Nonextensive realizations in interacting ion channels: Implications for mechano-electrical transducer mechanisms

We propose a theoretical model to investigate the thermodynamics of single and coupled two-state ion channels, associated with mechanoelectrical transduction (MET) and hair cell biophysics. The modeling was based on the Tsallis nonextensive statistical mechanics. The choice for a nonextensive framework in modeling ion channels is encouraged on the fact that we take into account the presence of interactions or long-range correlations in the dynamics of single and coupled ion channels. However, the basic assumptions that support Boltzmann-Gibbs statistics, traditionally used to model ion channel dynamics, state that the system is formed by independent or weakly interacting elements. Despite being well studied in many biological systems, the literature has not yet addressed the study of both entropy and mutual information related to isolated or physically interacting pairs of MET channels. Inspired by hair cell biophysics, we show how the presence of nonextensivity, or subadditivity and superadditivity modulates the nonextensive entropy and mutual information as functions of stereocilia displacements. We also observe that the magnitude of the interaction between the two channels, given by a nonextensive parameter, influences the amplitude of the nonextensive joint entropy and mutual information as functions of the hair cell displacements. Finally, we show how nonextensivity regulates the current versus displacement curve for a single and a pair of interacting two-state channels. The present findings shed light on the thermodynamic process involved in the molecular mechanisms of the auditory system.