Mathematical model of outer hair cell regulation including ion transport and cell motility

To understand the regulatory processes within the cochlea, and outer hair cells (OHCs) in particular, we have developed a mathematical model of OHC regulation that takes into account their known electrical properties, and includes fast and slow somatic motility. We model how cytosolic Ca2+ is involved in regulation of (i) the OHC membrane potential, (ii) the operating point of OHC mechano-electrical transduction (MET) channels via slow motility; (iii) basolateral wall K+ permeability via Ca2+-sensitive K+ channels; and (iv) cytosolic concentrations of Ca2+ itself, via Ca2+-ATPase-mediated sequestration within the OHCs and Ca2+-induced Ca2+-release (CICR) from the same intracellular Ca2+ storage organelles. To account for some aspects of the cochlea’s transient response to experimental perturbations, we have included a putative intracellular second-messenger cascade based on cytosolic Ca2+. Overall, the OHC basolateral permeability determines the resting membrane potential of the OHCs and their standing current, which influences the endocochlear potential, and also affects the AC receptor potential that drives the prestin-mediated somatic electromotility and active cochlear gain. The model we have developed provides a physiologically-plausible and internally-consistent explanation for the time-courses of the cochlear changes we have observed during a number of different experimental perturbations, including a slow oscillatory behaviour presumed due to oscillations in cytosolic Ca2+ concentration. We also show how the known ionic mechanisms within OHCs act to regulate membrane potential and hair bundle angle over a very wide range of strial current and intracochlear hydrostatic pressure. Not included in the model are osmotic effects, the nonlinear aspects of prestin’s electromotility, the intracellular role of Cl− in modifying this motility, nor adaptation of MET at the apex of OHCs. Only one Ca2+ sequestration compartment has been included in this implementation of the model, with the two types of basolateral Ca2+ cisternae combined into a single compartment. Despite these limitations, the model as presented offers insights into the regulation of OHC membrane potential and MET at the hair cell apex, and is our first step in understanding in a quantitative way the integrated function of the molecular components of ion transport and motility in these cells.