gold ncpa,olemiss.edu Tinevez, J.-Y. (5) Institut Curie, Section de Recherche, Laboratoire P.C.C. (UMR 168), 26, rue dWlm, 75005 Paris, FRANCE. [email protected] Tubis, A. (84) Purdue University, Department of Physics, 1396 Physics Building, West Lafayette, IN 47907-1396, USA. [email protected]

xxv

Ulfendahl, M. (54) Karolinska Institutet, Dept. of Clinical Neuroscience, Building M 1-Karolinska Hospital, SE- 171 76 Stockholm, SWEDEN. [email protected] van Netten, S.M. (4) University of Groningen, Department of Neurobiophysics, Nijenborgh 4, 9747 AG Groningen, THE NETHERLANDS. s.van,[email protected] VeteSnik, A. (28) U Klavirky 4, 150000 Prag, CZECH REPUBLIK. [email protected] Vilfan, A (23) Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, UK. [email protected] Wada,H. (56) Tohoku University, Department of Mechanical Engineering, Aoba-yama 0 1, Sendai 980-8579, JAPAN. [email protected] Winn, D. 1034 Keowee Avenue, Knoxville, TN 37919-7754, USA. [email protected] Withnell, R.H. (104) Indiana University, Department of Speech & Hearing Sciences, 200 South Jordan Avenue, Bloomington, IN 47405-7002, USA. [email protected] Wolfe, F. 1034 Keowee Avenue, Knoxville, TN 37919-7754, USA. jjivolfe@esper. corn Zinn, C. (1) Universitats-Hals-Nasen-Ohrenklinik, Elf?iede-Aulhom-Str. 5 , 72076 Tubingen, GERMANY. [email protected] Zweig, G. (47) Massachusetts Institute of Technology, Room 36-730, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA. [email protected]

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Contents I. Stereocilia

1

The contribution of transduction channels and adaptation motors to the hair cell’s active process P. Martin, F. Jiilicher and A . J Hudspeth

3

Active amplification by critical oscillations F. Jiilicher, S. Camalet, J. Prost and T. A. J. Duke

16

Formation and remodeling of hair bundles promoted by continuous actin polymerization at the tips of stereocilia: Mechanical considerations M. E. Schneider, A. Rzadzinska, C. Davies and B. Kachar

28

Mechanical-to-chemical transduction by motor proteins J. Howard

37

Investigation of the mechanoelectricaltransduction at single stereocilia by AFM M. G. Langer, S. Fink, K. Lofler, A. Koitschev and H.-P. Zenner

47

Immunocytochemical investigations of the distribution of calbindin and calretinin in the turtle cochlea C. M. Hackney, S. Mahendrasingam and R. Fettiplace

56

The effects of calcium on mechanoh-ansducerchannel kinetics in auditory hair cells R Fettiplace, A . C. Crawford and A. J Ricci

65

Signal processing by transducer channels in mammalian outer hair cells T. Dinklo, S. M. van Netten, W. Marcotti and C. J. Kros

73

Measured and modeled motion of kee-standing hair bundles in response to sound stimulation A . J. Aranyosi and D. M. Freeman

81

xxvii

xxviii

Viscoelasticity of active actin-myosin networks L. Le GoE F. Amblard and E. M. Furst

89

Mechanical stresses and forces in stereocilia bundles of inner and outer hair cells R Mueller, H. Maier, F. Boehnke and W. Arnold

91

Two adaptation processes in auditory hair cells together can provide an active amplifier A. Vilfan and T. A. J. Duke

93

11. Hair cells

95

Some pending problems in cochlear mechanics

97

P. Dallos

Functional properties of prestin - how the motormolecule works work B. FakIer and D. Oliver

110

Allosteric modulation of the outer hair cell motor protein prestin by chloride V. Rybalchenko and J. Santos-Sacchi

116

ROCK ‘n’ Rho in outer hair cell motility M. Zhang, G. Kalinec, F. Kalinec, D. D. Billadeau and R Urrutia

127

Ultrastructure of lateral walls of outer hair cells observed by atomic force microscopy H. Wada, M. Sugawara, H. Usukura, K. Kimura, Y. Katori, S. Kakehata, K. Ikeda and T. Kobayashi

136

The strain ratio of the outer hair cell motor protein R. Hallworth

144

Piezoelectric properties enhance outer hair cell high-frequency response A. A. Spector, A. S. Popel and W.E. Brownell

152

XXlX

Fast nonlinear currents in outer hair cells fiom the basal turn of the cochlea X-X. Dong, M. Ospeck and K. H. Iwasa

161

Membrane electromechanicsat hair-cell synapses W. E. Brownell, B. Farrell and R. M Raphael

169

Determination of the elastic modulus of thin gels using the atomic force microscope E. K. Dimitriadis, F. Horkay, B. Kachar, J. Maresca and R. S. Chadwick

177

Measurement of mechanical properties of the outer hair cell with atomic force microscopy M. Sugawara, H. Wada and Y. lshida

179

Mechanical responses of cochlear outer hair cells D. Z. Z. He

181

No correlates for somatic motility in freeze-fi-actured hair-cell membranes of lizards and birds C. Koppl, A. Forge and G. A. Manley

185

Tension-dependenceof the active and passive modes of energy generated in the outer hair cell wall A. A. Spector and R. P. Jean

187

Hair cell responses and harmonic phase M A. Cheatham and P. Dallos

189

Diverse and dynamic expression patterns of voltage-gated ion channel genes in rat cochlear hair cells K. W. Beisel and B. Fritzsch

191

A KCNQ-type potassium current in cochlear inner hair cells D. Oliver and B. Fakler

194

xxx

111. Whole-organ mechanics

197

Development of cochlear mechanics in the gerbil E. H. Overstreet, III, A. N. Ternchin and M. A. Ruggero

199

Measurement of basilar membrane vibration using a scanning laser interferometer T. Y. Ren, Y. Zou, J. F. Zheng, A. L. Nuttall, E. Porsov and S. Matthews

21 1

Cochlear mechanical distortion products for complex stimuli in the chinchilla basal region W. S. Rhode and A. Recio

220

Harmonic distortion in intracochlear pressure: Observations and interpretation E. S. Olson

228

The local mechanical response of the basilar membrane for electrical stimulation of the cochlea A. L. Nuttall, K. Grosh, J.F. Zheng, T.Y. Ren and E. de Boer

237

Fast effects of efferent stimulation on basilar membrane motion J. J. Guinan Jr. and N . P. Cooper

245

Response to amplitude modulated waves in the apical turn of the cochlea S. M. Khanna

252

Baseline position shifts and mechanical compression in the apical turns of the cochlea N. P. Cooper and W. Dong

26 1

High-kequency vibration of the organ of Corti in vitro M P. Scherer, M. Nowotny, E. Dalhofi H.-P. Zenner and A. W. Gummer

27 1

Micromechanics in the gerbil hemicochlea C.-P. Richter and P. Dallos

278

xxxi

Visualizing cochlear mechanics using confocal microscopy M. Urfendahl, J. Boutet de Monvel and A. Fridberger

285

Low-fi-equencyoscillations in outer hair cells and homeostatic regulation of the organ of Corti R. B. Patuzzi

292

Micromechanics of Drosophila audition M. C. Gopfert and D. Robert

300

Active auditory mechanics in insects D. Robert and M. C. Gopfert

308

Is the cochlear amplifier a fluid pump? K. D. Karavitaki and D, C. Mountain

310

IV. Cochlear models

313

Cellular cooperation in cochlear mechanics G. Zweig

315

Properties of amplifying elements in the cochlea E. de Boer and A. L. Nuttall

33 1

Nonlinear behavior in an active cochlear model with feed-forward K. M. Lim and C. R. Steele

343

Time-domain responses fiom a nonlinear sandwich model of the cochlea A. E. Hubbard. D. C. Mountain and F. Chen

35 1

Analysis of forces on inner hair cell cilia C. R. Steele and S. Puria

359

Notes on physical properties of the tectorial membrane S. M. Novoselova

368

An improved cochlea model with a general user interface H. Duifhuis, J. M Kruseman and P. W. J . van Hengel

376

xxxii

The role of micromechanics in explaining two-tone suppression and the upward spread of masking J. B. Allen and D. Sen

3 83

The helicotrema: Measurements and models D. C. Mountain, A. E. Hubbard, D. R. Ketten and J. Trehey O’Malley

393

Computation of modes and motion analysis in a transverse section of the cochlea H. Cai and R. S. Chadwick

400

A life-sized, hydrodynamical, micromechanical inner ear W. Hemmert, U. Diirig, M. Despont, U. Drechsler,

409

G. Genolet, P. Vettiger and D. M. Freeman

The silicon cochlea: From biology to bionics L. Turicchia and R. Sarpeshkar

417

Explanation of two curious phenomena regarding the relationship between tectorial membrane and basilar membrane dynamics R. Nobili

425

Dynamic behavior of the organ of Corti: Finite-element method analysis M. Andoh and H. Wada

427

Are outer hair cells pressure sensors? Basis of a SA W model of the cochlear amplifier A. Bell

429

Generalised description of the mammalian cochlear map E. L. LePage

432

Mathematical modelling of the role of outer hair cells in cochlear homeostasis G. A. O’Beirne and R. B. Patuzzi

434

xxxi ii

V. Emissions

437

Wave interference in the generation of reflection- and distortionsource emissions C. A. Shera

439

Growth of otoacoustic emissions with frequency: Inside the human cochlear vestibule S. Puria

454

Difference-tone response areas in rabbits G. K. Martin, B. B. Stagner and B. L. Lonsbury-Martin

464

Temporal characteristics of otoacoustic emissions R. H. Withnell, S. Dhar, C. L. Talmadge, L. A. Shafler, E. de Boer, R. Roberts and D. McPherson

472

The tectorial membrane stabilizes spontaneous otoacoustic emissions G. A. Manlq

480

Dynamic changes in spontaneous otoacoustic emissions produced by contralateral broadband noise J. Smurzymki, G. Lisowska, A. Grzanka, G. Namyslowski and R Probst

488

Contralateral DPOAE suppression in humans at very low sound intensities T. Jamsen, D. D. Gehr and Z. Kevanishvili

498

Effects of the medial olivocochlear reflex on cochlear mechanics: Experimental and modeling studies of DPOAE D. 0.Kim, X : M Yang and S. T. Neely

506

Modeling otoacoustic emissions and related psychoacoustic measures in humans and other mammals C. L. Talmadge, A. Tubis and G. R. Long

517

Otoacoustic emissions simulated in the time-domain by a hydrodynamic model of the human cochlea R Nobili, A. Veteinik, L. Turicchia and F. Mammano

524

XXXIV

Growth of distortion-productotoacoustic emissions in a nonlinear, active model of cochlear mechanics S. i? Neely, M. P. Gorga and P. A. Dorn

53 1

Modeling electrically evoked otoacoustic emissions K. Grosh, N . Deo, A. A. Parthasarathi, A. L. Nuttall, J.F. Zheng and T.Y. Ren

539

Developing a noninvasive measure of middle-ear sound transmission C. A. Shera and A. J. Miller

547

Assessment of sensitivity and compression of outer hair cell amplifiers by means of DPOAE VO-functions in humans J. Oswald, A. Klein and T. Janssen

549

DPOAE phase pattern: Evidence for a low frequency resonance in the fi place A. N. Lukashkin and I. J. Russell

55 1

Phenomenology of post-stimulus changes of DPOAE A. N . Lukashkin and I. J. Russell

553

Magnitude of distortion-product OAEs in a nonlinear model of the cochlea H, Taiji

555

Phase behavior of the primaries in distortion product analysis A. VeteSnik and R. Nobili

557

Two-tone interference caused by active amplification T. A. J. Duke, D. Andor and F. Jiilicher

559

VI. Discussion session

561

Hopf bikcation

564

Prestin

570

Stereociliary versus somatic motility

572

xxxv

An ideal approach to cochlear modelling

579

Low-frequency responses of the basilar membrane and the nerve

582

Multiple travelling waves on the basilar membrane

583

Kinocilium function

586

Fluid component of the travelling wave

587

Physical reason for the cochlear amplifier

588

Wilson’s hair-cell swelling model

589

Pressure at the round window

590

Shape of the stereocilia bundle

590

Author Index

593

Subject Index

597

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I. Stereocilia

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THE CONTRIBUTION OF TRANSDUCTIONCHANNELS AND ADAPTATION MOTORS TO THE HAIR CELL’S ACTIVE PROCESS P. MARTIN Laboratoire Physico-Chimie Curie, Unit&Mixte de Recherche 168 du CNRS, Institut Curie, 26, rue d’Ulm, F-75248 Paris cedex 05, France E-mail: [email protected] r F. JaICHEiR Max-Planck-Institutfur Physik komplexer Systeme Nothnitzer Str. 38, 01187 Dresden, Germany E-mail:julicher@mpiph-dresden. mpg.de A. J. HUDSPETH Howard Hughes Medical Institute and Laboratory of Sensory Neuroscience The Rockefeller Universi& 1230 YorkAvenue, New York, NY 10021-6399, USA E-mail: [email protected] When immersed in endolymph, hair bundles from the bullfrog’s sacculus oscillate spontaneously. Because the fluctuation-dissipationtheorem is not satisfied for an oscillatory hair bundle, these movements require the operation of energy-consuming elements within the hair cell. The interplay between the motor responsible for adaptation to sustained stimuli and an unstable region of negative stifhess in an oscillatory bundle’s displacement-force relation explains the active oscillation. Periodic forces as small as *0.3 pN applied at a bundle’s top can entrain the noisy oscillatory movements, thereby amplifiing the hair bundle’s response by as much as 28 dB. A bundle is most sensitive to faint stimuli; its response increases as the one-third power of the stimulus magnitude. Spontaneous oscillations, frequency-selective amplification, and nonlinear compression of a bundle’s response are hallmarks of a dynamical system that operates on the verge of an oscillatory instability, a Hopf bifurcation.

1

Introduction

The vertebrate ear can sing. Whether spontaneous or evoked by a click, otoacoustic emissions [I] constitute the most striking evidence that the ear is mechanically active. Because viscous dissipation in the inner-ear fluids hampers passive mechanical resonance of the ear’s moving structures, the ear’s exquisite sensitivity and sharp frequency selectivity must stem from an amplificatory process [2]. In addition, the active process is closely associated with nonlinear compression of the Spontaneous ear’s responsiveness to stimuli of increasing magnitude [3]. otoacoustic emissions (SOAEs), amplification, frequency selectivity, and compressive nonlinearity are the four essential characteristics that define the cochlear amplifier.

3

4

Although somata1length changes by electromotile outer hair cells are thought to mediate amplification in the mammalian cochlea [4], the auditory receptor organs of non-mammalian tetrapods, which evidently lack electromotile hair cells, display essentially identical sensitivity, tuning, nonlinearity, and emissions [ 5 ] . The active process necessary to explain the properties of hearing in these animals, and perhaps in mammals as well, must therefore stem from a different mechanism. An alternative candidate is active hair-bundle motility [6-81. We review here recent experimental findings demonstrating that a hair bundle can produce active oscillatory movements to amplifl a hair cell's response to sinusoidal mechanical stimuli [9-121. 2

Methods

Experiments were performed on hair bundles from the bullfrog's sacculus [9,10]. The saccular macula was secured in a two-compartment experimental chamber. The basolateral surfaces of the hair cells were immersed in standard saline solution, whereas their hair bundles projected into NMDG endolymph containing 2 mM Na", 3 mM K+, 0.25 mh4 Ca", 110 mM N-methyl-D-glucamine (NMDG), 111 mM Cl-, 3 mM D-glucose, and 5 mM HEPES. This arrangement mimicked the ionic circumstances in vivo, in particular by imposing a low Caz+concentration of 250 pM around the hair bundles. Because NMDG replaced most of the K" normally found in endolymph, this artificial endolymph supported little transduction current. NMDG, however, did not interfere with the permeation of other cations and with the active hair-bundle movements reported here. After removal of the otholitic membrane, the preparation was mounted on the stage of an upright microscope for observation through a 40x objective and differential-interference-contrastoptics. We used flexible glass fibers both to report movements of a hair bundle and deliver mechanical stimulation. The tip of the fiber was attached to a bundle's top whereas its base was secured to a piezoelectric actuator. The fiber's sti&ess and drag coefficient were respectively 80-400 pN.m" and 40-1 10 nN-sec-m-'. An image of the sputter-coated tip of the fiber was formed on a dual photodiode at a magnification of 1,OOOX. The photometric system produced an output linearly proportional to the displacement of the fiber's tip with a resolution of 1 nm. For measurement of a hair bundle's displacement-force relation, we recorded the forces necessary to displace the bundle various distances under displacementclamp control. To ensure that the bundle's position matched a command, we used negative feedback. The clamp circuit was able to track command steps with a time constant of 1 ms.

-

5

3

Results

Active spontaneous oscillations of a hair bundle

3. I

When immersed in artificial endolymph, hair buhdles from the bullfrog’s sacculus exhibited spontaneous oscillations at 5-50 Hz with a peak-to-peak magnitude as great as 80 nm. We attached a flexible fiber to a hair bundle’s top to monitor the bundle’s dynamical behavior. Composed of two distinct phases, the bundle movement appeared to be a relaxation oscillation [13]: a rapid stroke in one direction was followed by a slow excursion in the same direction (Fig. 1).

i.0

Figure 1. Properties of spontaneous oscillations by a hair bundle from the sacculus of the bullfrog’s inner ear. A: Monitoring the position of a glass fiber attached at the hair bundle’s top measured the bundle’s spontaneous movement. This oscillation had a rootmean-square magnitude of 27.6nm and a mean frequency of 8Hz. Note the irregularity of the oscillation’s size and frequency. 9: The probability distribution of bundle position was bimodal, with a local minimum near the bundle’s mean position.

-

T

nrn

500 rns

6 , 20

-30

-20

8

-10 0 10 Bundle position (nm)

20

30

The histogram of the bundle’s position was bimodal, a probability distribution resembling that observed for sound pressure at the frequency of an SOAE from the human ear [ 141. The spectral density of motion displayed a clear peak, centered at the bundle’s characteristic frequency of oscillation. The bundle movements, however, fluctuated both in amplitude and in phase. To determine whether noisy hair-bundle oscillations resulted from thermal bombardment or revealed the operation of energy-consuming elements within the hair cell, we invoked a general thermodynamical principle. With no assumption other than that the system under investigation is at thermal equilibrium, the fluctuation-dissipation theorem imposes a specific relation at all fkequencies between a system’s spontaneous fluctuations and its responsiveness to small external stimuli [15]. If the system is removed fkom thermal equilibrium by an active mechanism, this relation no longer holds. As a measure of the degree of violation of the fluctuation-dissipationtheorem, we defined an effective temperature TEFF(o):

in which E(w) is the system’s spectral density of spontaneous motion at angular frequency q is the imaginary part of the Fourier transform of the system’s

6

linear response function to small oscillatory forces, kB is the Boltzmann constant, and T is the temperature. By imposing small sinusoidal movements at the stimulus fiber’s base, we applied periodic forces at a hair bundle’s tip and measured the linear response function at various frequencies [12]. We calculated at each frequency the effective temperature at which the observed movements would have satisfied the fluctuation-dissipation theorem (Eq. 1). Because we found that TEFF differed from T at all measured frequencies (Fig. 2) both the hair bundle’s spontaneous motion and its response to sinusoidal stimulation must be active phenomena, governed by a process that requires a cellular energy source and can generate work.

. ::

100-

~

t“

0-

-100-

-200

0

10

20

30

40

50

Figure 2. The effective temperature of spontaneous hair-bundle motion. A: For an oscillatory hair bundle, the effective temperature, normalized by the actual temperature, changed its sign and exhibited a divergence near the bundle’s characteristic frequency, here 8 Hz, before reaching a value of -4 at the greatest frequencies explored. Because this ratio deviated kom unity, the hair bundle was active. B: For a control, non-oscillatory hair bundle, the normalized effective temperature remained near unity throughout the range of fiequencies. This behavior, which satisfies the fluctuation-dissipation theorem, suggests that these spontaneous bundle movements resulted from thermal bombardment.

3.2

A mechanism to explain hair-bundle oscillations

By examining the mechanical properties of active hair bundles, we sought to identify the basis of their spontaneous oscillations. Under displacement-clamp conditions, we measured the forces required to displace a bundle by various distances [lo]. An abrupt bundle deflection first elicited a viscous-force transient in the direction of bundle movement that concealed other fast components of the response. We estimated the elastic restoring force of the hair bundle soon after the viscous transient had vanished, but before adaptation to the static stimulus [16] had significantly affected the response. When displaced extensively along its axis of mechanosensitivity, the bundle behaved as an ordinary spring of constant stifhess (Fig. 3). The striking feature of our recordings was that, for displacements in the range of +_lonm,the hair bundle’s slope stiffness was negative. How does negative hair-bundle stiffness arise? Direct and concerted mechanical gating of transduction channels results in gating compliance [ 171. If this nonlinearity is great enough to dominate other elastic components, the hair bundle’s overall stifhess can become negative [18,19]. The gating force increases in proportion to the single-channel gating force z and to the channel open probability

7

po(X). In the simplest formulation of the gating-spring model [IS], the singlechannel gating force is given by z = yicd, in which y = 0.14 is a geometrical factor, is the gating-spring stiffness, and d is the distance by which a gating spring shortens as a channel opens. Our data were well fit by this model, indicating that ~ = 5 7 0 & 2 5pNm-’ 0 and d=8.2+ 1.5 run. This distance seems too large to reflect the movement of a channel’s pore-obstructing gate but would be plausible if the gating spring were attached to the gate by a molecular lever.

0 Displacement

Figure 3. Relation between hair-bundle displacement and applied force under displacement-clamp conditions. The continuous black line is the best fit to a gating-spring model in which the force FSFapplied by the stimulus fiber to deflect the bundle by a distance Xis F ~ ~ ( X ) = K , X - N ~ , ( X ) Z + F ~ , In this relation, K, is the bundle’s linear stiffness, N is the number of gating springs that operate in parallel, po is the channel’s open probability, z is the single-channel gating force, and FO is a constant offset. The grey cycle describes the putative trajectory during hairbundle oscillation.

Because positions in the domain of negative stiffness are unstable, the hair bundle cannot settle there. Mechanical biasing of the hair bundle in this unstable region would thus force the bundle to oscillate (Fig. 3). Two lines of evidence suggest that the myosin motor that mediates mechanical adaptation [16,20] constitutes the energy-consuming element that powers the hair-bundle oscillation. First, when the bundle is immersed in an ionic milieu containing 250 p M Ca*’, the adaptation motor reaches a steady state for a channel open probability near one-half [21,22]. This probability corresponds to a bundle position well within the unstable negative-stiffness region. Second, computer modeling of the bundle’s mechanical behavior using measured values for the rate of mechanoelectrical adaptation [22,23] generates spontaneous hair-bundle oscillation at the observed fiequency [lo]. 3.3

Frequency-selectiveamplijication of sinusoidal stimuli

By applying sinusoidal displacements at the stimulus fiber’s base, we inquired whether a hair cell can use active hair-bundle movements to amplify its inputs (Fig. 4). A hair bundle was most sensitive when stimulated near its characteristic fiequency [ 1I]. In this case, fiber displacements as small as *I nm, corresponding to forces of only &0.3pN, evoked partial entrainment of a bundle’s noisy oscillation. Stimuli 1- 10 nm in amplitude increased the phase-locking of the response; only after nearly perfect locking had been achieved did the magnitude of hair-bundle movement grow appreciably. This behavior resembles that of neural activity observed in vivo in all classes of tetrapods: the threshold for phase-locking may be 10-20 dB lower than that for increased firing of auditory-nerve fibers [24-261. Because the average work done in one cycle of stimulation by the stimulus fiber was

8

lower than the average amount of energy dissipated in the viscous fluid surrounding the moving bundle, the hair cell provided usefbl work and amplified its input [9]. Moreover, blockage of transduction-channel gating by gentamicin evoked a dramatic drop of the hair-bundle response, whose magnitude fell to one-tenth the control value (Fig. 4).

’

I

.

Figure 4. Comparison of a bundle’s active and passive responses to a sinusoidal stimulus. The bundle displayed a noisy spontaneous oscillation. A sinusoidal stimulus of f10 nm at 5 Hz entrained the bundle’s movements. Note that the ensuing response was almost twice as large as the stimulus. An iontophoretic pulse of gentamicin, applied near the top of the oscillating bundle during a period delimited by dashed vertical lines, reversibly blocked the active bundle response. Slow drifts in the baseline of bundle movement were subtracted. The fiber bad a stiffness of 220 a m - ’ .

3.4

Compressive nonlinearity of a bundle’s active response to stimulation

When an active hair bundle was subjected to stimuli of progressively increasing amplitude, the Fourier component of the bundle motion at the stimulus frequency exhibited a compressive nonlinearity (Fig. 5A). For moderate to intense stimuli, the response magnitude increased as the one-third power of the stimulus amplitude [I 11. The bundle’s sensitivity was correspondingly greatest for small stimuli and decliied as the minus two-thirds power of stimulus amplitude (Fig. 5B). Stimulation at ftequencies much higher than the bundle’s characteristic frequency, in contrast, evoked linear responses of constant sensitivity throughout the range of amplitudes. Moreover, this sensitivity did not vary markedly with stimulus frequency and equaled that of the bundle when stimulated at intense levels near its natural frequency. The ratio of a hair bundle’s active to its passive sensitivity defines the amplifier’s gain. The gain could be as great as 25, corresponding to 28 dB, for stimuli of *1 nm,but averaged -5 for small stimuli.

9 B

70 E60C

v

L

% 50C

J .

0

50

100

150

200

Base displacement (nm)

250

300

. . .. .* 1

.

,

. . . . . ., 10

,

.

. . . . . ..

Base displacement (nm)

loo

.

.

Figure 5. Nonlinear response compression for an active hair bundle. A: Stimulation at high frequencies relative to the bundle’s natural frequency (A, 153 Hz) elicited essentially linear responses, corresponding to passive behavior. By contrast, the RMS magnitude of the bundle motion’s Fourier component at the frequency of stimulation demonstrated strong amplification of small inputs at the characteristic frequency ( 0 , 9 Hz). The abscissa represents the amplitude of motion of the stimulus fiber’s base. B: Plotted in doubly logarithmic form, the hair-bundle sensitivity displayed saturation for small stimuli (upper horizontal line). For moderate to intense stimuli, the sensitivity declined as the negative two-thirds power of the stimulus amplitude (oblique line). The sensitivity reached a constant, low value for intense stimuli (lower horizontal line).

4

Discussion

Active hair-bundle motility displays correlates of all four essential properties that characterize the inner ear’s active process. First, hair bundles can oscillate spontaneously. Unprovoked mechanical oscillations of some constituent of the inner ear must underlie the production of spontaneous otoacoustic emissions. Second, the hair cell can make use of active hair-bundle movements to ampliQ its mechanical inputs, thereby enhancing its sensitivity. Amplification is one of the main benefits of the cochlear active process. Third, mechanical amplification by hair bundles is tuned. The bundle’s responsiveness to stimulation, like that of the mammalian basilar membrane, is greatest near its characteristic fiequency. Finally, amplification by hair bundles is nonlinear. Hair-bundle sensitivity varies over most of its range as the minus two-thirds power of the stimulus magnitude. The compressive nonlinearity of the mammalian basilar membrane in response to sounds is well described by the same power law in a range that covers four orders of magnitude of sound intensity (see Fig. 4 in ref. [3]). These results suggest that the hair-bundle amplifier at least obeys the same physical principles as the cochlear amplifier. All four properties of the active process have been recognized recently as signatures of a dynamical system that

10

operates on the verge of an oscillatory instability, a Hopf bifurcation [27-291. Proper operation of the amplifier probably requires a self-tuning mechanism to poise the system on the brink of the instability, for both amplification and frequency selectivity are greatest at this critical point [29]. In the case of active hair bundles, Ca2"-mediated adjustment of a bundle's negative stifhess to match the load's stifhess would achieve this end. The most important uncertainty about the potential use of active hair-bundle motility in hearing is its ability to operate at frequencies that can be as high as tens of kilohertz. Although hair bundles from the bullfrog's sacculus oscillate spontaneously at 5-50Hz, these fiequencies are within the range of saccular responsiveness, 5-130 Hz 1301. By using partial displacement clamping to oppose bundle motion, we observed that the frequency of a bundle's spontaneous oscillation increases upon effectively stiffening the stimulus fiber (unpublished observations). Because the magnitude of bundle movement decreases with increasing fiber stifhess and the oscillation become noisier, however, the range of well-defined oscillations that could be described by this means was limited to -50 Hz. It is plausible that auditory hair bundles, which can contain several hundred stereocilia and thus potentially a much larger number of active elements, would be less sensitive to thermal and stochastic fluctuations. Large collections of motors can potentially oscillate at several kilohertz [29,3 11. Active bundle movements may alternatively be powered by additional processes such as Ca2'-mediated channel reclosure [6,32,33]. This process has been shown by modeling to display a Hopf bifurcation with characteristic fi-equenciesthan span the auditory range [27]. Only two ingredients are necessary to endow hair bundles with the ability to amplify their mechanical inputs by the mechanism described here: a region of negative stifhess in the displacement-force relation and a biasing element such as that provided by the adaptation motor. Because both gating compliance [34,35] and adaptation [20,36,37] have been demonstrated in mammalian hair cells, active hairbundle motility may provide a source of amplification in the mammalian cochlea as well. Acknowledgments The original investigations on which this review is based were supported by National Institutes of Health grant DC00214. A. J. H. is an Investigator of Howard Hughes Medical Institute.

11

References 1 . Probst, R., 1990. Otoacoustic emissions: an overview. Adv. Otorhinolaryngol. 44, 1-97. 2. Gold, T., 1948. Hearing. 11. The physical basis of the action of the cochlea. Proc. R. SOC.Lond. B 135,492-498. 3. Ruggero, M.A., Rich, N.C., Robles, L., 1997. Basilar-membrane responses to tones at the base of the chinchilla cochlea. J. Acoust. SOC.Am. 104,2 15 1-2163. 4. Dallos, P., 1992. The active cochlea. J. Neurosci. 12,4575-4585. 5. Manley, G.A., 200 1. Evidence for an active process and a cochlear amplifier in nonmammals. J. Neurophysiol. 86, 54 1-549. 6. Hudspeth, A.J., 1997. Mechanical amplification of stimuli by hair cells. Curr. Opin. Neurobiol. 7,480-486. 7. Fettiplace, R., Ricci, A.J., Hackney, C.M., 200 1 . Clues to the cochlear amplifier from the turtle ear. Trends Neurosci. 24, 169-175. 8. Manley, G.A., Kirk, D.L., Koppl, C., Yates, G.K., 2001. In vivo evidence for a cochlear amplifier in the hair-cell bundle of lizards. Proc. Natl. Acad. Sci. USA 98,2826-283 1. 9. Martin, P., Hudspeth, A.J., 1999. Active hair-bundle movements can amplify a hair cell's response to oscillatory mechanical stimuli. Proc. Natl. Acad. Sci. USA 96, 14306-14311. 10. Martin, P., Mehta, A.D., Hudspeth, A.J., 2000. Negative hair-bundle stiflkess betrays a mechanism for mechanical amplification by the hair cell. Proc. Natl. Acad. Sci. USA 97, 12026-12031. 11. Martin, P., Hudspeth, A.J., 2001. Compressive nonlinearity in the hair bundle's active response to mechanical stimulation. Proc. Natl. Acad. Sci. USA 98, 14386-14391. 12. Martin, P., Hudspeth, A.J., Jiilicher, F., 2001. Comparison of a hair bundle's spontaneous oscillations with its response to mechanical stimulation reveals the underlying active process. Proc. Natl. Acad. Sci. USA 98, 14380-14385. 13. Strogatz, S.T., 1997. Nonlinear Dynamics and Chaos. Addison-Wesley, Reading, MA. 14. Bialek, W., Wit, H.P., 1984. Phys. Lett. A 104, 173-178. 15. Doi, M., Edwards, S.F., 1986. In: The Theory of Polymer Physics. Oxford Science Publications, Oxford, U.K., pp. 58-62. 16. Hudspeth, A.J., Gillespie, P.G., 1994. Pulling springs to tune transduction: adaptation by hair cells. Neuron 12, 1-9. 17. 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.

12

18. Markin, V.S., Hudspeth, A.J., 1995. Gating-spring models of mechanoelectrical transduction by hair cells of the internal ear. Annu. Rev. Biophys. Biomol. Struct. 24,59-83. 19. Denk, W., Keolian, R.M., Webb, W.W., 1992. Mechanical response of frog saccular hair bundles to the aminoglycoside block of mechanoelectrical transduction. J. Neurophysiol. 68, 927-932. 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. Corey, D.P., Hudspeth, A.J., 1983. Kinetics of the receptor current in bullfrog saccular hair cells. J. Neurosci. 3,962-976. 22. Hacohen, N., Assad, J.A., Smith, W.J., Corey, D.P., 1989. Regulation of tension on hair-cell transduction channels: displacement and calcium dependence. J. Neurosci. 9,3988-3997. 23. Eatock, R.A., Corey, D.P., Hudspeth, A.J., 1987. Adaptation of mechanoelectrical transduction in hair cells of the bullfi-og’s sacculus. J. Neurosci. 7, 2821-2836. 24. Kisppl, C., 1997. Phase locking to high fi-equencies in the auditory nerve and cochlear nucleus magnocellularis of the barn owl, Tyto alba. J. Neurosci. 17, 3312-3321. 25. Hillery, C.M., Narins, P.M., 1984. Neurophysiological evidence for a traveling wave in the amphibian inner ear. Science 225, 1037-1039. 26. Gleich, O., Narins, P.M., 1988. The phase response of primary auditory afferents in a songbird (Sturnw vulgaris L.). Hear. Res. 32,81-91. 27. Choe, Y., Magnasco, M.O., Hudspeth, A.J., 1998. A model for amplification of hair-bundle motion by cyclical binding of Ca” to mechanoelectricaltransduction channels. Proc. Natl. Acad. Sci. USA 95, 15321-15326. 28. Eguiluz, V.M., Ospeck, M., Choe, Y., Hudspeth, A.J., Magnasco, M.O., 2000. Essential nonlinearities in hearing. Phys. Rev. Lett. 84, 5232-5235. 29. Camalet, S., Duke, T., Julicher, F., Prost, J., 2000. Auditory sensitivity provided by self-tuned critical oscillations of hair cells. Proc. Natl. Acad. Sci. USA 97,3183-3188. 30. Yu, X.L., Lewis, E.R., Feld, D., 1991. Seismic and auditory tuning curves fi-om bullfiog saccular and amphibian papillar axons. J. Comp. Physiol. [A] 169,241 248. 3 1. Julicher, F., Prost, J., 1997. Spontaneous oscillations of collective molecular motors. Phys. Rev. Lett. 78,4510-4513. 32. Benser, M.E., Marquis, R.E., Hudspeth, A.J., 1996. Rapid, active hair bundle movements in hair cells fi-om the bullfrog’s sacculus. J. Neurosci. 16, 56295643.

13

33. 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, 713 17142. 34. Russell, I.J., Kossl, M., Richardson, G.P., 1992. Nonlinear mechanical responses of mouse cochlear hair bundles. Proc. R. SOC.Lond. B 250,217-227. 35. Geleoc, G.S., Lennan, G.W., Richardson, G.P., Kros, C.J., 1997. A quantitative comparison of mechanoelectrical transduction in vestibular and auditory hair cells of neonatal mice. Proc. R. SOC.Lond. B 264,611-62 1. 36. Russell, I.J., Richardson, G.P., Kossl, M., 1989. The responses of cochlear hair cells to tonic displacements of the sensory hair bundle. Hear. Res. 43,55-69. 37. Kros, C.J., Riisch, A., Richardson, G.P., 1992. Mechano-electrical transducer currents in hair cells of the cultured neonatal mouse cochlea. Proc. R. SOC. Lond. B 249, 185-193. Comments and Discussion J. Santos-Sacchi: Does the exquisite sensitivity of the model to amplitude and frequency changes actually fit the known sensitivity of the mammalian ear in a quantitative manner?

Answer: We observed a compressive nonlinearity in the response of a single hair bundle to stimuli of increasing magnitudes. The nature of this nonlinearity suggests that the hair bundle operates on the verge of an oscillatory instability, a Hopf bifurcation. Data collected in the chinchilla’s cochlea revealed very similar compression of the basilar-membrane response to sounds of increasing intensities over many orders of magnitude, suggesting that this organ might also take advantage of oscillatory instabilities. In a cochlea, however, many hair bundles are coupled together through the fluid, and the system is more complex than a single hair bundle. A careful description of how this coupling occurs is required before one can compare the data with the behavior a collection of coupled Hopf oscillators. J. Howard: Because most of the bundle displacements are 6 0 nm, most of the shear displacements between stereocilia are > term is unimportant and the response becomes linear

[f;’31

1B11/3~,the cubic

The response of the system given by Eq. (4) characterizes the main properties of an oscillator near the bifurcation point. This approach can be generalized to situations where more than one frequency is present [lo].

4

Oscillations generated by molecular motors

The generation of mechanical oscillations requires an energy input. In this section, we discuss a physical mechanism that could allow molecular motors which consume ATP to generate oscillations via a Hopf bifurcation. This mechanism requires many motor molecules to work together. It has the interesting property that it can generate frequencies over a large range, and in particular frequencies that are higher than the characteristic rate of ATP consumption of the motors. We consider a general physical model for force generation of molecular motors [22,23] where a large number of molecular motors are rigidly connected [24,25]. This system can undergo a Hopf bifurcation if coupled to elastic elements [26] (see Fig. 28). In the limit where a large number of motors is present, the system can be described by simple mean-field equations. We consider motors moving along a periodic linear structure of period l , which represents a cytoskeletal filament, see Fig. 2b. In the most simple case of a two-state model, we study the probability density Pi(c,t) to find a motor at position in state


100 ms) that may reflect slower processes such as regulation of the transducer channels by cyclic A M P (Ricci and Fettiplace, J. Physiol. 501, 111-124, 1997).

SIGNAL PROCESSING BY TRANSDUCER CHANNELS IN MAMMALIAN OUTER HAIR CELLS T. DINKLO AND S. M. VAN NETTEN Department of Neurobiophysics, Universityof Groningen,Nvenborgh 4, 9747 AG, Groningen, The Netherlands E-mail: [email protected] & [email protected]. nl

W. MARCO’M’I AND C . J. KROS School of Biological Sciences, Universityof Sussex, Falmer, Brighton, BNI 9QG, UK E-mail: [email protected] & [email protected] Transducer channels of mammalian outer hair cells may not be fully silenced during stimulation of the hair bundle into the inhibitory direction (< -50 nm). A recently formulated threestate model, assuming a state-dependent mechanical engagement of the transducer channel, accounts for this incomplete deactivation [l]. Moreover, the model suggests a specific function for calcium in controlling the transducer current, by modulating the energy gaps between the conformational states of the channel. Combining this differentially activating model with experimental results on the gating of transducer currents, we attempted to estimate the consequences of this mode of engagement for the processing of mechanical signals by sensory hair cells. We found that the channels transduce small mechanical signals most efficiently into transducer currents when the hair bundle is deflected some tens of nanometers away from its equilibrium position. The results are in line with a specific role of calcium in optimising the transducer efficiency and are possibly related to the calcium-dependent phenomenon of adaptation in mechano-electrical transduction.

1

Introduction

Hair cells encode the mechanical signals received by their hair bundles into electrical signals for subsequent transmission to the brain. The first stage in the cascade of events that underlies this mechano-electrical transduction process consists of a mechanically induced change in open probability of the hair cell’s transducer channels. These channels are located in the hair bundle’s tip region and are most likely engaged by elastic elements that are tensioned in response to a positive deflection of the hair bundle. Recently, in mammalian hair cells, in addition to the gating compliance [2-4], a discontinuous step in the bundle’s mechanics was found when deflected more negatively than approximately -50 nm [1,5]. This discontinuity was interpreted as a mechanical disengagement of the transducer channels and could be directly linked to the measured displacement-independent (finite) open probability of the transducer channels in this deflection range [l]. A new differentially engaging three-state (Cl,C ,, 0)model was proposed that accurately describes this mechanical aspect of elastic activation of the transducer channel.

73

74

The model is based on six parameters that directly relate to the underlying physics: three engaging positions (Xcl,Xcz,Xo), defining the bundle's deflection at which each of the individual states is being engaged, the spring constant (KF)of the engaging elastic element, which is assumed to be the same for all states, and fmally the two values of the energy gaps ( E ~ , , ,~ 0 , ~that ) energetically separate the three conformational states in the deactivated range (see Fig. I). Variation of these energy gap values has been shown [ 11 to describe the experimentally observed effects that variation of extracellular calcium concentration has on the open probability, po(X) [6]. Increasing the (summed) energy gap, AE, corresponds to increased calcium concentrations, which cause transducer current-displacement curves to shift to the right along the displacement axis, a process that physiologically has been described as adaptation. Lowering the energy gap value has the opposite effect. In the present paper the performance of the first step in hair cell transduction is investigated by estimating the signal-to-noise ratio of outer hair cell transducer channels. Related new experimental results are shown to be adequately described by the differentially activating model. It is concluded that the process of adaptation may be involved in adjusting and possibly optimising the signal-to-noise performance of this early stage in mechano-electricaltransduction in hair cells.

hair bundle deflection (nm) Figure 1. State energies of the 3 conformational states defmed by the differentially activating model of the transducer channel [l]. Parameters are: XC, = 4 2 nm;Xc2 = 16 nm;XO = 41 nm;Kgs = 7.3 pN/m; = 3.6 kT; ta,~ = 0.9 kT. Using these parameters, open probability,p,(@, is completely dictated by the Boltzmann distribution. Increasing A& = s2.1 + a.2simulates increased extracellular calcium and shifts the resultingp,(X) to the right, decreasing Ashas the opposite effect.

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2 2.1

Methods Signal-to-noiseratio of hair cell transducer channels

The transducer current signal, S , O , of a hair cell containing n identical operational transducer channels in response to a small change, AX,around a static displacement, X , of its hair bundle is defined here as:

with, i, the current flowing through one transducer channel with a unitary conductance of 112 pS [5], which amounts to about 9.4 pA at the holding potential used in this study (-84 mV). Equation (1) expresses that the change in the hair bundle's position is assumed to be the relevant signal to be processed and not its absolute position. In the experiments AX was about 10 nm. The results of SI are displayed as the current change caused by a change in hair bundle position of 1 nm. The hair cell transducer channel is assumed to possess 3 conformational states with just 2 conductance levels, open or closed. The probability of populating the open state is p o Q , that of the 2 closed states is (1- p o ( a ) .The total (r.m.s.) currentnoise, Nxx), of n independent channels can then be calculated:

which combines with Eq. (1) in the (power) signal-to-noise ratio of the summed transducer channels of a hair cell:

2.2

Experiments

Acute preparations of 6 to 7 day old CD1 mice (P6-7) were used to record transducer current in response to fluid-jet stimulation of the hair bundle. Transducer current of outer hair cells was measured using the tight-seal whole-cell configuration, with a holding potential of -84 mV. Extracellular solution contained (mM): 135 NaCl, 5.8 KCl, 1.3 CaC12, 0.9 MgC12, 0.7 NaH2P04, 2 NaPyruvate, 5.6 Dglucose and 10 HEPES, pH 7.5, vitamins and amino acids wereadded fiom concentrates. Intracellular solution contained (mM): 147 CsC1, 2.5 MgC12, 2.5 Na2ATP, 5 HEPES, 1 EGTA-NaOH, pH 7.3. Pipettes were pulled fiom soda glass and coated with wax. Hair bundle displacement was measured using a differential photodiode system and was recorded simultaneously with the transducer current [5]. The RCtime imposed on the measurements by the series resistance of the patch restricted current measurements to a bandwidth of approximately 10 kHz.

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Fluid jet stimuli were generated and measured signals recorded using a Power 1401 data acquisition board in combination with the Signal software package (CED, Cambridge UK). Stimuli were filtered at 2 kHz. Current and displacement recordings were filtered at 5 kHz and sampled at 50 kHz. A step protocol displaced the bundle with mcrementing steps of about 20 nm during 150 ms, alternating positive and negative hair-bundle deflection. Currentdisplacement curves were constructed by displaying the step-current response as a function of the simultaneously measured step-displacement of the hair bundle between 50 and 100 ms after stimulus onset (Fig. 2a, triangles). Another protocol (double-sine), consisting of a sum of two sine waves 49 Hz andfi 1563 Hz), displaced the bundle quasi-statically through a large part of its dynamic range at fiequency fi, while the transducer channel's signal sensitivity, SAX), was probed at X, with fiequencyfi and an amplitude of about 10 nm. Current-displacement relationships using the double-sine protocol were constructed by extracting the current response atfi fiom the total current and displaying it as a function of the associated hair-bundle displacement at f i (Fig. 2% squares). The envelope of the remainingfi component was calculated and plotted as a function of the associatedfi displacement to obtain signal-displacement curves, S, (A'), (Fig. 2b, squares). All experimentswere performed at room temperature.

vI-

3

-

Results and Discussion

Figure 2 shows the results as obtained from a mouse apical outer hair cell (P6). In Figure 2a the current-displacement functions are shown as obtained using the two different stimulus protocols described in the methods. The double-sine protocol (squares) produces steeper slopes, while similar currents are obtained at smaller hair-bundle deflections in comparison to the step protocol (triangles). A plausible explanation may lie in the different degree of adaptation evoked by the two protocols. The double-sine protocol, specifically designed to directly measure the signal, S, of transducer channels, obviously comprises a less adaptive way to induce transducer currents than the static step stimuli. The parameters used to fit the two curves (solid lines) also reflect a difference in adaptation. The (summed) energy gap, A&, is higher for the step-evoked currents (4.9 kT) than the double-sine-evoked currents (4.5 kT). It has been shown previously that an increase of AE can simulate an increased extracellular calcium concentration or a more adapted state [l]. In addition, the engaging position of the open state, Xo, is shifted 10 nm to the left for the stepevoked currents as compared to the double-sine-evokedsituation. Figure 2b shows the signal, S, as measured with the double-sine protocol. It shows that under this condition the transducer channels are most sensitive at a hairbundle displacement of about 40 nm, reaching a maximum of about 15 pA/nm.

0

OJ

-200

-1bo

i

160

2io

-

-200

-100

0

77

\ 100

200

hb. displacement (nm)

hb. displacement (nm) 0.4

hb. displacement (nm)

hb. displacement (nm)

Figure 2. Signal, noise and their ratio of current through transducer channels in a mouse apical OHC. a: Transducer current of an OHC in response to a fluid jet producing forces with increasing steps (trian-

gles) and, measured continuously, in response to a fluid jet producing low frequency (49 Hz) forces using the double-sine protocol (a small selection of data points is shown as squares). b: Current signal in response to small variations (dx=lnm) of the hair bundle around a quasi-static position X, measured using the double-sine protocol in the same OHC as shown in a. e: Noise (r.m.s.) of the same OHC measured during the step responses displayed in a (triangles). To facilitate comparison with the responses measured with the double-sine protocol, the noise measured during the step stimuli is displayed with a contractedX-axis (factor 1.6) commensuratewith the apparent difference in the two transfer-curves in a. d: Signal-to-noise ratio of transducer current obtained by dividing the signal displayed in b by the noise shown in c. Apart from the solid line through the triangles in a (step protocol), all solid lines in a, b, c and d are based on the parameter set of the model given in the caption of Figure 1 and Eqs. 1,2 and 3. n = 85. The solid line through the triangles (step protocol) is based on: XCI= -42 nm; X C =16 ~ nm; XO = 31 nm; Kgs= 7 W/m; ~ , 1 =3.2 kT; t b , = ~ 1.7 kT; n = 74.

The measured signal (squares 2b) was modelled (solid curve 2b) by applying Eq. 1 to the solid curve in Fig. 2% describing the current in response to the (s1ow)fi component (- 49 Hz) of the double-sine protocol. Values so obtained had to be multiplied by a factor of 1.5 (solid curve 2b) to fit the measured signal (squares 2b), reflecting the smaller degree of adaptation at the higherfi component (- 1563 Hz). Figure 2c depicts the r.m.s. noise of the same outer hair cell, as measured during the step responses over a 50 ms time period. The values are displayed as a function

78

of hair-bundle displacement, which was reduced with a factor of 1.6 with respect to the actual measurement. This rescaling of the X-axis effectively describes the differences between the two measurement protocols and facilitates a proper comparison of the measured noise data with the signal, S , obtained using the double-sine protocol. Also, the measured r.m.s. noise was actually a factor 2.13 less than plotted in Fig. 2c. This multiplication factor was used to obtain a best match between the measured and calculated noise (solid curve 2c). A probable explanation lies in the limited bandwidth (0-5 MIz) that was used to measure the current noise during the step responses. The noise spectrum of a three-state channel can be shown to consist of a double Lorenzian with cut-off fiequencies related to the rate constants of the transitions between the states [7]. Transducer channel current noise spectra have been measured in fiog saccular- and turtle auditory hair cells with cut-off fiequencies of 250 Hz and 1185 Hz respectively [8,9]. The present outer hair cell current noise was found to be flat within the filter bandwidth used (5 kHz). Since cochlear outer hair cells may have rate constants that exceed this bandwidth, we may have measured only a fraction of the current noise present. An estimate based on the ratio (0.22) between measured and calculated (power) noise predicts a channel noise spectrum bandwidth of at least 20 kHz, suggesting relatively fast rate constants in mammalian hair cells. In this estimate we neglected the effect of bundle noise and other sources that could contribute to the current noise. Figure 2d finally shows the signal-to-noise ratio as obtained by taking the ratio of the measured data shown in Fig. 2b and the solid curve in Fig. 2c. The solid line depicts the signal-to-noise ratio resulting from the model. Both results shows that the signal-to-noise ratio peaks at a hair-bundle deflection of about 40 nm where it reaches a value of 0.37. It should be noted that this is the signal-to-noise in response to a change in hair-bundle position of 1 nm. Another way to characterise this result is to define the noise-equivalent stimulus amplitude (NESA) as the change in hairbundle position that produces a response signal equal to the noise. The NESA ranges fiom a minimum of about 2.7 nm around a static deflection of 40 nm to very high values at negative deflections. At the equilibrium position of the hair bundle, the NESA amounts to 5.3 nm. Adaptation has been shown to effectively shift a hair cell’s operational point and may also affect the slope of current-displacement curves. The related signal-to-noise ratio will therefore also be controlled by adaptation. The present results were obtained at extracellular calcium concentrations of 1.3 mM. However, the calcium concentration of the cochlear endolymph is much lower (-30 pM,[lo]). At such low extracellular calcium concentrations the current-displacement curve may shift several tens of nanometers to the left [6]. Under in vivo conditions hair-cell transducer channels may therefore be expected to reach the optimal signal-to-noise ratio closer to the resting position of the hair bundle than found under the present experimental conditions.

79

Acknowledgments T. Dinklo is supported by the Netherlands Organisation for Scientific Research (NWO). W. Marcotti and C.J. Kros are supported by the MRC and the Wellcome TIUSt.

References 1. 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. 2. Howard, J., Hudspeth, A.J., 1988. Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfiog’s saccular hair cell. Neuron 1, 189-199. 3. van Netten, S.M., Khanna, S.M., 1994. Stifkess changes of the cupula associated with the mechanics of hair cells in the fish lateral line. Proc. Natl. Acad. Sci. USA 9 1, 1549-1553. 4. Ricci, A.J., Crawford, A.C., Fettiplace, R., 2002. Mechanisms of active hair bundle motion in auditory hair cells. J. Neurosci. 22,44-52. 5. Gkleoc, G.S.G., Lennan, G.W.T., Richardson, G.P., Kros, C.J., 1997. A quantitative comparison of mechanoelectrical transduction in vestibular and auditory hair cells of neonatal mice. Proc. R SOC.Lond. B 264,6 1 1-621. 6. Crawford, A.C., Evans, M.G., Fettiplace, R., 1991. The action of calcium on the mechano-electrical transducer current of turtle hair cells. J. Physiol. 434, 369398. 7. Colquhoun, D., Hawkes, A.G., 1995. The principles of the stochastic interpretation of ion-channel mechanisms. In: Sakmann B., Neher, E. (Eds.), SingleChannel Recording, 2nd edition, Plenum Press, New York, pp. 397-482. 8. Holton, T., Hudspeth, A.J., 1986. The transduction channel of hair cells fiom the bull-fi-og characterized by noise analysis. J. Physiol. 375, 195-227. 9. Ricci, A., 2002. Differences in mechano-transducer channel kinetics underlie tonotopic distribution of fast adaptation in auditory hair cells. J. Neurophysiol. 87, 1738-1748. 10. Bosher S.K., Warren, R.L., 1978. Very low calcium content of cochlear endolymph, an extracellular fluid. Nature 273,377-378.

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Comments and Discussion J. Howard: The important information you should get fkom the noise recordings is the number of channels. Did you do so?

Answer: In this paper we obtained the number of channels using the fits of the current-displacement curves and dividing the resulting maximal current by the unitary transducer current taken fkom the data of GelCoc et ul. (proc. R. SOC.Lond. B 264, 61 1-621, 1997). The method referred to by Howard uses the variance in the current noise to estimate the unitary current, i, and the number of channels, n. From Equation 3 in this paper it can be easily shown that the variance in the current noise, oI,can be described by: oI= - 1 2 / n + i - l . A parabolic fit to the current variance plotted against the mean current then gives the values for n and i. The danger of this method, however, is that you may overestimate the value for n and underestimatethe value for i if the measuring bandwidth is too small. J.B. Allen: Did you work out the dynamic range of the hair cell?

Answer: The dynamic range can be estimated using the outer hair cell’s maximal accuracy of approximately 3 nm (see this paper) and the effective operational range of hair-bundle displacements of about 100 nm for the outer hair cell. This yields a dynamic range of about 30 ds.

E. Dalhoff: What is the integration time, to which the 3-nm accuracy or the signalto-noise ratio is referred to? Answer: The displacement accuracy of the transducer channels of an outer hair cell of about 3 nm has been obtained using the noise equivalent stimulus amplitude (NESA), according to the definition in the paper. It is therefore defined as the change in bundle position AX, that causes a difference in the transducer current AZ = S, (Eq. 1) equal to the r.m.s. current noise NI, resulting fi-om the spontaneous transitions of the channel between its different conductance states (Eq. 2). This means that the accuracy is referred to the noise integrated over the channel’s fill bandwidth. This bandwidth follows fi-om a double Lorentzian in the case of a channel possessing 3 conformational states and is related to its 2 time constants (e.g. [7]). The slowest time constant of the transducer channel can thus be considered to be the effective integration time.

MEASURED AND MODELED MOTION OF FREESTANDING HAIR BUNDLES IN RESPONSE TO SOUND STIMULATION A. J. ARANYOSI AND D. M. FREEMAN Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, M A 02139, USA E-mail: [email protected] Although there has been a long-standing debate about whether hair bundles can be mechanically resonant, existing measurements do not resolve the issue. To test the possibility of resonance, and t o determine which fluid properties are important for deflection of hair bundles, we have made detailed measurements of the sound-induced motion of freestanding hair bundles as a function of frequency. The measurements, which relate hair-bundle deflection 6 t o reticular lamina velocity Ub, show a strong frequency dependence. At low frequencies, H ( f ) = 6/Ub is nearly independent of frequency, with a positive phase. At high frequencies, H ( f ) magnitude falls with frequency at -20 dB/decade, with a phase near -7r/2 radians. A 2D hydrodynamic model accurately predicts both magnitude and phase of H ( f ) with only a single free parameter. A low-pass filter model with two free parameters fits the magnitude of H ( f ) , but predicts a larger phase lag than observed at low frequencies. These results are consistent with the idea that that both viscous and inertial fluid properties drive hair-bundle deflection at low frequencies, while inertial fluid properties drive deflection at high frequencies.

1

Introduction

Hair-cell receptor potentials are initiated by deflections of sensory hair bundles. However, the mechanical processes that cause these deflections are not well understood, particularly in the cochlea. Although computational models provide some insight for example, in most models hair bundle deflection at high frequencies is attenuated by the fluid [l-31 - existing measurements of sound-induced hair-bundle deflection [4,5] do not reveal the physical processes governing hair-bundle deflection, or provide sufficient information to evaluate the predictions of current models. The alligator-lizard cochlea provides a unique opportunity to study the interaction of hair bundles with fluid. Unlike most hair-cell organs, in which hair bundles project into overlying gelatinous structures, the alligator-lizard cochlea has hair cells whose hair bundles project freely into endolymph. Consequently, this system provides a simpler context in which to study hair-bundle dynamics at audio frequencies. In this paper, we present measurements of the sound-induced motion of such free-standing hair bundles in response to acoustic stimulation. The measurements demonstrate that inertial as well as viscous properties of the ~

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fluid determine the motion of hair bundles, and t,hat hair-bundle motion can be accurately predicted with simple hydrodynamic models. 2

Methods

Cochleae from adult alligator lizards were dissected and clamped between two fluid spaces in an experiment chamber. An artificial endolymph was perfused in the apical space, and an artificial perilymph was perfused in the basal space. A piezoelectric disk generated pressures in the basal space to drive motion of the organ. Stroboscopic illumination was used to take images of the cochlea at multiple phases of the acoustic stimulus. This process was repeated at multiple focal planes to generate three-dimensional images of the cochlea in motion. Computer vision algorithms [6,7] were used to extract the three-dimensional motion of both the bases and tips of individual hair bundles. The length and orientation of each hair bundle were determined from the images. The velocity u b of the reticular lamina at the base of each hair bundle was measured in the direction to which the hair bundles are presumed to be maximally sensitive [8]. The deflection of each hair bundle was measured as the difference in displacement of the tip and base of the bundle in this same direction. Hair-bundle rotation 8 was computed from this deflection and the measured hair-bundle height. The measured motions were plotted as the ratio H ( f ) = 8 ( f ) / u b ( f ) , which describes the transformation from velocity at the reticular lamina to rotation of the hair bundle. Measurements were fit with a simple hydrodynamic model [9]. In this twodimensional ‘flap’ model, the hair bundle is represented as a rigid flap attached to the reticular lamina by a compliant hinge. Motion of the reticular lamina drives motion of the fluid, which in turn drives hair-bundle deflection. The model incorporates both viscous and inertial properties of the fluid, assumed to be those of water, to describe H ( f ) . Although this model has two free parameters - the height L and the rotational compliance c b of the bundle - L was fixed at the measured height, so only a single free parameter was allowed. In addition, the model predictions at high frequencies are independent of c b , so at these frequencies the model was entirely deterministic. For comparison, the measurements vs. frequency were also fit with a first-order low-pass filter, for which the free parameters were the cutoff frequency and the low-frequency gain. Because slow drift of the tissue is aliased to the stimulus frequency and its harmonics by the measurement system, measurements with higher harmonic amplitudes within 10 dB of the fundamental were excluded. Although this p r e cedure excludes any potentially non-sinusoidal motions of the hair bundles, our observations were that when visible drift of the tissue was small the motions

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Figure 1. Images of the free-standing region of the alligator lizard cochlea. A: Top-down view as seen through the microscope. The neural edge is to the left, the apical end is toward the top of the image. The bases of several hair bundles are visible toward the left, and the tips of others arc visible toward the right. Individual stereo cilia are resolved. B: Reconstructed cross-sectional view. This image was created by taking a single row of pixels from each of eighty top-down images taken at different focal planes. Individual hair bundles can be seen projecting from the circular basilar papilla. Scale bar =10 /j,m.

were primarily sinusoidal. 3

Results

Three-dimensional images of the basilar papilla in motion were acquired in four preparations. Figure 1 shows some typical images. Both the bases and tips of each hair bundle, and even individual stereocilia, are clearly resolved. As is typical for this region of the alligator lizard cochlea, the hair bundles have no overlying tcctorial structure. From such images taken at multiple phases of the stimulus, measurements of reticular-lamina velocity [/6 and hair-bundle rotation 9 as a function of frequency were made for 136 hair bundles. Of the hair bundles studied, the motions of 24 typically showed no discernible trend with frequency and were not well-fit by the flap model. For an additional 36, H(f) fell with frequency by about —20 dB/decade at all frequencies measured. These measurements were well-fit by the flap model for C& > 108 rad/N, but the precise value of Cb could not be determined. The results reported here are for the remaining 80 hair bundles. For these bundles, H(f) magnitude was constant or increased with frequency at low frequencies, with a phase at or above zero. The best fit of the flap model had 10r < Cb < 108, with a magnitude peak between 0.5 and 10 kHz. Figure 2 shows the magnitude and phase of H(f) vs. frequency for three hair bundles. The magnitudes were mostly between 0.01 and 0.1 rad-s/cm. At low frequencies, magnitudes were largely independent of frequency, and phases were at or

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Figure 2. Measured and best-fit H(f) for three hair bundles. The top plots show the magnitudes, the bottom plots show the phases. The circles represent the individual measurements. The solid line is the best fit of the flap model, using the parameters listed above each pair of plots. The dashed line is the fit when the best-fit compliance c b is doubled, and the dotted line is the fit when c b is halved. Fits were determined using both the magnitude and phase of Wf).

above zero. At high frequencies, magnitudes fell with frequency by about -20 dB/decade, and phases rolled off to radians. The solid lines show the best fit of the flap model to the measurements, made by varying the single free parameter Cb.The fits fell near the measured magnitude and phase at most frequencies. The dashed and dotted lines show the effect of doubling or halving the best-fit compliance, respectively. Note that changing the best-fit compliance does not have a significant effect on the magnitude of the fit at high frequencies. In addition to fits of the flap model, the data were fit by a first-order low-pass filter model. To facilitate the comparison of H ( f) measurements from different hair bundles, the measured H ( f) values were normalized based on each type of fit. Frequency was normalized by the peak frequency of the flap model, or the cutoff frequency of the low-pass filter model, to give a normalized frequency fn. Magnitudes were normalized so that the high-frequency asymptote of each fit fell on the line 1/ fn. Normalization was performed separately for each hair bundle. The resulting normalized transfer function H,( f) is plotted for 80 hair bundles for both types of fits in figure 3. Because the normalization was different for each model, the distribution of data is different in the top and bottom plots. For both methods of normalization, Hn(f) magnitude decreased with frequency above fn = 1, and Hn(f) phase approached at high f n . In this frequency range, both models fit the data quite well. Below fn = 1, the

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Figure 3. Normalized Hn(f) values vs. normalized frequency. The top plots show the magnitude and phase of H , (f) normalized by the fits of the flap model. Dots represent the individual measurements. The solid lines show the predictions of this model. The bottom plots show the magnitude and phase of Hn(f) normalized by the fit of a first-order low-pass filter t o the data. The solid lines show the response of this filter. Because the fitting and normalization were done separately for each hair bundle, the distribution of data differs in the two sets of plots.

measurements were more scattered. Although there were few measurements below fn = 0.5 when the data were normalized to the flap model, most of the Hn(f) magnitudes in this frequency range were larger than predicted by the model. However, the measurements typically showed a phase lead at low frequencies, consistent with the flap model predictions. When the data were normalized to the low-pass filter fits, the measured &(f) magnitudes below fn = 0.5 also fell above the model prediction. In addition, the measured phases were typically more positive than predicted by the low-pass filter model. 4

Discussion

At high frequencies, measured H ( f ) fell with frequency at -20 dB/decade, with a phase near That is, hair-bundle rotation 8 was proportional to the displacement of the reticular lamina. This proportionality indicates that at high

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frequencies, fluid inertia retarded hair-bundle motion such that deflection depended on the inertial rather than the viscous fluid properties. For 36 hair bundles not included in figure 3, this behavior was seen at all frequencies measured. We suspect that these hair bundles were damaged during dissection, so their compliance became large. At low frequencies, hair-bundle deflection appears to be driven by a different mechanism. The magnitude of H ( f ) was roughly constant, suggesting that hair bundles were driven largely by viscous forces. However, the phase was positive, suggesting that the fluid accelerated the hair bundles relative to the reticular lamina. That is, at low frequencies both viscous and inertial forces are important for driving hair-bundle motion, but fluid inertia accelerates rather than retards the hair bundle. To a first approximation, H ( f ) rnagnitudcs wcre described equally well by the flap model and the low-pass filter model. For both models, the measured magnitudes were consistent with model predictions at high frequencies, and somewhat larger than predicted at low frequencies. This difference may be caused by measurement noise: at low frequencies the tip and base of the hair bundle move nearly in phase, so measurements of 8 are the small difference of two large numbers. Noise in the measured 8 can bias the magnitude of H ( f ) to higher values. However, it is possible that processes not considered in the models, such as viscous forces between stereocilia [2], increase hair-bundle deflection at low frequencies. The phase below fn = 1 was well fit by the flap model, but not by the low-pass filter model. In particular, H ( f ) phase was typically positive at low frequencies. The low-pass filter model, in which 8 IX Ub below the cutoff frequency, predicts a phase of zero at low frequencies. However, the flap model predicts a phase lead at low frequencies. Thus the measured phase favors the flap model over the low-pass filter model. At high frequencies, the flap model has no free parameters; the predicted magnitude and phase of H ( f) are determined entirely by the hair-bundle length and fluid properties. Nonetheless, the model accurately predicts both the magnitude and phase of H ( f ) at high frequencies for nearly all hair bundles measured. At low frequencies, only one free parameter is necessary to fit the measurements. In contrast, the low-pass filter model needs one free parameter at high frequencies, and a second at low frequencies. The low-pass filter model is also a ‘black box’ model, while the flap model is physically-based. Thus, the flap model provides a more parsimonious as well as a more accurate description of the measured hair bundle deflections. These measurements show that the fluid properties important for hair-bundle deflection depend on stimulus frequency. Both viscous and inertial properties of

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the fluid play a key role in driving the deflection of hair bundles. This result also confirms the least intuitive prediction of the flap model, that for free-standing hair bundles, hair-bundle deflection leads reticular-lamina velocity at low frequencies. However, the frequency dependence of hair-bundle motion seen in this study does not account for the frequency selectivity seen in hair-cell and auditory-nerve electrical responses to sound.

Acknowledgments

Supported by NIH grant R01-DC00238. A. J. Aranyosi was supported in part by an NIH grant to the Harvard-MIT Speech and Hearing Biosciences and Technology program.

References

1. Freeman, D.M., Weiss, T.F., 1990. Hydrodynamic forces on hair bundles at high frequencies. Hear. Res. 43, 31-36. 2. Zetes, D.E., Steele, C.R., 1997. Fluid-structure interaction of the stereocilia bundle in relation to mechanotransduction. J. Acoust. SOC. Am. 101, 3593-3601. 3. Shatz, L.F., 2000. The effect of hair bundle shape on hair bundle hydrodynamics of inner ear hair cells at low and high frequencies. Hear. Res. 141, 39-50. 4. Frishkopf, L.S., DeRosier, D.J., 1983. Mechanical tuning of free-standing stereociliary bundles and frequency analysis in the alligator lizard cochlea. Hear. Res. 12, 393-404. 5. Holton, T., Hudspeth, A.J., 1983. A micromechanical contribution to cochlear tuning and tonotopic organization. Science 222, 508-510. 6. Horn, B.K.P., Weldon Jr., E.J., 1988. Direct methods for recovering motion. Intl. J. Comp. Vis. 2, 51-76. 7. Davis, C.Q., Freeman, D.M., 1998. Using a light microscope to measure motions with nanometer accuracy. Opt. Eng. 37, 1299-1304. 8. Shotwell, S.L., Jacobs, R., Hudspeth, A.J., 1981. Directional sensitivity of individual vertebrate hair cells to controlled deflection of their hair bundles. Ann. NY Acad. Sci. 374, 1-10. 9. Freeman, D.M., Weiss, T.F., 1990. Hydrodynamic analysis of a twodimensional model for micromechanical resonance of freestanding hair bundles. Hear. Res. 43, 37-68.

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Comments and Discussion J. Howard: What is the Reynolds number associated with hair-bundle motion? Answer: The Reynolds numbers involved are quite low, typically less than one for the velocities we have measured. At these low numbers inertial effects would normally not be important. However, the inertial effects in the flap model come not from the bundle (the only characteristic length available in this model), but from the infinite plate representing the reticular lamina. Velocity of this plate sets up a boundary layer due to the distributed viscosity and inertia of the fluid. This distributed impedance introduces a 45 degree phase lead at low frequencies; also, the relative velocity of the fluid increases as the boundary layer shrinks, increasing hair-bundle deflection. In reality, the basilar papilla is not an infinite plate, and this difference may explain the discrepancies between the measurements and models at low frequencies. H. Duifhuis: I want to compliment you on your approach, but I do not consider the interpretation as final. From your Fig. 3, for example, it appears that, whereas the flap model predicts a better fit for the phase data, the low-pass filter model does so for the amplitude data. Actually, if one would abstract from the physical constraints, all four data sets seem to be fitting a straight line. Answer: Many cochlear models treat hair bundles as either velocity sensors or displacement sensors. Our measurements are not consistent with either of these representations. At high frequencies, the magnitude of H ( f ) = O ( f ) / U b ( f )falls with frequency, indicating that inertial properties dominate hair-bundle deflection. At low frequencies, hair-bundle deflection leads reticular-lamina velocity, indicating that the forces on the hair bundle are viscous as well as inertial. The low-pass filter and flap models have only two and one free parameters, respectively, but still quantitatively match both the magnitude and phase of measured hair-bundle deflection over a wide frequency range. These models highlight the importance of different fluid properties at different frequencies, and are the simplest models that are consistent with our data.

VISCOELASTICITY OF ACTIVE ACTIN-MYOSIN NETWORKS L. LE GOFF AND F. AMBLARD Institut Curie, Physico-Chimie Curie, UMR CNRS/IC 168, 26 rue d'Ulm, 75248 Paris Cedex 05, fiance E-mail: Loic. [email protected] E.M. FURST Colburn Laboratory, Department of Chemical Engineering, University of Delaware, Newark, DE 19716, USA The effect of myosin motor-protein activity on the filamentous actin (F-actin) r h w logical response is studied using diffusing wave spectroscopy.

1

Introduction

The mechanics and dynamics of biological semi-flexible polymers, such as filaments formed by actin proteins, underlie a cell's ability to generate morphology, motility and resist deformation. To date, rheological and dynamical studies of F-actin have relied on probing passive reconstituted systems through either mechanical rheometry, light scattering or microrheological techniques [l]. In frequency regimes governed by single' polymer relaxation, the linear viscoelastic storage G'(w) and loss G"(w) shear moduli scale as G'(w) G"(w) w 3 / 4 , a direct consequence of the dominant stress relaxation by end-to-end response upon f i n e deformation of the polymer. Here, we take advantage of the mechanochemical activity of the singleheaded molecular motor protein myosin S1 to induce local stresses on filaments in a reconstituted network. The act& myosin cycle proceeds perpetually as long as ATP is present. In the absence of ATP, myosin remains attached to filaments with a low dissociation Kd = 500 nM in what is known as the rigor state. N

2

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Methods

We probe the viscoelastic modulus of the actin-myosin network measuring the thermal motion of embedded microsphere[l]. This so-called micro-rheology technique is the Brownian analogy of mechanical rheology. The movement of the microspheres is measured by dynamic light scattering in the multiple scattering regime (Diffusing wave spectroscopy). We plot the complex viscoelastic modulus in terms of its amplitude and phase angle G * ( w ) = Gd(w)eiG("). Within small corrections, 6 is related to Gd by a Kramer-Kroenigs like relation

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Figure 1. A: viscoelastic shear modulus amplitude G ~ ( w and ) B: phase angle 6(w) for 13.7 pM F-actin (open circles) and 5 pM myosin S1 (crossed circles) compared t o actin alone (crosses). During myosin activity (open circles), we observe a new scaling G ~ ( w ) w0,89(represented by a solid line superimposed on the data) corresponding to b(w) ‘v 1.37. After depletion of the ATP reservoir (crossed circles), myosin binds t o actin in the rigor state, with a factor 2 increase in G d ( w ) and similar b(w) compared to actin alone. The passive and rigor scaling agrees with previous reports, G d ( w ) w 3 I 4 (solid line superimposed on rigor data). N

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d(w) [dhGd/dInt]t=a?r,w, which essentially gives the scaling of Gd(w) with respect to w. N

3

Results

Under conditions of saturating motor activity, we find an enhancement of filament fluctuations corresponding to a scaling of the viscoelastic shear modulus Gd(W) w0.89 (s. Fig. 1). As the ATP reservoir sustaining motor activity is depleted, we find an abrupt transient to a passive, “rigor state” and a return to dissipation dominated by transverse filament modes, G ~ ( w ) w0.75. Singlefilament measurements of the apparent persistence length support the notion that motor activity leads to an increase in the effectivetemperature for the Brownian dynamics of filaments (data not shown). Investigation of the dependence on S1 concentration, and interpretation in terms of the molecular mechanisms of acto-myosin interactions have been previously reported [2].

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References 1. Gisler T., Weitz D. A., 1999. Scaling of the microrheology of semidilute F-actin solutions. Phys. Rev. Lett. 82, 1606-1609. 2. Le Goff, L., Amblard, F., F‘urst, E.M., 2002. Excited lifetimes of far-infrared collective modes in proteins. Phys. Fkv. Lett. 88, 018101-1-018101-4.

MECHANICAL STRESSES AND FORCES IN STEREOCILIA BUNDLES OF INNER AND OUTER HAIR CELLS R. MUELLER AND H. MAIER Bundeswehrkrankenhaus Ulm, Dept. of Otorhinolaryngolou, Head and Neck Surgery, Oberer Eselsberg 40, 89081 Ulm, Germany E-mail: [email protected] F. BOEHNIE AND W. ARNOLD Klinikum rechts der Isar, ENT-Department, Technical University of Munich, Ismaninger Str. 22, 81675 Muenchen, Germany E-mail:frank [email protected] The precise mechanism of mechanoelectrical transduction in stereocilia bundles is not known. It is very difficult to measure the extremely small stresses, which occur at the stereocilia bundles. Therefore we developed 3-D finite element models of stereocilia bundles (guinea pig) to obtain quantitative results. The stereocilia bundles of the outer hair cells show a characteristic W-form. Therefore, it is interesting to compare the mechanical behavior of the stereocilia bundle of an outer hair cell with that of an inner hair cell with its linear arrangement. Our analysis provides estimates of forces and stresses on the transducer channels of mammalian hair bundles, although the model does not include active mechanisms yet.

1

Introduction

In order to obtain estimates of the mechanical stresses in the tip-links of the stereocilia bundles of inner and outer hair cells (MC, OHC), finite element models of whole bundles of IHC and OHC were developed. By this means, we are able to quantiQ the stress gradients which occur in tip-links from upper to lower stereocilia. 2

Methods

Based on morphological parameters, the geometry of the W-shaped bundles of OHC stereocilia and the linear arranged stereocilia of M C is futed. Additionally, the tipand side-links of the stereocilia are included (Fig. 1). Their extremely small cross sections are 78.5 x 10 pm2. Young’s modulus of elasticity for the stereocilia is chosen as 20 MPa representing a value for actin filaments. As the tip-links are significantlymore rigid, we chose their Young’s modulus to be 500 MPa. The bundles are statically displaced by a number of discrete forces (F=50 pN) applied to the top of the stereocilia orthogonally to the stereocilia axes.

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Figure 1. Part of an inner hair cell slereocilia bundle showing three rows of stereocilia with different lengths and their connections with tip-links from the top of the two lower stereocilia. The maximum stress is found in the upper tip-links to be 343 kPa.

3

Results and Discussion

The main result is the large difference (factor 3) in stress between the upper and lower tip-links of IHC (maximum stress upper tip-links: 343 kPa, maximum stress lower tip-links: 120 kPa). The corresponding stresses of OHC tip-links are 2.2 MPa (upper) and 1.0 MPa (lower). Therefore we conclude that in the case of excessive noise exposure, those upper tip-links would be destroyed first. Another finding is the similar values of stress in the excitatory and inhibitory directions of displacement. The excitatory stiffness of the OHC bundle is found to be 1.48 mN/m and therefore confirms former experimental results.

TWO ADAPTATION PROCESSES IN AUDITORY HAIR CELLS TOGETHER CAN PROVIDE AN ACTIVE AMPLIFIER A. VILFAN AND T. A. J. DUKE Cauendish Laboratory, Madingley Road, Cambridge CB3 OHE, UK E-mail: [email protected] Two adaptation mechanisms are known t o modify the ionic current flowing through the transduction channels of the hair bundles: a rapid process involves Ca2+ ions binding t o the channels; and a slower adaptation is associated with the movement of myosin motors. We present a mathematical model of the hair cell which demonstrates that the combination of these two mechanisms can produce 'self-tuned critical oscillations', i.e. maintain the hair bundle at the threshold of an oscillatory instability. The characteristic frequency depends on the geometry of the bundle and on the Ca2+ dynamics, but is independent of channel kinetics. Poised on the verge of vibrating, the hair bundle acts as an active amplifier.

1

Introduction

The concept of self-tuned critical oscillations has recently been introduced to explain the remarkable sensitivity, dynamic range and frequency selectivity of auditory hair cells [l], but its physical basis is yet to be established. In this contribution we propose a mechanism based on the two known adaptation processes in hair bundles [2], namely the fast Ca2+-mediated channel closure and the slow adaptation mediated by myosin motors, whereby the first adaptation process provides the amplification while the second one keeps it on the verge of spontaneous oscillation. 2

Results

To describe the transduction channel we use a three-state model [3], with two closed and one open state. The states have different lever arm displacements, with different tensions in the tip link. The free-energy difference between these states additionally depends on the Ca2+ concentration within the stereocilia, as Ca2+ promotes channel closure. The transitions between the channel states are assumed to be faster than the characteristic frequency of the bundle. For a constant Ca2+ concentration, this channel model shows a range of negative stiffness in the force-displacement relation, as observed in [4]. The Ca2+ feedback (the concentration increase due to influx through the open channel), combined with negative stiffness can lead to a dynamic instability and spontaneous oscillations. The existence of oscillations depends on the position of adaptation

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Adaptation motor position (nm)

Figure 1. The bundle deflection as a function of the position of adaptation motors. In the oscillating region the two curves show the maximum and the minimum deflection during a cycle.

motors (Fig. 1). A second, slower, feedback mechanism which detects the voltage oscillations and additionally increases the inside Ca2+ concentration in their presence can control the force exerted by the myosin motors and thus poise the system on the working point with maximum amplification. The characteristic frequency of the bundle depends mainly on two parameters: the viscoelastic relaxation rate of the bundle and the relaxation rate of the Ca2+ concentration. It does not depend on the channel kinetics, therefore a large range of characteristic frequencies can be achieved without its variation. The amplitude of spontaneous oscillations is determined by the Brownian noise and is typically of the order of a few nanometers, which allows detection of stimuli in the sub-nanometer range. If the feedback mechanism is weaker or perturbed, other dynamical regimes are possible. These include the slow relaxation oscillations as observed with saccular hair cells [4]. References 1. Camalet, S., Duke, T., Julicher, F., Prost, J., 2000. Auditory sensitivity provided by self-tuned critical oscillations of hair cells. Proc. Natl. Acad. Sci. USA 97, 3183-3188. 2. Wu, Y.C., Ricci, A.J., Fettiplace, R., 1999. Two components of transducer adaptation in auditory hair cells. J. Neurophysiol. 82, 2171-2181. 3. Corey, D.P., Hudspeth A.J., 1983. Kinetics of the receptor current in bullfrog saccular hair cells. J. Neurosci. 3, 962-976. 4. Martin, P., Mehta, A.D., Hudspeth, A.J., 2000. Negative hair-bundle stiffness betrays a mechanism for mechanical amplification by the hair cell. Proc. Natl. Acad. Sci. USA 97, 1202G12031.

11. Hair cells

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SOME PENDING PROBLEMS IN COCHLEAR MECHANICS P. DALLOS Auditory Physiologv Laboratory, The Hugh Knowles Center and Neuroscience Institute, Departments of Neurobiology and Physiologv and Communication Sciences and Disorders Northwestern University, Evanston, IL 60208, USA E-mail: [email protected] The internal workings of the organ of Corti and their relation to basilar-membrane motion are examined with the aid of several simple models. Assuming that cochlear processing may be approximated as a feedback system, it is asked how dynamic variables are related at different points in the feedback loop. Next, considering the system as two coupled resonances, the influence of one of these subsystems upon the other is investigated as a h c t i o n of coupling between them. Finally, a simple kinematic model of the organ of Corti is examined in the context of transferring displacements from basilar membrane to stereocilia and vice versa.

1

Introduction

The past dozen years have brought remarkable advances in our understanding of the ear’s operation. Of particular note are coherent, experimentally based, theories of transduction and adaptation in hair cells, particularly as they pertain to nonmammalian vertebrates (for summaries see: [l-31). Also, accurate and seemingly complete descriptions of basilar-membrane motion patterns are now available both for the cochlear base and apex (for summary see: [4]).We also start to understand the molecular mechanisms of cochlear homeostasis, fluid and ion-balance (for summary see: [ 5 ] ) . Great strides are made in identifying deahess genes, along with their phenotypes and appropriate mouse models (for summary see: [6]). The motor protein of outer hair cells, prestin, has been identified and some of its unique properties have been elucidated (for summary see: [7]). Yet, age-old questions remain unanswered. Some of these are the subject of the following discussion. 2

Cochlear micromechanics

By definition, micromechanics describes the motions of elements of the organ of Corti and tectorial membrane (TM) that are a consequence of the presumed primary event: motion of the basilar membrane (BM). The aim of micromechanics is to relate the final non-molecular mechanical step, inner hair cell (IHC) ciliary displacement, to its precursor events. This inquiry dates back to ter Kuile [S], with significant contributions by von B6k6sy [9]. In spite of its hundred-year history, the subject is poorly understood; experimental data being scarce, limited, and largely confined to preparations in non-physiological condition. To dramatize the status of

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research on micromechanics, it is sufficient to note that there are no in vivo data available on the internal movements of the organ of Corti and that the prospect of seeing some soon is dim. This lack of information forces us to attempt to deduce intervening processes, aside from in vitro measurements, fiom comparisons between BM motion patterns on the one hand, and neural (e.g., [lo]) or hair-cell responses (e.g., [l 11) on the other hand. Such comparisons produce some interesting results, one of which I examine below. Von Bkkksy emphasized the role of organ of Corti micromechanics in impedance matching. Contemporary formulations of his concern might pose two questions. Assuming that outer hair cell (OHC) somatic motility constitutes the cochlear amplifier [12], how well-matched is the cells’ mechanical impedance to that of the basilar membrane’s? Similarly, if the reciprocal operation of hair-cell transducer channels forms the basis of amplification [13], what are the mechanical impedance relations between cilia and organ of Corti and BM? As a general question, reaching to the heart of inquiries about micromechanics, we need to know: are there multiple resonances, or multiple degrees of freedom, associated with the elements of the organ of Corti and TM. This inquiry is usually answered in the affirmative (e.g., [14-171). However, in vivo experimental evidence might appear as to place severe constraints on implementation. Let us start with this matter. Narayan et al. [ 101 recently published a set of remarkable data demonstrating that, as measured in the same animal, BM and neural tuning curves are indistinguishable around best fkequency. The implication is that, at the best-frequency place, the motion of the BM is fully representative of the process that culminates in neural spike generation. Or,saying it another way, that macro- and micromechanics are so tightly coupled as to make their distinction moot. This is a potentially troublesome conclusion and needs further examination. 2.1

Cochlear micromechanics

Assume first that either OHC somatic electromotility or ciliary processes constitute a feedback mechanism that produces cochlear amplification. A simple linear feedback loop is clearly inadequate fully to represent the interrelated cochlear macro- and micromechanics. However, for the present purpose, we assume as a modification of Mountain et al. [18], that GI in Figure 1 represents BM macromechanics, while G2 stands for micromechanics. The variable x is the pressure gradient across the cochlear partition while variable y is BM displacement. The IHC receptor potential, or its surrogate, neural response is designated u. IHC input is tapped off between the blocks representing micromechanics and OHC. Feedback (z) is assumed to be provided by OHCs. Clearly, the dynamic properties of OHC and IHC receptor potentials, the OHC mechanical feedback process (somatic and/or ciliary motility), and the complex hydromechanical input process to IHCs makes the system exceedingly complex. However, for simplicity, both OHC and IHC transfer functions are taken as unity; so in this case u=z.

99

pressure gradient macro mec h a n i c s basilar membrane motion

Figure I. Feedback representation of cochlear operation.

feedback signal

IHC receptor potential (neural)

If one examines signals at various locations within a feedback loop (Fig. 1), it is evident that the input (x), the output (y), the feedback signal (z) and the error signal (w) are different: l + GtG2

= x-

G,G,

1

w-x1 + C,G2

(1)

In order to emphasize the meaning of these formulae, simple resonant systems are assumed to be represented by Gj and G2 (Fig. 2, left column). The two variables of interest, y/x and z/x are plotted in Figure 2, right column. In the example chosen, G; and Gj are second-order systems that differ only in their resonant frequencies, which are one-half octave apart andjc=l.

50100

50100

0.5

Frequency (kHz)

Figure 2. Two simple resonant elements, G i andG; incorporated in the feedback loop of Fig, 1 (leil) and responses at different points in the loop (right).

100

TO

50100

50

150 100 50 0-

-50

-50-100

roc

-100

I 0,5 1

-150-

5 10

50100

0.5 1

5 10

50100

Figure 3. Two resonant elements, Gt andGj incorporated in the feedback loop of Fig. 1 (left) and responses at different points in the loop (right).

Frequency (kHz) The two variables are significantly divergent, especially in their terminal slopes. The only condition that makes x, y andz equal is the obvious one: G;=C?=1. As is apparent from this somewhat trivial example, measurements at different points in a feedback loop ought to yield different results as long as the constituent elements possess significant dynamic properties in the frequency band of interest. Let us study this problem a bit more. In Figure 3 computations are shown for the case when the two resonant frequencies are again one-half octave apart, the feedback function is the same simple resonant filter as before, but the forward path contains a high-order resonance (5'1'). We see that precise measurements should still be able to discriminate frequency responses at different points in the loop. However, the magnitude plots for variables y and u are similar enough that their differences could be missed. Obviously, it can be difficult to tell apart two steep slopes. Careful highfrequency phase measurements should still separate the different functions. 2.2

Resonant subsystems

Assume next that the BM, organ of Corti, TM system is constituted of two resonant subsystems. One representation would be two coupled mass-stifrbess-damping systems. One can examine the motion of elements in one of these systems and inquire about the detectability of influence by the second. Results of some computations are demonstrated in Figure 4. The curves provide magnitude of motions of the mass-elements in both systems. One system is a simple resonance at 1000 Hz (dark curve), whereas the other is a composite of 10 parallel mass-stiffnessdamping elements. In the latter, the resonant frequencies of the individual branches range from 1322 Hz to 1592 Hz, with the composite peaking at 1445 Hz (light curve). It is assumed that the two systems are coupled by a spring. By changing the

101

stiffness of the spring, one adjusts the coupling between the two systems. Computational results are shown for four cases: weak and very strong coupling, and for two intermediate cases. As expected, in the weak-coupling case the responses of the two systems are essentially independent, as one system does not affect the response of the other. In all other cases the two systems influence one another's response to varying degrees. This is manifested by a strong influence on the resonance frequencies of the systems, as well as non-monotonicities in the response of the higher order system. The computations suggest that, for a range of intermediate coupling, the presence of one subsystem might be detectable in the response pattern of the other. The most interesting situation is reflected in the "strong coupling" case. Here, while the simple system influences the response of the complex one, if one were to measure only the latter, it is not likely that the simple system's presence could be detected. weak coupling 1DOD

gj o

^^

\

medium coupling

2001

1000

2000

strong coupling 10011 20CM

very strong coupling ion me

\

1000

0-

MOD

Frequency (Hz) Figure 4. Responses of two coupled resonant systems with different degrees of coupling.

2.3

Organ ofCorti mechanics

Next, we consider the relation between BM displacement and cilia displacement. A simple representation of the mechanical system to be modeled is given in Figure 5. The BM and pillar cells are represented as a rigid frame, hinged at the insertion into the osseous spiral lamina (OSL). The reticular lamina (RL) is assumed to be a rigid beam hinged at the top of

L'I-V.

Figure 5. Simplified schematic diagram of organ of Corli components (not to scale).

102

the pillar cells. The TM is also taken as a rigid beam; it rotates around its attachment at the spiral limbus (SL). OHCs and Deiters' cells are represented as a spring. Finally, a single ciliary bundle is hinged between reticular lamina and TM. The analysis is an update of the work of mo d e and Geisler [19]. Rotational stiaesses are assigned to the TM (k2), the base of the cilium (k3),and the rotational center of the reticular lamina at the pillar-head (k,). A simple stiffness is assigned to the BM (KO),as well as to the OHCs ( K J . The TM also possesses a simple radial stif€hess (K2). The input is a linear deflection of the BM under the OHC (6), while the output is the angular position of the cilia (7112-a). All elements are assumed to be inertialess and no damping is considered. A Cartesian coordinate system is placed so that the origin corresponds to the center of rotation of the TM. Initial computations assume that KO=k2=k3=KFO Object Dimension and kl=K2=m. In other words, springs K,,,k2,k3and K4 are ignored and the reticular lamina-pillar junction and TM are made rigid. As the BM is deflected by 6, the bottom of the cilium moves fi-om its resting coordinate (Ll,-x,) to a new location (Xl,Yl). To 128 obtain the coordinates of the new position of the top A-x, of the cilium (X2,Y2), one solves the simultaneous XO 1.9 equations for the intersection of two circles, one formed by the rotation of the TM around the origin, the other by the rotation of the cilium around (Xl,Yl). The analytical solution is complex, consequently we demonstrate numerical results obtained with Mathematicam. Approximate organ of Corti dimensions for the basal turn of the gerbil are derived fiom data obtained fiom unfmed hemicochlea material ([20] and unpublished data), ciliary height is taken fiom Wright ([21] and Strelioff and Flock [22]); they are given in the Table above. Figure 6 demonstrates computational results. In the top panel, the change in cilia angle (fiom the resting 90") is given as a fictio n of BM displacement (6). The middle panel gives angular gain (in dB), obtained as the ratio of cilia angle (nR-a) and BM angle (cp) at a given 6. Finally, in the bottom panel the ratio of cilia anglechange and BM displacement is plotted. We note that the range of BM deflections is severely limited. This is imposed by the known range of angular rotation of the ciliary bundle between the limits where most mechanotransducer channels are either open or closed [23]. Taking this limit as *lo, the corresponding useful range of excursions of the BM is f 32 nm,a remarkably small number. The angular gain, (d2-a)/cp7 is -24 dB at small displacements, and the ratio of angle-change and BM displacement is -32 O/pm. If the springs are incorporated, the above gain becomes a complex function of the variously transformed stifbesses and the geometry of the floating lever system of Figure 5. The corrected gain will be lower than the figure obtained above for the rigid organ of Corti. We now consider some aspects of this, more realistic, case.

pi

103

2.4

Computations with springs

The rigid-beam, or even a lumped-parameter representation of the TM is an approximation at best [24]. Nevertheless, there is sufficient information available to estimate the value of the TM’s sti&ess as seen by the stereocilia, and thus assess the validity of the mode of ciliary displacement as modeled here. Abnet and Freeman [24] provide the most comprehensive data for the material properties of the TM and Emadi et al. [25] deliver evidence that stifkess properties are cochlearlocation dependent. Zwislocki and Ceferatti [26] demonstrated that the TM’s radial and transversal stiaesses are approximately the same. The space constants of the TM are 27.1 pm in the longitudinal and 20.7 pm in the radial directions [24]. Within this rectangular area there are -3.3 outer hair cells. From [25] we have for the basal TM radial stifhess 0.3 N/m, obtained with a 20 pm diameter probe. Scaling this to the 20.7-times-27.1 pm’ area, we obtain 0.54 N/m applicable stifkess. From the work of Strelioff and Flock [22], we obtain the translational stifhess of an average single basal-turn ciliary bundle as -0.03 N/m. Then, the combined stifkess of 3.3 OHC ciliary bundles is 0.099 N/m. Clearly, the TM stifhess is greater than the ciliary stifkess, consequently the model used is acceptable. For computational purposes, all stifbesses are derived for a spatial extent that corresponds to the 3 &-down spatial bandwidth fi-om traveling wave measurements obtained at low sound levels by Nilsen and Russell [27]: -260 pm. This segment is approximately 3.8 OHCs wide, or 49.4 pm. Let us now catalogue all necessary stifiess values and the means of deriving them. The measured stifhess at the midpoint of the BM’s pectinate zone is 1.1 N/m, obtained with a 20-pm diameter probe [28]. When the 3-dB spatial bandwidth is taken into account, we obtain K0=45.7N/m. When electrically stimulated, an OHC moves the reticular lamina approximately -8.5-times more than the BM (at least in the apex [29]). Consequently, K, +

K2K3 ~

K2 + K 3

- KO

= -= 5.37 N/m 8.5

where Kl is the translational stifhess of the reticular lamina, K2=kJL12, is that of the TM, and K3 is that of the ciliary bundles. In the equation, we readily obtain K3 fi-om [22] by scaling single cilia-bundle stifhess to the number of OHCs within the spatial bandwidth. The parallel translational cilia stifhess of 24 rows of OHCs (260 pm), 3.8 cells per row, is 2.74 N/m. The TM’s stifhess in the basal turn is 0.3 N/m, obtained with a 20-pm diameter probe [25]. From this, we compute for the 260-pm length, 3.8 hair cells wide: K2=12.46 N/m. With these values, Kl, the reticular lamina translational stifkess is obtained fi-om Eq. 2 as 3.12 N/m.

104

The individual OHC somatic stifkess, extrapolated to the cochlear base, is 1 8 ~ 1 0 N/m ‘ ~ [30]. The parallel axial stifkess of 24 rows of OHCs (260 p), 3.8 cells per row, is K4=l .64 N/m. If springs are included, the ratio of angular rotations of the reticular lamina (y) and BM (q)will be largely controlled by the stiffness-divider:

Substitution into Eq. 3 yields a ratio of 0.24. Inclusion of springs thus diminishes reticular lamina angle. However, any reduction in y l q has minimal effect on ciliary angle. The reason is that the radial motion of the reticular lamina is largely controlled by the displacement of its attachment point at the pillar head, its rotation being of secondary importance. Thus the plots of Figure 6 change little due to the reduction in reticular lamina rotation. (It is noted parenthetically that a simple approximation of ciliary angle may be had by assuming that it is only the radial motion of the bundle’s base that causes the angle change. In this case, a= cos’[h(sin cp)/xJ=cos-’[hS/~L,]. Plots based on this approximation are included in Figure 6 with thin lines.) Finally, we ask what happens if the driving 1 2 3 force comes not fkom the BM but fkom “active” -3 OHCs or fkom “active” cilia. One can compute, based on the simple rigid configuration of Figure 5, that a 1 - p lengthchange of OHCs would produce 0.6” ciliary angle change and a corresponding 0.025-pm 1 y 3 5 y displacement of the BM. The approximate .c 341 effect of incorporating springs is a 0.23-times 33/ ,/ reduction in the above numbers. Thus, a I-pm _L ,.--_,_ OHC length change produces 4.14” ciliary -3 -2 -i.--+--iz 3 angle change and -5.8 nm displacement of the / i, 5 40;i BM. It is recalled that the sensitivity of OHC LA-:..

_._>

y31)

motile response is -20 nm/mV. Consequently, , a one millivolt OHC membrane-potential \ a fi 30 change is expected to produce 4.003O cilia rotation and -0.12-nm BM displacement. 3 In the rigid organ of Corti representation, -3 -2 the gain of transformation fi-om single hair cell Basilar m m b r m e displacement ( I J ~ ciliary angle-change to reticular lamina radial displacement is xosin[pi/2-a]. T h q a full 1” Fiere 6. Computational results O f O r k W of Corti kinematics. rotation of the bundle would produce -33 nm 7

-

105 radial reticular-lamina displacement at the base of the ciliary bundle and -31.2 nm BM movement. These transformations need to be modified, however, by taking into account the driving and load stiffnesses. For the reticular lamina, the approximate multiplier is obtained as:

K?

(4)

Substitution gives a value of 0.44, yielding -14.6 nm reticular-lamina displacement for each degree of cilia rotation. Computation for the BM produces an additional multiplier in the approximate form:

with the value of -0.094, giving a total reduction vis-a-vis the rigid frame of 0.041fold. Consequently, the resulting BM displacement is -1.29 nm for each degree of cilia rotation. 3

Conclusions

The questions posed above are not original. Many of our colleagues have concerned themselves with similar inquiries. A particularly lucid exposition is by Allen and Neely [3 I]. Here I am simply revisiting some timely issues. Our first question pertained to the implications of the Narayan et ul. [lo] data for the nature of cochlear micromechanics. A few simple simulations of feedback and coupled systems implied that, in magnitude plots, it might be easy to overlook the influence of a subsidiary system upon the principal system's response. This is especially the case for strong coupling. Detailed comparisons of phase Characteristics at different measuring locations ought to distinguish system components possessing different dynamic properties. Such comparisons, based on in vivo measurements, are as yet lacking. Inner hair cell receptor potentials are more suitable for such measurements than neural spike trains. In the second inquiry I studied the relation between stereocilia deflection and BM displacement. A greatly simplified kinematic model was examined. Several conclusions arise fiom the use of the model. First, due to the floating lever system embodied in the organ of Corti elements, there is a significant transformer action present, as envisioned by von Bekksy. The transfonner gain was estimated for the basal turn as -32' ciliary-angle change for each pm of BM deflection. The consequence of this high gain is a very limited permissible dynamic range of BM

106

deflections, if cilia deflection is to be maintained within its normal operating range of approximately f 1-2". Further considerations indicated that, if reasonable estimates of stifkess magnitudes are taken into account, all components are fairly well-matched. Thus, BM displacement is effectively transferred to cilia rotation. Also, the TM can be construed as stifhess-controlled at low fi-equencies and it is capable of restraining the cilia. Further, somatic motility of OHCs can produce cilia deflection, with an estimated gain of O.O03"/mV membrane potential change. At threshold, the receptor potential is -1 mV and the BM displacement is -2 nm. The latter corresponds to a cilia angle of 0.005", to be compared to that produced via OHC somatic motility by a 1 mV receptor potential, -0.003". Clearly, OHC motile response can be effective. Finally, the mismatch between cilia and organ of Corti stifkesses does not appear to be great enough to prevent cilia deflection, due to ciliary motility, by the organ of Corti load. Of course, the transduction process itself could be further affected by processes indigenous to the cilia without significant reflection in BM motion. The latter would be quite small, about 1.3 nm for a full degree of cilia rotation. Deriving an estimate for active bundle angle-change at threshold of -lo-' degrees (fiom displacement of -0.37 nm:Ref. [32]), gives 13-pm BM displacement. This value is probably too small to be reflected in sound-pressure driven motion. Acknowledgments Supported by NIH Grant DC00089. I thank Drs. M.A. Cheatham and C.-P. Richter for their comments.

References 1. Hudspeth, A.J., 1997. How hearing happens. Neuron 19,947-950. 2. Fettiplace R., Fuchs, P.A., 1999. Mechanisms of hair cell tuning. Ann. Rev. Physiol. 61,809-834. 3. Gillespie, P.G., Walker, R.G., 200 1. Molecular basis of mechanosensory transduction. Nature 413, 194-202. 4. Robles, L., Ruggero, M.A., 2001. Mechanics of the mammalian cochlea. Physiol. Rev. 81, 1305-1352. 5. Wangemann, P., Schacht, J., 1996. Homeostatic mechanisms in the cochlea. In: Dallos, P., Popper, A.N., Fay, R.R. (Eds.), The Cochlea. Springer, New York, pp. 130-185. 6. Steel, K.P., Kros, C.J., 2001. A genetic approach to understanding auditory function. Nat. Genet. 27, 143-149. 7. Dallos, P., Fakler, B., 2002. Prestin, a new type of motor protein. Nature Rev. Mol. Cell Biol. 3, 104-111.

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8. ter Kuile, E., 1900. Die Ubertragung der Energie von der Grundmembran auf die Haarzellen. Pfliig. Arch. Ges. Physiol. 79, 146-157. 9. Bkkesy, G. von, 1960. Experiments in Hearing. McGraw-Hill, New York. 10. Narayan, S.S., Temchin, A.N., Recio, A., Ruggero, M.A., 1998. Frequency tuning of basilar membrane and auditory nerve fibers in the same cochleae. Science 282, 1882-1884. 11. Cheatham M.A., 1993. Cochlear h c t i o n reflected in mammalian hair cell responses. Progr. Brain Res. 97, 13-19. 12. Nobili, R., Mammano, F., Ashmore, J., 1998. How well do we understand the cochlea? Trends Neurosci. 2 1, 159-167. 13. Hudspeth, A.J., 1997. Mechanical amplification of stimuli by hair cells. Cur. Opin. Neurobiol. 7 , 4 8 0 4 6 . 14. Allen, J.B., 1980. Cochlear micromechanics - a physical model of transduction. J. Acoust. SOC.Am. 68, 1660-1670. 15. Zwislocki, J.J., 1980. Five decades of research on cochlear mechanics. J. Acoust. SOC.Am. 67, 1679-1685. 16. Neely, S.T., 1993. A model of cochlear mechanics with outer hair cell motility. J. AcOust. SOC.Am. 94, 137-146. 17. Gummer, A.W., Hemmert, W., Zenner, H.-P., 1996. Resonant tectorial membrane motion in the inner ear: its crucial role in fi-equency tuning. Proc. Natl. Acad. Sci. USA 93, 8727-8732. 18. Mountain, D.C., Hubbard, A.L., McMullen T.A., 1983. Electromechanical processes in the cochlea. In: de Boer, E., Viergever, M.A. (Eds.), Mechanics of Hearing. Martinus Nijhoff, Delft, pp. 119-126. 19. Rhode, W.S., Geisler, C.D., 1966. Model of the displacement between opposing points on the tectorial membrane and reticular lamina. J. Acoust. SOC. Am. 42, 185-190. 20. Edge, R.M., Evans, B.N., Pearce, M., Richter, C.-P., Hu, X., Dallos, P., 1998. Morphology of the unfixed cochlea. Hear. Res. 124, 1-16. 21. Wright, A., 1984. Dimensions of the cochlear stereocilia in man and the guinea pig. Hear. Res. 13,89-98. 22. Strelioff, D., Flock, w., 1984. Stiffness of sensory-cell hair bundles in the isolated guinea pig cochlea. Hear. Res. 15, 19-28. 23. Hudspeth, A.J., Corey, D.P., 1977. Sensitivity, polarity, and conductance change in the response of vertebrate hair cells to controlled mechanical stimuli. Roc. Natl. Acad. Sci. USA 74,2407-24 1 I. 24. Abnet, C.C., Freeman, D.M., 2000. Deformations of the isolated mouse tectorial membrane produced by oscillatory forces. Hear. Res. 144,2946. 25. Emadi, G., Richter, C.-P., Dallos, P., 2002. Tectorial membrane stiffhess at multiple longitudinal locations. Abstract #906 of the 25. Midwinter Meeting of the Association for Research in Otorhinolaryngology, St. Petersburg Beach, Florida, USA.

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26. Zwislocki, J.J., Cefaratti, L.K., 1989. Tectorial membrane 11: Stiffhess measurements in vivo. Hear. Res. 42,2 1 1-228. 27. 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. USA 97, 11751-1158. 28. Emadi, G., Richter, C.-P., Dallos, P., 2002. The hemicochlea as a tool for measurement of mechanics in the passive cochlea Abstract #907 of the 25. Midwinter Meeting of the Association for Research in Otorhinolaryngology, St. Petersburg Beach, Florida, USA. 29. Mammano, F., Ashmore, J.F., 1993. Reverse transduction measured in the isolated cochlea by laser Michelson interferometry. Nature 365, 838-84 1 . 30. He, D.Z.Z., Dallos, P., 2000. Properties of voltage-dependent somatic stiffhess of cochlear outer hair cells. J. Assoc. Res. Otolaryngol. 1, 64-8 1. 31. Allen, J.B., Neely, S.T., 1992. Micromechanical models of the cochlea. Physics Today 45,40-47. 32. 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. USA. 95, 15321-15326. Comments and Discussion D.O. Kim: Peter, I enjoyed your presentation very much. You set up a very good framework to address an important issue. I want to make a suggestion regarding how your analysis may be extended to the organ of Corti in a dynamic situtation. Let us consider the impedance, Zs(f), of an internal power source. The latter may be the hair bundles or the somata of outer hair cells (OHC). We will call the impedance of the load (the rest of the organ of Corti), ZL(f). An impedance, Z(f), as a fhnction of frequency, f, has a resistive part, R(f), and a reactive part, X(f); Z(f) = R(f) + iX(f), X(f) = (27cPM-W(27cf)), R = resistance, M = mass, K = stifhess, i = (-i)O5. The reactive part will approach zero for fiequency near the resonant frequency, fo = (1/ 2 n ) * ( ~ ) 0 . 5 . Power transfer from a source to a load is optimal when Zs(f) is a complex conjugate of ZL(f). Accordingly, the requirement of matching the two impedances would be much facilitated if the two resonant frequencies are matched, i.e., if Ks/Ms is similar to KLML, whereby the reactive parts of the source and load both approach zero near the resonant frequency; the subscripts S and L represent the source and load, respectively. In this consideration, the requirement is not to match Ks with KL but to match KsMs with KL/ML. The absolute values of Ks and KL may be allowed to have a mismatch of orders of magnitude. For example, let us consider the situation where the OHC hair bundle is postulated to be the active power source. We may estimate the value of ML/Msfrom the corresponding ratio of the two volumes, those of the organ of Corti and the hair

109

bundle of one OHC in a transverse slice of the organ of Corti. This volume ratio would be large, say 1000. Then, the optimal KL& should be 1000 rather than unity. That is, the optimal stiikess of the hair bundle of one OHC, in this case, should be one thousandth of KLrather than KL. The above consideration applies to the condition where the stimulus fiequency is equal to the resonant fiequency, 4. Even if the stimulus fiequency is away fiom fo, the above consideration can still make a substantial difference if the stimulus frequency is within a limited range of frequncies, say within one octave, around fo.

Editor's comment: refer also to the comment by E.S. Olson in the Discussion session, pp. 576-577.

FUNCTIONAL PROPERTIES OF PRESTIN - HOW THE MOTORMOLECULE WORKS WORK B. FAKLER AND D. OLIVER Department of Physiologv II, Hermann-Herder-Str.7,79104 Freiburg,Germany E-mail: [email protected] Outer hair cells (OHC) of the mammalian cochlea exhibit electromotility that occurs at acoustic frequencies and is thought to produce the amplification of vibrations required for the high sensitivity and fiequency selectivity of the mammalian hearing organ. Recent work showed that electromotility is brought about by voltage-driven conformational changes of prestin, a member of the SLC26 family of anion transporters, which is highly expressed in the lateral membrane of the OHC. Prestin binds intracellular anions, predominantly chloride, and uses them as a voltage-sensor. Thus, anions are translocated across the membrane, a process that promotes the structural rearrangements that change the width of prestin in the membrane plane. Accordingly, voltage sensitivity of prestin is strongly affected by the anion species present on the cytoplasmicside as well as by the concentrationof the respective anion.

1

Introduction

Outer hair cells (OHC) of the mammalian cochlea actively change their cell length in response to changes in membrane potential [l]. This electromotility occurs at acoustic frequencies and is assumed to produce the amplification of vibrations in the cochlea that enables the high sensitivity and frequency selectivity of the mammalian hearing organ [2,3]. Electromotility results from a protein in the OHC basolateral membrane that undergoes structural rearrangements in response to changes in the transmembrane voltage. Coupling of protein conformation to transmembrane voltage is mediated by a charged 'voltage-sensor' within the protein that moves through the electrical field and thus gives rise to a non-linear capacitance ('gating current'; NLC). Recently, Dallos and coworkers identified prestin, a gene coding for an integral membrane protein of OHCs [4]. Upon heterologous expression, prestin reproduces the 'piezoelectrical' properties of the OHC motor protein: (i) it generates mechanical force with constant amplitude and phase upon electrical stimulation up to a stimulus frequency of at least 20 kHz, (ii) the voltage-dependence of its NLC is shifted in response to mechanical stimulation [ 5 ] . 2

Methods

Phase-sensitive capacitance measurements in excised patches from rat OHCs were used to characterize charge movement produced by prestin's voltage sensor (for details see [6]). Briefly, lock-in phase angles, yielding signals proportional to

110

111

changes in C, and conductance, were calculated by dithering the C,-compensation setting of the patch-clamp amplifier by 100 @. Capacitance was then calibrated by again changing the C,-compensation setting. Command sinusoid (f = 2.6 kHz; 10 mV) was filtered at 8 kHz with an 8-pole Bessel filter, and 16 periods were averaged to generate each capacitance point. To obtain the voltage dependence of membrane capacitance, voltage ramps were summed to the sinusoid command. Capacitance was fitted with the derivative of a first-order Boltzmann function,

where Cli, is residual linear membrane capacitance, V is membrane potential, Qmaxis maximum voltage-sensor charge moved through the membrane electrical field, V1,2 is voltage at half-maximal charge transfer and a is the slope factor of the voltage dependence. Processing and fitting of data was performed with IgorPro; all data are given as mean f SD. 3

Results

Motivated by the failure in identifying a charged residue as the voltage-sensor of the prestin molecule via site-directed mutagenensis [7], we removed mobile charges, i.e. the usual bulk ions of the solutions contacting the intra- and extracellular surfaces of prestin. Cations and anions on either side of the membrane were replaced by Nmethyl-D-glucamine (NMDG’) or tetra-ethyl-ammonium (TEA+) and pentanesulfonate or sulfate, respectively. These experiments demonstrated that NLC and, concomittantly, electromotility were reversibly eliminated by removing chloride ions (Cl-) kom the cytoplasmic side of the membrane. In contrast, NLC was not affected by exchange of cations. More detailed analysis subsequently showed that (i) about 6 mM C1- was required for half-maximal activation of prestin, that (ii) quite a number of other monovalent anions (small anorganic anions as well as carboxylic acids) effectively promoted NLC, but divalents failed to do so, and that (iii) the voltage-dependence (slope) of NLC in the presence of all small anorganic anions tested matched that of Cl- (ao 35 mV), while it considerably decreased with chain length in carboxylic acids [7]. Furthermore, replacement of either anions or cations on the extracellular side of the membrane did not affect NLC mediated by prestin. The specific requirement of small intracellular monovalent anions suggested that prestin function depends on the translocation of an anion through the membrane electrical field without dissociation kom the protein into the external solution; in other words, anions undergoing an ‘incomplete transport cycle’ work as prestin‘s

112

voltage sensor. These findings and the resulting model as well as other molecular hallmarks of prestin have been reviewed in detail in the recent past [S]. In addition to these results, Figures 1 and 2 summarize some aspects of NLC with respect to anion species and concentration, that were obtained in recent experiments: (i) the maximal charge transfer (Q-) observed with a series of small A Cnowlin (fF)

*0°

1 I

.-

100 -

0 -1 50

-1 00

-50

0

50

membrane potential (mV)

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Figure 1 . Q- and V1/2 as a function of the anion species present at the cytoplasmic side of prestin. A: NLC was measured in an inside-out patch from a rat OHC with the anions indicated as the only anion present at the cytoplasmic face of the patch ([A1 = 150 mM). Note that both, amplitude and VI/Zchange with the anion species. Continous lines are fits of equation (1) to the data. B: Dependence of the amplitude of NLC on anion species, derived from experiments as in (A). Total charge moved (Q-) was derived from fits to equation (1) and normalized to the value with Cf in each patch. C: Dependence of Vl/z on anion species, derived from the same set of data as in @). A V V is ~ the difference in VVZwith respect to the value with C1- in each patch.

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Figure 2. Dependence of V1/2 on the CI- concentration. A: NLC measured in an excised patch with the and V1/2 vary with [CI-] as indicated present at the intracellular side of the patch. Note, that both, CnOa-lm [Cl-1. Sulfate was substituted for CI- such that a constant ionic strength was maintained. NLC from the same patch prior to excision is labelled 'cell-attached'. B: Summary of V1/2 data from 4 patches, measured as in (A).Straight line indicates a fit of a logarithmic function to the data. AVl/2 is the difference in Vl/z with respect to the value with 150 mM Cf in each patch.

monovalents was found to depend on the anion species (Fig. 1A) and to be systematically correlated with the voltage for half-maximal charge transfer (V112; Fig. 1B); (ii) the V1,2value strongly depended on the anion concentration present at the cytoplasmic side of the prestin molecule. Surprisingly, the hyperpolarization required to drive the molecules into their elongated state increased with an increasing concentration of the intracellular anion (Fig. 2). 4

Discussion

The above data on prestin's behaviour with respect to voltage and ion species support a model in which the intracellular anions Cf and HCOY act as the voltagesensor of prestin [7,8]. After binding to a site with millimolar affinity, these anions are translocated across the membrane by the transmembrane voltage: towards the extracellular surface upon hyperpolarization, towards the cytoplasmic side in response to depolarization. As a consequence, this translocation triggers conformational changes of the protein that finally change its dimensions in the plane of the plasma membrane. The area occupied by prestin decreases when the anion is near the cytoplasmic face of the membrane (short state, equivalent to cell

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contraction), it increases when the ion has crossed the membrane to the outer surface (long state equivalent to cell elongation). Thus, prestin works as an ‘incomplete transporter’ that shuttles anions across the membrane without allowing them to dissociate at the extracellular surface of the cell. A refined model will have to account for the dependence of the properties of NLC (VIRin particular) on anion species and concentration.

References 1. Brownell, W.E., Bader, C.R., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses in isolated cochlear outer hair cells. Science 227, 194-196. 2. Dallos, P., 1992. The active cochlea. J. Neurosci. 12,4575-4585. 3. Frank, G., Hemmert, W., Gummer, A.W., 1999. Limiting dynamics of highfiequency electromechanical transduction of outer hair cells. Proc. Natl. Acad. Sci. USA 96,4420-4425. 4. 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, 149-155. 5. Ludwig, J., Oliver, D., Frank, G., Klbcker, N., Gummer, A.W., Fakler, B., 2001. Reciprocal electromechanical properties of rat prestin: the motor molecule fiom rat outer hair cells. Proc. Natl. Acad. Sci. USA 98,4 178-4183. 6. Oliver, D., Fakler, B., 1999. Expression density and fimctional characteristics of the outer hair cell motor protein are regulated during postnatal development in rat. J. Physiol. 5 19, 79 1-800. 7. Oliver, D., He, D.Z., Klbcker, N., Ludwig, J., Schulte, U., Waldegger, S., Ruppersberg, J.P., Dallos, P., Fakler, B., 200 1. Intracellular anions as the voltage sensor of prestin, the outer hair cell motor protein. Science 292,2340-2343. 8. Dallos, P., Fakler, B., 2002. Prestin, a new type of motor protein. Nat. Rev. Mol. Cell Biol. 3, 104-111.

Comments and Discussion J. Howard: You argue that prestin is an “incomplete transporter”. What kind of transporters are the prestin-family proteins (symport, antiport), and can you rule out that it is not a transporter? Answer: Data on anion transport properties of members of the SLC26A family are still very sparse. These transporters appear to be passive, but detailed data with respect to transport mechanisms are not available. Interestingly, the anion selectivity established for pendrin (SLC26A4) is very similar to the anion specificity that we found for charge movement by prestin. We do not find an influence of extracellular anion concentration on non-linear capacitance, indicating that there is no access to

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the intracellularly accessible anion binding site(s) fkom the extracellular side. This suggests that prestin does not mediate anion flux across the membrane, or that transport rates are very low compared with the charge translocation rates that we measure. C.-P. Richter: It has been demonstrated that Gd3+,a three times positively charged ion, interferes significantly with outer hair cell motility. Are you able to comment on the mechanisms of Gd3+within the scope of your model?

Answer: Gd3+ acts ftom the extracellular side and our data and model do not provide a clue to its action on charge movement and electromotility. However, Gd3+ is known to block quite a number of different ion channels with low structural similarity, thus it may act in a relatively unspecific way.

ALLOSTERIC MODULATION OF THE OUTER HAIR CELL MOTOR PROTEIN PRESTIN BY CHLORIDE V. RYBALCHENKO AND J. SANTOS-SACCHI Yale University School of Medicine, Otolaryngologv and Meurobiology, BML 244, 333 Cedar Street, Mew Haven, CT 06510, USA E-mail:[email protected] A variety of ionic channels control cationic content of outer hair cells (OHC). However, little is known about mechanisms that control intracellular anions. In this work we demonstrate that monovalent anions (CI-) and cations (K+, Na+) can permeate the OHC membrane through a voltage dependent, aniodcation non-selective pathway. Moreover, CI- flux through these putative channels sufficiently modulates intracellular C1- concentration to influence the behavior of the OHC membrane motor protein prestin. Depletion of OHC intracellular and extracellular C1- ions does not eliminate the OHC’s nonlinear capacitance that derives from the molecule’s mobile charge. That is, total charge, Q- was not reduced upon intracellular and extracellular CI- substitution by HEPES for prolonged periods of time. Additionally, following intracellular Cl- substitution by the divalent anion sulfate, the apparent valence of prestin’s mobile charge was stable (0.7-0.8) and Qmaxremained substantial. Our data argue against the hypothesis that C1- is an exogenous voltage sensor for prestin.

1

Introduction

Electromotility of outer hair cells (OHCs) is believed to enable mammals to discriminate high ffequency sounds. There exist several models to explain this voltage dependent motility. One of them suggests that cell elongatiodcontraction results fiom OHC surface area changes produced by voltage-dependent resizing of intrinsic plasma membrane structures. This model obtained strong support after successll cloning and transfection of the voltage-sensitive protein prestin [11, abundantly expressed in the OHC lateral wall and responsible for OHC membrane surface changes up to 11% [2]. The model posits that the molecular size of prestin varies for different conformational states primarily depending on transmembrane potential. Transitions between different conformational states occur due to the voltage-driven translocation of prestin’s charged residue within the membrane and normal to its plane. This mobile intra-membrane charge contributes a large nonlinear component (C,) to the total OHC membrane capacitance (Cm), which can be monitored to study molecular events pertaining to OHC motility. The origin and location of prestin’s mobile charge is not clear. It has recently been shown that a C1presence at the inner aspect of the plasma membrane is necessary to maintain normal prestin voltage sensitivity [3]. Analogous to some types of Cl- channels, those authors hypothesized that the C1- ion itself functions as the mobile “gating” charge of prestin. In this article we present results of our experiments that challenge the

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gating role of Cl-. Rather, our data indicate that C1- ions function as allosteric modulators of prestin’s intrinsic voltage sensor mechanism.

2

Methods

OHCs were isolated fiom apical turns of the guinea-pig organ of Corti after 15 min treatment with dispase (1 mg/ml). Voltage-clamp recordings were performed at room temperature using an Axopatch 200B amplifier controlled with the patchclamp software program jClamp (SciSoft, CT). To monitor OHC membrane resistance and to record currents in the absence of major physiological ions, TrisHEPES based intracellular (mM: HEPES-190, EGTA-10, MgS04-2; pH -> 7.25 with TrisOH, 310 mOsm) and extracellular (mM: HEPES-210, MgS04-5, CaS0,0.2; pH -> 7.30 with TrisOH, 3 15 mOsm ) solutions were used. To evaluate the nonselective, voltage-dependentconductance, currents were measured in the presence of equal amounts of monovalent ions in extracellular solution: (80 mM C1-) HEPES108, TrisC1-80, MgS04-5, CaS04-0.2; (80 mM K+) HEPES-220, KOH-80, MgS045 , CaS04-0.2; (80 mM Na’) HEPES-220, NaOH-80, MgS04-5, CaS04-0.2. The pH and osmolarity were adjusted with HEPES/Tris to match those values in the reference (Tris-HEPES) solution. Membrane resistance 1-3 GR, and series resistance 7-20 MR were typical for OHCs in reference solutions. Cm vs. Vm (C-V) functions were measured using a two-sine voltage stimulus (20 mV peak at 390.6 and 781.2 Hz) [4] superimposed on linear voltage ramps. Prestin mobile charge translocation was approximated with a Boltzmann function:

where Qmax - total prestin-mediated mobile charge, z -apparent valence, e - electron charge, V,-membrane potential, Vh - half maximal charge transfer potential, k Boltzmann’s constant and T - absolute temperature. Qmm, z and Vh values were obtained fiom dQ/dVm fits to the experimental Cm functions as in [5]. Intracellular Tris-HEPES (mM: HEPES-154, EGTA-10; pH -> 7.25 with TrisOH) and Trissulfate (mM: Tris-S04-l 10, HEPES-10, EGTA-10, MgS04-2; pH -> 7.25 with TrisOH) solutions were used to study Cm function changes during washout following accumulation of C1- during preliminary exposure (5 min) to 140-mM extracellular chloride (mM: TrisC1-140, HEPES-10, MgS04-5, CaS0,-0.2). TrisHEPES based solution (see above) was reapplied then to stop steady-state C1- influx into the cell.

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3

Results

3. I

OHCs possess a voltage-dependent anion-cation, non-selective conductance permeable to C t anions

Isolated OHCs possess a characteristic low membrane resistance even in the presence of K" and Ca" channel blockers [2]. We initially focused our attention on the origin of this low membrane resistance. Our finding was that in the presence of K' channel blockers (1 mM 4-Ap and 200 pM linpirdine) or stereocilia channel blockers (streptomicin 500 pM), in low-Ca2' extracellular solutions, a voltagedependent conductance exists, which is linear within -60 to +40 mV, but is moderately outwardly rectifying at potentials more positive to +40 mV, and strongly inwardly rectifying at potentials more negative to -80 mV. On the other hand, in the absence of K', Na+, Ca2' and CI- in intracellular and extracellular (low-Ca*') TrisHEPES based solutions, only small currents were observed with characteristic inward rectification at hyperpolarizing potentials (Fig. 1A). They likely reflected a small leakage through the putative channels for HEPES andor Tris ions. Currents were increased noticeably, when 80 mM K', Na" or C1- were applied extracellularly, substituting the equivalent amount of low-permeable ions (K+ and Na* for Tris, C1for HEPES; Fig. 1A). No similar currents appeared in isolated supporting Deiter's cells. Additionally, we failed to separate outwardly and inwardly rectifying

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components of currents, as well as cationic from anionic components. Instead, we observed that Na’ and C1- currents appear in similar proportion (and never exist separately) in all OHCs tested, and exhibit the same voltage dependence in both hyperpolarizing and depolarizing directions (disregarding the direction of opposite charges). They are modulated simultaneously and in the same direction by partial blockers (Gd3’, quinine, tamoxifen) and activators (octanol, NPPB, niflumic acid, Hg23. These observations strongly suggested that small monovalent cations and anions are able to pass with nearly equal efficiency through the putative channels that are responsible for the observed currents. The observation that currents were increased by conventional blockers of gap-junction hemichannels, aquaporins and chloride channels/transportersruled out their contribution to the currents. 3.2

C t current modulates voltage sensitivity and charge-transferfunctions of prestin

Since prestin possesses a functional intracellular C1--binding site [3], we tested whether C1‘ flux through the non-selective channels described above may influence prestin behavior. Isolated OHCs where initially maintained in 140-mM TrisCl extracellular solution to permit the accumulation of chloride intracellularly. Subsequently, gigohm seals were made with patch pipettes filled with CT-free intracellular solutions. The frst C-V h c t i o n was recorded after patch rupture (5-10 sec) to obtain the initial prestin-generated C, component when [Cl-Ii was maximal. Over the next 220 seconds, functions were recorded every 20 seconds to monitor changes during washout of intracellular Cl- through the patch pipette. C-V functions recorded from representative cells with Tris-HEPES and Tris-sulfate filled pipettes are shown in Figure 2A and B, respectively. The function’s characteristics changed significantly during the washout, and finally stabilized after 100 s. Following equilibration, the extracellular (140 mM TrisC1) solution was replaced by TrisHEPES solution. This operation further changed the C-V function’s characteristics, indicating that the steady-state influx of C1- through the non-selective channels was sufficient to influence prestin’s behavior, even though the cell was continuously perfbsed with Cl--fiee patch pipette solutions. Qma, z and Vh values were extracted from least square fits to the C-V functions. The fits are presented in Figure 2C (pipette: Tris-HEPES) and Figure 2D (pipette: Tris-sulfate) for three different conditions: after patch rupture, following intracellular solution equilibration and following equilibration in the presence of extracellular CI--free solution. For the cell perfused with intracellular Tris-HJZPES solution (Fig. 2C) the amount of prestin’s mobile charge, Qmm,remained stable (-2.5 pC) upon washout of intracellular C1- and following removal of extracellular Cl-. During the washout of intracellular Cl-, the apparent valence of “gating ” charge, z, was reduced from

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Figure 2. Changes in Cv functions of OHCs upon washout of intracellular and extracellular Cl-. A: Cm vs. membrane potential (Vm) functions were collected in 140 mh4 TrisCl extracellular solution (see Methods) during 220-s period (20 s intervals) after patch rupture with Tris-HEPES filled pipette. First collection (int: 0 mM HEPES) was at the time t;5-10 s. Additional (final) Cm collection (ext: 0 mM Cl-) was done 4 min after substitution of 140 mM TrisCl extracellular solution by CI--free solution. B: The same experiment as in A was carried out in different OHC perfused with Tris-sulfate (see Methods) filled pipette. C: Bell-shaped fits (first derivatives of Boltvnann functions, see Methods) to three Cm functions (bold traces) from part A (extended to k.300 mv). Fitting parameters: (at t;5-10 s, int: 0 mM HEPES) Qmax=2.56pC, ~ 0 . 7 9 Vh=-23 , mV; (at F220 s, int: 154-mM HEPES) Qm=2.42 pC, ~ 0 . 6 8 , v h = - l mV; (at F460 s, ext: 0 mM C1.) Qm=2.54 pc, F0.50, Vh=+46 mV. D: Bell-shaped fits (same as in C) to three Cm h c t i o n s (bold traces) from part B. Fitting parameters: (at t-5-10 s, int: 0 mM ~ 0 4 ~ ‘Qm=2.66 ) pc, ~ 0 . 7 8 vh=-5 , mV; (at ~ 2 2 0s, int: 110 mM SO:-) Qmax=2.77pc, ~ 0 . 7 5 , Vh=-+103 mV; (at t=460 s, ext: 0 mM Cl-) Qm=0.95 pC, F0.70, Vh=+137 mV.

-0.8 to -0.7,and the half maximal charge transfer potential Vh was shifted fiom -23 to -1 mV. Extracellular C1- removal resulted in fhrther reduction of z to -0.5 and shift Of Vh t0 +46 mv. For the cell perfused with intracellular Tris-sulfate solution (Fig. 2D) Qm remained stable (-2.7 pC) upon washout of intracellular Cl-, but it dropped to -I .O pC after removal of extracellular Cl-. z was stable (0.75-0.8),but Vh was shifted strongly to the right (fiom -5 to +lo3 mV) upon intracellular C1- washout. Extracellular C1- removal did not change z markedly (0.7), but shifted Vh further to the right (to +137 mV). Similar results to those presented in Figure 2 were obtained with more than 5 cells perfused with Tris-HEPES and Tris-sulfate solutions.

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4

Discussion

In this work we show that OHCs possess a catiodanion non-selective conductance capable of sustaining significant macroscopic currents of monovalent ions. The Clcurrent through these putative channels strongly modulates the behavior of prestin. We carried out our series of experiments to examine the recently proposed hypothesis [3] that C1- ions, bound to an intracellular residue of prestin, function as the motor’s voltage sensor. We monitored three parameters of prestin-mediated charge displacement: total mobile charge, Q-, apparent valence, z, of “gating” charge and half maximal charge transfer potential, Vh. Q- reflects both macroscopic (number of prestin molecules involved) and microscopic (real electric charge transferred by one prestin molecule) parameters. z is a microscopic parameter, being a product of the amount of mobile electric charge of one prestin molecule multiplied by the distance this charge travels within the membrane field in the direction normal to its plane. (1 is for a unit charge moved through the distance of the full field). Vh is a microscopic parameter characterizing the voltage component of the fiee energy level at which mobile charges are evenly distributed between two conformational states of prestin. Based on our data, several conclusions can be drawn about the molecular processes underlying voltage-dependent conformational transitions of prestin. 1. z remains stable (0.7-0.8) when intracellular C1- ions are substituted entirely by SOi2 ions, and C1- ions are eliminated fi-om extracellular solution to prevent their influx. Under these conditions, the only anion available to bind the intracellular residue of prestin and drive its voltage-dependent translocation according to Oliver et al. [3] is SOi2. If this were the case, the values of z and Qmaxmight be expected to double (-2e charge of the anion). Instead, the magnitude of z remains stable, while Qmaxis reduced. 2. In the analogous conditions with HEPES as the only major intracellular and extracellular anion, Qremained unchanged relative to the initial extracellular/intracellular CT-containing conditions. According to the Oliver et al. hypothesis, no prestin-mediated charge transfer is expected in HEPES perfused OHCs deprived of other functional anions. These two observations seriously challenge the hypothesis that C1- ions act as exogenous voltage sensors for prestin. Alternatively, we suggest that an intrinsic charged residue exists, which drives voltage-dependent conformational transitions of prestin. Our data are in agreement with Oliver et al. [3] that intracellular CI- ions strongly influence prestin’s voltage sensor mechanism. Presumably, Cl- ions interact with prestin’s intracellular binding site to allosterically modulate the structure of a mobile charge residue and/or the energy profile for its displacement. One may suggest the existence of more than one functional anionic binding site in the cytoplasmic residue, which allosterically modulate independent properties of

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prestin’s voltage sensor. Indeed, Vh was shifted to more positive membrane potentials while Qmarremained stable upon intracellular perfusion with either TrisHEPES or Tris-sulfate based solutions. Furthermore, total deprivation of chloride following replacement of extracellular high-Cl- by CT-free solution resulted mainly in a Qm reduction for Tris-sulfate perfused cells but a z reduction for Tris-HEPES perfused cells. The observed effects might be explained if one intracellular lowaffinity C1- binding site influenced through allosteric interactions the local electrostatic field (and vh) in which the mobile charge is moving. Another, highaffinity binding site, could allosterically modulate the extent of polarization (real charge) of prestin’s mobile residue. This could independently change apparent Qm andor z values. Finally, the existence of an extracellular low-affinity C1- binding site that modulates prestin behavior cannot be ruled out. Acknowledgments This work was supported by NIDCD grant DC00273 to JSS. We thank Margaret Mazzucco for technical assistance. References 1. 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, 149-155. 2. Santos-Sacchi, J., Navarrete, E., 2002. Voltage-dependent changes in specific membrane capacitance caused by prestin, the outer hair cell lateral membrane motor. Pflugers Arch. 444,99-106. 3. Oliver, D., He, D.Z., Klocker, 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, 23402343. 4. 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. (Lond.) 5 10,225-235. 5. Santos-Sacchi, J., 1991. Reversible inhibition of voltage-dependent outer hair cell motility and capacitance. J. Neurosci. 1 1,3096-3 1 10.

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Comments and Discussion K.H. Iwasa: What is the range of physiological chloride concentration? It is usually lower than the external medium but it would be about 20 mh4. In this range, is prestin sensitive enough to external chloride influx to have a significant effect on motility?

Answer: Under normal physiological conditions, homeostatic mechanisms to control chloride levels may come into play, for example, pumps, transporters and sequestration mechanisms; see Frings et ul. (Prog. Neurobiol. 60, 247-289, 2000), just as they do in calcium metabolism. Most cells maintain an intracellular chloride concentration that is substantially below the typical extracellular concentration of 140 mM, as in perilymph. Nevertheless, in many cell types chloride is maintained at levels higher than the predicted electrochemical equilibrium levels. This is usually achieved by Na-K-2Cl cotransport (Russell, Physiol. Rev. 80, 21 1-276, 2000). However, there is an apparent absence of NKCC1 transporter in OHCs (Crouch et ul., J. Histochem. Cytochem. 45, 773-778, 1997); this may indicate that levels in the OHC are close to equilibrium levels, namely, for a resting potential < -70 mV, < 10 mM. Furthermore, efficient mechanisms for the control of chloride must exist within the very localized region of the lateral subplasma lemma1 space (LSpS), since an incessant flux of chloride across the lateral membrane is predicted to accompany acoustically induced (or basilar-membrane vibration induced) mechanical deformations of the cell. This results l?om the stretch sensitivity of the lateral membrane chloride conductance that we find. As noted in our report and in previous presentations (IEB meeting abstracts, 200 1, ARO meeting abstracts, 2002), changes in chloride levels in the LSpS will have an enormous impact on OHC mechanical function, since the state probability of prestin is greatly affected, as evidenced through shifts in Vpkcm.We speculate that the subsurface cisternae and associated mitochondria aid in controlling LSpS chloride levels. Indeed, it may be that interference with chloride homeostatic mechanisms underlies the cochlea amplifier’s susceptibilityto insult.

R.B. Patuzzi: I have two questions. You have said very little about the role of Ca” in modulating the motility you have observed. I remember Peter Dallos and colleagues commenting some years ago about the role of Ca” in modulating outer hair cell motility in vitro. Could you please comment on any role it might have? The second question is really more of a comment. Since the cochlea is an organ sensitive to atomic movements, it would seem to me to be very bad design to install chloride transport into the basolateral wall (especially C1- channels). In a cell that is only permeable to K+, large membrane potential shifts can occur without significant ion flux through the wall (the cell is “Nernstian”), and if the cell is permeable to K+ and

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Na’, then you may have ion exchange between cations, but not a large salt flux. If you install C1- transport, however, there can be a nett salt transport during cell depolarization, which would evoke slow osmotic water movements during sound transduction which could then stimulate the cell’s sensitive mechanotransduction. This would seem like a very poor design in a system “designed” to detect atomic movements by producing receptor potentials. My only point is that, if I were God, I would make sure I had the cell’s osmoregulation clearly under control before I played with C1- transport. The other comment is that I seem to remember Don Robertson from our laboratory performing perilymphatic C1- substitution experiments in the late ‘70’s in which he perfused sulphate perilymph through scala tympani. This produced very little change in hearing threshold. This seems consistent with no sensitivity of the prestin motility to extracellular chloride, but does not seem consistent with the idea that the outer hair cells have a significant CIpermeability (by whatever transport mechanism: channel or carrier). Can you comment? Answer: Ca2’ may influence OHC motility via interactions with the cytoskeleton and/or by its modulation of phosphorylation in the OHC; see Szonyi et uf. (Brain Res. 922, 65-70, 2001). It is certainly clear, however, that Ca2’ is not required for prestin activity. As far as the chloride currents we measure, Ca2’ does not seem to play a role. Cells typically regulate chloride levels remarkably well (see reply to Iwasa above). We do not know the concentration of chloride in the sub-membranous space at the OHC lateral wall; nonetheless, we would predict that the OHC has machinery necessary to carefully regulate such an important ion as chloride. Furthermore, while chloride may be a significant factor in controlling osmotic effects on a variety of cell types, this has not kept those cells from using chloride for very important tasks such as synaptic signaling. Indeed, the ability of some synapses (even in the auditory system) to switch from inhibitory to excitatory, or visa versa, underscores the cell’s ability to tightly control chloride levels within microenvironments (Ehrlich et uf., J. Physiol. 520, 121-137, 1999). We feel that chloride levels in the compartment beneath the OHC lateral membrane are important for the cell to control owing to prestin’s chloride sensitivity. Thus, we would predict that levels are maintained below the saturation level for prestin effects, and the stretch-sensitiveconductance that we find might be expected to modulate that steady state level even at high frequencies. Indeed, modulation of the steady-state level may also be physiologically important; for example, it may be that the shift in Vpkcm observed during OHC development (Oliver and Fakler, J. Physiol. 5 19, 791-800, 1999) is driven by changes in intracellular chloride levels. Finally, it seems to me that Nature would take advantage of a well-developed mechanism, such as osmoregulation, to deal with another important task - high-flequency tuning. It may be significant that these two important cellular h c t i o n s are so widely separated in frequency such that they do not interfere with each other.

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Regarding the interpretation of perilymphatic perfusion of any type, we must remain cognizant of the possibility that preparation for these kinds of experiments can sometimes reduce response levels significantly such that threshold (active) effects can be missed. Indeed, in the manuscript of Desmedt and Robertson (J. Physiol. 247, 407-428, 1975), where perilymphatic perfusions with altered chloride concentrations were made, the authors described their preparations as ‘‘fairly intact”, and found variations of up to 20% in CM and N l thresholds during control perfkions. In those experiments, slow perhsion rates typically reduced chloride levels (which they measured) to values at or above 35 mM. When perfusion rates were increased so as to drop chloride levels down to 5 mM, N1 threshold levels did deteriorate. D. Oliver: First comment: The whole-cell approach is problematical with respect to completely removing a certain intracellular anion. It appears that you do not remove all of the relevant anions and therefore a large portion of the non-linear capacitance (NLC) remains. Moreover, bicarbonate also promotes NLC. It is probably impossible to get rid of bicarbonate in a cell that constantly produces COz. Thus, for studying the basic biophysical properties of prestin with respect to anion species and concentration, excised patches are more appropriate, as they allow for precise control of all ion species. Secondly, you propose an allosteric mechanism by which chloride shifts Vh along the voltage axis. If C1‘ binds to prestin and thereby alters Vh, would you not expect to have 2 populations of molecules, i.e., experimentally find the overlay of two Boltzmann-type capacitances with different Vh, instead of the observed gradual shift at constant slope, when lowering C1- ? Answer: To be sure, there are potential problems with either the whole-cell or patch approach, and native cell vs. transfected cell approach. For example, removal of a patch from a cell or measurement of an attached patch in a transfected cell will drastically alter membrane structure, not to mention the intracellular environment that a transmembrane protein normally experiences (Milton and Caldwell, Pfliigers Arch. 416, 758-762, 1990). How this affects a protein is difficult to assess. For example, both cell-attached and excised patches of oocyte expressed Shaker-IR channels display anomalous mechanical sensitivity because normal cellular mechano-control mechanisms are absent (Gu et al., Biophys. J. 80, 2678-2693, 2001). Obviously, we use our techniques and try to deal with potential problems. In this regard, we believe that we do have control over solutes delivered to the intracellular aspect of the lateral membrane (LSpS), at least in steady state. So, in the presence of the lateral membrane conductance that we find, the presence of chloride-fiee intracellular and extracellular solutions will eventually deplete chloride in the LSpS. This we are sure of because we find washout rates of chloride (based on prestin activity) typical for whole-cell washout (- 1-3 minutes; Pusch and Neher,

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Pfliigers Arch. 41 1, 204-2 1 1, 1988); indeed, we have perfUsed for greater than 4 hours and our results remain consistent. Reversal potentials also indicate that we can rapidly change LSpS chloride concentrations. As far as bicarbonate is concerned, carbonic anhydrase is not located at the lateral wall but at the apical and basal ends of the OHC (Okamura el al., Histochem. Cell Biol. 106, 425-430, 1996); so, under our conditions, the little bicarbonate that might be produced in the absence of energy substrates (i.e., in the absence of robust C02 generation) would be readily washed out from the cell’s cytosol. Since we first demonstrated the shift in V, or Vpkmwith changes in chloride levels (Rybalchenko and Santos-Sacchi, Inner Ear Biology meeting abstracts, Rome, Italy, 2001), we realized that the simple voltage sensor scheme of Oliver et al. (Science 292, 2340-2343, 2001) was problematic. The dependence of V,, Qand z on control anion species that we find cannot be reconciled with an anion functioning simply as a voltage sensor. Something else must be happening here. We conclude that the effect of chloride is most likely due to an allosteric action on the motor protein, prestin. That is, as is typical of indirect allosteric interactions (Monod et al., J. Mol. Biol. 6, 306-329, 1963; Changeux and Edelstein, Neuron 21,959-980, 1998), a modulator, in this case Cl-, binds to a site that is distinct from the active site responsible for the main function of the protein, namely the intrinsically charged voltage sensing moiety. The binding produces a reversible conformational change in prestin that is measurable as a shift in the motor charge’s Boltzmann function along the voltage axis. Allosteric modulation such as this is not unusual. For example, allosteric modulation of the HERG potassium channel by Ca2’ induces voltage shifts in the channel’s activation curve (Johnson et al., J. Neurosci. 21,4143-4153,2001). The expectation that two sub-populations, one CI--bound, and one not, would produce distinct double Boltananns might be met if the number of state transitions were as simple as you suggest. However, in our data we find differential changes in V,,,,, z and Qm that depend on the control anions (pentane sulfonate, sulfate or HEPES) that we use to replace chloride. We would suggest that there are multiple binding sites of different affinities not only for chloride but also for other anions, each having differential effects on V,,,. Thus, our data indicate that multiple populations of anion-bound prestin may exist simultaneously. For the whole cell, and large patches, we must also be cognizant that still other restricted populations of motors (with different Boltzmann characteristics) may also exist as a result of local forces other than chloride, e.g., tension, phosphorylation (Santos-Sacchi, Pfliigers Arch. in press; DOI: 10.1007/s00424-002-0928-4). Thus, because of distributed populations, the resulting single Boltzmann fits that we make may not demonstrate any apparent discontinuities.

ROCK ‘N’RHO IN OUTER HAIR CELL MOTILITY M. ZHANG*, G. KALINEC AND F. KALINEC Leslie and Susan Gonda Department of Cell and Molecular Biology, House Ear Institute, Los Angeles, CA, USA, and *Department of CommunicationDisorders, Texas Tech University Health Sciences Center, Lubbock, TX 79430, USA E-mail:fkalinec@hei. org D. D. BILLADEAU AND R. URRUTIA Division of Developmental Oncology Research and the Department of Biochemistry and Molecular Biology, Mayo Clinic, Rochester, MN 55905, USA E-mail: [email protected] Rho& Cdc42 and Racl, small GTPases of the Rho family, are crucial regulators of the actin cytoskeleton and mediate different types of cell motility. They also help to maintain cellular homeostasis, actively regulating the structure and mechanical properties of the cells. We investigated the expression in the guinea-pig cochlea of the serinehreonine kinase ROCK, a well-known effector of Rho4 and measured electromotile amplitude in outer hair cells (OHCs) internally perfused with C3 and Y-27632, pharmacological inhibitors of RhoA and ROCK respectively, and dominant-negative mutants of Racl and Cdc42. We found that a RhoA/ROCK-mediated signaling pathway is important for mechanical homeostasis of cochlear OHCs, and identified ROCK as a potential target to selectively modulate outer hair cell electromotility.

1

Introduction

The electromotility of outer hair cells (OHCs) results from a membrane-based force generator mechanism associated with conformational changes and rearrangement of a voltage-sensitive integral membrane protein [1,2]. The OHC motor protein has been recently identified as a novel anion transporter (SLC26A5-prestin) [3], with voltage sensitivity conferred by the intracellular anions chloride and bicarbonate [4] (for review see [2]). It has been suggested that the vectorial component to the forces generated in the OHC plasma membrane is provided by the cortical cytoskeleton, an actin-spectrin meshwork placed immediately underneath the plasma membrane and connected to it through thousands of 25-nm long, rod like structures [5]. Therefore, OHC electromotility amplitude would depend on both prestin performance and the mechanical load applied to the motors by the cytoskeleton. OHC motility would require tight spatial and temporal regulation of cytoskeletal structures for optimum performance [6-81. The homeostatic regulation of structures as precisely ordered as the OHC cortical cytoskeleton presents a unique challenge for the cell signaling pathways that control cytoskeletal dynamics [ 6 ] .

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In animal cells, the actin cytoskeleton is regulated by the Rho family of small GTPases [9]. Rho GTPases comprises three main subgroups termed Cdc42, Rac, and (confusingly) Rho. All share two fundamental characteristics: 1) they are controlled by extracellular stimuli, and 2) they cycle between an inactive GDPbound state and an active GTP-bound state, with the ratio of the two forms being regulated by the opposing effects of guanine nucleotide exchange factors (GEFs), GTPase activating proteins (GAPS), and guanine nucleotide dissociation inhibitors (GDIs) [9,10]. We have recently provided evidence that ACh affects OHC electromotility by activating a signaling pathway mediated by the small GTPases RhoA, Racl and Cdc42 [S]. We suggested that the ACh-activated, Rho-mediated pathway could be triggering a functional reorganization of the cytoskeleton. To address this hypothesis, we are now investigating the signaling pathways downstream of Rho GTPases that are involved in the regulation of OHC electromotility. We focused our attention on the serine-threonine kinase ROCK, a molecular target of RhoA. ROCK (a.k.a. Rho-kinase or pl60ROCK) is known to regulate dynamic reorganization of cytoskeletal proteins, such as stress-fibre and focal adhesion formation [ 111. ROCK also regulates the contractile force in cells through the inhibition of myosin light chain (MLC) phosphatases. This results in the accumulation of phosphorylated MLC generated by MLC-kinase and consequently cytoskeletal contraction. In addition, ROCK induces phosphorylation of FERh4 proteins, important for plasma membrane-cytoskeleton interaction [ 121, and adducin, a membrane skeletal protein that promotes actin-spectrin binding [ 131. Here we report that a RhoA/ROCK-mediated signaling pathway is important for mechanical homeostasis of cochlear OHCs, and identified ROCK as a potential target to selectively modulate OHC electromotility. 2

Methods

Young guinea pigs (200-300 g) were euthanized following procedures and protocols approved by the Institutional Animal Care and Use Committee (IACUC). Immunolabeling and Western blotting experiments were performed following standard protocols [ti].Anti-ROCK rabbit polyclonal antisera against amino acids 1 29 (MSTGDSFETRFEKMDNLLRDPKSEVNSDC) of human ROCK [ 141 was used as primary antibody. Samples were observed with Zeiss LSM-410 laser confocal microscope with objectives C-Apo 40X and C-Apo 63X (NA=1.2). For electromotility experiments, OHCs were isolated by microdissection, and suspended in Leibowitz L- 15 media (Gibco, Gaithersburg, MD, USA) in a perfusion chamber on an Axiovert 135 inverted microscope stage. Only cells from the second and third turn of the guinea-pig cochlea (30-60 pm long) that met established criteria for healthy OHCs were used in these studies. L-15 media was continuously

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renovated at a rate of 50 pL/min using a two-way perfusion system (KDS-120, KD Scientific, Boston, MA, USA). OHCs were patch-clamped (-70 mV holding potential; 4-5 MR pipette access resistance) at or immediately above the nuclear region using an EPC-9 amplifier (HEKA, Germany) and a Patchman electronic micromanipulator (Eppendorf, Germany). Patch pipettes were filled with internal perfusion buffer (KF, 120 mM; KC1,20 mM; MgC12, 2 mM; Mg-ATP, 2 mM; Na-GTP, 0.1 mM; HEPES, 10 mM) adjusted with Trizma Base to pH 7.4 and with glucose to 300 mOsm. Experimental conditions included internal p erh io n buffer alone (control) or with the addition of exotransferase C3 (100 pM. Cytoskeleton, Denver, CO, USA), the synthetic compound Y-27632 (10 pM. Upstate Biotechnology, Lake Placid, NY, USA), the dominant-negative constructs dnRac1 and dnCdc42 (100 pg/mL. Kindly provided by Dr. J.Silvio Gutkind, NIDCR-NM), or combinations of these compounds at identical concentrations. Since dnRacl and dnCdc42 are fusion proteins composed by the mutant and Glutathione S-Transferase (GST. Calbiochem), internal perfusion of OHCs with the internal buffer plus GST (100 @mL) was used as a control for all those conditions including dnRacl or dnCdc42. After being patch-clamped, cells were permitted to stabilize in their new mechanical conditions for 8 to 10 minutes. Cells were electrically stimulated with bursts of three depolarization (+50 mV)/hyperpolarization (-140 mV) cycles (3 Hz) to elicit electromotility. The cell response was recorded in video and analyzed offline. The electrical and structural integrity of every OHC was continuously evaluated through the whole experiment. The osmolarity of every solution used in these experiments was controlled and adjusted to 30W2 mOsm with a pOsmette 5004 freezing-point osmometer (Precision Systems Inc. Natick, MA, USA). Changes in electromotile amplitude were measured with a resolution better than 0.1 pm as described elsewhere [ 151. 3

Results

We first examined the expression and distribution of ROCK in the guinea-pig cochlea. A rabbit polyclonal antiserum [14] provided consistent labeling of ROCK in outer and inner hair cells, but considerable lower levels in other organ of Corti cell populations such as Deiters’, and Hensen’s cells. Interestingly, labeling of ROCK in pillar cells as well in cells of the stria vascularis was negligible (Figs. lA, B). Confocal microscopy of whole mount preparations confirmed that ROCK is expressed abundantly in OHCs, and is localized primarily to the cell cortex (Figs. 1 C, D). Thus, these results suggest that ROCK is localized either immediately adjacent to or at the areas involved in OHC electromotility.

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Figure 1. Immunolocalization of ROCK in guinea-pig cochlea A: ROCK labeling was strong in the organ of Corti and weak in the stria vascularis (arrows). B: [n Ihe organ of Corti, ROCK, appears to be abundantly expressed in inner and OHCs (arrows), but nearly absent in pillar's (arrowheads). C: Confocal sections of whole mount preparations of guineapig organ of Corti con firm the expression of ROCK in OHCs. D: Isolated OHCs were also labeled with anti-ROCK. E: Westem-blol analysis confirmed the expression of ROCK in ROCK guinea-pig cochlea Given the abundant expression of ROCK in OHCs and its association with RhoA, we hypothesized that inhibition of ROCK might result in changes in the mechanical properties of OHCs and consequently, in their electromotile response. To test this hypothesis, we inhibited the function of RhoA and ROCK and investigated their effect on OHC electromotility. To inhibit RhoA- and ROCKmediated signaling pathways we used C3 exoenzyme from Clostridium botulinum, which ADP-rybosylate RhoA (but not Rac and Cdc42) at Asn41 thereby blocking RhoA-mediated signals, and the synthetic compound Y-27632 that inhibits ROCK with high specificity by competing with ATP for binding to the kinases [16]. As shown in Figure 2, internal perfusion of OHCs with C3 or Y27632 resulted in a significant decrease in electromotility amplitude respect to the control condition, from 3.5±0.1 % (control) to 2.6±0,2% (C3) and 2.7±0.2% (Y27632) of the total cell length, respectively. Co-perfusion of C3 and Y-27632 induced a response statistically undistinguishable from that observed with Y-27632 alone (2.9±0.3%). These results suggest that a RhoA/ROCK-mediated Figure 2. Electromotile amplitude in isolated OHCs internally perfused with inhibitors of RhoA (C3), signaling cascade may be ROCK (Y-27632). Values are meansiSEM from at antagonizing a parallel pathway that least 8 cells per condition, * = P