An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping

Wonryull Koh; Kim T Blackwell

doi:10.1063/1.3572335

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An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping

Journal article

Open access

Peer reviewed

An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping

Wonryull Koh and Kim T Blackwell

The Journal of chemical physics, Vol.134(15), pp.154103-154103-13

04/21/2011

DOI: 10.1063/1.3572335

PMCID: PMC3089647

PMID: 21513371

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https://europepmc.org/articles/pmc3089647View

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Abstract

Stochastic simulation of reaction-diffusion systems enables the investigation of stochastic events arising from the small numbers and heterogeneous distribution of molecular species in biological cells. Stochastic variations in intracellular microdomains and in diffusional gradients play a significant part in the spatiotemporal activity and behavior of cells. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system's state over time, it can be too slow for many practical applications. We present an accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems designed to improve the speed of simulation by reducing the number of time-steps required to complete a simulation run. This method is unique in that it employs two strategies that have not been incorporated in existing spatial stochastic simulation algorithms. First, diffusive transfers between neighboring subvolumes are based on concentration gradients. This treatment necessitates sampling of only the net or observed diffusion events from higher to lower concentration gradients rather than sampling all diffusion events regardless of local concentration gradients. Second, we extend the non-negative Poisson tau-leaping method that was originally developed for speeding up nonspatial or homogeneous stochastic simulation algorithms. This method calculates each leap time in a unified step for both reaction and diffusion processes while satisfying the leap condition that the propensities do not change appreciably during the leap and ensuring that leaping does not cause molecular populations to become negative. Numerical results are presented that illustrate the improvement in simulation speed achieved by incorporating these two new strategies.

Algorithms

Cyclic AMP - pharmacology

Diffusion

Enzyme Activation - drug effects

Models, Chemical

Poisson Distribution

Protein Kinases - chemistry

Protein Kinases - metabolism

Stochastic Processes

Details

Title: Subtitle: An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping
Creators: Wonryull Koh - George Mason University
Kim T Blackwell - George Mason University
Resource Type: Journal article
Publication Details: The Journal of chemical physics, Vol.134(15), pp.154103-154103-13
DOI: 10.1063/1.3572335
PMID: 21513371
PMCID: PMC3089647
NLM abbreviation: J Chem Phys
ISSN: 0021-9606
eISSN: 1089-7690
Grant note: R01 AA016022 / NIAAA NIH HHS R01 AA16022 / NIAAA NIH HHS R01 AA018060 / NIAAA NIH HHS
Language: English
Date published: 04/21/2011
Academic Unit: Roy J. Carver Department of Biomedical Engineering; Iowa Neuroscience Institute
Record Identifier: 9984446260602771

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