The interplay between active hair bundle motility and electromotility in the cochlea

Journal of the Acoustical Society of America

Volumn 128, Issue 3, 2010, Pages 1175-1190

  Maoiléidigh, Dáibhid Ó ^a   Jülicher, Frank ^a  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ACTIVE FORCE GENERATION; ACTIVE PROCESS; BASILAR MEMBRANES; CELLULAR PROCESS; COCHLEAR AMPLIFIERS; DYNAMIC RANGE; ELECTROMOTILITY; FREQUENCY-TUNING; HAIR BUNDLES; HAIR CELLS; INTEGRATED SYSTEMS; MECHANOSENSORY HAIR; NON-LINEAR RESPONSE; NON-LINEARITY; NONLINEAR AMPLIFICATION; OSCILLATORY BEHAVIORS; OUTER HAIR CELL;

ACOUSTICS; AUDIO FREQUENCY AMPLIFIERS; HOPF BIFURCATION; INTEGRATED OPTICS; MAMMALS;

AMPLIFICATION;

ANIMAL; ARTICLE; BASILAR MEMBRANE; BIOLOGICAL MODEL; CELL MEMBRANE POTENTIAL; CELL MOTION; COCHLEA; FEEDBACK SYSTEM; HAIR CELL; HEARING; HISTOLOGY; HUMAN; MECHANOTRANSDUCTION; NONLINEAR SYSTEM; PHYSIOLOGY; STATISTICAL MODEL; TIME; VIBRATION;

ANIMALS; BASILAR MEMBRANE; CELL MOVEMENT; COCHLEA; FEEDBACK, PHYSIOLOGICAL; HAIR CELLS, AUDITORY, OUTER; HEARING; HUMANS; LINEAR MODELS; MECHANOTRANSDUCTION, CELLULAR; MEMBRANE POTENTIALS; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; TIME FACTORS; VIBRATION;

EID: 77956414648     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.3463804     Document Type: Article

References (94)

1. A. J. Hudspeth, " Making an effort to listen: Mechanical amplification in the ear.," Neuron NERNET 0896-6273 59, 530-545 (2008). 10.1016/j.neuron.2008.07.012
2. P. Dallos, " The active cochlea.," J. Neurosci. JNRSDS 0270-6474 12, 4575-4585 (1992).
3. G. A. Manley, " Cochlear mechanisms from a phylogenetic viewpoint.," Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 97, 11736-11743 (2000). 10.1073/pnas.97.22.11736
4. M. A. Ruggero, N. C. Rich, A. Recio, S. S. Narayan, and L. Robles, " Basilar-membrane responses to tones at the base of the chinchilla cochlea.," J. Acoust. Soc. Am. JASMAN 0001-4966 101, 2151-2163 (1997). 10.1121/1.418265 (Pubitemid 27163980)
5. L. Robles and M. A. Ruggero, " Mechanics of the mammalian cochlea.," Physiol. Rev. PHREA7 0031-9333 81, 1305-1352 (2001).
6. W. S. Rhode, " Observations of the vibrations of the basilar membrane using the Mössbauer technique.," J. Acoust. Soc. Am. JASMAN 0001-4966 49, 1218-1231 (1971). 10.1121/1.1912485
7. P. M. Sellick, R. B. Patuzzi, and B. M. Johnstone, " Measurement of basilar membrane motion in the guinea-pig using the Mössbauer technique.," J. Acoust. Soc. Am. JASMAN 0001-4966 72, 131-141 (1982). 10.1121/1.387996
8. D. T. Kemp, " Stimulated acoustic emissions from within the human auditory system.," J. Acoust. Soc. Am. JASMAN 0001-4966 64, 1386-1391 (1978). 10.1121/1.382104
9. J. P. Wilson, " Evidence for a cochlear origin for acoustic re-emissions, threshold fine structure and tinnitus.," Hear. Res. HERED3 0378-5955 2, 233-252 (1980). 10.1016/0378-5955(80)90060-X (Pubitemid 10034130)
10. W. S. Rhode, " An investigation of postmortem cochlear mechanics using the Mössbauer effect.," Basic Mechanisms of Hearing (Academic, New York, 1973), pp. 49-67.
11. M. A. Ruggero and N. C. Rich, " Application of a commercially-manufactured Doppler-shift laser velocimeter to the measurement of basilar-membrane vibration.," Hear. Res. HERED3 0378-5955 51, 215-230 (1991). 10.1016/0378-5955(91)90038-B
12. T. Gold, " Hearing. II. the physical basis of the action of the cochlea.," Proc. R. Soc., London, Ser. B PRLBA4 0950-1193 135, 492-498 (1948). 10.1098/rspb.1948.0025
13. 2+ to mechanoelectrical-transduction channels.," Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 95, 15321-15326 (1998). 10.1073/pnas.95.26.15321 (Pubitemid 29018697)
14. S. Camalet, T. Duke, F. Jülicher, and J. Prost, " Auditory sensitivity provided by self-tuned critical oscillations of hair cells.," Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 97, 3183-3188 (2000). 10.1073/pnas.97.7.3183 (Pubitemid 30183276)
15. V. M. Eguíluz, M. Ospeck, Y. Choe, A. J. Hudspeth, and M. O. Magnasco, " Essential nonlinearities in hearing.," Phys. Rev. Lett. PRLTAO 0031-9007 84, 5232-5235 (2000). 10.1103/PhysRevLett.84.5232
16. P. Martin, Active Processes and Otoacoustic Emissions (Springer, New York, 2008), Chap., pp. 93-143.
17. R. Hallworth and H. C. Jensen-Smith, Active Processes and Otoacoustic Emissions (Springer, New York, 2008), Chap., pp. 145-189.
18. P. Dallos, The Cochlea (Springer, New York, 1996), Chap., pp. 1-43.
19. C. J. Kros, The Cochlea (Springer, New York, 1996), Chap., pp. 318-385.
20. M. C. Holley, The Cochlea (Springer, New York, 1996), Chap., pp. 386-434.
21. W. E. Brownell, C. R. Bader, D. Bertrand, and Y. De Ribaupierre, " Evoked mechanical responses of isolated cochlear outer hair cells.," Science SCIEAS 0036-8075 227, 194-196 (1985). 10.1126/science.3966153
22. B. Kachar, W. E. Brownell, R. Altschuler, and J. Fex, " Electrokinetic shape changes of cochlear outer hair-cells.," Nature (London) NATUAS 0028-0836 322, 365-368 (1986). 10.1038/322365a0
23. J. Ashmore, " A fast motile response in guinea-pig outer hair cells.," J. Physiol. 388, 323-347 (1987). 0022-3751
24. J. Ashmore, " Cochlear outer hair cell motility.," Physiol. Rev. PHREA7 0031-9333 88, 173-210 (2008). 10.1152/physrev.00044.2006
25. X. Dong, M. Ospeck, and K. H. Iwasa, " Piezoelectric reciprocal relation of the membrane motor in the cochlear outer hair cell.," Biophys. J. BIOJAU 0006-3495 82, 1254-1259 (2002). 10.1016/S0006-3495(02)75481-7
26. R. Patuzzi, The Cochlea (Springer, New York, 1996), Chap., pp. 186-257.
27. E. DeBoer, The Cochlea (Springer, New York, 1996), Chap., pp. 258-317.
28. S. Preyer, R. Renz, W. Hemmert, H. Zenner, and A. W. Gummer, " Receptor potential of outer hair cells isolated from base to apex of the adult guinea-pig cochlea: Implications of cochlear tuning mechanisms.," Aud. Neurosci. AUNEEJ 1023-618X 2, 145-157 (1996).
29. J. Santos-Sacchi, " On the frequency limit and phase of outer hair cell motility: Effects of the membrane filter.," J. Neurosci. JNRSDS 0270-6474 12, 1906-1916 (1992).
30. A. C. Crawford and R. Fettiplace, " The mechanical properties of ciliary bundles of the turtle cochlear hair cells.," J. Physiol. 364, 359-379 (1985). 0022-3751
31. P. Martin and A. J. Hudspeth, " Active hair-bundle movements can amplify a hair cell's response to oscillatory mechanical stimuli.," Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 96, 14306-14311 (1999). 10.1073/pnas.96.25.14306 (Pubitemid 30000646)
32. P. Martin, D. Bozovic, Y. Choe, and A. J. Hudspeth, " Spontaneous oscillations by the hair bundles of the bullfrog's sacculus.," J. Neurosci. JNRSDS 0270-6474 23, 4533-4548 (2003).
33. H. J. Kennedy, A. C. Crawford, and R. Fettiplace, " Force generation by the mammalian hair bundle supports a role in cochlear amplification.," Nature (London) NATUAS 0028-0836 433, 880-883 (2005). 10.1038/nature03367 (Pubitemid 40314898)
34. W. Denk and W. W. Webb, " Forward and reverse transduction at the limit of sensitivity studied by correlating electrical and mechanical fluctuations in frog saccular hair cells.," Hear. Res. HERED3 0378-5955 60, 89-102 (1992). 10.1016/0378-5955(92)90062-R
35. P. Martin and A. J. Hudspeth, " Compressive nonlinearity in the hair bundle's active response to mechanical stimulation.," Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 98, 14386-14391 (2001). 10.1073/pnas.251530498 (Pubitemid 33121401)
36. D. K. Chan and A. J. Hudspeth, " Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro.," Nat. Neurosci. NANEFN 1097-6256 8, 149-155 (2005). 10.1038/nn1385 (Pubitemid 40194044)
37. M. C. Liberman, J. Gao, D. Z. Z. He, X. Wu, S. Jia, and J. Zuo, " Prestin is required for electromotility of the outer hair cell and for the cochlear amplifier.," Nature (London) NATUAS 0028-0836 419, 300-304 (2002). 10.1038/nature01059
38. P. Dallos, X. Wu, M. Cheatham, J. Gao, J. Zheng, C. Anderson, S. Jia, X. Wang, W. Cheng, and S. Sengupta, " Prestin-based outer hair cell motility is necessary for mammalian cochlear amplification.," Neuron NERNET 0896-6273 58, 333-339 (2008). 10.1016/j.neuron.2008.02.028 (Pubitemid 351615184)
39. G. Frank, W. Hemmert, and A. W. Gummer, " Limiting dynamics of high-frequency electromechanical transduction of outer hair cells.," Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 96, 4420-4425 (1999). 10.1073/pnas.96.8.4420 (Pubitemid 29190351)
40. G. D. Housley and J. F. Ashmore, " Ionic currents of outer hair cells isolated from the guinea-pig cochlea.," J. Physiol. 448, 73-98 (1992). 0022-3751
41. E. K. Weitzel, R. Tasker, and W. E. Brownell, " Outer hair cell piezoelectricity: Frequency response enhancement and resonance behavior.," J. Acoust. Soc. Am. JASMAN 0001-4966 114, 1462-1466 (2003). 10.1121/1.1596172 (Pubitemid 37075720)
42. A. A. Spector, A. S. Popel, R. A. Eatock, and W. E. Brownell, " Mechanosensitive channels in the lateral wall can enhance the cochlear outer hair cell frequency response.," Ann. Biomed. Eng. ABMECF 0090-6964 33, 991-1002 (2005). 10.1007/s10439-005-5749-0 (Pubitemid 41172447)
43. Z. Liao, S. Feng, A. S. Popel, W. E. Brownell, and A. A. Spector, " Outer hair cell active force generation in the cochlear environment.," J. Acoust. Soc. Am. JASMAN 0001-4966 122, 2215-2225 (2007). 10.1121/1.2776154 (Pubitemid 47493348)
44. K. Dierkes, B. Lindner, and F. Jülicher, " Enhancement of sensitivity gain and frequency tuning by coupling of active hair bundles.," Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 105, 18669-18674 (2008). 10.1073/pnas.0805752105
45. J. B. Allen, " Cochlear micromechanics-A physical model of transduction.," J. Acoust. Soc. Am. JASMAN 0001-4966 68, 1660-1670 (1980). 10.1121/1.385198 (Pubitemid 11185447)
46. W. F. Sewell, The Cochlea (Springer, New York, 1996), Chap., pp. 503-533.
47. J. Zwislocki, " Theorie der schneckenmechanik (Theory of cochlear mechanics).," Acta Oto-Laryngol., Suppl. AOLSA5 0365-5237 72, 1-76 (1948).
48. G. Zweig, " Basilar membrane motion.," Cold Spring Harb Symp. Quant Biol. ZZZZZZ 0091-7451 40, 619-633 (1976).
49. J. Lighthill, " Energy flow in the cochlea.," J. Fluid Mech. JFLSA7 0022-1120 106, 149-213 (1981). 10.1017/S0022112081001560
50. D. O. Kim, X. M. Yang, and S. T. Neely, " An active cochlear model with negative damping in the partition: Comparison with Rhode's ante- and post-mortem observations.," Psychophysical, Physiological, and Behavioral Studies in Hearing (Delft University Press, Delft, 1980), pp. 7-14.
51. E. de Boer, " No sharpening? A challenge for cochlear mechanics.," J. Acoust. Soc. Am. JASMAN 0001-4966 73, 567-573 (1983). 10.1121/1.389002
52. R. Nobili and F. Mammano, " Biophysics of the cochlea II: Stationary nonlinear phenomenology.," J. Acoust. Soc. Am. JASMAN 0001-4966 99, 2244-2255 (1996). 10.1121/1.415412 (Pubitemid 26123233)
53. T. K. Lu, S. Zhak, P. Dallos, and R. Sarpeshkar, " Fast cochlear amplification with slow outer hair cells.," Hear. Res. HERED3 0378-5955 214, 45-67 (2006). 10.1016/j.heares.2006.01.018 (Pubitemid 44321900)
54. T. Reichenbach and A. J. Hudspeth, " A ratchet mechanism for amplification in low-frequency mammalian hearing.," Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 107, 4973-4978 (2010). 10.1073/pnas.0914345107
55. N. B. Slepecky, The Cochlea (Springer, New York, 1996), Chap., pp. 44-129.
56. R. M. Edge, B. N. Evans, M. Pearce, C. -P. Richter, X. Hu, and P. Dallos, " Morphology of the unfixed cochlea.," Hear. Res. HERED3 0378-5955 124, 1-16 (1998). 10.1016/S0378-5955(98)00090-2 (Pubitemid 28483061)
57. C. -P. Richter, R. Edge, D. Z. Z. He, and P. Dallos, " Development of the gerbil inner ear observed in the hemicochlea.," J. Assoc. Res. Otolaryngol. ZZZZZZ 1525-3961 1, 195-210 (2000). 10.1007/s101620010019
58. P. Dallos, " Organ of Corti kinematics.," J. Assoc. Res. Otolaryngol. ZZZZZZ 1525-3961 4, 416-421 (2003). 10.1007/s10162-002-3049-z (Pubitemid 37187820)
59. H. J. Kennedy, M. G. Evans, A. C. Crawford, and R. Fettiplace, " Depolarization of cochlear outer hair cells evokes active hair bundle motion by two mechanisms.," J. Neurosci. JNRSDS 0270-6474 26, 2757-2766 (2006). 10.1523/JNEUROSCI.3808-05.2006 (Pubitemid 43357859)
60. D. K. Chan and A. J. Hudspeth, " Mechanical responses of the organ of Corti to acoustic and electrical stimulation in vitro.," Biophys. J. BIOJAU 0006-3495 89, 4382-4395 (2005). 10.1529/biophysj.105.070474 (Pubitemid 41725656)
61. A. W. Gummer, W. Hemmert, and H. P. Zenner, " Resonant tectorial membrane motion in the inner ear: Its crucial role in frequency tuning.," Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 93, 8727-8732 (1996). 10.1073/pnas.93.16.8727 (Pubitemid 26269628)
62. F. Mammano and J. F. Ashmore, " Reverse transduction measured in the isolated cochlea by laser Michelson interferometry.," Nature (London) NATUAS 0028-0836 365, 838-841 (1993). 10.1038/365838a0 (Pubitemid 23341025)
63. B. Nadrowski, P. Martin, and F. Jülicher, " Active hair-bundle motility harnesses noise to operate near an optimum of mechanosensitivity., " Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 101, 12195-12200 (2004). 10.1073/pnas.0403020101 (Pubitemid 39145419)
64. J. Tinevez, F. Jülicher, and P. Martin, " Unifying the various incarnations of active hair-bundle motility by the vertebrate hair cell.," Biophys. J. BIOJAU 0006-3495 93, 4053-4067 (2007). 10.1529/biophysj.107.108498 (Pubitemid 350223820)
65. P. Wangemann and J. Schacht, The Cochlea (Springer, New York, 1996), Chap., pp. 130-185.
66. B. Hille, Ionic Channels of Excitable Membranes, 3rd ed. (Sinauer Associates Inc., Sunderland, 2001), Chap., pp. 1-22.
67. M. M. Mellado Lagarde, M. Drexl, A. N. Lukashkin, J. Zuo, and I. J. Russell, " Prestin's role in cochlear frequency tuning and transmission of mechanical responses to neural excitation.," Curr. Biol. CUBLE2 0960-9822 18, 200-202 (2008). 10.1016/j.cub.2008.01.006
68. F. Mammano and R. Nobili, " Biophysics of the cochlea: Linear approximation.," J. Acoust. Soc. Am. JASMAN 0001-4966 93, 3320-3332 (1993). 10.1121/1.405716 (Pubitemid 23165748)
69. T. Duke and F. Jülicher, " Active traveling wave in the cochlea.," Phys. Rev. Lett. PRLTAO 0031-9007 90, 158101 (2003). 10.1103/PhysRevLett.90.158101
70. H. J. Kennedy, M. G. Evans, A. C. Crawford, and R. Fettiplace, " Fast adaptation of mechanoelectrical transducer channels in mammalian cochlear hair cells.," Nat. Neurosci. NANEFN 1097-6256 6, 832-836 (2003). 10.1038/nn1089 (Pubitemid 36929704)
71. W. Dong and E. S. Olson, " Middle ear forward and reverse transmission in gerbil.," J. Neurophysiol. JONEA4 0022-3077 95, 2951-2961 (2006). 10.1152/jn.01214.2005
72. I. J. Russell and A. N. Lukashkin, Active Processes and Otoacoustic Emissions (Springer, New York, 2008), Chap., pp. 343-379.
73. J. J. Guinan, The Cochlea (Springer, New York, 1996), Chap., pp. 435-502.
74. H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, MA, 1980), Chap., pp. 1-34.
75. A. W. Gummer, B. M. Johnstone, and N. J. Armstrong, " Direct measurement of basilar membrane stiffness in the guinea pig.," J. Acoust. Soc. Am. JASMAN 0001-4966 70, 1298-1309 (1981). 10.1121/1.387144
76. C. E. Miller, " Structural implications of basilar membrane compliance measurements.," J. Acoust. Soc. Am. JASMAN 0001-4966 77, 1465-1474 (1985). 10.1121/1.392041 (Pubitemid 15090340)
77. E. S. Olson and D. C. Mountain, " In vivo measurement of basilar membrane stiffness.," J. Acoust. Soc. Am. JASMAN 0001-4966 89, 1262-1275 (1991). 10.1121/1.400535
78. E. S. Olson and D. C. Mountain, " Mapping the cochlear partition's stiffness to its cellular architecture.," J. Acoust. Soc. Am. JASMAN 0001-4966 95, 395-400 (1994). 10.1121/1.408331
79. R. C. Naidu and D. C. Mountain, " Measurements of the stiffness map challenge a basic tenet of cochlear theories.," Hear. Res. HERED3 0378-5955 124, 124-131 (1998). 10.1016/S0378-5955(98)00133-6 (Pubitemid 28483073)
80. G. Emadi, C. -P. Richter, and P. Dallos, " Stiffness of the gerbil basilar membrane: Radial and longitudinal variations.," J. Neurophysiol. JONEA4 0022-3077 91, 474-488 (2003). 10.1152/jn.00446.2003
81. C. -P. Richter, G. Emadi, G. Getnick, A. Quesnel, and P. Dallos, " Tectorial membrane stiffness gradients.," Biophys. J. BIOJAU 0006-3495 93, 2265-2276 (2007). 10.1529/biophysj.106.094474 (Pubitemid 47437609)
82. B. Shoelson, E. K. Dimitriadis, H. Cai, B. Kachar, and R. S. Chadwick, " Evidence and implications of inhomogeneity in tectorial membrane elasticity.," Biophys. J. BIOJAU 0006-3495 87, 2768-2777 (2004). 10.1529/biophysj.104.040774
83. R. Gueta, D. Barlam, R. Z. Shneck, and I. Rousso, " Measurement of the mechanical properties of isolated tectorial membrane using atomic force microscopy.," Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 103, 14790-14795 (2006). 10.1073/pnas.0603429103 (Pubitemid 44527807)
84. R. Gueta, D. Barlam, R. Z. Shneck, and I. Rousso, " Sound-evoked deflections of outer hair cell stereocilia arise from tectorial membrane anisotropy.," Biophys. J. BIOJAU 0006-3495 94, 4570-4576 (2008). 10.1529/biophysj.107.125203
85. R. Fettiplace, " Active hair bundle movements in auditory hair cells.," J. Physiol. 576, 29-36 (2006). 10.1113/jphysiol.2006.115949 0022-3751 (Pubitemid 44426216)
86. K. H. Iwasa and M. Adachi, " Force generation in the outer hair cell of the cochlea.," Biophys. J. BIOJAU 0006-3495 73, 546-555 (1997). 10.1016/S0006-3495(97)78092-5
87. D. Z. Z. He, J. Shuping, and P. Dallos, " Mechanoelectrical transduction of adult outer hair cells studied in a gerbil hemicochlea.," Nature (London) NATUAS 0028-0836 429, 766-770 (2004). 10.1038/nature02591 (Pubitemid 38833128)
88. A. J. Ricci, A. C. Crawford, and R. Fettiplace, " Tonotopic variation in the conductance of the hair cell mechanotransducer channel.," Neuron NERNET 0896-6273 40, 983-990 (2003). 10.1016/S0896-6273(03)00721-9 (Pubitemid 37522055)
89. S. Preyer, W. Hemmert, M. Pfister, H. P. Zenner, and A. W. Gummer, " Frequency response of mature guinea-pig outer hair cells to stereociliary displacement.," Hear. Res. HERED3 0378-5955 77, 116-124 (1994). 10.1016/0378-5955(94)90259-3 (Pubitemid 24201336)
90. J. A. Tolomeo and C. R. Steele, " Orthotropic piezoelectric properties of the cochlear outer hair cell wall.," J. Acoust. Soc. Am. JASMAN 0001-4966 97, 3006-3011 (1995). 10.1121/1.411865
91. B. J. Dannhof, B. Roth, and V. Bruns, " Length of hair cells as a measure of frequency representation in the mammalian inner ear?," Naturwiss. NATWAY 0028-1042 78, 570-573 (1991). 10.1007/BF01134454
92. M. Beurg, M. G. Evans, C. M. Hackney, and R. Fettiplace, " A large-conductance calcium-selective mechanotransducer channel in mammalian cochlear hair cells.," J. Neurosci. JNRSDS 0270-6474 26, 10992-11000 (2006). 10.1523/JNEUROSCI.2188-06.2006 (Pubitemid 44772189)
93. M. P. Scherer and A. W. Gummer, " Impedance analysis of the organ of Corti with magnetically actuated probes.," Biophys. J. BIOJAU 0006-3495 87, 1378-1391 (2004). 10.1529/biophysj.103.037184 (Pubitemid 39095114)
94. C. -P. Richter and A. Quesnel, " Stiffness properties of the reticular lamina and the tectorial membrane.," Auditory Mechanisms (World Scientific, Singapore, 2006), pp. 70-78.