The rate of equilibration in a competitive n drug system and the auto-inhibitory equations of enzyme kinetics: some properties of simple models for passive sensitization

Abstract

The solution of the equation for the rate of equilibration of n drugs all competing for the same receptors is presented and the two-drug case is given explicitly. The case of two com­peting drugs with the same rate constants is discussed in detail as it is the simplest plausible model for the rate of passive sensitization. The predictions of this model are compared with present knowledge about the rate of onset and the persistence of sensitization. The model suggests that if the observed rate of sensitization depends on the rates of reaction with receptors then (1) equilibration will be too slow to be seen in the usual length of passive sensitization experiment in vitro , (2) there will be no fast initial phase of sensitization, and (3) sensitizing immunoglobulins which persist for a long time (e. g. those of man and rat) will have a slower rate of onset than those which persist for a shorter time (e. g. those of the guinea-pig). It is also emphasized that there are at present no firm grounds for supposing that the more persistent sensitizing antibodies have a higher affinity for cells than the less persistent since the association rate constants are unknown. The model proposed by Mongar & Winne, which accounted for the auto-inhibition observed during passive sensitization by a mechanism involving two-point attachment of antibody to cells, is discussed in relation to uncompetitive and non-competitive models for auto­-inhibition. These models all fit the available observations equally well but the last of them does not involve two-point attachment of antibody. The presence of non-specific immuno­globulin in the antibody preparation used is shown to have a potentially very serious effect on some of the parameter estimates in all three models, and corrections for errors from this source are discussed.