A Much better replacement of the Michaelis-Menten equation and its application

TL;DR

This paper introduces a quartic equation as a more accurate and informative replacement for the Michaelis-Menten equation in enzyme kinetics, improving approximation during reaction and near completion.

Contribution

It proposes a new quartic equation A(S,E)=0 that surpasses Michaelis-Menten in accuracy and information content, with potential applications in enzyme reaction analysis.

Findings

Quartic equation A(S,E)=0 offers better approximation during the quasi-steady state.

The new equation approaches reaction end with matching tangent lines.

It differs from Michaelis-Menten less than 1/S^3 as substrate concentration increases.

Abstract

Michaelis-Menten equation is a basic equation of enzyme kinetics and gives 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 $+\infty$. 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 $dP/dt=k_2C(t)$.