Physiology of the cell in a minimal model
description of the membrane potential
H.G.J van Mil
Graduate School of Neuroscience, Institute Neurobiology: Cell Biophysics
group,
University of Amsterdam, The Netherlands
In the thermodynamical sense the living cell is an open system that exchanges matter and energy with its environment. By using fluxes of free energy and matter the living cell keeps itself out of thermodynamical equilibrium. One of the manifestations of this in living cells is the membrane potential (Vm): the electrical part of the weighted electro-chemical gradients of the ions involved. Since the fifties a quantitative description known as the Goldman-Hodgkin-Katz equation is used. It relates Vm to the gradients and membrane permeabilities of sodium, potassium and chloride as a reformalization related to a steady state condition. If one describes Vm dynamically, using the established ideas of a pump that actively translocates ions and dissipative dynamical currents through the membrane permeabilities (as described in the Hodgkin Huxley) no stable point of attraction is generated. For models' bases on these current equations, the rank of the system will always by smaller than its dimension. From experimental observations and biological considerations however a stable attractor should be expected. A second observation in cell biology is that metabolism of the cell influences the ions activities underlying Vm. On the other hand transport of matter through the membrane is powered by Vm, that by itself influences the macromolecules physical and biochemical activity underlying cellular metabolism. In this way the anabolism and catabolism of the cell are related to properties in Vm. This results in a strong chemical asymmetry between the intra- and extra-cellular space. In my poster presentation I shall analyse and discuss the model structure that is needed for a minimal model of Vm to generate a stable point. In this model stochastic and deterministic theories are combined. They may thus link physiological properties of the cell to the behaviour of Vm and visa versa. The consequence for existing models is discussed.