Mathematical modeling of the mechanical response of coupled inner-ear hair cells with opposite polarity

Abstract

Hair cells are specialized receptors that detect mechanical forces in the auditory and vestibular systems of vertebrates. In vivo hair-cell bundles are typically anchored to an overlying structure which provides mechanical coupling between neighboring hair cells. Cooperativity between hair bundles has been previously proposed to have strong effects on signal detection. While the coupling of hair cells with the same polarity as those in the auditory organs has been extensively studied, the dynamics of hair cells with opposite polarity in the vestibular system and the inner ear of lizards remain unexplored. In this study, we aim to investigate the dynamics of two hair cells arranged with opposite polarity under a coupling spring using a mathematical model previously proposed to describe hair bundle motility. We focused on three scenarios: spontaneous dynamics, responses to sinusoidal force stimulation, and responses to step force stimulation. Through our analyses, we showed that the coupling force applied to each hair cell by the coupling element served as an additional force that modulated the individual cell's dynamics. Notably, when coupled with opposite polarity, the coupling force counteracted the applied constant force, which affected the hair cell's operating point. Under sinusoidal force stimulation, the coupling force oscillated at twice the frequency of the driving force. This oscillatory force could affect the response of the coupled hair bundle at the driving frequency, leading to reduced responses at high force amplitudes and frequencies below the resonance frequency. This phenomenon could improve the hair cell's compressive nonlinearity and frequency selectivity. Furthermore, we observed that the coupling force increased the responses to positive step forces while decreasing responses to negative forces. Our study contributes to the understanding of coupled hair-bundle dynamics which could play important roles in the signal detections by the vestibular systems and inner ear of lizards.