Parametric Sensitivity Analysis: Local and Global Approaches in Stochastic Biochemical Models

The recent advancements in mathematical modeling of biochemical systems have generated increased interest in sensitivity analysis methodologies. There are two primary approaches for analyzing these mathematical models: the stochastic approach, which employs chemical master equations (CME), and the deterministic approach, which utilizes ordinary differential equations (ODEs). The intractable discrete states present in most biochemical processes render the direct simulation of the CME infeasible. Moment closure approximations are recognized for their numerical efficiency in estimating the statistics of the CME solution. Since classical sensitivity analysis is not directly applicable to stochastic modeling, this work conducts sensitivity analysis using moment-based ordinary differential equations (ODEs) to identify key parameters that significantly influence the dynamics of the model. We conduct numerical tests to evaluate the effectiveness of both local and global sensitivity analyses of the moment-based ODEs. These tests enable us to examine how variations in input parameters influence the model's output.