Free energy dissipation of the spontaneous gating of a single voltage-gated potassium channel.

Potassium channels mainly contribute to the resting potential and re-polarizations, with the potassium electrochemical gradient being maintained by the pump Na ⁺ /K ⁺ -ATPase. In this paper, we construct a stochastic model mimicking the kinetics of a potassium channel, which integrates temporal evolving of the membrane voltage and the spontaneous gating of the channel. Its stationary probability density functions (PDFs) are found to be singular at the boundaries, which result from the fact that the evolving rates of voltage are greater than the gating rates of the channel. We apply PDFs to calculate the power dissipations of the potassium current, the leakage, and the gating currents. On a physical perspective, the essential role of the system is the K ⁺ -battery charging the leakage (L-)battery. A part of power will inevitably be dissipated among the process. So, the efficiency of energy transference is calculated.