A transformed time-dependent Michaelis-Menten enzymatic reaction model and its asymptotic stability

作者：Mallory Kristina; Van Gorder Robert A^*

来源：Journal of Mathematical Chemistry, 2014, 52(1): 222-230.

DOI：10.1007/s10910-013-0257-1

• Dynamic Michaelis-Menten model
• Nonlinear dynamics
• Stability
• Enzyme reactions

The dynamic form of the Michaelis-Menten enzymatic reaction equations provide a time-dependent model in which a substrate reacts with an enzyme to form a complex which in turn is converted into a product and the enzyme . In the present paper, we show that this system of four nonlinear equations can be reduced to a single nonlinear differential equation, which is simpler to solve numerically than the system of four equations. Applying the Lyapunov stability theory, we prove that the non-zero equilibrium for this equation is globally asymptotically stable, and hence that the non-zero steady-state solution for the full Michaelis-Menten enzymatic reaction model is globally asymptotically stable for all values of the model parameters. As such, the steady-state solutions considered in the literature are stable. We finally discuss properties of the numerical solutions to the dynamic Michaelis-Menten enzymatic reaction model, and show that at small and large time scales the solutions may be approximated analytically.

• 出版日期2014-1