# Path mutual information for a class of biochemical reaction networks

## TL;DR

This paper introduces a method to estimate the mutual information between the complete trajectories of two interacting molecular species in biochemical reaction networks, addressing mathematical challenges in stochastic systems.

## Contribution

It presents a novel approach for calculating path mutual information in biochemical networks, enabling better understanding of cellular information processing.

## Key findings

- Method successfully applied to three case studies
- Provides a quantitative measure of interdependence in biochemical systems
- Addresses mathematical challenges in stochastic reaction network analysis

## Abstract

Living cells encode and transmit information in the temporal dynamics of biochemical components. Gaining a detailed understanding of the input-output relationship in biological systems therefore requires quantitative measures that capture the interdependence between complete time trajectories of biochemical components. Mutual information provides such a measure but its calculation in the context of stochastic reaction networks is associated with mathematical challenges. Here we show how to estimate the mutual information between complete paths of two molecular species that interact with each other through biochemical reactions. We demonstrate our approach using three simple case studies.