Potassium conductance models related to an interactive subunit membrane II: Monte Carlo analysis and subunit migration

Abstract

A model of membrane potassium conductance is proposed based on the concept of a fluid mosaic membrane where subunit migration and interaction are responsible for important features of the conductance kinetics. In the mathematical description of this model the statistical correlations normally present when considering interacting subunits can be ignored because of rapid subunit migration which ensures a random distribution of subunits in the pro- and anti-conductance states. Similarly potassium conductance pores, which occur whenever there is an appropriate grouping of subunits in the pro-conductance state, will also be randomly distributed. The validity of these assertions, which were also implied in an earlier description of our model, is indicated by the present computer solutions of the master equation for the membrane by Monte Carlo methods. It is shown however, that the rate of subunit migration is required to be at least an order of magnitude greater than the fastest subunit transition rate for effective randomization to occur. The usual criteria for an effective potassium conductance model, those of satisfactory “induction” and “superposition”, are met by this model. Calculations have also been made for the condition where subunits cannot migrate. Even with this restriction the model is capable of accurately simulating experimentally determined potassium conductances provided that polarizations outside the range of the normal action potential are not encountered. The implications of subunit migration, of restriction of migration and of interaction between migrating subunits are discussed for membrane conductance in general.