2019
DOI: 10.1063/1.5096774
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Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks

Abstract: Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on adaptive and heterogeneous scaling of reaction rates and stoichiometric coefficients. The algorithm is conceptually related to the commonly used idea of accelerating a stochastic simulation by considering a sub-volume λΩ (0 < λ < 1) within a system of interest, which reduces … Show more

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Cited by 6 publications
(10 citation statements)
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References 57 publications
(121 reference statements)
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“…Stochastic kinetic Monte Carlo simulations were performed in BioNetGen 79 . To accelerate simulations of the model the scaling method was applied 80 . Fractions of apoptotic cells for each protocol were calculated based on 1,000 stochastic simulations.…”
Section: Methodsmentioning
confidence: 99%
“…Stochastic kinetic Monte Carlo simulations were performed in BioNetGen 79 . To accelerate simulations of the model the scaling method was applied 80 . Fractions of apoptotic cells for each protocol were calculated based on 1,000 stochastic simulations.…”
Section: Methodsmentioning
confidence: 99%
“…We also impose the boundary conditions that p i , j , k , l = 0 if i < 0 or j < 0. The deterministic dynamics of the stochastic processes governed by Eqs. (14) and (16) can be derived by performing the Kramers–Moyal expansion to the lowest-order expansion 𝒪 (Ω 0 ) (van Kampen, 2007; Gardiner, 2009; Lin et al, 2019). The procedure yields a Liouville equation describing the correspond- ing deterministic dynamics in the infinite population limit Ω → ∞, in which regime the gene expression noise diminishes to zero.…”
Section: Stochastic Formulation Of the Repressilator And Circadian Clockmentioning
confidence: 99%
“…We followed the standard procedure to construct a set of stochastic differential equations (SDEs), by first formulating a master equation, then performing the Kramers-Moyal expansion to obtain the approximate continuum-limit Fokker-Planck equation in the large-population limit, and formulating the corresponding SDEs. The procedure has been described, for example, by Lin et al (41, 42) . In simulations, we used the Euler-Maruyama integrator to evolve the SDEs with a time step of 0.05 (d). We checked to make sure the timestep was sufficiently small. We adopted a standard particle filter technique to identify the Maximum Likelihood Estimator of the parameters of the stochastic model, noting that our process is not time-homogeneous due to different episodes of distinct social-distancing practices.…”
Section: Full Description Of the Mechanistic Compartmental Modelmentioning
confidence: 99%
“…We followed the standard procedure to construct a set of stochastic differential equations (SDEs), by first formulating a master equation, then performing the Kramers-Moyal expansion to obtain the approximate continuum-limit Fokker-Planck equation in the large-population limit, and formulating the corresponding SDEs. The procedure has been described, for example, by Lin et al (41, 42) .…”
Section: Full Description Of the Mechanistic Compartmental Modelmentioning
confidence: 99%