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 the number of reaction events per unit time occurring in a simulation by a factor 1/λ at the cost of greater error in unbiased estimates of first moments and biased overestimates of second moments. Our new approach offers two unique benefits. First, scaling is adaptive and heterogeneous, which eliminates the pitfall of overaggressive scaling. Second, there is no need for an a priori classification of populations as discrete or continuous (as in a hybrid method), which is problematic when discreteness of a chemical species changes during a simulation. The method requires specification of only a single algorithmic parameter, N c , a global critical population size above which populations are effectively scaled down to increase simulation efficiency. The method, which we term partial scaling, is implemented in the open-source BioNetGen software package. We demonstrate that partial scaling can significantly accelerate simulations without significant loss of accuracy for several published models of biological systems. These models characterize activation of the mitogen-activated protein kinase ERK, prion protein aggregation, and T-cell receptor signaling. arXiv:1903.08615v2 [q-bio.QM]

Model-based optimization of combination protocols for irradiation-insensitive cancers

“…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.…”

Gene expression noise accelerates the evolution of a biological oscillator

“…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.…”

Daily Forecasting of New Cases for Regional Epidemics of Coronavirus Disease 2019 with Bayesian Uncertainty Quantification

“…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.…”

“…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) .…”