# Sensitivity and Network Topology in Chemical Reaction Systems

## TL;DR

This paper extends a framework for analyzing biochemical reaction networks to include conserved concentrations, introduces new measures of robustness, and demonstrates that E. coli's metabolic network is more robust than random networks.

## Contribution

It generalizes the law of localization to reaction systems with conserved concentrations and proposes novel network metrics for robustness analysis.

## Key findings

- E. coli metabolic network exhibits higher robustness than random networks.
- The generalized framework applies to any reaction system with conserved quantities.
- Network topology influences response patterns and robustness.

## Abstract

In living cells, biochemical reactions are catalyzed by specific enzymes and connect to one another by sharing substrates and products, forming complex networks. In our previous studies, we established a framework determining the responses to enzyme perturbations only from network topology, and then proved a theorem, called the law of localization, explaining response patterns in terms of network topology. In this paper, we generalize these results to reaction networks with conserved concentrations, which allows us to study any reaction systems. We also propose novel network characteristics quantifying robustness. We compare E. coli metabolic network with randomly rewired networks, and find that the robustness of the E. coli network is significantly higher than that of the random networks.