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H.G.J. van Mil+,#, M. Bier*, R.J. Geukes Foppen+, J. Siegenbeek van Heukelom+.
+Institute of Neurosciences, Cell Biophysics, Faculty of Biology, University of Amsterdam, Kruislaan 320, 1098 SM Amsterdam, the Netherlands.
#Theory of Complex Fluids, Faculty of Applied Sciences, Delft Universtity of Technology, Delft, the Netherlands.
*Department of Biochemistry and Molecular Biology and Department of Surgery MC6035, University of Chicago, 5841 South Maryland Avenue, Chicago, IL 60637, USA.

Decreasing the extra cellular potassium concentration (Ko) leads to a hyperpolarization of the membrane if no voltage sensitive phenomena are activate. However, lowering Ko below a certain threshold value, in mammalian skeletal muscle fibers, resulted in a sudden depolarization due to the voltage sensitive inwarly rectifing potassium channel (IRK).
A model of coupled differential equations was constructed containing passive currents for sodium, chloride and potassium (including the IRK), as described by the Goldman flux equation, and a kinetic description of an ATP driven sodium potassium pump. Intra celullar ionic charges are related to the electrical potential (Vm) by a integrated version of the Kirchhoff current law, containing a integration constant identified as the excess intracellular impermeable charge.
Analysis of the model revealed as an underlying dynamical mechanism hysteresis. Using physiological realistic values for the parameters involved, the model fitted the data with quantitatively accuraty. Measurement of the hysteresis in mammalian muscle fibers directly verified the existence of hysteresis. The introduction of a osmolarity sensitive cotransporting system resulted in the observed shift of the bistability to higher concentrations of Ko as observed in experiments. Although strikly speaking the equations are derived for the steady state, the model described the trajectories between the steady state quantitatively well.
Extentions of the model to include more moleculair details of potassium channels like the IRK are discused.