A theoretical model of the competition between hydrolase and carboxylesterase in protection against organophosphorus poisoning

Abstract

A system of coupled non-linear differential equations describing interactions between organophosphorus compounds (OPs), OP hydrolase, acetylcholinesterase (AChE), and carboxylesterase (CaE) in a single compartment was derived incorporating irreversible combination of OP with AChE, hydrolytic breakdown of OP, and irreversible combination of OP with CaE. The equations were then uncoupled, providing non-linear differential equations on AChE, CaE and OP concentrations. One steady state solution of the AChE equation provided theoretical expressions for the amounts of OP hydrolyzed, bound with CaE, and bound with AChE. Assuming that the LD50 of an OP reflects the dose that depletes AChE to a `minimal essential' level and that a single compartment model is applicable in vivo, the steady state solution becomes an equation predicting the LD50 from rate constants, initial enzyme levels, and the allowable AChE depletion. Normalization by initial AChE concentration produced a dimensionless relationship describing an `OP toxicity surface' that clearly demonstrates regions where hydrolysis and CaE offer protection against OP poisoning. The surface can be used to theoretically predict an LD50 given only kinetic rate constants and effective whole-body AChE and CaE levels. Predictions of LD50s of seven OPs in rats were compared with published data. The relationship was found to adequately predict published LD50s spanning 5 orders of magnitude. The OP toxicity surface relationship provides a conceptual tool for use in OP toxicity research but should be particularly useful in predicting the relative protective effects of catalytic and stoichiometric scavenger mechanisms for an OP.