The mechanism of acute toxicity of the organophosphorus insecticides has been known for many years to be inhibition of the critical enzyme acetylcholinesterase (EC 3.1.1.7), with the resulting excess acetylcholine accumulation leading to symptoms of cholinergic excess. The bimolecular inhibition rate constant k(i) has been used for decades to describe the inhibitory capacity of organophosphates toward acetylcholinesterase. In the current study, a new approach based on continuous systems modeling was used to determine the appk(i)s of paraoxon and methyl paraoxon towards mouse brain acetylcholinesterase over a wide range of oxon concentrations. These studies revealed that the bimolecular inhibition rate constants for paraoxon and methyl paraoxon appeared to change as a function of oxon concentrations. For example, the appk(i) found with a paraoxon concentration of 1000 nM was 0.16 nM-1h-1, whereas that for 0.1 nM paraoxon was 1.60 nM-1h-1, indicating that the efficiency of phosphorylation appeared to decrease as the paraoxon concentration increased. These data suggested that the current understanding of how these organophosphates interact with acetylcholinesterase is incomplete. Modeling studies using several different kinetic schemes, as well as studies using recombinant monomeric mouse brain acetylcholinesterase, suggested the existence of a second binding site in addition to the active site of the enzyme, to which paraoxon and methyl paraoxon bound, probably in a reversibly manner. Occupation of this site likely rendered more difficult the subsequent phosphorylation of the active site by other oxon molecules, probably by steric hindrance or allosteric modification of the active site. It cannot be ascertained from the current study whether the putative second binding site is identical to or shares common elements with the well-characterized propidium-specific peripheral binding site of acetylcholinesterase.