Auditory Performances and Hopf Bifurcation: From Global Coupling to Out-of-Equilibrium Criticality
Thomas Risler
Lab. Physicochimie Curie (CNRS-UMR 168), Institut Curie, Paris
Mon, Jan. 12th 2009, 14:15
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
Our auditory organ is capable of impressive performances in terms of intensity threshold of sound detection, amplitude range and frequency discrimination. It has been proposed that to achieve such performances, the mechano-sensory cells of the inner ear actively regulate their operating point close to a noisy Hopf bifurcation. This highly nonlinear behavior relies on the cooperativity of their mechano-transduction ion channels which, numbering typically several tens per cell, need to be mechanically globally coupled for maximal sensitivity to occur. To assess the degree of cooperativity among channels, we studied data acquired with a dual-beam laser interferometer that measures the displacements of two different locations within a single mechano-sensitive structure with sub-nanometer spatial resolution and sub-millisecond temporal precision. We first show how multi-taper spectral analysis techniques allow us to quantify the degree of correlation among mechano-transduction channels with constrained bias and good statistical confidence, despite the presence of low-frequency drift in the data. We then show how the noisy nonlinear behavior of these mechano-sensory cells has led us to study the oscillatory transition of a large collection of active oscillators in the vicinity of a synchronization transition. In the thermodynamic limit, this universal transition corresponds to an out-of-equilibrium critical point, of which we characterize the universal properties using dynamical renormalization-group techniques.
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