Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom.
J Chem Phys. 2011 Feb 28;134(8):084109. doi: 10.1063/1.3554385.
The stochastic simulation algorithm was introduced by Gillespie and in a different form by Kurtz. There have been many attempts at accelerating the algorithm without deviating from the behavior of the simulated system. The crux of the explicit τ-leaping procedure is the use of Poisson random variables to approximate the number of occurrences of each type of reaction event during a carefully selected time period, τ. This method is acceptable providing the leap condition, that no propensity function changes "significantly" during any time-step, is met. Using this method there is a possibility that species numbers can, artificially, become negative. Several recent papers have demonstrated methods that avoid this situation. One such method classifies, as critical, those reactions in danger of sending species populations negative. At most, one of these critical reactions is allowed to occur in the next time-step. We argue that the criticality of a reactant species and its dependent reaction channels should be related to the probability of the species number becoming negative. This way only reactions that, if fired, produce a high probability of driving a reactant population negative are labeled critical. The number of firings of more reaction channels can be approximated using Poisson random variables thus speeding up the simulation while maintaining the accuracy. In implementing this revised method of criticality selection we make use of the probability distribution from which the random variable describing the change in species number is drawn. We give several numerical examples to demonstrate the effectiveness of our new method.
随机模拟算法由 Gillespie 提出，Kurtz 以不同的形式提出。已经有许多尝试通过不偏离模拟系统的行为来加速算法。显式 τ 跳跃过程的关键是使用泊松随机变量来近似在仔细选择的时间段 τ 内每种类型的反应事件发生的次数。只要满足跳跃条件，即倾向函数在任何时间步长内都不会“显著”变化，这种方法是可以接受的。使用这种方法，物种数量可能会人为地变为负数。最近有几篇论文展示了避免这种情况的方法。其中一种方法将那些有将物种数量发送到负值危险的反应归类为关键反应。在下一个时间步中，最多只允许发生其中一个关键反应。我们认为，反应物种的临界性及其相关的反应通道应该与物种数量变为负值的概率有关。这样，只有那些如果被触发，就会产生很高的将反应物种群数量驱动为负值的概率的反应才被标记为关键反应。可以使用泊松随机变量来近似更多反应通道的触发次数，从而在保持准确性的同时加快模拟速度。在实现这种修正的关键反应选择方法时，我们利用了描述物种数量变化的随机变量所来自的概率分布。我们给出了几个数值示例来演示我们新方法的有效性。
