Sensitivity of chemical reaction networks: a structural approach 3. Regular multimolecular systems

TL;DR

This paper introduces a structural mathematical framework for analyzing how steady states in large, complex reaction networks respond to rate changes, using only network structure without numerical rate data.

Contribution

It develops a purely structural sensitivity analysis method for reaction networks, enabling the identification of influential reactions and functional subunits without numerical parameters.

Findings

Derived influence graphs for reaction networks.

Identified sensitive and insensitive steady-state concentrations.

Applied method to glycolytic and citric acid cycle variants.

Abstract

We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions, multiple reaction products, nonmonotone rate functions, and non-closed autonomous systems. Our structural sensitivity analysis is based on the stoichiometry of the reaction network, only. It does not require numerical data on reaction rates. Instead, we impose mild and generic nondegeneracy conditions of algebraic type. From the structural data, only, we derive which steady-state concentrations are sensitive to, and hence influenced by, changes of any particular reaction rate - and which are not. We also establish transitivity properties for influences involving rate perturbations. This allows us to derive an influence graph which globally summarizes the influence pattern of the given network. The influence graph allows the computational, but meaningful, automatic identification of functional subunits in general networks, which hierarchically influence each other. We illustrate our results for several variants of the glycolytic citric acid cycle. Biological applications include enzyme knockout experiments, and metabolic control.