Related papers: The Quasi-Steady-State Approximations revisited: T…
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…
We analyze the standard model of enzyme-catalyzed reactions at various substrate-enzyme ratios to identify the regions of validity of the quasi-steady-state approximation. Certain prevalent conditions are checked and compared against the…
In this paper we prove that the well-known quasi-steady state approximations, commonly used in enzyme kinetics, which can be interpreted as the reduced system of a differential system depending on a perturbative parameter, according to…
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…
Quasi-steady state reductions for the irreversible Michaelis--Menten reaction mechanism are of interest both from a theoretical and an experimental design perspective. A number of publications have been devoted to extending the parameter…
Scaling transformations involving a small parameter ({\em degenerate scalings}) are frequently used for ordinary differential equations that model (bio-) chemical reaction networks. They are motivated by quasi-steady state (QSS) of certain…
The application of the standard quasi-steady-state approximation to the Michaelis--Menten reaction mechanism is a textbook example of biochemical model reduction, derived using singular perturbation theory. However, determining the specific…
There is a vast amount of literature concerning the appropriateness of various perturbation parameters for the standard quasi-steady state approximation in the Michaelis-Menten reaction mechanism, and also concerning the relevance of these…
The standard two-step model of homogeneous-catalyzed reactions had been theoretically analyzed at various levels of approximations from time to time. The primary aim was to check the validity of the quasi-steady-state approximation, and…
We study, from a purely quantitative point of view, the quasi-steady-state assumption for the fundamental mathematical model of the general enzymatic reaction: we re-establish, on a rigorous basis, certain already known results and we…
In this paper we derive several quasi steady-state approximations (QSSAs) to the stochastic reaction network describing the Michaelis-Menten enzyme kinetics. We show how the different assumptions about chemical species abundance and…
In biochemical systems the Michaelis-Menten (MM) scheme is one of the best-known models of the enzyme- catalyzed kinetics. In the academic literature the MM approximation has been thoroughly studied in the context of differential equation…
The application of the quasi-steady-state approximation to the Michaelis-Menten reaction embedded in large open chemical reaction networks is a popular model reduction technique in deterministic and stochastic simulations of biochemical…
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…
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…
The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found…
We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and…
Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions,…
The quasi-steady state assumption (QSSA) forms the basis for rigorous mathematical justification of the Michaelis-Menten formalism commonly used in modeling a broad range of intracellular phenomena. A critical supposition of QSSA-based…
With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…