Rational polynomial equation as an unbiased approach for the kinetic studies of Drosophila melanogaster acetylcholinesterase reaction mechanism

The hydrolysis of substrates by cholinesterases does not follow the Michaelis–Menten reaction mechanism. The well-known inhibition by excess substrate is often accompanied by an unexpectedly high activity at low substrate concentrations. It appears that these peculiarities are the consequence of an unusual architecture of the active site, which conducts the substrate molecule over many stages before it is cleaved and released. Structural and kinetic data also suggest that two substrate molecules can attach at the same time to the free, as well as to the acetylated, enzyme. We present a procedure which provides an unbiased framework for mathematical modelling of such complex reaction mechanisms. It is based on regression analysis of a rational polynomial using classical initial rate data. The determination of polynomial degree reveals the number of independent parameters that can be evaluated from the available information. Once determined, these parameters can substantially facilitate the construction and evaluation of a kinetic model reflecting the expected molecular events in an enzymic reaction. We also present practical suggestions for testing the postulated kinetic model, using an original thermodynamic approach and an isolated effect in a specifically mutated enzyme.