A scalable computational framework for establishing long-term behavior of stochastic reaction networks

Area of Science:

• Systems Biology
• Computational Biology
• Biochemistry

Background:

• Stochastic models are essential for biochemical reaction networks with small populations to capture interaction randomness.
• Existing analysis tools for stochastic models lag behind deterministic counterparts.

Purpose of the Study:

• To develop a constructive framework for analyzing long-term behavior and stability of stochastic reaction dynamics.
• To address ergodicity, bounded statistical moments, and steady-state convergence in these networks.

Main Methods:

• Combines probability theory, linear algebra, and optimization theory.
• Recasts theoretical conditions into efficient and scalable linear programs.
• Demonstrates computational complexity often linear in the number of species.

Main Results:

• Provides a framework for assessing stability properties of biological networks.
• Establishes conditions for ergodicity and convergence of statistical moments.
• Shows efficient and scalable analysis through linear programming.

Conclusions:

• The developed framework bridges the gap in analyzing stochastic reaction networks.
• Offers efficient and widely applicable methods for assessing biological network dynamics.
• Highlights biological implications and provides examples of non-ergodic networks.