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

Although there are theoretical studies on the thermodynamics of ion channels, an investigation involving the thermodynamics of coupled channels has not been proposed. To overcome this issue, we developed calculations to present a thermodynamic scenario associated with mechanoelectrical transduction channels as a single and coupling of two-state channels. The modeling was inspired by the Tsallis theory, in which we derived the open and closed probability distributions, the joint probability distribution, the Tsallis entropy, and the Shannon mutual information. Despite being well studied in many biological systems, the literature has not addressed both entropy and mutual information related to isolated and a pair of physically interacting mechanoelectrical transduction channels. Inspired by the hair cell biophysics, we revealed how the presence of nonextensivity modulates the degree of entropy and mutual information as a function of stereocilia displacements. In this sense, we showed how the non-extensivity regulates the current versus displacement curve for a single and two interacting channels made up of a single open and closed states. Overall, subadditivity and superadditivity yielded increments and decrements in the entropy and mutual information compared with the extensive regime. We also observed that the magnitude of the interaction between the two channels significantly influences the amplitude of the joint entropy and the mutual information. These results are directly related to the modulation of the channel kinetics, given by changes evoked by hair cell displacements. Finally, we found that the gating force modulates the contribution of subadditivity and superadditivity present in the joint entropy and the mutual information. The present findings shed light on the thermodynamic process involved in the molecular mechanisms of the auditory system.