A method for defining steady-state unidirectional fluxes through branched chemical, osmotic and chemiosmotic reactions.

A general mathematical technique is described for deriving analytical expressions and obtaining numerical solutions for the steady-state unidirectional fluxes between two chemical states via any set of intermediate states present within any hypothetical system of unbranched or branched and overlapping elementary processes. The technique is a restricted application of the theory of Markov processes with conditional probabilities being assigned to the chemical state transitions constituting the system of reactions. While, in principle, the technique requires the summation of an infinite power series of a matrix defining the conditional probabilities of single state transitions, the power series is evaluated by means of the Taylor series expansion for matrices. As this technique allows isotopic exchange velocity equations to be derived from systems of reactions in which no distinction between the labelled and unlabelled species is required it provides a distinct and independent alternative to previously proposed methods. The technique is illustrated by application to a mechanism for second-order carrier-mediated transport.