arXiv subjects

James N. Cobley

Publications and source records attributed to James N. Cobley.

5 recordsLinked to original sources

arXiv2026

Oxi-Shapes: Tropical geometric analysis of bounded redox proteomic state spaces

Redox proteomics generates bounded biochemical measurements that are categorically mismatched to conventional linear algebraic formalisms. This work introduces Oxi-Shapes, a tropical geometric framework for the measurement-native analysis of bounded redox proteomic data. Oxi-Shapes represents cysteine oxidation as a scalar field over a discrete lattice, enabling global and site-wise analysis without rescaling, interpolation, or kinetic assumptions. At the global level, the framework yields internal redox entropy, lattice curvature, and derived energy functionals that characterise the geometric structure of the redox proteome. At the site level, Oxi-Shapes defines a bounded change space that makes explicit hard geometric constraints on admissible redox transitions and enables a normalised signed representation of site-wise change as a fraction of available redox freedom. Applied to an ageing mouse brain dataset, Oxi-Shapes reveals that a small decrease in mean oxidation arises from a profound redistribution of site-wise redox states, with thousands of residues shifting toward the reduced absorbing boundary. These results demonstrate that categorically correct algebraic representations expose structure in proteomic data that is inaccessible to mean-centric or unbounded analyses.

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arXiv2026

A Mathematical Theory of Redox Biology

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.

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arXiv2026

A tropical geometry for bounded biochemical state spaces

Many biochemical measurements define state spaces that are bounded, absorbing, and physically irreversible, yet are routinely analysed using linear and Euclidean frameworks that assume global invertibility, symmetry, and translation invariance. This mismatch can irretrievably obscure biological structure, independent of data quality, scale, or preprocessing. This work formalises the structure of bounded biochemical state spaces using cysteine redox regulation as a representative example and identify the minimal algebraic properties required for categorically correct representation. Hard boundaries, absorbing states, and irreversible ensemble dynamics render linear algebra incompatible with these objects. This work demonstrates that tropical algebra provides a natural realisation of the required properties by replacing additive linear structure with order-based, piecewise-linear operations that encode dominance, saturation, and path dependence without contradiction. By making non-invertibility and absorption explicit rather than implicit, this framework resolves a fundamental algebraic mismatch and establishes a principled foundation for the representation and analysis of bounded biochemical data.

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arXiv2025

Local Electromagnetic Fields Enable Fast Redox Sensing by Physically Accelerating Cysteine Oxidation

Hydrogen peroxide oxidises cysteine residues to control protein function, yet bulk rate constants predict hours for changes that occur in cells in seconds. Here, this work shows that local electromagnetic fields (EMFs), ubiquitous in proteins, membranes and nanodomains, can lawfully modulate the Eyring barrier and orientate reactants, accelerating cysteine oxidation without changing the underlying chemistry. Embedding a field term into the Eyring expression, demonstrated that plausible local EMFs with realistic dipole changes accelerate rate constants by orders of magnitude. This local acceleration reconciles the discrepancy between predicted vs. observed rates of H2O2-mediated cysteine oxidation. The framework generates falsifiable predictions, such as vibrational Stark readouts in thiolate peroxide complexes should fall within predicted ranges, and reframes rate-constants as mutable, field conditioned parameters. Cysteine redox sensing is fast not because the chemistry is exotic, but because the physics is local.

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arXiv2025

Modal Geometry Governs Proteoform Dynamics

The fundamental laws governing proteoform dynamics have yet to be formulated. As a result, it is unclear how a specific proteoform, a distinct molecular variant of a protein, dynamically shapes its own future by evolving into new modes that exist only in potential until realised. Here, Modal Geometric Field (MGF) Theory couples real and abstract proteoform transitions through four axioms. Axioms 1 to 3 (invariant) dictate that only first-order transitions occur on the discrete, volume-invariant, non symplectic modal manifold. Axiom 4 (mutable) projects the occupancy and shape of a real, instantiated molecule into the modal manifold, generating occupancy-induced curvature. By coupling what is real to what is abstract, curvature, which is always conserved, governs proteoform dynamics by dictating the least-action modal transition. Because curvature distribution renders activation energy relative, barriers are mutable, and entropy emerges inevitably from curvature transport. This unification of energy, entropy, and curvature yields hysteresis, path dependence, fractal self similarity, and trajectories that oscillate between order and chaos. As a scale invariant and universal framework, MGF Theory reveals how modal geometry governs proteoform dynamics

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