相关论文: Quasi-steady state reduction for the Michaelis-Men…

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…

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 equilibration of enzyme and complex concentrations in deterministic Michaelis-Menten reaction networks underlies the hyperbolic dependence between the input (substrates) and output (products). This relationship was first obtained by…

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…

Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with…

All biological processes are controlled by complex systems of enzymatic chemical reactions. Although the majority of enzymatic networks have very elaborate structures, there are many experimental observations indicating that some turnover…

To understand the behaviour of complex systems it is often necessary to use models that describe the dynamics of subnetworks. It has previously been established using projection methods that such subnetwork dynamics generically involves…

It is well known in enzyme kinetics that the Michaelis-Menten (MM) equation is applicable only to enzymes in the steady state. We show that the result obtained in the previous work [Phys. Rev. Lett. 107, 218301 (2011)] is inconsistent with…

A comparison is made between conventional Michaelis-Menten kinetics and two models that take into account the duration of the conformational changes that take place at the molecular level during the catalytic cycle of a monomer. The models…

In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. Based on a discrete kinetic network model, we use the integrated probability flux balance method to derive the…

The linear noise approximation models the random fluctuations from the mean-field model of a chemical reaction that unfolds near the thermodynamic limit. Specifically, the fluctuations obey a linear Langevin equation up to order…

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…

Mathematical analysis of mass action models of large complex chemical systems is typically only possible if the models are reduced. The most common reduction technique is based on quasi-steady state assumptions. To increase the accuracy of…

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,…

The mass-based Maxwell-Stefan approach to one-phase multicomponent reactive mixtures is mathematically analyzed. It is shown that the resulting quasilinear, strongly coupled reaction-diffusion system is locally well-posed in an…

Partial equilibrium approximation (PEA) and quasi-steady-state approximation (QSSA) are two classical methods for reducing complex macroscopic chemical reactions into simple computable ones. Previous studies mainly focus on the accuracy of…

The paper is to study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion system with Dirichlet boundary condition, which is comparable with uniformly stable strongly order-preserving system. By appealing to…

Model reduction methods are relevant when the computation time of a full convection-diffusion-reaction simulation based on detailed chemical reaction mechanisms is too large. In this article, we review a model reduction approach based on…

We discuss parameter dependent polynomial ordinary differential equations that model chemical reaction networks. By classical quasi-steady state (QSS) reduction we understand the following familiar heuristic: Set the rate of change for…

The paper has two goals: It presents basic ideas, notions, and methods for reduction of reaction kinetics models: quasi-steady-state, quasi-equilibrium, slow invariant manifolds, and limiting steps. It describes briefly the current state of…