Distance of the reduced Brusselator from equilibrium

Abstract

The new concept of a nonequilibrium parameter P is applied to a reduced Brusselator, considered as a kinetic model for cellular processes. The reduction corresponds to omitting a monomolecular reaction. The deviation from equilibrium is due to a fixed nonequilibrium value of an extracellular concentration B, responsible for energizing and determining the steady-state value of the overall chemical affinity ?. The value of ? is insensitive to different steady states possible for a given set of rate constants. In contrast, the parameter P is state dependent. In particular, it may jump together with state variables. Two limiting cases of high ? are investigated, B→ 0 and B→ 1. In the first case P grows monotonically with ?. In the second case there is always a steady state solution with P→ 0. The physical interpretation of this effect of “equilibrium far from equilibrium” reveals the real predictive power of the parameter P. Relaxation regimes are investigated for a doubly reduced Brusselator. Both P and ? are in general time dependent and have jumps in their time derivatives. The canonical form of P is compared with the noncanonical one in the context of robustness of the new concept with respect to incomplete information about the system studied. These forms of P are different in relaxation to a nonequilibrium state and coincide in relaxation to an equilibrium state.