A measure for the distance from equilibrium

Abstract

Subcellular systems represented by macromolecules (enzymes, ion channels etc.) function far from equilibrium. We propose a characterization of such systems in terms of their distance from equilibrium (DFE). Standard chemical and physical approaches are not always applicable because they need too detailed kinetic and thermodynamic information. We suggest a general measure for DFE in systems described by fluxes. Each connection between subsystems corresponds to two unidirectional fluxes, f and b. These fluxes form forward and backward vectors, ? and ?, respectively. The forward direction is defined by a net flux, so that 0≤b≤f. The flux vec-tors ℜ={?, ?} and ?={?, –?} are introduced. DFE is defined as P=(ℜ?/??)²=cos² α, α being the angle between the ℜ- and ?-vectors, with 0≤α≤π/2. The distance from strict irreversibility, E, is defined symmetrically: E=cos²(π/2–α)=1–P. For a single-stage reaction, parameter P is strictly equivalent to the chemical affinity. For multi-stage reactions P reflects DFE better than chemical affinity. Near equilibrium P is equivalent to excess Gibbs energy. Away from equilibrium, P scales DFE better.