A much better replacement of the Michaelis–Menten equation and its application

Abstract

Michaelis-Menten equation is a basic equation of enzyme kinetics andgives an acceptable approximation of real chemical reaction processes. Analyzing the derivation of this equation yields the fact that its good performance of approximating real reaction processes is due to Michaelis-Menten curve (15). This curve is derived from Quasi-Steady-State Assumption(QSSA), which has been proved always true and called Quasi-Steady-State Law by Banghe Li et al [19].Here, we found a quartic equation A(S, E) = 0 (22), which gives more accurate approximation of the reaction process in two aspects: during the quasi-steady state of a reaction, Michaelis-Menten curve approximates the reaction well, while our quartic equation A(S, E) = 0 gives better approximation; near the end of the reaction, our equation approaches the end of the reaction with a tangent line same to that of the reaction, while Michaelis-Menten curve does not. In addition, our quartic equation A(S, E) = 0 differs to Michaelis-Menten curve less than the order of 1/S 3 as S approaches +∞.By considering the above merits of A(S, E) = 0, we suggest it as a replacement of Michaelis-Menten curve. Intuitively, this new equation is more complex and harder to understand. But, just because its complexity, it provides more information about the rate constants than Michaelis-Menten curve does.Finally, we get a better replacement of the Michaelis-Menten equation by combing A(S, E) = 0 and the equation dP/dt = k2C(t).keywords : rate constants of enzyme kinetics; quasi-steady-state assumption; quasi-steady-state law. a.

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“…The Michaelis-Menten Curve is an indicator that can be used to describe changes in enzyme kinetics and to provide inhibitory characteristics for enzyme activity 19 . Km and Vmax values are two main parameters in the enzyme kinetics study, each of which represents the Michaelis-Menten constanta which can be used to estimate the number of substrates and acceleration reaction 20 .…”