Nonlinear Stochastic Dynamics and Signal Amplifications in Sensory Hair Cells

Abstract

Hair cells are mechanosensors specializing in detection and amplification of weak mechanical stimuli in the auditory and vestibular peripheral sensory systems in vertebrates. In amphibians, hair cells exhibit two distinct mechanisms of amplification: via active motility of the hair bundle and via nonlinear resonant properties of the membrane potential. We use computational and theoretical approaches to study how the interaction of these two mechanisms a ect spontaneous dynamics of hair cells and shape their responses to weak mechanical stimuli. We develop a two-compartment model incorporating a Hodgkin– Huxley type system for the membrane potential and a nonlinear stochastic oscillator for the hair bundle. We show that the bidirectional coupling between two compartments a ects significantly the dynamics of the cell. Self-sustained oscillations of the hair bundles and membrane potential can result from coupling of initially quiescent mechanical and electrical compartments. The coherence of stochastic spontaneous oscillations can be maximized by tuning the coupling strength. Consistent with previous experimental work, we show that dynamical regimes of the hair bundle change in response to variations in the conductances of basolateral ion channels. Randomness of the hair bundle compartment is a limiting factor of the sensitivity. We found that sensitivity of the hair cell to weak mechanical perturbation is maximized by varying coupling strength. Using an analytical approach we show that such a non-monotonic dependence of sensitivity on coupling strength is a generic property of bidirectionally coupled unequally noisy oscillators. Furthermore, we show analytically that the phase coherence in such systems changes nonmonotonically in response to increasing noise levels in the less coherent oscillator, a novel counter–intuitive e ect.