A dissipative Lagrangian formulation of the network thermodynamics of (pseudo)-first-order reaction–diffusion systems

Abstract

A formulation of the equilibrium and dynamic properties of reaction–diffusion systems is developed which is analogous to the Lagrangian formulation of dissipative mechanical systems and electrical networks. Since the formulation uses ‘‘kinetic’’ forces for the chemical reactions, not thermodynamic forces, the Lagrangian and dissipation function are only apparent quantities. Nonetheless, the Lagrangian determines equilibrium properties completely, and the dissipation function contains all dissipative effects. The formulation shows that no modulation of the potentials in diffusional pathways is caused by the presence of the chemical reactions, as was previously claimed, if the same scale is used for all reactions and diffusion steps in the system. Furthermore, the formulation renders the system in a network form which guarantees symmetry in the force-flow relations at the stationary state. This is shown explicitly for the special case of King–Altman–Hill systems. Unfortunately, the Lagrangian approach using kinetic forces seems to be limited to systems with only first-order or pseudo-first-order reactions. To treat higher order reactions, the thermodynamic forces must be used.