Variance decomposition in stochastic simulators.

Area of Science:

• Computational Chemistry
• Mathematical Biology
• Biophysics

Background:

• Stochastic simulations are crucial for understanding chemical reaction networks.
• Quantifying sources of randomness and their sensitivities remains a challenge.

Purpose of the Study:

• To develop a mathematical and computational approach for quantifying stochasticity sources and sensitivities in chemical reaction networks.
• To enable a quantitative characterization of inherent stochasticity in chemical systems.

Main Methods:

• Reformulating system dynamics using independent standardized Poisson processes.
• Employing Sobol-Hoeffding decomposition for orthogonal variance decomposition.
• Implementing algorithms for analyzing stochastic simulations.

Main Results:

• The approach allows straightforward identification of stochastic dynamics for each reaction channel.
• Quantitative characterization of inherent stochasticity sources is achieved.
• Variance-based sensitivities of individual reaction channels and their interactions are quantified.

Conclusions:

• The developed method provides a robust framework for analyzing stochasticity in chemical reaction networks.
• This approach enhances the understanding of system dynamics by quantifying sources of randomness and their sensitivities.
• Applicable to various models, including birth-death, Schlögl, and Michaelis-Menten systems.