The derivation of second degree rate equations arising from two-substrate, two-product enzyme catalysed reactions whose catalytic cycle is branched

Abstract

A selection of two-substrate, two-product enzyme catalysed reactions with alternate catalytic cycles and second degree rate equations was examined by the computer program described by Kinderlerer and Ainsworth (1976). It is shown that the numerator terms of the rate equations are particularly simple, easy to derive and capable of creating a broad division of the mechanisms considered. The numerator terms also have the advantage of being unaffected by dead end inhibition or the presence of Theorell-Chance reactions. It is then shown that the relatively small group of mechanisms, isolated by the numerator analysis, can be distinguished from each other by considering the denominator terms of the rate equation that are second degree in the concentration of the varied substrate.