相关论文: Techniques of Model Reductions in Biochemical Cell…
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…
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…
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…
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…
The relationship between components of biochemical network and the resulting dynamics of the overall system is a key focus of computational biology. However, as these networks and resulting mathematical models are inherently complex and…
Quasi-steady state (QSS) reduction is a commonly used method to lower the dimension of a differential equation model of a chemical reaction network. From a mathematical perspective, QSS reduction is generally interpreted as a special type…
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…
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…
This limited review is intended as an introduction to the fast growing subject of mathematical modelling of cell metabolism and its biochemical pathways, and more precisely on pathways linked to apoptosis of cancerous cells. Some basic…
The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is…
We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the…
Simplified stochastic models are widely used in the study of frequency-resolved noise propagation in biochemical reaction networks, a common measure being the coherence between random fluctuations in molecule number trajectories. Such…
We use the Litvinov-Maslov correspondence principle to reduce and hybridize networks of biochemical reactions. We apply this method to a cell cycle oscillator model. The reduced and hybridized model can be used as a hybrid model for the…
We derive and simulate a mathematical model for mechanotransduction related to the Rho GTPase signalling pathway. The model addresses the bidirectional coupling between signalling processes and cell mechanics. A numerical method based on…
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…
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…
Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions. These systems may be modeled as state transition systems with transitions representing individual reaction…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
Apoptosis is one of the most basic biological processes. In apoptosis, tens of species are involved in many biochemical reactions with times scales of widely differing orders of magnitude. By the law of mass action, the process is…
We propose a new approach to model composition, based on reducing several models to the same level of complexity and subsequent combining them together. Firstly, we suggest a set of model reduction tools that can be systematically applied…