Branched reaction mechanism for the Na/K pump as an alternative explanation for a nonmonotonic current vs. membrane potential response.

Nonmonotonic velocity vs. membrane potential curves are often taken as evidence that two steps involve charge movement through the electric field. However, a branched reaction scheme in which only one step involves charge movement per cycle can lead to a nonmonotonic response. A similar case occurs in enzyme kinetics: nonmonotonic velocity vs. substrate curves are often taken as evidence for two different substrate-binding sites. However, a branched reaction scheme in which only one substrate binds per complete cycle can lead to a nonmonotonic response (see Segel, I.H. 1975, Enzyme Kinetics, pp. 657-659. John Wiley & Sons, New York). Some analytical constraints on the relative sizes of the rate constants of a branched reaction mechanism that give rise to nonmonotonic responses are derived. There are two necessary conditions. (i) The rate of at least one step in the branched pathway must be less than the rate of the step after the branch. (ii) The rate of the pathway in which S binds first must be slower than the rate of the other pathway. Analogous cases give rise to nonmonotonic current vs. membrane potential curves. A branched mechanism for the Na/K pump provides an alternative explanation for a nonmonotonic pump current vs. membrane potential relationship.