Parametric Sensitivity Analysis for Biochemical Reaction Networks based on Pathwise Information Theory

TL;DR

This paper introduces a pathwise information-theoretic sensitivity analysis method for complex stochastic biochemical networks, enabling efficient parameter sensitivity assessment in high-dimensional models without gradient computations.

Contribution

The authors develop a novel pathwise sensitivity analysis approach based on Relative Entropy Rate and Fisher Information Matrix, suitable for large-scale stochastic reaction networks.

Findings

The method efficiently quantifies parameter sensitivities using path-space information measures.

The Fisher Information Matrix reveals hidden parameter dependencies.

The approach reduces computational cost compared to traditional finite difference methods.

Abstract

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.