Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically  such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the  sensitivity analysis of the reaction network's parameters is a crucial mathematical and computational tool since it allows to infer information about the robustness and the identifiability of the model 's parameters. We develop a sensitivity analysis methodology suitable for complex stochastic reaction networks with a high number of parameters. The proposed approach is based on Information Theory  and relies on the quantification of information loss due to parameter perturbations between time-series distributions , hence referred to as "pathwise". This is achieved by employing the rigorously-derived Relative Entropy Rate (RER), which is directly computable from the propensity functions. A key aspect of the method is that an associated pathwise Fisher Information Matrix (FIM) is defined, which in turn constitutes a gradient-free approach to quantify the parameter sensitivities. The study of the structure of the FIM which turns out to be block-diagonal reveals hidden parameter dependencies and sensitivities in reaction networks . The proposed method is tested and validated on two biochemical systems, namely: (a) the p53 reaction network where quasi-steady stochastic oscillations of the concentrations are observed and (b) an Epidermal Growth Factor Receptor (EGFR) model which is an example of a high-dimensional stochastic reaction network with more than 200 reactions and a corresponding number of parameters .
Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically , such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the parameter sensitivity analysis of reaction networks is an essential mathematical and computational tool , yielding information regarding the robustness and the identifiability of model parameters. However, existing sensitivity analysis approaches such as variants of the finite difference method can have an overwhelming computational cost in models with a high-dimensional parameter space. We develop a sensitivity analysis methodology suitable for complex stochastic reaction networks with a large number of parameters. The proposed approach is based on Information Theory methods and relies on the quantification of information loss due to parameter perturbations between time-series distributions . For this reason, we need to work on path-space, i.e., the set consisting of all stochastic trajectories, hence the proposed approach is referred to as "pathwise". The pathwise sensitivity analysis method is realized by employing the rigorously-derived Relative Entropy Rate (RER), which is directly computable from the propensity functions. A key aspect of the method is that an associated pathwise Fisher Information Matrix (FIM) is defined, which in turn constitutes a gradient-free approach to quantifying parameter sensitivities. The structure of the FIM turns out to be block-diagonal , revealing hidden parameter dependencies and sensitivities in reaction networks .
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