加速化学反应网络动力学Monte Carlo模拟的标度方法
Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks
摘要：
各种动力学蒙特卡罗算法变得低效时，在一个系统中的一些群体的大小是大的，这会引起大量的反应事件，每单位时间。在这里，我们提出了一个新的加速算法的基础上自适应和异构缩放的反应速率和化学计量系数。该算法在概念上涉及到常用的想法加速随机模拟，通过考虑一个子体积$λΩ$（$0<λ<1$）内的系统的利益，这减少了反应事件的数量，每单位时间发生在模拟的一个因素$1/λ$在成本更大的错误，在无偏估计的第一时刻和偏高估的第二时刻。我们的新方法提供了两个独特的好处。首先，扩展是自适应的和异构的，这消除了过度扩展的陷阱。第二，不需要将群体分类为离散或连续的\emph{a priori}（如在混合方法中），当化学物质的离散性在模拟期间改变时，这是有问题的。该方法只需要指定一个单一的算法参数，$N_c$，一个全球性的关键人口规模以上的人口有效地缩小，以提高模拟效率。该方法，我们称之为部分缩放，在开源BioNetGen软件包中实现。我们证明，部分缩放可以显着加快模拟，而不会显着损失的准确性，几个已发表的生物系统模型。这些模型表征了丝裂原活化蛋白激酶ERK、朊病毒蛋白聚集和T细胞受体信号传导的活化。
英文摘要：
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 \emph{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.
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