多粒子复合物基于规则的建模的代数与图形化方法
Algebraic and diagrammatic methods for the rule-based modeling of multi-particle complexes
AI总结：
本文提出一种基于Fock空间的算子代数与图形化方法，统一了基于规则的生化复合物建模与统计物理分析，并给出非平衡系统的随机模拟算法。
摘要：
多粒子复合物的形成、解离和动力学在随机化学系统研究中具有根本意义。1976年，Masao Doi引入了一种用于建模经典粒子的Fock空间形式化方法。然而，Doi的形式化方法不支持多个粒子组装成复合物。从2000年代开始，多个研究团队开发了基于规则的方法，用于计算模拟涉及大分子复合物的生化系统。但这些方法基于图重写规则和/或进程代数，在数学上与通常用于分析平衡和非平衡系统的统计物理方法相脱节。本文通过引入一种用于多粒子复合物基于规则建模的算子代数，将这两种方法连接起来。我们的形式化方法基于一个Fock空间，该空间不仅支持经典粒子的产生和湮灭，还支持多个粒子组装成复合物，以及复合物分解为其组分。规则由代数算子指定，这些算子通过Wick定理的一种表现形式作用于粒子。我们进一步描述了便于规则指定和解析计算的图形化方法。我们在处于热平衡和非热平衡的系统上展示了我们的形式化方法，并且对于非平衡系统，我们提出了一种基于该形式化方法的随机模拟算法。这些结果为随机化学系统的数学和计算研究提供了一种统一方法，其中多粒子复合物发挥着重要作用。
英文摘要：
The formation, dissolution, and dynamics of multi-particle complexes is of fundamental interest in the study of stochastic chemical systems. In 1976, Masao Doi introduced a Fock space formalism for modeling classical particles. Doi's formalism, however, does not support the assembly of multiple particles into complexes. Starting in the 2000's, multiple groups developed rule-based methods for computationally simulating biochemical systems involving large macromolecular complexes. However, these methods are based on graph-rewriting rules and/or process algebras that are mathematically disconnected from the statistical physics methods generally used to analyze equilibrium and nonequilibrium systems. Here we bridge these two approaches by introducing an operator algebra for the rule-based modeling of multi-particle complexes. Our formalism is based on a Fock space that supports not only the creation and annihilation of classical particles, but also the assembly of multiple particles into complexes, as well as the disassembly of complexes into their components. Rules are specified by algebraic operators that act on particles through a manifestation of Wick's theorem. We further describe diagrammatic methods that facilitate rule specification and analytic calculations. We demonstrate our formalism on systems in and out of thermal equilibrium, and for nonequilibrium systems we present a stochastic simulation algorithm based on our formalism. The results provide a unified approach to the mathematical and computational study of stochastic chemical systems in which multi-particle complexes play an important role.
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