Co-operative response of chemically excitable membrane III. Three-state model

Abstract

The general three-state model is formulated first, which is the direct extension of the unified two-state model previously formulated ( Kijima & Kijima, 1978). In this model, each protomer in a symmetrically interacting system (oligomers or lattices) can take three states, S, R and Q, where S and R states are the same as in the two-state model and Q state is another state either corresponding to a different open-state of ionophore from R open-state or corresponding to another closed state of ionophore. The model has no restriction on the value of Hill coefficient at the midpoint of the dose-response curves in contrast to two-state models. It is applied on GABA sensitive inhibitory synapse of crayfish muscle to account for anomalous behaviour of the membrane in I − solution. The simplified versions of the above general three-state model are also formulated (simplified three-state model), in which it is assumed that R and Q state are equivalent in regard to the nearest neighbor interaction. By this assumption, R and Q state are collectively treated as state A and mathematical formula obtained on Ising model are applicable on this model. This model is applied on the insect sugar receptor which was shown to be incompatible with the two-state models ( Kijima & Kijima, 1980). Further simplification of the above simplified model results in two convenient models: three-state KNF model and three-state MWC model, which have minimum parameters but sufficient to account for most experiments. They give plausible physico-chemical base on the “classical model” in which the existence of both inactive and active ligand-receptor complex is assumed.