Properties of membrane stationary states. 2. The isobaric isothermal ensemble

Abstract

A multi-state membrane transport system serves as the basic model for a comparison of equilibrium and stationary state distributions of ions within an ensemble of membrane channels. Transition probabilities for intramembrane transitions are developed for consistency with an equilibrium Donnan potential and the magnitude of the flux in the stationary state can be controlled with either the bath concentrations or an externally applied potential. The stationary state distribution and operational thermodynamic parameters for the stationary state are expressed as functions of the ratio (jnet/p) where jnet is the observable net membrane flux and p is a characteristic decay constant for the intramolecular transitions. Both parameters are experimentally accessible so that their time independent ratio serves as an experimental measure of the membrane configuration. When operational thermodynamic parameters are expressed as functions of the ratio (j/p) for systems which obey the condition of detailed balance, the free energy varies quadratically with the ratio while the enthalpy, expressed as an average membrane potential, varies linearly with the ratio. As the system is driven from its equilibrium configuration by the net membrane flux the free energy increases relative to the enthalpy of the membrane. The free energy is localized in the membrane region at the expense of dissipation in the bathing solutions.