Onset Dynamics of Type A Botulinum Neurotoxin-Induced Paralysis

Experimental studies have demonstrated that botulinum neurotoxin serotype A BoNTA causes flaccid paralysis by a multi-step mechanism. Following its binding to specific receptors at peripheral cholinergic nerve endings, BoNTA is internalized by receptor-mediated endocytosis. Subsequently its zinc-dependent catalytic domain translocates into the neuroplasm where it cleaves a vesicle-docking protein, SNAP-25, to block neurally evoked cholinergic neurotransmission. We tested the hypothesis that mathematical models having a minimal number of reactions and reactants can simulate published data concerning the onset of paralysis of skeletal muscles induced by BoNTA at the isolated rat neuromuscular junction NMJ and in other systems. Experimental data from several laboratories were simulated with two different models that were represented by sets of coupled, first-order differential equations. In this study, the 3-step sequential model developed by Simpson J Pharmacol Exp Ther 21216-21,1980 was used to estimate upper limits of the times during which anti-toxins and other impermeable inhibitors of BoNTA can exert an effect. The experimentally determined binding reaction rate was verified to be consistent with published estimates for the rate constants for BoNTA binding to and dissociating from its receptors. Because this 3-step model was not designed to reproduce temporal changes in paralysis with different toxin concentrations, a new BoNTA species and rate kS were added at the beginning of the reaction sequence to create a 4-step scheme. This unbound initial species is transformed at a rate determined by kS to a free species that is capable of binding. By systematically adjusting the values of kS, the 4-step model simulated the rapid decline in NMJ function kS or 0.01, the less rapid onset of paralysis in mice following i.m. injections k S0.001, and the slow onset of the therapeutic effects of BoNTA kS0.001 in man.