Geometric gain approximation dictates the accuracy of hair bundle models

Sound perception arises from oscillations of stereocilia, hair-like structures that convert mechanical motion into electrical signals via ion channels. These signals, depending on the stereocilia's location, drive neural activation and nonlinear sound amplification, crucial for normal hearing. Mathematical models of isolated hair bundles (HBs), composed of stereocilia, provide a mechanistic understanding of these processes. A key parameter in these models is geometric gain, which estimates how mechanical deflections impact gating spring extension, modulating ion channel activity. Traditionally, this gain is approximated as the ratio of horizontal spacing between adjacent stereocilia pivots to their average height. However, this simplified ratio can lead to inaccuracies in predictions of HB sensitivity and stiffness. We analyzed gain at five cochlear locations in adult mice, comparing two definitions: the approximated “stick geometric gain,” based on two infinitesimally thin stereocilia, and the “true geometric gain” derived using our nonlinear two-row isolated HB model with complete morphology. We found that the stick model overpredicts gain by a factor of 1.5–2, resulting in overestimated changes in gating spring tension, sensitivity, stiffness, and narrower activation curves. We discuss the implications of gain-overprediction on the interpretation of experimental results and theoretical models. [Work supported by NIH-R01-NIDCD04084].