The Journal of Membrane Biology

, Volume 13, Issue 1, pp 37–60 | Cite as

Properties of membrane stationary states

I. The microcanonical membranes
  • Michael E. Starzak


The flux of permeant species through a membrane is examined using discrete state stochastic models for the transport process within the membrane. While a membrane flux is maintained due to a concentration gradient between bathing solutions, the distribution of species within the membrane evolves to a time invariant configuration which can differ significantly from the equilibrium configuration. Some special properties of these stationary states are examined using linear, microcanonical models for the membrane transport process. Analysis of these models reveals properties which are masked by the phenomenological analysis of irreversible thermodynamics. For example, the models can be used to study the nature of multi-state relaxation within the membrane by observation of the time dependence of the net membrane flux when the membrane is perturbed from its stationary state distribution. Under some conditions, multi-state models will produce relaxation similar to that observed for single-state processes. The symmetry within the membrane is a critical factor for monitoring relaxation processes within the membrane. Because of the stationary nature of the membrane configuration, statistical thermodynamic variables can be defined for the membrane configuration. The total system is not in equilibrium since the baths must still be described by dissipation functions. In the stationary state, the configurational entropy of the membrane is lowered relative to equilibrium and is shown to depend quadratically on the time independent parameter (j/p) wherej is the membrane flux andp is a characteristic transition probability for intra-membrane transitions. The basic membrane system serves as a quantitative example of the entropy reduction possible in a stationary state system. An allosteric transition mediated by the stationary state configuration is examined as a means of utilizing this negentropy production.


Stationary State Allosteric Transition Configurational Entropy Invariant Configuration Membrane Flux 
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Copyright information

© Springer-Verlag New York Inc 1973

Authors and Affiliations

  • Michael E. Starzak
    • 1
  1. 1.Department of ChemistryState University of New York at BinghamtonBinghamton

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