Past exam of the mathematics and the environment and mathematical physiology course of the University of Oxford / 2009 / B / 4 / d / ii

The relation $B_i=-J$ means $k_{-}{p}_i=k_{+}{s}_i{c}_i+J$. Put $K=k_{-}/k_{+}$ and substitute the preceding expression for $c_i$:The first term is the equilibrium binding contribution from the outward free-carrier pool; the additional terms account for the maintained current and the excess inward-facing free carriers. This is a steady throughput relation, not a detailed-balance assumption.