Parametric Sensitivity Analysis for Models of Reaction Networks within Interacting Compartments

TL;DR

This paper develops and compares computational methods for sensitivity analysis of reaction network models within interacting compartments, extending techniques from stochastic reaction networks to this more complex setting.

Contribution

It introduces and evaluates several unbiased and coupling-based sensitivity estimation methods tailored for RNIC models, adapting existing stochastic network techniques.

Findings

Girsanov transformation method performs well in RNIC context

Coupling methods provide efficient finite difference estimates

Performance aligns with standard stochastic reaction network results

Abstract

Models of reaction networks within interacting compartments (RNIC) are a generalization of stochastic reaction networks. It is most natural to think of the interacting compartments as "cells" that can appear, degrade, split, and even merge, with each cell containing an evolving copy of the underlying stochastic reaction network. Such models have a number of parameters, including those associated with the internal chemical model and those associated with the compartment interactions, and it is natural to want efficient computational methods for the numerical estimation of sensitivities of model statistics with respect to these parameters. Motivated by the extensive work on computational methods for parametric sensitivity analysis in the context of stochastic reaction networks over the past few decades, we provide a number of methods in the basic RNIC setting. Provided methods include the (unbiased) Girsanov transformation method (also called the Likelihood Ratio method) and a number of coupling methods for the implementation of finite differences, each motivated by methods from previous work related to stochastic reaction networks. We provide several numerical examples comparing the various methods in the new setting. We find that the relative performance of each method is in line with its analog in the "standard" stochastic reaction network setting. We have made all of the Matlab code used to implement the various methods freely available for download.