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A Web Tool for Generating High Quality Machine-readable Biological Pathways

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Transition graph decomposition for complex balanced reaction networks with non-mass-action kinetics.

Daniele Cappelletti¹, Badal Joshi²

¹DISMA-Dipartimento di Scienze Matematiche "G.L. Lagrange", Politecnico di Torino, Torino, Italy.

Mathematical Biosciences and Engineering : MBE

|July 8, 2022

Summary

This study identifies specific finite state subsets, called copies, within reaction networks. These copies enable exact calculation of stationary distributions for stochastic models, simplifying analysis of biochemical processes.

Keywords:

reaction networks state space truncation stationary distribution stochastic models

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Area of Science:

Computational Biology
Biochemical Systems Theory
Stochastic Modeling

Background:

Reaction networks are crucial for modeling biochemical processes.
Stochastic fluctuations in small biomolecular populations necessitate discrete, continuous-time models.
Stationary distributions are key to understanding model behavior at equilibrium.

Purpose of the Study:

To determine conditions under which stationary distributions of infinite state-space models match truncated finite state-space models.
To introduce a novel graphical characterization for complex balancing in stochastic reaction networks.

Main Methods:

Identification of finite subsets of states, termed 'copies', inspired by modular network topology.
Analysis of stationary distributions for both original and truncated models.
Development of a graphical method for complex balancing.

Main Results:

Conditions are established for the exact coincidence of stationary distributions between infinite and finite (copy-truncated) state spaces.
A novel graphical characterization of complex balancing for stochastic reaction network models is proven.
Results are applicable to mass-action kinetics and more general reaction settings.

Conclusions:

The concept of 'copies' provides a powerful tool for analyzing stationary distributions in complex biochemical reaction networks.
The graphical characterization simplifies the understanding and identification of complex balancing in stochastic models.
This work offers a more tractable approach to studying the long-term behavior of biochemical systems.