Ion flow through a membrane: effect of chemical reaction on time dependence

The membrane model previously described [Hays, T.R., Buckwalter, C.Q., Lin S.H. & Eyring, H. (1978) Proc. Natl. Acad. Sci. USA 75, 1612-1615] for ion flow through a membrane is expanded to include the effect of binding of the mobile ion at the occupiable sites in the membrane. Two different effects were investigated: alteration of the association-dissociation rates at constant equilibrium constant and alteration of the equilibrium constant at constant dissociation constant. Increasing the rates of association and dissociation initially causes an increased slowing of the relaxation to the final steady state, though ultimately the curves for the faster rates cross those for the slower states. Increasing the equilibrium constant causes a greater delay in the relaxation curve, with the curves for different equilibrium constants not crossing. Overall, the effect of binding is not very great unless the equilibrium constant for binding is quite large.