Using a fluctuation analysis of limit cycle oscillations in inner ear hair bundles as a new test of low dimensional dynamical models

The transduction of sound in the inner ear is an active process involving elastic elements, molecular motors, and ion channels. A manifestation of this process in inner ear hair cells is the presence of spontaneous bundle oscillation, observed in vitro in some species. This limit cycle oscillation has been modelled using both a simple two-dimensional Hopf oscillator and more complex variants that explicitly incorporate the physiological variables. The models include stochastic noise in one or more variables representing implicitly the effect of other degrees of freedom.
We study the effects of noise on these stable limit cycles using both analytic calculations and numerical simulations. We show that d-dimensional noisy oscillators generically display phase diffusion at long time scales and (d-1) degrees of freedom that behave roughly as overdamped oscillators. On shorter time scales, we show that noise in the dependent variables which are hidden from measurement, e.g., motor activity, are coupled back to observable variables in ways that allow one to use noise measurements to access otherwise “hidden” features of the system. We compare our theoretical results to data from Rana catesbeiana hair cells.