Reaction-diffusion master equation: A comparison with microscopic simulations

Baras, F.; Mansour, M. Malek

doi:10.1103/physreve.54.6139

Cited by 98 publications

(88 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The inequality (8) requires that the variation in each molecular amount X i does not exceed some small parameter ε i , but the change in the population number will not be altered by less than one molecule. The value of ε i depends on the user-specified tolerance ε (with 0 < ε < 1), as follows:…”

Section: A Leap Conditionmentioning

confidence: 99%

“…4,5 Mathematically, the dynamics of these biochemical systems may be modelled using Markov processes. 6 The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation, 7,8 known also as the Multivariate Master Equation. 9 This discrete stochastic model has been successfully employed to analyze key cellular processes, such as intracellular signaling chemical pathways, 10,11 or morphogenesis 12 where the influence of the spatial distribution of the reacting species on the system behaviour cannot be neglected.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems

Padgett

Ilie

2016

AIP Advances

View full text Add to dashboard Cite

Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating the solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.

show abstract

Section: A Leap Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems

Padgett

Ilie

2016

AIP Advances

View full text Add to dashboard Cite

show abstract

“…The values of the parameters are 1 = 150, 2 = 2, 3 = 200, 4 = 1, corresponding to and in (2.11), the diffusion = 4 for all species, = 0 04 and the volume Î = (250 ) 3 . The initial system has seven molecules, see the upper left panel of Figure 5.3, two , three , and two molecules.…”

Section: Two Reversible Reactionsmentioning

confidence: 99%

“…For example, no accurate mesoscopic description is known for crowding and a particle model is the only alternative (4; 29). Another reason is that the mesoscopic SSA is valid only when its voxel sizes are of the same order as the average distance traveled by a particle between two reactions or the reactive mean free path (3). Hence, sharp gradients in the concentrations may not be sufficiently resolved on a mesoscopic mesh (20; 26).…”

Section: Introductionmentioning

confidence: 99%

Flexible single molecule simulation of reaction–diffusion processes

Hellander

Lötstedt

2011

Journal of Computational Physics

View full text Add to dashboard Cite

An algorithm is developed for simulation of the motion and reactions of single molecules at a microscopic level. The molecules diffuse in a solvent and react with each other or a polymer and molecules can dissociate. Such simulations are of interest e.g. in molecular biology. The algorithm is similar to the Green's function reaction dynamics (GFRD) algorithm by van Zon and ten Wolde where longer time steps can be taken by computing the probability density functions (PDFs) and then sample from its distribution function. Our computation of the PDFs is much less complicated than GFRD and more flexible. The solution of the partial differential equation for the PDF is split into two steps to simplify the calculations. The sampling is without splitting error in two of the coordinate directions for a pair of molecules and a molecule-polymer interaction and is approximate in the third direction. The PDF is obtained either from an analytical solution or a numerical discretization. The errors due to the operator splitting, the partitioning of the system, and the numerical approximations are analyzed. The method is applied to three different systems involving up to four reactions. Comparisons with other mesoscopic and macroscopic models show excellent agreement.

show abstract

“…£ àÕÑÏ ÔÎÖÚÂÇ ÏÑÉÇÕ ÑÍÂÊÂÕßÔâ (Ä ÊÂÄËÔËÏÑÔÕË ÑÕ ÕÑÅÑ, ÍÂÍËÇ ÔÎÖÚÂÌÐÞÇ ÚËÔÎÂ ÄÞÒÂAEÖÕ), ÚÕÑ ÊÂ ËÐÕÇÓÄÂÎ Dt ÐÇ ÒÓÑËÊÑÌAEÇÕ ÐË ÑAEÐÑÌ ÓÇÂÍÙËË ËÎË ÒÓÑËÊÑÌAEÖÕ ÄÔÇ n ÓÇÂÍÙËÌ. £ÇÓÑâÕÐÑ, ËÊ-ÊÂ ÕÓÖAEÐÑÔÕÇÌ Ä ÄÞÃÑÓÇ t (ËÎË Dt), Â ÕÂÍÉÇ ËÊ-ÊÂ ÏÇAEÎÇÐÐÑÔÕË ÓÂÃÑÕÞ ÒÓÑÅÓÂÏÏÞ ÔÖÜÇÔÕÄÖÇÕ ÏÂÎÑ ÓÂÃÑÕ, Ä ÍÑÕÑÓÞØ ÏÇÕÑAE DSMC ÒÓËÏÇÐâÇÕÔâ Í ËÔÔÎÇAEÑ-ÄÂÐËá ÒÓÑÔÕÓÂÐÔÕÄÇÐÐÑ ÓÂÔÒÓÇAEÇÎÇÐÐÞØ ÔËÔÕÇÏ [43].…”

unclassified

Study of spatially extended dynamical systems using probabilistic cellular automata

Vanag¹

1999

Usp. Fiz. Nauk

View full text Add to dashboard Cite

Reaction-diffusion master equation: A comparison with microscopic simulations

Cited by 98 publications

References 50 publications

An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems

An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems

Flexible single molecule simulation of reaction–diffusion processes

Study of spatially extended dynamical systems using probabilistic cellular automata

Contact Info

Product

Resources

About