Comparison Theorems for Stochastic Chemical Reaction Networks.

Area of Science:

• Systems Biology
• Stochastic Modeling
• Computational Chemistry

Background:

• Continuous-time Markov chains model chemical reaction networks in systems biology.
• Understanding parameter dependence in Stochastic Chemical Reaction Networks (SCRNs) is crucial but challenging.
• Existing methods lack sufficient tools for analyzing parameter influence on SCRN dynamics.

Purpose of the Study:

• Develop theoretical tools (comparison theorems) for analyzing parameter dependence in SCRNs.
• Provide sufficient conditions for monotonic dependence of SCRN behavior on reaction rate parameters.
• Enable comparison of SCRNs with different parameters or initial conditions.

Main Methods:

• Development of novel comparison theorems for SCRNs.
• Exploitation of specific structural properties of SCRNs.
• Derivation of theorems for comparing stationary distributions and mean first passage times.
• Application of coupling methods for simultaneous simulation when propensity functions are bounded.

Main Results:

• Comparison theorems provide stochastic ordering results for SCRNs.
• Sufficient conditions for monotonic parameter dependence are established.
• Theorems allow insights into transient and steady-state behaviors.
• New methods facilitate comparison of stationary distributions and mean first passage times.
• Explicit coupling methods enable simultaneous simulation of comparable SCRNs.

Conclusions:

• The developed comparison theorems offer powerful tools for analyzing parameter sensitivity in SCRNs.
• These methods advance the understanding of stochastic dynamics in biological systems.
• The findings are applicable to a broad range of SCRNs, including non-mass-action models and specific biological processes.