Effect of bidirectional mechanoelectrical coupling on spontaneous oscillations and sensitivity in a model of hair cells

Abstract

Sensory hair cells of amphibians exhibit spontaneous activity in their hair bundles and membrane potentials, reflecting two distinct active amplification mechanisms employed in these peripheral mechanosensors. We use a two-compartment model of the bullfrog's saccular hair cell to study how the interaction between its mechanical and electrical compartments affects the emergence of distinct dynamical regimes, and the role of this interaction in shaping the response of the hair cell to weak mechanical stimuli. The model employs a Hodgkin-Huxley-type system for the basolateral electrical compartment and a nonlinear hair bundle oscillator for the mechanical compartment, which are coupled bidirectionally. In the model, forward coupling is provided by the mechanoelectrical transduction current, flowing from the hair bundle to the cell soma. Backward coupling is due to reverse electromechanical transduction, whereby variations of the membrane potential affect adaptation processes in the hair bundle. We isolate oscillation regions in the parameter space of the model and show that bidirectional coupling affects significantly the dynamics of the cell. In particular, self-sustained oscillations of the hair bundles and membrane potential can result from bidirectional coupling, and the coherence of spontaneous oscillations can be maximized by tuning the coupling strength. Consistent with previous experimental work, the model demonstrates that dynamical regimes of the hair bundle change in response to variations in the conductances of basolateral ion channels. We show that sensitivity of the hair cell to weak mechanical stimuli can be maximized by varying coupling strength, and that stochasticity of the hair bundle compartment is a limiting factor of the sensitivity.

Nonequilibrium limit-cycle oscillators: Fluctuations in hair bundle dynamics

“…Here, P 0 denotes the opening probability of mechanoelectrical transduction channels and its equation is given in appendix A. Variations of the membrane potential modulate calcium influx, which affects the myosin motor activity; a dimensionless parameter α controls the strength of this reverse coupling [39].…”

Signal-Coupled Subthreshold Hopf-Type Systems Show a Sharpened Collective Response

“…While Refs. [32][33][34][35][36] used very detailed hair-cell models (involving a multitude of equations and parameters), we obtain what we see as the most salient results [34] by coupling subthreshold normal-form Hopf systems [cf. Fig.…”

The Remarkable Frog Ear: Implications for Vertebrate Hearing

“…If the assumption is made that the body of the hair cell contains some highly compressible element, perhaps even air, then when the pressure in the surrounding fluid increases, the hair cell is squeezed and pressure-sensitive channels in the wall of the cell are activated. An alternative model is that the compressible element might reside in the tectorial membrane itself, an idea following from consideration of Figure 6, or The active process within hair cells arises by two separate mechanisms, one relying on the motility of the hair bundle and the other by the motility of the cell body [28][29][30].…”