BioSystems 47 (1998) 37–60 Enzymatic reaction rate limits with constraints on equilibrium constants and experimental parameters Douglas R. Bish a , Michael L. Mavrovouniotis b, * a Department of Biomedical Engineering, Northwestern Uniersity, Eanston, IL 60208, USA b Department of Chemical Engineering, Northwestern Uniersity, 2145 Sheridan Road, Eanston, IL 60208, USA Abstract A general methodology is presented for estimating maximum rates of enzymatic reactions based on general characteristics of enzymatic reaction mechanisms, kinetic limits and thermodynamics. The useful range of experimen- tally derived kinetic parameters can also be extended by the methodology. The methodology divides the reaction mechanism into physical and chemical steps. Maximum rates that comply with kinetic and thermodynamic constraints are calculated by setting the physical rate constants to their diffusion limits and optimising the chemical rate constants subject to constraints of the reaction mechanism and overall equilibrium constant. Rate estimates from this methodology can be subject to additional constraints from experimental data, and thus conform to the distinctive features of the enzymatic reaction. The methodology is demonstrated using a reversible enzymatic reaction model involving ordered binding of two reactants and ordered release of two products (bi – bi mechanism). Numerical results are shown for alcohol dehydrogenase (EC 1.1.1.1), which has a bi – bi mechanism. Pyrophosphatase (EC 3.6.1.1) with a uni – bi mechanism and triosephosphate isomerase (EC 5.3.1.1) with a uni – uni mechanism are also examined. © 1998 Elsevier Science Ireland Ltd. All rights reserved. 1. Introduction An irreversible enzymatic reaction with a single reactant has a maximum rate (r max ) equal to the rate of encounter between an enzyme and a reac- tant (Hiromi, 1979; Fersht, 1985), as follows: r max =ke t [A] (1) where k is the bimolecular encounter rate con- stant, e t is the enzyme concentration, and [A] is the concentration of the reactant. The theoretical upper-bound on the reaction rate, estimated using this simple equation, depends only on the diffu- sion of a single reactant to the enzyme. While some enzymes with efficient binding and intramolecular rearrangements might approach this maximum rate, Eq. (1) is an unrealistic sim- plification for most enzymatic reaction mecha- nisms. The rate expression does not take into account multiple reactants that would involve bi- * Corresponding author. Tel.: +1 847 4917043; fax: +1 847 4913728; e-mail: mlmavro@nwu.edu 0303-2647/98/$19.00 © 1998 Elsevier Science Ireland Ltd. All rights reserved. PII S0303-2647(98)00012-4