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

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.