Reconstructing biochemical cluster networks

TL;DR

This paper introduces a computational algebra method to reconstruct biochemical cluster networks, enabling the determination of connectivity between states and enumeration of reaction pathways, with applications to chemical reactions like permanganate/oxalic acid.

Contribution

It presents a novel algebraic approach for reconstructing cluster graphs in biochemical systems, addressing connectivity and pathway enumeration problems.

Findings

Successfully applied to permanganate/oxalic acid reaction

Decided state connectivity using algebraic methods

Reconstructed full cluster graph for biochemical states

Abstract

Motivated by fundamental problems in chemistry and biology we study cluster graphs arising from a set of initial states $S\subseteq\Z^n_+$ and a set of transitions/reactions $M\subseteq\Z^n_+\times\Z^n_+$. The clusters are formed out of states that can be mutually transformed into each other by a sequence of reversible transitions. We provide a solution method from computational commutative algebra that allows for deciding whether two given states belong to the same cluster as well as for the reconstruction of the full cluster graph. Using the cluster graph approach we provide solutions to two fundamental questions: 1) Deciding whether two states are connected, e.g., if the initial state can be turned into the final state by a sequence of transition and 2) listing concisely all reactions processes that can accomplish that. As a computational example, we apply the framework to the permanganate/oxalic acid reaction.