Maximum Entropy Prediction of Non-Equilibrium Stationary Distributions for Stochastic Reaction Networks with...

Area of Science:

• Biochemistry
• Chemical Kinetics
• Computational Biology

Background:

• Biological systems exhibit complex oscillatory dynamics in processes like gene regulation and cell cycles.
• Stochastic models, such as the Chemical Master Equation (CME), are limited by computational challenges and the need for extensive simulations.
• The low molecule counts in many biological reactions deviate from thermodynamic equilibrium assumptions.

Purpose of the Study:

• To develop an efficient computational method for predicting non-equilibrium stationary distributions in stochastic chemical reaction networks.
• To address the limitations of existing methods in solving the Chemical Master Equation (CME) for oscillatory systems.
• To explore the application of maximum entropy principles for truncating moment equations.

Main Methods:

• Truncation of infinite stationary moment equations using maximum entropy principles.
• Application to stochastic Brusselator and Schnakenberg oscillatory reaction networks.
• Numerical comparison with kinetic Monte Carlo simulations.

Main Results:

• The maximum entropy method provides accurate predictions for stationary distributions of oscillatory chemical reactions.
• Prediction accuracy improves exponentially with the chosen closure order for the moment equations.
• The approach successfully truncates the infinite set of moment equations.

Conclusions:

• Maximum entropy models offer an efficient alternative closure scheme for moment equations in stochastic chemical kinetics.
• This method accurately predicts non-equilibrium stationary distributions without prior system knowledge or biased assumptions.
• The findings are applicable to various biological systems with complex oscillatory dynamics.