Mode-locking dynamics of hair cells of the inner ear

Abstract

We explore mode-locking of spontaneous oscillations of saccular hair cell bundles to periodic mechanical deflections. A simple dynamic systems framework is presented that captures the main features of the experimentally observed behavior in the form of an Arnold Tongue. We propose that the phase-locking transition can proceed via different bifurcations. At low stimulus amplitudes F, the transition to mode-locking as a function of the stimulus frequency ω has the character of a saddle-node bifurcation on an invariant circle. At higher stimulus amplitudes, the mode-locking transition has the character of a supercritical Andronov-Hopf bifurcation.

Hydrodynamics Versus Intracellular Coupling in the Synchronization of Eukaryotic Flagella

“…Controlled hydrodynamic forces are applied on the cell by generating external periodic background flows. Controlled perturbations have been imposed on biological systems in previous investigations of hair cells and flagella [14,[18][19][20]. Our experiments reveal that flagellar beating can be controlled solely via hydrodynamic forces generated by an external periodic flow.…”

Frequency locking in auditory hair cells: Distinguishing between additive and parametric forcing

“…We focus this study on the 1:1 resonant response [31,45]. The amplitude equation (2) with n = 1 has been employed in several contexts, such as studies of fluctuations and the response to pitches [57,58].…”

“…Yet, theoretical models have typically included only additive forcing terms [31,39,42]. We develop a general theoretical framework that allows a systematic study of the impact of parametric versus additive forcing on the resonant response in the cochlea.…”

“…Synchronization of hair bundle oscillations by periodic perturbations, exhibited over a wide range of frequencies [15,30,31], suggests that the auditory system is analogous to general forced oscillatory media, similar to autocatalysis in chemical media or enzymatic dynamics in physiology [32][33][34][35]. To explain the role of active amplification in hearing, theoretical mod-els proposed that hair cell response follows temporal dynamics that arise through a Hopf bifurcation [36][37][38][39][40][41][42], a generic mechanism that describes the birth of oscillatory behavior once the critical value of a control parameter is exceeded [43].…”

Periodic Oscillation in Neutrophil Models with Time Delays

“…From point view of dynamics, stable equilibrium solution can enter into instability regime to bifurcate into oscillation mode periodically via super-critical Hopf/sub-critical Hopf bifurcation [10]- [15]. Commonly, people use method of linearization model near the steady states to get the exponential polynomial characteristic equation to analyze its asymptotic stability via roots attribution to such polynomials [4] [5].…”