A theoretical expression for the protection associated with stoichiometric and catalytic scavengers in a single compartment model of organophosphorus poisoning

The ability of certain organophosphorus (OP) compounds to inhibit acetylcholinesterase (AChE) has made them useful for industrial (insecticides) and military (nerve agents) purposes. We have previously published a single compartment mathematical model of the interactions between OP nerve agents and the enzymes affected by these agents. That model, which could be used to predict the LD50 of seven nerve agents in rats, has been extended to include the protective actions of stoichiometric and catalytic OP–scavenger enzymes (delivered as pretreatments) so that protective ratios attributable to the scavengers may be predicted. Prediction of expected human protection from in vitro rate constant and initial enzyme level measurements is the ultimate goal for this work. The enhanced model predicts the LD50 from rate constants of the OP agent’s binding reactions with AChE, carboxylesterase (CaE) and a stoichiometric scavenger (S); a first-order OP elimination rate (including a contribution due to a catalytic scavenger); and whole body estimates of AChE, CaE and S. The ratio of the scavenger-treated LD50 estimate to the scavenger-free LD50 estimate provided a theoretical expression describing the scavenger’s contributions to the protective ratio. Published in vivo protective ratios for two stoichiometric scavengers (fetal bovine serum AChE and human utyrylcholinesterase) against challenge by several OP agents in mice were compared with ratios predicted by the model. A linear regression analysis of in vivo protective ratios in mice versus the ratios predicted by the model from the in vitro measurements resulted in an R2 value of 0.902. The catalytic scavenger portion of the theory could not be validated due to a lack of published data. We conclude that the one-compartment model can be used to make reasonable estimates of the protective ratio attributable to stoichiometric scavengers, but can make no conclusions regarding the ability of the model to predict catalytic scavenger protection ratios.