A Mathematical Theory of Redox Biology

TL;DR

This paper introduces a comprehensive mathematical framework for redox biology, modeling it as a structured, dynamical, and spatially embedded system that explains complex behaviors without ad hoc assumptions.

Contribution

It develops a formal, geometric theory of redox systems, linking molecular transformations to biological functions through a structured state space and dynamics.

Findings

Redox behavior emerges from constrained biochemical organization.

The framework explains nonlinearity, hysteresis, and memory in redox systems.

It provides a predictive basis for interpreting redox measurements.

Abstract

Redox biology underpins signalling, metabolism, immunity, and adaptation, yet lacks a unifying theoretical framework capable of formalising structure, function, and dynamics. Current interpretations rely on descriptive catalogues of molecules and reactions, obscuring how redox behaviour emerges from constrained biochemical organisation. Here, we present a mathematical theory of redox biology that resolves this gap by treating redox systems as finite, compositional, dynamical, and spatially embedded objects. We define a structured redox state space in which admissible molecular transformations form a neutral algebra of possibilities. Biological function emerges when this structure is embedded within a wider molecular network and interpreted through weighted flux distributions. Time-dependent reweighting of these transformations generates redox dynamics, while spatial embedding enforces locality and causality, yielding a distributed redox field. Within this framework, context dependence, nonlinearity, hysteresis, and memory arise naturally from bounded state spaces and irreversible transformations, without requiring ad hoc assumptions. This theory provides a working, predictive interpretative basis for redox biology: it constrains admissible states and trajectories, clarifies the meaning of redox measurements, and links chemical transformation to biological behaviour. Redox biology emerges as a geometric, dynamical process governed by lawful organisation.