New Methods for Modeling Multi-Particle Complexes in Stochastic Chemical Systems

Recent advancements in the modeling of multi-particle complexes have been presented in a paper titled "Algebraic and diagrammatic methods for the rule-based modeling of multi-particle complexes" by Rebecca J. Rousseau and Justin B. Kinney. The paper, submitted on September 3, 2024, introduces a new formalism that bridges existing methodologies in the field of stochastic chemical systems.

Historically, the modeling of classical particles was addressed by Masao Doi in 1976 through a Fock space formalism. However, this approach did not accommodate the assembly of multiple particles into complexes. In the 2000s, various groups began to develop rule-based methods for simulating biochemical systems involving large macromolecular complexes, yet these methods often relied on graph-rewriting rules and process algebras that lacked a connection to statistical physics methods typically used for analyzing equilibrium and nonequilibrium systems.

The authors propose an operator algebra that supports both the creation and annihilation of classical particles, along with the assembly and disassembly of these particles into complexes. This is achieved through algebraic operators that act on particles, utilizing a manifestation of Wick's theorem. Additionally, the paper outlines diagrammatic methods that simplify rule specification and facilitate analytical calculations.

The formalism is demonstrated on systems both in and out of thermal equilibrium. For nonequilibrium systems, a stochastic simulation algorithm based on the new formalism is presented. The findings aim to provide a unified approach for the mathematical and computational study of stochastic chemical systems where multi-particle complexes are significant.

This work is expected to impact the understanding and simulation of complex biochemical interactions, potentially leading to more accurate models in biological physics and related fields. The paper can be cited as arXiv:2409.01529.