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A novel approach to measure all rate constants in the simplest enzyme kinetics model. (English) Zbl 1182.92037

Summary: Enzymes play vital roles in life processes. Almost all biochemical reactions are mediated by enzymes. The rate constants of enzyme kinetics are the most important parameters for the reactions catalyzed by enzymes. A. Brown [Enzyme action. J. Chem. Soc. 81, 373–386 (1902)] proposed a simple single-substrate-single-product model which contains only three rate constants \(k _{1}, k _{ - 1}\) and \(k _{2}\). So far, biologists can measure the Michaelis constant \(K _{M }\) and the catalytic constant \(k _{cat }\), which actually is equal to \(k _{2}\), according to the L. Michaelis and M. L. Menten equation [Biochem. Z. 49, 333–369 (1913)]. Using the temperature jump method or transient state kinetics, \(k _{1}, k _{ - 1}\) and \(k _{2}\) can be determined. However, these methods are complicated. We design a novel simple method that could determine the rate constants \(k _{1}\) and \(k _{ - 1}\) based on knowing \(k _{cat }\) and \(K _{M }\). Our numerical experiments show that the three rate constants can be calculated rather precisely. Hence, we believe that biochemists could design experiments to measure the rate constants based on our method.

MSC:

92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
92-08 Computational methods for problems pertaining to biology
37N25 Dynamical systems in biology
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