Computational Systems Biology Section, Laboratory of Immune System Biology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA.
J Chem Phys. 2021 Apr 28;154(16):164111. doi: 10.1063/5.0037266.
Computational models of reaction-diffusion systems involving low copy numbers or strongly heterogeneous molecular spatial distributions, such as those frequently found in cellular signaling pathways, require approaches that account for the stochastic dynamics of individual particles, as opposed to approaches representing them through their average concentrations. Efforts to remedy the high computational cost associated with particle-based stochastic approaches by taking advantage of Green's functions are hampered by the need to draw random numbers from complicated, and therefore costly, non-standard probability distributions to update particle positions. Here, we introduce an approach that permits the reconstruction of entire molecular trajectories, including bimolecular encounters, in retrospect, after a simulated time step, while avoiding inefficient draws from non-standard distributions. This means that highly accurate stochastic simulations can be performed for system sizes that would be prohibitively costly to simulate with conventional Green's function based methods. The algorithm applies equally well to one, two, and three dimensional systems and can be readily extended to include deterministic forces specified by an interaction potential, such as the Coulomb potential.
涉及低拷贝数或强烈异质分子空间分布的反应扩散系统的计算模型，如细胞信号通路中经常遇到的模型，需要采用能够描述单个粒子随机动力学的方法，而不是通过它们的平均浓度来表示它们的方法。通过利用格林函数来弥补基于粒子的随机方法相关的高计算成本的努力受到阻碍，因为需要从复杂且因此昂贵的非标准概率分布中随机抽取数字来更新粒子位置。在这里，我们引入了一种方法，允许在模拟时间步之后回顾性地重建整个分子轨迹，包括双分子遭遇，同时避免从非标准分布中进行低效抽取。这意味着可以对系统大小进行非常精确的随机模拟，而这些模拟对于传统基于格林函数的方法来说成本过高。该算法同样适用于一维、二维和三维系统，并且可以很容易地扩展到包括由相互作用势能（如库仑势能）指定的确定性力。
