# Optimisation of simulations of stochastic processes by removal of opposing reactions

Research output: Contribution to journal › Article › peer-review

## Standard

**Optimisation of simulations of stochastic processes by removal of opposing reactions.** / Spill, Fabian; Maini, Philip K.; Byrne, Helen M.

Research output: Contribution to journal › Article › peer-review

## Harvard

*Journal of Chemical Physics*, vol. 144, no. 8, 084105. https://doi.org/10.1063/1.4942413

## APA

*Journal of Chemical Physics*,

*144*(8), [084105]. https://doi.org/10.1063/1.4942413

## Vancouver

## Author

## Bibtex

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## RIS

TY - JOUR

T1 - Optimisation of simulations of stochastic processes by removal of opposing reactions

AU - Spill, Fabian

AU - Maini, Philip K.

AU - Byrne, Helen M.

PY - 2016/2/24

Y1 - 2016/2/24

N2 - Models invoking the chemical master equation are used in many areas of science, and, hence, their simulation is of interest to many researchers. The complexity of the problems at hand often requires considerable computational power, so a large number of algorithms have been developed to speed up simulations. However, a drawback of many of these algorithms is that their implementation is more complicated than, for instance, the Gillespie algorithm, which is widely used to simulate the chemical master equation, and can be implemented with a few lines of code. Here, we present an algorithm which does not modify the way in which the master equation is solved, but instead modifies the transition rates. It works for all models in which reversible reactions occur by replacing such reversible reactions with effective net reactions. Examples of such systems include reaction-diffusion systems, in which diffusion is modelled by a random walk. The random movement of particles between neighbouring sites is then replaced with a net random flux. Furthermore, as we modify the transition rates of the model, rather than its implementation on a computer, our method can be combined with existing algorithms that were designed to speed up simulations of the stochastic master equation. By focusing on some specific models, we show how our algorithm can significantly speed up model simulations while maintaining essential features of the original model.

AB - Models invoking the chemical master equation are used in many areas of science, and, hence, their simulation is of interest to many researchers. The complexity of the problems at hand often requires considerable computational power, so a large number of algorithms have been developed to speed up simulations. However, a drawback of many of these algorithms is that their implementation is more complicated than, for instance, the Gillespie algorithm, which is widely used to simulate the chemical master equation, and can be implemented with a few lines of code. Here, we present an algorithm which does not modify the way in which the master equation is solved, but instead modifies the transition rates. It works for all models in which reversible reactions occur by replacing such reversible reactions with effective net reactions. Examples of such systems include reaction-diffusion systems, in which diffusion is modelled by a random walk. The random movement of particles between neighbouring sites is then replaced with a net random flux. Furthermore, as we modify the transition rates of the model, rather than its implementation on a computer, our method can be combined with existing algorithms that were designed to speed up simulations of the stochastic master equation. By focusing on some specific models, we show how our algorithm can significantly speed up model simulations while maintaining essential features of the original model.

KW - diffusion

KW - random walks

KW - mean field theory

KW - mining

KW - chemical reactions

UR - http://www.scopus.com/inward/record.url?scp=84959450093&partnerID=8YFLogxK

U2 - 10.1063/1.4942413

DO - 10.1063/1.4942413

M3 - Article

AN - SCOPUS:84959450093

VL - 144

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

M1 - 084105

ER -