Related papers: The Quasi-Steady State Assumption in an Enzymatica…
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…
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…
We consider a stochastic model of the Michaelis-Menten (MM) enzyme kinetic reactions in terms of Stochastic Differential Equations (SDEs) driven by Poisson Random Measures (PRMs). It has been argued that among various Quasi-Steady State…
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…
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…
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 Michaelis-Menten equation has played a central role in our understanding of biochemical processes. It has long been understood how this equation approximates the dynamics of irreversible enzymatic reactions. However, a similar…
From molecular, cellular, to ecological systems, the modeling of biological processes often stands on the assumption that fast components immediately reach the equilibrium at each moment (quasi-steady state) and only slow components govern…
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…
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 assumption (QSSA) is an approximation that is widely used in chemistry and chemical engineering to simplify reaction mechanisms. The key step in the method requires a solution by radicals of a system of multivariate…
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…
Computational feasibility of turbulent reacting flows hinges on the reduction of large chemical kinetics systems to smaller more manageable reaction sets. Recently, several sophisticated reduction techniques have been developed but they…
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…
We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is…
Enzyme kinetics has historically been described by deterministic models, with the Michaelis-Menten (MM) equation serving as a paradigm. However, recent experimental and theoretical advances have made it clear that stochastic fluctuations,…
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…
Michaelis-Menten equation is a basic equation of enzyme kinetics and gives an acceptable approximation of real chemical reaction processes. Analyzing the derivation of this equation yields the fact that its good performance of approximating…
Stochastic models for biochemical reaction networks are widely used to explore their complex dynamics but face significant challenges, including difficulties in determining rate constants and high computational costs. To address these…