Simplifications of the derivations and forms of steady-state equations for non-equilibrium random substrate-modifier and allosteric enzyme mechanisms

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Abstract
The steady-state equations for “random” enzymic mechanisms (ones with alternative routes for substrate and enzyme to form enzyme-substrate complexes) are non-Michaelian and very complicated when a quasi-equilibrium approximation cannot be used. General methods for simplifying their forms and derivations are given and applied to several single-substrate mechanisms of general or topical interest. The special simplifications resulting from partial ordering of reaction mechanism, from gross inequalities of rate constants, and from special relationships between catalytic and dissociation rate constants, are considered with reference to allosteric mechanisms. Some equations mentioned, but not given here, and more detailed working out of some of those given, have been deposited as Supplementary Publication SUP 50069 (18 pages) at the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms given in Biochem. J. (1976) 153, 5.