A network thermodynamic approach to Hill and King–Altman reaction–diffusion kinetics

Abstract

The major graphical approaches to kinetics—Hill diagrams and the King–Altman rules—can be considerably simplified using network techniques. An algorithmic procedure is developed and applied to several concrete examples which permits systems described in terms of first order transitions to be represented as connected networks. The utility of this representation is: (1) it permits powerful results from network thermodynamics and network theory to be applied to complex kinetic networks such as those representing biological dynamic systems. (2) The intrinsic role played by the thermodynamic principle of microscopic reversibility in networks containing cycles is emphasized: microscopic reversibility implies Onsager reciprocity for perturbed equilibrium systems. It now becomes clear that Onsager reciprocity is a topological property of systems to which thermodynamics is applicable. Reciprocity, or its lack can be rigorously established for macroscopic systems far outside the domain of Onsager’s original demonstration. These ideas are applied to produce a complete analysis of a complex active transport system previously studied by Hill diagrams.