The collusion of flexoelectricity and Hopf bifurcation in the hearing mechanism

Abstract

How do the weak sound waves get amplified in a cochlea? This deceptively simple question has attracted a fair amount of attention and several creative mechanisms have been proposed that purport to understand how the inner ear’s hair cells actively collude to achieve the requisite sensitivity, frequency selectivity, range and nonlinear amplification. Some of the proposed mechanisms target the nature of the mechanoelectric transduction mechanism while others adopt a more dynamical systems approach and focus on the fact that stereocilia of the hair cells operate on the verge of an instability phenomenon—the so-called Hopf bifurcation. In this work, we propose a physics-based model to understand how flexoelectricity, a universal electromechanical coupling that exists in all dielectric substances, facilitates the mechanics of the active motion of hair bundles. A key feature of our model is that we eschew a “black-box” approach, and all parameters are well-defined physical quantities such as membrane bending modulus, geometrical characteristics and others. Furthermore, the model is derived from the well-accepted principles of mechanics and soft matter physics. While the role of flexoelectricity in the hearing mechanism has been noted before, we show for the first time that flexoelectricity is an essential ingredient in inducing the Hopf bifurcation state considered responsible for several highly nonlinear and peculiar features of the hearing mechanism. We find that the biomembranes’ bending modulus and the intracellular charge concentration (which for instance could represent K+ or Ca2+) are the two key control parameters that significantly impact the stability of the system and hence the hearing mechanism. Our work highlights the importance of flexoelectricity, confirms earlier assertions that the cochlea amplifies the acoustic stimuli through its exceptional electromechanical energy conversion property, and provides insights into how physical properties such as biomembranes’ bending modulus impact the performance of the hearing system.