On the pseudo-steady-state approximation and Tikhonov theorem for general enzyme systems
The dynamical behaviour of enzymatic networks is given by a set of nonlinear autonomous differential equations. They are usually solved by a pseudo-steady-state approximation (PSSA), corresponding to the adiabatic approximation in physics, such that the slowest reaction determines the overall velocity. The authors consider the mathematical background and establish sufficient conditions applying Tikhonov's theorem to this situation, and propose some statements about uniqueness and stability. The PSSA does not hold in open systems or in closed systems such that the crucial small parameter \(\epsilon =E_ 0/S_ 0\) (total amount of enzym by total amount of ligands) approaches zero by \(1/S_ 0\to O\) instead of \(E_ 0\to O\).
nonlinear autonomous differential equations
scientific article; zbMATH DE number 3930783