Efficient Finite Difference Method for Computing Sensitivities of Biochemical Reactions

TL;DR

This paper introduces a novel finite difference method that efficiently computes sensitivities in biochemical reactions by coupling simulations to reduce variance, requiring minimal data structures, and suitable for large networks.

Contribution

The paper presents a new coupling-based finite difference approach that improves efficiency and accuracy in sensitivity analysis of biochemical reactions, especially for large networks.

Findings

Reduces variance of sensitivity estimators

Requires only a single data structure for propensity bounds

Demonstrates efficiency on biological reaction models

Abstract

Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities, however, poses many computational challenges when taking stochastic noise into account. This paper proposes a new finite difference method for efficiently computing sensitivities of biochemical reactions. We employ propensity bounds of reactions to couple the simulation of the nominal and perturbed processes. The exactness of the simulation is reserved by applying the rejection-based mechanism. For each simulation step, the nominal and perturbed processes under our coupling strategy are synchronized and often jump together, increasing their positive correlation and hence reducing the variance of the estimator. The distinctive feature of our approach in comparison with existing coupling approaches is that it only needs to maintain a single data structure storing propensity bounds of reactions during the simulation of the nominal and perturbed processes. Our approach allows to computing sensitivities of many reaction rates simultaneously. Moreover, the data structure does not require to be updated frequently, hence improving the computational cost. This feature is especially useful when applied to large reaction networks. We benchmark our method on biological reaction models to prove its applicability and efficiency.