Exact Hybrid Particle/Population Simulation of Rule-Based Models of Biochemical Systems

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This “network-free” approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of “partial network expansion” into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.

生化系统的精细化建模与仿真常因组合复杂度（combinatorial complexity）问题变得复杂——海量的蛋白质-蛋白质相互作用与翻译后修饰（post-translational modifications）会导致分子物种与反应数量呈爆炸式增长。基于规则的建模（rule-based modeling）通过将分子表示为结构化对象、将分子间相互作用编码为基于模式的规则，解决了这一难题。这极大简化了模型构建流程，规避了手动枚举系统中所有潜在分子物种与反应的繁琐且易出错的任务。从仿真视角来看，若反应网络规模未过度庞大，基于规则的模型可通过算法扩展为完全枚举的反应网络，并采用多种基于网络的仿真方法进行模拟，如常微分方程（ordinary differential equations）或吉莱斯皮算法（Gillespie's algorithm）。此外，基于规则的模型也可直接采用基于粒子的动力学蒙特卡洛方法（particle-based kinetic Monte Carlo methods）进行仿真。这种“无网络”方法可生成精确的随机轨迹（stochastic trajectories），其计算成本与网络规模无关，但内存与运行时间成本会随粒子数量增加而上升，限制了可有效仿真的系统规模。本文提出一种结合基于网络与无网络方法优势的混合粒子/群体模拟方法（hybrid particle/population simulation method）。该方法以基于规则的模型与用户指定的分子物种子集作为输入，将这些物种作为群体变量而非粒子进行处理。随后通过“部分网络扩展”流程将模型转换为动态等价形式，即可采用适配群体的无网络仿真器进行模拟。该转换方法已在开源基于规则的建模平台BioNetGen中实现，生成的混合模型可通过基于粒子的仿真器NFsim进行仿真。性能测试表明，新方法可显著节省内存，且成本分析可为其应用价值提供量化参考。