ﻻ يوجد ملخص باللغة العربية
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-steady-state approximation to model enzyme catalyzed reactions and estimate kinetic parameters in enzymatic assays at much lower enzyme to substrate ratios than was previously thought. Moreover, we show for the first time that the critical manifold of the reverse quasi-steady-state approximation contains a singular point where normal hyperbolicity is lost. Associated with this singularity is a transcritical bifurcation, and the corresponding normal form of this bifurcation is recovered through scaling analysis.
The estimation of the kinetic parameters requires the careful design of experiments under a constrained set of conditions. Many estimates reported in the literature incorporate protocols that leverage simplified mathematical models known as quasi-ste
The quasi-steady-state approximation is widely used to develop simplified deterministic or stochastic models of enzyme catalyzed reactions. In deterministic models, the quasi-steady-state approximation can be mathematically justified from singular pe
In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dim
The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis--Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the sys
We discuss various bifurcation problems in which two isolated periodic orbits exchange periodic ``bridge orbit(s) between two successive bifurcations. We propose normal forms which locally describe the corresponding fixed point scenarios on the Poinc