Computing Weakly Reversible Linearly Conjugate Chemical Reaction Networks with Minimal Deficiency

TL;DR

This paper introduces a mixed-integer linear programming method to identify weakly reversible chemical reaction networks with minimal deficiency that are linearly conjugate to a given network, aiding the analysis of their dynamical properties.

Contribution

It presents a novel algorithm to compute weakly reversible networks with minimal deficiency linearly conjugate to a specified network, enhancing the understanding of their dynamics.

Findings

Algorithm successfully finds minimal deficiency weakly reversible networks

Enables analysis of network dynamics via linear conjugacy

Supports systems biology modeling with improved network characterization

Abstract

Mass-action kinetics is frequently used in systems biology to model the behaviour of interacting chemical species. Many important dynamical properties are known to hold for such systems if they are weakly reversible and have a low deficiency. In particular, the Deficiency Zero and Deficiency One Theorems guarantee strong regularity with regards to the number and stability of positive equilibrium states. It is also known that chemical reaction networks with disparate reaction structure can exhibit the same qualitative dynamics. The theory of linear conjugacy encapsulates the cases where this relationship is captured by a linear transformation. In this paper, we propose a mixed-integer linear programming algorithm capable of determining weakly reversible reaction networks with a minimal deficiency which are linearly conjugate to a given reaction network.