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 inter
Electrochemically redox-active halide (eREAL) materials are an emerging class of materials that combine high Li-ion conductivity with transition-metal redox activity, making them promising candidates for cathode or catholyte applications. As a redox-active catholyte, they could significantly increase the energy density of solid-state batteries. In this work, we perform first-principles calculations on Li-M-Cl (M = 3d transition metals) ternaries to establish such a theoretical foundation for their stability and electrochemical activity. We map the phase stability of eREAL structures with varying metal-to-Cl ratio, transition-metal species, oxidation states, and anion frameworks, and compute cation and anion redox potentials. We find that the high ionicity of metal-Cl bonds elevates cation redox potentials above those of conventional oxide cathodes, but also will promote Cl oxidation and Cl-Cl dimerization at high voltages, which may limit the stability of these materials. Anion substitution effectively tunes both cation and anion redox potentials, with F substitution standing out as a viable route to extend the reversible voltage window. Beyond the anion redox issue, eREAL compound
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 representatio
Volatile outgassing from planetary interiors controls the composition of rocky exoplanets' secondary atmospheres. However, observations indicate that disequilibrium processes, such as photochemistry and vertical transport, can strongly alter the chemical structure of Hot Jupiters. Which process dominates under different types of rocky planets, and how outgassing and photochemistry jointly determine the atmospheric composition, remain open questions. Sulfur species are promising tracers of interior-atmosphere coupling because their atmospheric abundances are sensitive to both mantle redox state and stellar irradiation. The PROTEUS planetary interior-atmosphere evolution modelling framework is coupled to two chemical models, FastChem and VULCAN, for post-processed chemistry calculations. We run a grid of planetary evolution simulations spanning diverse mantle redox states, instellation fluxes, and Solar versus M-star host-star spectra. For each case, we compare atmospheric compositions under thermochemical equilibrium, only vertical transport, and vertical transport plus photochemistry. The bulk atmospheric composition remains controlled by the redox state of the mantle and outgassin
Describing Li-ion battery positive electrodes in terms of distinct transition metal or oxygen redox regimes can lead to confusion in understanding metal-ligand hybridisation, oxygen dimerisation, and degradation. There is a pressing need to study the electronic structure of these materials and determine the role each cation and anion plays in charge compensation. Here, we employ transition metal L-edge X-ray Resonance Photoemission Spectroscopy in conjunction with Single Impurity Anderson models, Self-consistent Real Space Multiple Scattering spectral simulations, and Dynamical Mean-Field theory calculations to directly evaluate the redox mechanisms in (de-)lithiated battery electrodes. This approach reconciles the redox description of two canonical cathodes -- LiMn$_{0.6}$Fe$_{0.4}$PO$_{4}$ and LiNiO$_{2}$ -- in terms of varying degrees of charge transfer using the established Zaanen-Sawatzky-Allen framework, common to condensed matter physics. In LiMn$_{0.6}$Fe$_{0.4}$PO$_{4}$, the absence of charge transfer means capacity arises due to the depopulation of metal $\textit{3d}$ states, i.e. conventional metal redox. Whereas, in LiNiO$_{2}$, charge transfer dominates and redox occur
Understanding how the electronic structure of electrodes influences electrocatalytic reactions has been a longstanding topic in the electrochemistry community, with predominant attention paid to metallic electrodes. In this work, we present a defect physics perspective on the effect of semiconductor band structure on electrochemical redox reactions. Specifically, the Haldane-Anderson model, originally developed to study multiple charge states of transition-metal defects in semiconductors, is extended to describe electrochemical redox reactions by incorporating the solvent effect, inspired by the Holstein model. The solvent coordinate and the actual charge on the redox species in reduced and oxidized states are assumed to be instant equilibrium, and the transitions between these states are defined by the framework of Green's function. With these treatments, we treat the charge state transition in a self-consistent manner. We first confirm that this self-consistent approach is essential to accurately depict the hybridization effect of band structure by comparing the model-calculated ionization potential (IP), electron affinity (EA), and redox potential of the species with those obtai
Numerous aqueous systems host elements in multiple redox states, with wide ranging implications such as their influence on the formation/dissolution of minerals, water toxicity, and nutrient cycling. To uncover governing mechanisms and complex chemical interactions in aqueous systems, reactive-transport models have increasingly gained importance. However, their predictive capabilities remain limited because existing approaches struggle to accurately account for the full complexities of redox reactions. Here, we develop a reactive-transport framework that leverages recent advancements in thermodynamic modelling, speciation chemistry, and redox kinetics. Distinct from traditional models, we uniquely treat redox kinetics along with transport as transient phenomena, decoupled from Gibbs free energy minimisation. Ensuring ion concentrations are governed by non-equilibrium rate laws, this approach allows predicting the tempo-spatial distribution of speciation and precipitation of species across oxidation states. We illustrate the versatility of our framework through two case studies: manganese speciation in natural waters and the fate of dissolved iron in aqueous/porous media. Our framew
Antioxidants operate in biological environments where solvent effects dramatically alter their redox properties. Using ascorbic acid (vitamin C) as a paradigmatic example, we present a comprehensive quantum-chemical investigation of its global chemical reactivity indices -- ionization potential, electron affinity, HOMO-LUMO gap, hardness, softness, electronegativity, electrophilicity, and electrodonating/accepting powers -- computed at the compound chemistry CBS-QB3 and various DFT levels in vacuo and across six solvents. The results demonstrate that solvation stabilizes charged species so strongly that reactivity indices shift by several electronvolts, following a roughly Born-like dependence on dielectric constant. Most importantly, we show unequivocally that Koopmans' theorem, often used to estimate these indices from orbital energies, fails catastrophically in solution: it predicts solvent-independent values that are qualitatively and quantitatively wrong, missing the essential physics of dielectric screening and geometric relaxation. We therefore conclude that Koopmans' theorem must be abandoned for antioxidant studies in condensed phases; adiabatic calculations with solvent a
Capture of anthropogenic CO2 is critical for mitigating climate change, and reducing the energy cost is essential for wide-scale deployment. Solubility of inorganic carbon in aqueous solutions depends on the pH, and electrochemical modulation of the pH has been investigated as a means of CO2 capture and release. However, reported methods incur unavoidable energy costs due to thermodynamic penalties. In this study, we introduce a pH-independent redox chemistry that greatly lowers the thermodynamic energy costs by changing the pH without directly changing the [H+]. We show that the redox reaction of TEMPO molecules modulates the pH for capture and release of CO2 in a flow cell with an energy cost as low as 2.6 kJ/mol of CO2 corresponding to 0.027 eV/molecule. A molecular model, supported by MD and DFT simulations, is proposed of how the pH is decreased by 7.6 while largely avoiding the entropic energy cost associated with increasing the [H+]. We believe that this work showcases the potential of pH-independent redox chemistries for practical and cost-effective CO2 capture.
This paper proposes Redox, a training data management system designed to achieve high I/O efficiency. The key insight is a new observation of file redirection: for model training, when training data in one file is requested, the system has the flexibility to return the data of another file. Based on this property, Redox starts with a bold design principle that chunks of data files are always read from disk in batch, and once loaded, all files in the chunk will be consumed without being loaded again. We propose efficient local and distributed file read protocol based on this principle that both minimizes the wasted data read and enables opportunistic prefetch from remote node. Moreover, we analyze file redirection's impact on randomness, and show that it has little effects on training efficiency. Experimental results indicate that Redox significantly accelerates data fetching in training, achieving up to a 4.57x improvement in end-to-end training compared to PyTorch.
The participation of oxygen or other anionic species in redox activities in cathode materials for lithium and sodium-ion battery systems is known to play a role in governing the useful capacity of these batteries. Directly probing anionic redox mechanisms is not possible, rather the computational analysis by density functional theory poses the main approach towards gleaning insights into anionic redox activity and harnessing these effects to maximize capacity in future electrode materials. Here we showcase material systems exhibiting this mechanism of ion insertion and removal, and present the key computational considerations in studying anionic redox activities in battery materials. Aided by new computationally derived understandings of the role of anionic redox in emerging battery materials, increasingly greater levels of useable capacities can be extracted through informed materials design.
Industrial polymeric materials often rely on antioxidants to achieve long-term reliability. Previous studies have frequently discussed the stabilization effect in the presence of macroscopic additive migration. However, the micro- to meso-scale coupling between polymer dynamics and antioxidant molecular dynamics remains insufficiently understood. In this study, we extend a polymer dynamics simulation framework that can account for oxidative aging. We also update the model so that it can explicitly incorporate antioxidant molecules into the simulation. As a result, the framework enables us to quantify how molecular architecture of antioxidants affects oxidation kinetics, which has previously been inferred only indirectly from apparent changes in reaction rates. It also allows us to evaluate the effects of antioxidant concentration and molecular architecture on the spatial heterogeneity of oxidative aging.
FLASH radiotherapy (FLASH-RT) achieves tumor control comparable to conventional dose-rate irradiation (CONV-RT) while significantly reducing radiation damage to normal tissues. However, the physical conditions triggering the FLASH sparing effect remain unclear, and mechanisms related to oxidative stress and redox regulation are poorly understood. This study utilizes a murine acute intestinal toxicity model to investigate how beam parameters influence the FLASH sparing effect and tumor control using innovative FLASH-RT and CONV-RT combined irradiation. Results demonstrate for the first time that a substantially reduced FLASH dose can still elicit sparing effect, provided a total dose threshold is met. Kinetic simulation and experimental validation demonstrate that FLASH-RT enhances peroxyl radical recombination, reducing reactive oxygen species (ROS) and malondialdehyde levels. Antioxidant interventions further confirm the essential role of free radicals. RNA sequencing and molecular analyses reveal that FLASH-RT activates the nuclear factor E2-related factor 2 (NRF2) antioxidant pathway while suppressing extracellular signal-regulated kinases (ERK) signaling, thereby enhancing cell
A thermodynamic integration (TI) protocol incorporating dummy atoms is introduced to calculate free energy differences for disulfide bond formation in proteins. This method successfully reproduces experimental redox potentials for multiple proteins, providing improved insights into the redox regulation of various proteins.
Redox potentials of electron transfer reactions are of fundamental importance for the performance and description of electrochemical devices. Despite decades of research, accurate computational predictions for the redox potential of even simple metals remain very challenging. Here we use a combination of first principles calculations and machine learning to predict the redox potentials of three redox couples, $\mathrm{Fe}^{2+}$/$\mathrm{Fe}^{3+}$, $\mathrm{Cu}^{+}$/$\mathrm{Cu}^{2+}$ and $\mathrm{Ag}^{+}$/$\mathrm{Ag}^{2+}$. Using a hybrid functional with a fraction of 25\% exact exchange (PBE0) the predicted values are 0.92, 0.26 and 1.99 V in good agreement with the best experimental estimates (0.77, 0.15, 1.98 V). We explain in detail, how we combine machine learning, thermodynamic integration from machine learning to semi-local functionals, as well as a combination of thermodynamic perturbation theory and $Δ$-machine learning to determine the redox potentials for computationally expensive hybrid functionals. The combination of these approaches allows one to obtain statistically accurate results.
The tunable design of protein redox potentials promises to open a range of applications in biotechnology and catalysis. Here we introduce a method to calculate redox potential changes by combining fluctuation relations with molecular dynamics simulations. It involves the simulation of reduced and oxidized states, followed by the instantaneous conversion between them. Energy differences introduced by the perturbations are obtained using the Kubo-Onsager approach. Using a detailed fluctuation relation coupled with Bayesian inference, these are post-processed into estimates for the redox potentials in an efficient manner. This new method, denoted MD+CB, is tested on a de novo four-helix bundle heme protein (the m4D2 `maquette') and five designed mutants, including some mutants characterized experimentally in this work. The MD+CB approach is found to perform reliably, giving redox potential shifts with reasonably good correlation (0.85) to the experimental values for the mutants. The MD+CB approach also compares well with redox potential shift predictions using a continuum electrostatic method. The estimation method employed within the MD+CB approach is straightforwardly transferable t
Machine learning potentials (MLPs) represent atomic interactions with quantum mechanical accuracy offering an efficient tool for atomistic simulations in many fields of science. However, most MLPs rely on local atomic energies without information about the global composition of the system. To date, this has prevented the application of MLPs to redox reactions in solution, which involve chemical species in different oxidation states and electron transfer between them. Here, we show that fourth-generation MLPs overcome this limitation and can provide a physically correct description of redox chemical reactions. For the example of ferrous (Fe$^{2+}$) and ferric (Fe$^{3+}$) ions in water we show that the correct oxidation states are obtained matching the number of chloride counter ions irrespective of their positions in the system. Moreover, we demonstrate that our method can describe electron-transfer processes between ferrous and ferric ions, paving the way to simulations of general redox chemistry in solution.
We develop a systems approach based on an energy-landscape concept to differentiate interactions involving redox activities and conformational changes of proteins and nucleic acids interactions in multi-layered protein-DNA regulatory networks under light disturbance. Our approach is a data-driven modeling workflow using a physics-informed machine learning algorithm to train a non-linear mathematical model for interpreting gene expression dynamics and to lead discovery for protein regulators using redox proteome analysis. We distinguish light-responsive elements within central carbon metabolism pathways from independent variables like circadian time using the publicly available transcriptome datasets of Synechococcus elongatus over diel cycles responding to light perturbations. Our approach provides interpretable de novo models for elucidating events of reactions in complex regulatory pathways in response to stressful disturbance from the environment. We discovered protein regulators in response to light disturbance in the proteome analysis involving shifts in protein abundance as well as cysteine redox states under constant illumination and after two hours of darkness. We discovere
Redox processes are important in chemistry, with applications in biomedicine, chemical analysis, among others. As many redox experiments are also performed at a fixed value of pH, having an efficient computational method to support experimental measures at both constant redox potential and pH is very important. Such computational techniques have the potential to validate experimental observations performed under these conditions and to provide additional information unachievable experimentally such as an atomic level description of macroscopic measures. We present the implementation of discrete redox and protonation states methods for constant redox potential Molecular Dynamics (CEMD), for coupled constant pH and constant redox potential MD (C(pH,E)MD), and for Replica Exchange MD along the redox potential dimension (E-REMD) on the AMBER software package. Validation results are presented for a small system that contains a single heme group: N-acetylmicroperoxidase-8 (NAcMP8) axially connected to a histidine peptide. The methods implemented allow one to make standard redox potential (Eo) predictions with the same easiness and accuracy as pKa predictions using the constant pH molecul
In charged water microdroplets, which occur in nature or in the lab upon ultrasonication or in electrospray processes, the thermodynamics for reactive chemistry can be dramatically altered relative to the bulk phase. Here, we provide a theoretical basis for the observation of accelerated chemistry by simulating water droplets of increasing charge imbalance to create redox agents such as hydroxyl and hydrogen radicals and solvated electrons. We compute the hydration enthalpy of OH^- and H^+ that controls the electron transfer process, and the corresponding changes in vertical ionization energy and vertical electron affinity of the ions, to create OH* and H* reactive species. We find that at ~20-50% of the Rayleigh limit of droplet charge the hydration enthalpy of both OH^- and H^+ have decreased by >50 kcal/mol such that electron transfer becomes thermodynamically favorable, in correspondence with the more favorable vertical electron affinity of H^+ and the lowered vertical ionization energy of OH^-. We provide scaling arguments that show that the nanoscale calculations and conclusions extend to the experimental microdroplet length scale. The relevance of the droplet charge for c