Competition of two time scales determines the performance of a voltage-gated potassium channel

The dynamics of a voltage-gated potassium channel in real environments represents a crucial bridge between its molecular structure and functions. However, it is still missing due to the mathematical difficulty that arises from the high dimensionality and nonlinear interregulation. Here we present a method for solving the stationary distribution of a hybrid process that contains two negatively interregulating kinetics: channel gating and voltage decay. The results can be summarized as follows: first, the voltage distribution is determined by the competition of their time scales; second, the fluctuation structures in parameter space illustrate that, to perform the voltage-controlling task, the channel gating is elastic while the membrane produces the stabilizing function; third, the power dissipated by the capacitive currents and the internal battery current are calculated and explained. Based on these findings, we examine the manner in which macroscopic functions of potassium channels are manifested. Our methodology provides an accurate characterization of hybrid processes that are pervasive in the life sciences.