Solution of carrier-type transport models: General solution for an arbitrarily complex rapid equilibrium model

Abstract

A general framework for solving and analyzing rapid equilibrium carrier models is given. The basis of this work is the demonstration that the solution of an arbitrarily complex model of this type can be written in the form $$J_S^{1 \to 2} = \frac{{C_o A_{12} F_{21} }}{{\alpha _1 F_{21} + \alpha _2 F_{12} }}$$ whereJs1→2 is the unidirectional flux of the substrateS from side 1 to side 2 of the membrane,C0 is the total number of carriers andA12,F12,F21, α1 and α2 are sums of terms which can be written down simply and directly from knowledge of the basic properties of the model. The above relation not only leads to a simple and convenient method for solving transport models of this type, but also provides a powerful algebraic tool for analyzing the properties of individual models or groups of models. In this regard several examples of the potential utility of this formalism are given. The effects of “dead-end” inhibitors on rapid equilibrium carrier models are analyzed. Also the properties of carriers with one substrate binding site are studied in some detail. A parameterization ofJs1→2 entirely in terms of experimentally measurable kinetic parameters as well as a set of generalized rejection criteria are derived for these models. Since the existence of a single substrate binding site is the only assumption made in these latter derivations, the results obtained necessarily apply to all rapid equilibrium models of this type, irrespective of complexity.