{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T18:37:00Z","timestamp":1791311820028,"version":"4.3.1"},"reference-count":38,"publisher":"National Academy of Sciences","issue":"33","content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2004,8,17]]},"abstract":"<jats:p>\n                    The ear relies on nonlinear amplification to enhance its sensitivity and frequency selectivity to oscillatory mechanical stimuli. It has been suggested that this active process results from the operation of dynamical systems that operate in the vicinity of an oscillatory instability, a Hopf bifurcation. In the bullfrog's sacculus, a hair cell can display spontaneous oscillations of its mechanosensory hair bundle. The behavior of an oscillatory hair bundle resembles that of a critical oscillator. We present here a theoretical description of the effects of intrinsic noise on active hair-bundle motility. An oscillatory instability can result from the interplay between a region of negative stiffness in the bundle's force-displacement relation and the Ca\n                    <jats:sup>2+<\/jats:sup>\n                    -regulated activity of molecular motors. We calculate a state diagram that describes the possible dynamical states of the hair bundle in the absence of fluctuations. Taking into account thermal fluctuations, the stochastic nature of transduction channels' gating, and of the forces generated by molecular motors, we discuss conditions that yield a response function and spontaneous noisy movements of the hair bundle in quantitative agreement with previously published experiments. We find that the magnitude of the fluctuations resulting from the active processes that mediate mechanical amplification remains just below that of thermal fluctuations. Fluctuations destroy the phase coherence of spontaneous oscillations and restrict the bundle's sensitivity as well as frequency selectivity to small oscillatory stimuli. We show, however, that a hair bundle studied experimentally operates near an optimum of mechanosensitivity in our state diagram.\n                  <\/jats:p>","DOI":"10.1073\/pnas.0403020101","type":"journal-article","created":{"date-parts":[[2004,8,9]],"date-time":"2004-08-09T20:16:45Z","timestamp":1092082605000},"page":"12195-12200","update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":176,"title":["Active hair-bundle motility harnesses noise to operate near an optimum of mechanosensitivity"],"prefix":"10.1073","volume":"101","author":[{"given":"Bj\u00f6rn","family":"Nadrowski","sequence":"first","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Physik komplexer Systeme, N\u00f6thnitzerstrasse 38, 01187 Dresden, Germany; and Laboratoire Physico-Chimie Curie, Centre National de la Recherche Scientifique\u2013Unit\u00e9 Mixte de Recherche 168, Institut Curie Recherche, 26, Rue d'Ulm, 75248 Paris Cedex 05, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pascal","family":"Martin","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Physik komplexer Systeme, N\u00f6thnitzerstrasse 38, 01187 Dresden, Germany; and Laboratoire Physico-Chimie Curie, Centre National de la Recherche Scientifique\u2013Unit\u00e9 Mixte de Recherche 168, Institut Curie Recherche, 26, Rue d'Ulm, 75248 Paris Cedex 05, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Frank","family":"J\u00fclicher","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Physik komplexer Systeme, N\u00f6thnitzerstrasse 38, 01187 Dresden, Germany; and Laboratoire Physico-Chimie Curie, Centre National de la Recherche Scientifique\u2013Unit\u00e9 Mixte de Recherche 168, Institut Curie Recherche, 26, Rue d'Ulm, 75248 Paris Cedex 05, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2004,8,9]]},"reference":[{"key":"e_1_3_2_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0959-4388(97)80026-8"},{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.12-12-04575.1992"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1152\/jn.2001.86.2.541"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.96.25.14306"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.251530598"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.251530498"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.041604998"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.23-11-04533.2003"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.95.26.15321"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.97.7.3183"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.84.5232"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.75.2618"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0896-6273(94)90147-3"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0896-6273(88)90139-0"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.16-18-05629.1996"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1152\/jn.1999.82.5.2171"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.20-19-07131.2000"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(03)74465-8"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.210389497"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1101\/SQB.1990.055.01.053"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.bb.24.060195.000423"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.14-10-06217.1994"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.09-11-03988.1989"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0959-4388(03)00094-1"},{"key":"e_1_3_2_25_2","unstructured":"Strogatz S. 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