Thermodynamics of a voltage-gated potassium channel

In order to know how a single potassium channel works in its microscopic niche, a hybrid process about the observables of channel state and voltage is constructed, which comprises the interweaving kinetics of channel gating, voltage decay, and thermal noise. The formula of entropy production rates (i.e., power dissipation) is derived and the stationary probability distribution is solved analytically. It is found that gating is thermally robust, and the underlying mechanism is explained. Using the mutual information between the distributions of the channel state and voltage to characterize how much information of gating can be broadcasted by voltage evolution, and the entropy production rate per unit area to represent the energy costs of the system, we plot the Pareto front from the perspective of accuracy-energy trade-off, and find that, in terms of information broadcasting, the channel works most efficiently without the extrinsic driving current.