Past exam of the biological physics course of the University of Oxford / 2015 / 2 / b / Solution

Here $V_m$ is the inside-minus-outside membrane potential, $V_K$ is the potassium Nernst equilibrium potential, and ${\bar{g}}_K$ is the maximum potassium conductance, or conductance per area if $I_K$ is a current density. The factor $n\in [0,1]$ is the permissive-state probability of an activation gate. Four independent permissive gates in an ion channel give the open fraction $n^4$, henceThe model assumes identical independent gating units, additive currents from many ion channels, an approximately ohmic open-pore current, and fixed ionic activities setting $V_K$. Outward positive electric current is obtained for $V_m>V_K$. The original delayed-rectifier term omits rapid ion-channel inactivation. The fourth power is a successful phenomenological gating description, rather than a deduction of the molecular structure from this equation alone.