The Quasi-State-State Approximations revisited: Timescales, small parameters, singularities, and normal forms in enzyme kinetics.

The Quasi-State-State Approximations revisited: Timescales, small parameters, singularities, and normal forms in enzyme kinetics.
Math Biosci. 2020 Mar 14;:108339
Authors: Eilertsen J, Schnell S
Abstract
In this work, we revisit the scaling analysis and commonly accepted conditions for the validity of the standard, reverse and total quasi-steady-state approximations through the lens of dimensional Tikhonov-Fenichel parameters and their respective critical manifolds. By combining Tikhonov-Fenichel parameters with scaling analysis and energy methods, we derive improved upper bounds on the approximation error for the standard, reverse and total quasi-steady-state approximations. Furthermore, previous analyses suggest that the reverse quasi-steady-state approximation is only valid when initial enzyme concentrations greatly exceed initial substrate concentrations. However, our results indicate that this approximation can be valid when initial enzyme and substrate concentrations are of equal magnitude. Using energy methods, we find that the condition for the validity of the reverse quasi-steady-state approximation is far less restrictive than was previously assumed, and we derive a new "small" parameter that determines the validity of this approximation. In doing so, we extend the established domain of validity for the reverse quasi-steady-state approximation. Consequently, this opens up the possibility of utilizing the reverse quasi-stead...

Source: Mathematical Biosciences - March 13, 2020 Category: Statistics Authors: Eilertsen J, Schnell S Tags: Math Biosci Source Type: research