Quasi-Steady-State Approximations of the Chemical Master Equation in enzyme kinetics - application to the double phosphorylation/dephosphorylation cycle

2014 ◽  
Author(s):  
A. M. Bersani ◽  
A. Borri ◽  
F. Carravetta ◽  
G. Mavelli ◽  
P. Palumbo
Keyword(s):  
Steady State ◽  
Master Equation ◽  
Enzyme Kinetics ◽  
Chemical Master Equation ◽  
Quasi Steady State

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

2019 ◽  
Vol 12 (01) ◽  
pp. 1950008
Author(s):  
Banghe Li ◽  
Bo Li ◽  
Yuefeng Shen
Keyword(s):  
Steady State ◽  
Enzyme Kinetics ◽  
Polynomial Equation ◽  
Mass Action ◽  
Reaction Process ◽  
Quasi Steady State ◽  
State Laws ◽  
New Equation ◽  
Reaction Processes ◽  
State Assumption

Michaelis–Menten equation is a basic equation of enzyme kinetics and gives acceptable approximations 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 (8). 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. [Quasi-steady state laws in enzyme kinetics, J. Phys. Chem. A 112(11) (2008) 2311–2321]. Here, we found a polynomial equation with total degree of four [Formula: see text] (14), which gives more accurate approximation of the reaction process in two aspects: during the quasi-steady-state of the reaction, Michaelis–Menten curve approximates the reaction well, while our equation [Formula: see text] gives better approximation; near the end of the reaction, our equation approaches the end of the reaction with a tangent line the same to that of the reaction process trajectory simulated by mass action, while Michaelis–Menten curve does not. In addition, our equation [Formula: see text] differs to Michaelis–Menten curve less than the order of [Formula: see text] as [Formula: see text] approaches [Formula: see text]. By considering the above merits of [Formula: see text], we suggest it as a replacement of Michaelis–Menten curve. Intuitively, this new equation is more complex and harder to understand. But, just because of 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 [Formula: see text] and the equation [Formula: see text].

scholarly journals Quasi-Steady-State Approximations Derived from the Stochastic Model of Enzyme Kinetics

2019 ◽  
Vol 81 (5) ◽  
pp. 1303-1336 ◽  
Author(s):  
Hye-Won Kang ◽  
Wasiur R. KhudaBukhsh ◽  
Heinz Koeppl ◽  
Grzegorz A. Rempała
Keyword(s):  
Steady State ◽  
Stochastic Model ◽  
Enzyme Kinetics ◽  
Quasi Steady State
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