ArticleRoyal Society open science2016
A hybrid continuous-discrete method for stochastic reaction-diffusion processes.
Article in Royal Society open science, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
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Who cites it
11 citing papers in PubMed.
- Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles.PLoS computational biology · 2023Article
- Close agreement between deterministic versus stochastic modeling of first-passage time to vesicle fusion.Biophysical journal · 2022Article
- Generalized Solutions of Parrondo's Games.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2020Article
- The blending region hybrid framework for the simulation of stochastic reaction-diffusion processes.Journal of the Royal Society, Interface · 2020Article
- Stochastic Simulation of Pattern Formation in Growing Tissue: A Multilevel Approach.Bulletin of mathematical biology · 2019Article
- Multiscale Stochastic Reaction-Diffusion Algorithms Combining Markov Chain Models with Stochastic Partial Differential Equations.Bulletin of mathematical biology · 2019Article
- Analysis and remedy of negativity problem in hybrid stochastic simulation algorithm and its application.BMC bioinformatics · 2019Article
- Hybrid CME-ODE method for efficient simulation of the galactose switch in yeast.IET systems biology · 2018Article
- Exploring intermediate cell states through the lens of single cells.Current opinion in systems biology · 2018Article
- Spatially extended hybrid methods: a review.Journal of the Royal Society, Interface · 2018Review
- Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning.The Journal of chemical physics · 2017Article
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Authors and funding
3 authors.
Funding
Abstract
Stochastic fluctuations in reaction-diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method.
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