A Much better replacement of the Michaelis-Menten equation and its application
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 $dP/dt=k_2C(t)$.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Relaxation to statistical equilibrium in stochastic Michaelis-Menten kinetics
The equilibration of enzyme and complex concentrations in deterministic Michaelis-Menten reaction networks underlies the hyperbolic dependence between the input (substrates) and output (products). This relationship was f…
Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli l…
Michaelis-Menten dynamics in protein subnetworks
To understand the behaviour of complex systems it is often necessary to use models that describe the dynamics of subnetworks. It has previously been established using projection methods that such subnetwork dynamics gene…
Unbounded solutions of models for glycolysis
The Selkov oscillator, a simple description of glycolysis, is a system of two ordinary differential equations with mass action kinetics. In previous work the authors established several properties of the solutions of thi…
Deterministic and Stochastic Models in Enzyme Kinetics
Enzyme kinetics has historically been described by deterministic models, with the Michaelis-Menten (MM) equation serving as a paradigm. However, recent experimental and theoretical advances have made it clear that stocha…