MODELLING ACETYLCHOLINESTERASE KINETICS: THE IDENTIFIABILITY PROBLEM IN PARAMETER ESTIMATION

Abstract

Acetylcholinesterase (E.C. 3.1.1.7) is a typical hydrolase showing substrate inhibition. Classical works stated a two-step kinetics for the catalytic mechanism. We analyse here a full interacting model for the substrate bound to an inhibitory site different to the catalytic one, in agreement with current tridimensional data. A mixed model derived from equilibrium-steady state analysis fits fairly well to experimental data. We conclude that both catalytic steps are susceptible of partial inhibition, with 15% of remaining activity for substrate saturated enzyme. Indeed, substrate inhibition would be preferentially exerted on one of the catalytic steps, leading to particular cases which fit to data as well. The parametric identity among the mathematical expressions from restricted models disables identifiability of kinetic constants solely by fitting to data. Thus, additional information is required from other experimental approaches. Based on the cited closeness between both rate constants for the substrate acetylthiocholine, dissociation constants at the catalytic and inhibitory sites are estimated in ~ 63 μM and ~ 0.35 mM respectively, while interaction between binding sites might enhance the latter up to 16 mM. We also emphasise the relevance of considering substrate inhibition in kcat extrapolations even at low substrate concentrations. Finally, we are able to predict total acetylated enzyme values in the order of those done from direct experimental measurements.