Cooperative response of chemically excitable membrane II. Two-state models and their limitations

Abstract

Various types of two-state models, classified by the type of direct receptorionophore coupling, were formulated based on the previously presented generalized two-state model of cooperativity (Kijima & Kijima, 1978) and their dose-response relationships were examined. Hill coefficient at the mid-point of dose-response curve n H o the measure of the cooperativity of curves, is restricted for partial agonists in any two-state models because n H o is expressed by the product of two terms, one of which decreases when the other increases. In the independent gating unit model in which the channel opens only when the independent gating units are all in the activated state, the restriction of n H o is the most stringent: it never exceeds 2. In 2 ÷ 1·39 even for full agonist. It appears to be incompatible with most of the cooperative responses observed on chemically excitable membrane. In the basic model or one protomer-one channel model, n H o never exceeds 2·0 when 〈 p〉 ∞, the maximum fraction of open-channel, is less than 2 3 . In the cooperative gating unit model, n H o is the least restricted, which is less than 2·8 when 〈 p〉 ∞ ≤ 0·5, but if the number of gating units, N in a receptor is practically reasonably small ( N ≤ 12), n H o ≤ 2·0 when 〈 p〉 ∞ ≤ 0·58. It is discussed whether or not several representative drug-receptive membranes can be accounted for by two-state models. Response of the insect sugar receptor is out of the above limitations of two-state models and can be accounted for by three-state model. The origin of cooperative interaction can be inferred by the shapes of dose-response curves. Cooperative dose-response curves of two dimensional lattices or oligomerc systems with large number of protomers weakly interacting by long range forces bend upward more markedly at lower region than the curves of strongly interacting oligomers, when curves with the same n H o are compared.