Results 11  20
of
427
Modelling and Simulation of IntraCellular Dynamics: Choosing an Appropriate Framework
 IEEE Transactions on NanoBioscience
, 2004
"... Systems biology, that is, mathematical modelling and simulation of biochemical reaction networks in intracellular processes has gained renewed interest in recent years. For most simulation tools and publications they are usually characterized by either preferring stochastic simulation or rate equati ..."
Abstract

Cited by 44 (2 self)
 Add to MetaCart
(Show Context)
Systems biology, that is, mathematical modelling and simulation of biochemical reaction networks in intracellular processes has gained renewed interest in recent years. For most simulation tools and publications they are usually characterized by either preferring stochastic simulation or rate equation models. The use of stochastic simulation is occasionally accompanied with arguments against rate equations. Motivated by these arguments, in this paper we discuss the relationship between these two forms of representation. Towards this end we provide a novel compact derivation for the stochastic rate constant that forms the basis of the popular Gillespie algorithm. Comparing the mathematical basis of the two popular conceptual frameworks of generalized mass action models and the chemical master equation, we argue that some of the arguments that have been put forward are ignoring subtle differences and similarities that are important for answering the question in which conceptual framework one should investigate intracellular dynamics.
Efficient attenuation of stochasticity in gene expression through posttranscriptional control
 J MOL BIOL
, 2004
"... ..."
ProductForm Stationary Distributions for Deficiency Zero Chemical Reaction Networks
, 2010
"... We consider stochastically modeled chemical reaction systems with massaction kinetics and prove that a productform stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically modeled system with massaction kinetics admits a complex bala ..."
Abstract

Cited by 40 (16 self)
 Add to MetaCart
(Show Context)
We consider stochastically modeled chemical reaction systems with massaction kinetics and prove that a productform stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically modeled system with massaction kinetics admits a complex balanced equilibrium. Feinberg’s deficiency zero theorem then implies that such a distribution exists so long as the corresponding chemical network is weakly reversible and has a deficiency of zero. The main parameter of the stationary distribution for the stochastically modeled system is a complex balanced equilibrium value for the corresponding deterministically modeled system. We also generalize our main result to some nonmassaction kinetics.
Error bound for piecewise deterministic processes modeling stochastic reaction systems
, 2012
"... ..."
(Show Context)
Modeling and simulating chemical reactions
 SIAM Review
, 2007
"... Many students are familiar with the idea of modeling chemical reactions in terms of ordinary differential equations. However, these deterministic reaction rate equations are really a certain largescale limit of a sequence of finerscale probabilistic models. In studying this hierarchy of models, st ..."
Abstract

Cited by 34 (1 self)
 Add to MetaCart
(Show Context)
Many students are familiar with the idea of modeling chemical reactions in terms of ordinary differential equations. However, these deterministic reaction rate equations are really a certain largescale limit of a sequence of finerscale probabilistic models. In studying this hierarchy of models, students can be exposed to a range of modern ideas in applied and computational mathematics. This article introduces some of the basic concepts in an accessible manner, and points to some challenges that currently occupy researchers in this area. Short, downloadable MATLAB codes are listed and described. 1
P (2008) Colored extrinsic fluctuations and stochastic gene expression. Mol Sys Biol 4
"... expression ..."
(Show Context)
Computing the moments of high dimensional solutions of the master equation
 Appl. Math. Comput
"... Derived from the Markov character only, the master equation of chemical reactions is an accurate stochastic description of quite general systems in chemistry. Exact solutions of this equation are rare and the most frequently used approximative solution method is to write down the corresponding set o ..."
Abstract

Cited by 32 (2 self)
 Add to MetaCart
(Show Context)
Derived from the Markov character only, the master equation of chemical reactions is an accurate stochastic description of quite general systems in chemistry. Exact solutions of this equation are rare and the most frequently used approximative solution method is to write down the corresponding set of reaction rate equations. In many cases this approximation is not valid, or only partially so, as stochastic effects caused by the natural noise present in the full description of the problem are poorly captured. In this paper it is shown how a certain set of higher order equations can be derived. It is shown by theory and example that stochastic effects are better captured using this technique while still maintaining the computational advantages of the reaction rate approach.
SA: A general modeling strategy for gene regulatory networks with stochastic dynamics
 Journal of Computational Biology
"... A stochastic genetic toggle switch model that consists of two identical, mutually repressive genes is built using the Gillespie algorithm with time delays as an example of a simple stochastic gene regulatory network. The stochastic kinetics of this model is investigated, and it is found that the del ..."
Abstract

Cited by 32 (13 self)
 Add to MetaCart
A stochastic genetic toggle switch model that consists of two identical, mutually repressive genes is built using the Gillespie algorithm with time delays as an example of a simple stochastic gene regulatory network. The stochastic kinetics of this model is investigated, and it is found that the delays for the protein productions can highly weaken the global fluctuations for the expressions of the two genes, making the two mutually repressive genes coexist for a long time. Starting from this model, we propose a practical modeling strategy for more complex gene regulatory networks. Unlike previous applications of the Gillespie algorithm to simulate specific genetic networks dynamics, this modeling strategy is proposed for an ensemble approach to study the dynamical properties of these networks. The model allows any combination of gene expression products, forming complex multimers, and each one of the multimers is assigned to a randomly chosen gene promoter site as an activator or inhibitor. In addition, each gene, although it has only one promoter site, can have multiple regulatory sites and distinct rates of translation and transcription. Also, different genes have different time delays for transcription and translation and all reaction constant rates are initially randomly chosen from a range of values. Therefore, the general strategy here proposed may be used to simulate real genetic networks. Key words: gene regulatory networks (GRNs), genetic toggle switch, Gillespie algorithm, nonMarkov Processes, random Boolean networks, stochastic dynamics 1.
P systems, a new computational modelling tool for Systems Biology
 Transactions on Computational Systems Biology VI. Lecture
, 2006
"... Abstract. In this paper we present P systems as a reliable computational modelling tool for Systems Biology that takes into account the discrete character of the quantity of components of biological systems, the inherently randomness in biological phenomena and the key role played by membranes in th ..."
Abstract

Cited by 31 (14 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we present P systems as a reliable computational modelling tool for Systems Biology that takes into account the discrete character of the quantity of components of biological systems, the inherently randomness in biological phenomena and the key role played by membranes in the function of living cells. We will introduce two different strategies for the evolution of P systems, namely, Multicompartmental Gillespie’s Algorithm based on the well known Gillespie’s Algorithm but running on more than one compartment; and Deterministic Waiting Times Algorithm, an exact deterministic method. In order to illustrate these two strategies we have modelled two biological systems: the EGFR Signalling Cascade and the Quorum Sensing System in the bacterium Vibrio Fischeri. Our simulations results show that for the former system a deterministic approach is valid whereas for the latter a stochastic approach like Multicompartmental Gillespie’s Algorithm is necessary. 1
Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations
 SIAM Journal on Scientific Computing
"... Abstract. A method is developed for incorporating diffusion of chemicals in complex geometries into stochastic chemical kinetics simulations. Systems are modeled using the reactiondiffusion master equation, with jump rates for diffusive motion between mesh cells calculated from the discretization w ..."
Abstract

Cited by 30 (3 self)
 Add to MetaCart
(Show Context)
Abstract. A method is developed for incorporating diffusion of chemicals in complex geometries into stochastic chemical kinetics simulations. Systems are modeled using the reactiondiffusion master equation, with jump rates for diffusive motion between mesh cells calculated from the discretization weights of an embedded boundary method. Since diffusive jumps between cells are treated as first order reactions, individual realizations of the stochastic process can be created by the Gillespie method. Numerical convergence results for the underlying embedded boundary method, and for the stochastic reactiondiffusion method, are presented in two dimensions. A twodimensional model of transcription, translation, and nuclear membrane transport in eukaryotic cells is presented to demonstrate the feasibility of the method in studying cellwide biological processes.