具有最优装箱的常数复杂度随机模拟算法
Constant-complexity Stochastic Simulation Algorithm with Optimal Binning
摘要：
在细胞尺度上，生物化学过程由具有小拷贝数的反应物分子之间的随机相互作用控制，导致固有随机的行为。这些系统通常被建模为连续时间马尔可夫跳跃过程，可以通过化学主方程来描述。Gillespie的随机模拟算法（SSA）生成这些系统的精确轨迹。原始SSA的每个步骤所需的计算工作量与反应通道的数量成比例，导致计算复杂性随着问题大小的增加而线性扩展。因此，原来的SSA是效率低下的大问题，这促使了几个替代配方的发展与改进的缩放性能。我们描述了一个确切的SSA，它使用一个表的数据结构与事件时间分仓，以实现恒定的计算复杂性。最佳的算法参数和合并策略进行了讨论。我们比较现有的方法的算法的计算效率，并表现出良好的规模大的问题。这种方法非常适合于生成精确的轨迹的大型模型，可以描述的反应扩散主方程所产生的空间离散的反应扩散过程。
英文摘要：
At the cellular scale, biochemical processes are governed by random interactions between reactant molecules with small copy counts, leading to behavior that is inherently stochastic. Such systems are often modeled as continuous-time Markov jump processes that can be described by the Chemical Master Equation. Gillespie's Stochastic Simulation Algorithm (SSA) generates exact trajectories of these systems. The amount of computational work required for each step of the original SSA is proportional to the number of reaction channels, leading to computational complexity that scales linearly as the problem size increases. The original SSA is therefore inefficient for large problems, which has prompted the development of several alternative formulations with improved scaling properties. We describe an exact SSA that uses a table data structure with event time binning to achieve constant computational complexity. Optimal algorithm parameters and binning strategies are discussed. We compare the computational efficiency of the algorithm to existing methods and demonstrate excellent scaling for large problems. This method is well suited for generating exact trajectories of large models that can be described by the Reaction-Diffusion Master Equation arising from spatially discretized reaction-diffusion processes.
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