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A generalization of the van-der-Pol oscillator underlies active signal amplification in Drosophila hearing

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Abstract

The antennal hearing organs of the fruit fly Drosophila melanogaster boost their sensitivity by an active mechanical process that, analogous to the cochlear amplifier of vertebrates, resides in the motility of mechanosensory cells. This process nonlinearly improves the sensitivity of hearing and occasionally gives rise to self-sustained oscillations in the absence of sound. Time series analysis of self-sustained oscillations now unveils that the underlying dynamical system is well described by a generalization of the van-der-Pol oscillator. From the dynamic equations, the underlying amplification dynamics can explicitly be derived. According to the model, oscillations emerge from a combination of negative damping, which reflects active amplification, and a nonlinear restoring force that dictates the amplitude of the oscillations. Hence, active amplification in fly hearing seems to rely on the negative damping mechanism initially proposed for the cochlear amplifier of vertebrates.

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References

  • Boekhoff-Falk G (2005) Hearing in Drosophila: development of Johnston’s organ and emerging parallels to vertebrate ear development. Dev Dyn 232:550–558

    Article  PubMed  Google Scholar 

  • de Boer E (1996) Mechanics of the cochlea: modeling efforts. In: Dallos P, Popper A, Fay R (eds) The Cochlea. Springer Handbook of Auditory Research, Springer, Berlin Heidelberg New York

  • Camalet S, Duke T, Jülicher F, Prost J (2000) Auditory sensitivity provided by self-tuned critical oscillations of hair cells. Proc Natl Acad Sci USA 97:3183–3188

    Article  PubMed  ADS  Google Scholar 

  • Chan DK, Hudspeth AJ (2005) Ca 2+ current-driven nonlinear amplification by the mammalian cochlea in vitro. Nat Neurosci 8:149–155

    Article  PubMed  Google Scholar 

  • Choe Y, Magnasco MO, Hudspeth AJ (1998) A model for amplification of hair-bundle motion by cyclical binding of Ca 2+ to mechanoelectrical-transduction channels. Proc Natl Acad Sci USA 95:15321–15326

    Article  PubMed  ADS  Google Scholar 

  • Duke T, Jülicher F (2003) Active traveling wave in the cochlea. Phys Rev Lett 90:158101-1–158101-4

    Article  ADS  Google Scholar 

  • Eguíluz VM, Ospeck M, Choe Y, Hudspeth AJ, Magnasco MO (2000) Essential nonlinearities in hearing. Phys Rev Lett 84:5232–5235

    Article  PubMed  ADS  Google Scholar 

  • Gold T (1948) Hearing ii: the physical basis of the action of the cochlea. Proc R Soc Lond B 135:492–498

    Article  ADS  Google Scholar 

  • Göpfert MC, Robert D (2001) Active auditory mechanics in mosquitoes. Proc R Soc Lond B 268:333–339

    Article  Google Scholar 

  • Göpfert MC, Robert D (2003) Motion generation by Drosophila mechanosensory neurons. Proc Natl Acad Sci USA 100:5514–5519

    Article  PubMed  ADS  Google Scholar 

  • Göpfert MC, Humpfries ADL, Albert JT, Robert D, Hendrich O (2005) Power gain exhibited by motile neurons in Drosophila ears. Proc Natl Acad Sci USA 102:325–330

    Article  PubMed  ADS  Google Scholar 

  • Jülicher F, Andor D, Duke T (2001) Physical basis of two-tone interference in hearing. Proc Natl Acad Sci USA 98:9080–9085

    Article  PubMed  ADS  Google Scholar 

  • Kennedy HJ, Crawford AC, Fettiplace R (2005) Force generation by mammalian hair bundles supports a role in cochlear amplification. Nature 433:880–883

    Article  PubMed  ADS  Google Scholar 

  • Kern A, Stoop R (2003) Essential role of couplings between hearing nonlinearities. Phys Rev Lett 91:128101-1–128101-4

    Article  ADS  Google Scholar 

  • Kern A, Steeb W-H, Stoop R (2000) Projective noise cleaning with dynamic neighborhood selection. Int J Mod Phys C 11:125–146

    Article  ADS  Google Scholar 

  • Kuramoto Y (2003) Chemical oscillations, waves, and turbulence. Dover Publications, Dover

    Google Scholar 

  • Magnasco MO (2003) A wave traveling over a Hopf instability shapes the cochlear tuning curve. Phys Rev Lett 90:058101-1–058101-4

    Article  ADS  Google Scholar 

  • Martin P, Mehta AD, Hudspeth AJ (2000) Negative hair-bundle stiffness betrays a mechanism for mechanical amplification by the hair cell. Proc Natl Acad Sci USA 97:12026–12031

    Article  PubMed  ADS  Google Scholar 

  • Robert D, Göpfert MC (2002) Novel schemes for hearing and orientation in insects. Curr Opin Neurobiol 12:715–720

    Article  PubMed  Google Scholar 

  • Robles L, Ruggero M (2001) Mechanics of the mammalian cochlea. Physiol Rev 81:1305–1352

    PubMed  Google Scholar 

  • Savitsky A, Golay MJE (1964) Smoothing and differentiation of data by simplified least square procedures. Anal Chem 36:1627–1639

    Article  ADS  Google Scholar 

  • Sisto R, Moleti A (1999) Modeling otoacoustic emissions by active nonlinear oscillators. J Acoust Soc Am 106:1893–1906

    Article  PubMed  ADS  Google Scholar 

  • Stoop R, Kern A (2004) Two-tone suppression and combination tone generation as computations performed by the Hopf cochlea. Phys Rev Lett 93:268103-1–268103-4

    Article  PubMed  ADS  Google Scholar 

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Stoop, R., Kern, A., Göpfert, M.C. et al. A generalization of the van-der-Pol oscillator underlies active signal amplification in Drosophila hearing. Eur Biophys J 35, 511–516 (2006). https://doi.org/10.1007/s00249-006-0059-5

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  • DOI: https://doi.org/10.1007/s00249-006-0059-5

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