Quantum chemistry reveals thermodynamic principles of redox biochemistry

Machine Learning Approach to Vertical Energy Gap in Redox Processes

A straightforward approach to calculating the free energy change (ΔG) and reorganization energy of a redox process is linear response approximation (LRA). However, accurate prediction of redox properties is still challenging due to difficulties in conformational sampling and vertical energy-gap sampling. Expensive hybrid quantum mechanical/molecular mechanical (QM/MM) calculations are typically employed in sampling energy gaps using conformations from simulations. To alleviate the computational cost associated with the expensive QM method in the QM/MM calculation, we propose machine learning (ML) methods to predict the vertical energy gaps (VEGs). We tested several ML models to predict the VEGs and observed that simple models like linear regression show excellent performance (mean absolute error ∼0.1 eV) in predicting VEGs in all test systems, even when using features extracted from cheaper semiempirical methods. Our best ML model (extra trees regressor) shows a mean absolute error of around 0.1 eV while using features from the cheapest QM method. We anticipate our approach can be generalized to larger macromolecular systems with more complex redox centers.

Repurposing Kraft black Liquor as Reductant for Enhanced Lithium-Ion Battery Leaching

The economic advantages of H2SO4 make it the acid of choice for the hydrometallurgical treatment of waste lithium-ion batteries (LIBs). However, to facilitate the full dissolution of the higher valency metal oxides present in the cathode black mass, a suitable reducing agent is required. Herein, the application of industrial black liquor (BL) obtained from the Kraft pulping for papermaking is investigated as a renewable reducing agent for the enhanced leaching of transition metals from LIB powder with H2SO4. The addition of acidified BL to H2SO4 significantly improved the leaching efficiency for a range of LIB cathode chemistries, with the strongest effect observed for manganese-rich active material. Focusing on NMC111 (LiMnxCoyNizO2) material, a linear correlation between the BL concentration and the leaching yield of Mn was obtained, with the best overall leaching efficiencies being achieved for 2.0 mol L-1 H2SO4 and 50 vol % of BL at 353 K. A quasi-total degradation of oxygenated and aromatic groups from the BL during NMC111 dissolution was observed after leaching, suggesting that these chemical groups are essential for LIB reduction. Finally, the leached transition metals could be easily recovered by pH adjustment and oxalic acid addition, closing the resource loop and fostering resource efficiency.

Functional convergence in slow-growing microbial communities arises from thermodynamic constraints

The dynamics of microbial communities is complex, determined by competition for metabolic substrates and cross-feeding of byproducts. Species in the community grow by harvesting energy from chemical reactions that transform substrates to products. In many anoxic environments, these reactions are close to thermodynamic equilibrium and growth is slow. To understand the community structure in these energy-limited environments, we developed a microbial community consumer-resource model incorporating energetic and thermodynamic constraints on an interconnected metabolic network. The central element of the model is product inhibition, meaning that microbial growth may be limited not only by depletion of metabolic substrates but also by accumulation of products. We demonstrate that these additional constraints on microbial growth cause a convergence in the structure and function of the community metabolic network-independent of species composition and biochemical details-providing a possible explanation for convergence of community function despite taxonomic variation observed in many natural and industrial environments. Furthermore, we discovered that the structure of community metabolic network is governed by the thermodynamic principle of maximum free energy dissipation. Our results predict the decrease of functional convergence in faster growing communities, which we validate by analyzing experimental data from anaerobic digesters. Overall, the work demonstrates how universal thermodynamic principles may constrain community metabolism and explain observed functional convergence in microbial communities.

Stoichiometric ratios for biotics and xenobiotics capture effective metabolic coupling to re(de)fine biodegradation

Preserving human and environmental health requires anthropogenic pollutants to be biologically degradable. Depending on concentration, both nutrients and pollutants induce and activate metabolic capacity in the endemic bacterial consortium, which in turn aids their degradation. Knowledge on such 'acclimation' is rarely implemented in risk assessment cost-effectively. As a result, an accurate description of the mechanisms and kinetics of biodegradation remains problematic. In this study, we defined a yield 'effectivity', comprising the effectiveness at which a pollutant (substrate) enhances its own degradation by inducing (biomass) cofactors involved therein. Our architecture for calculation represents the interplay between concentration and metabolism via both stoichiometric and thermodynamic concepts. The calculus for yield 'effectivity' is biochemically intuitive, implicitly embeds co-metabolism and distinguishes 'endogenic' from 'exogenic' substances' reflecting various phenomena in biodegradation and bio-transformation studies. We combined data on half-lives of pollutants/nutrients in wastewater and surface water with transition-state rate theory to obtain also experimental values for effective yields. These quantify the state of acclimation: the portion of biodegradation kinetics attributable to (contributed by) 'natural metabolism', in view of similarity to natural substances. Calculated and experimental values showed statistically significant correspondence. Particularly, carbohydrate metabolism and nucleic acid metabolism appeared relevant for acclimation (R² = 0.11-0.42), affecting rates up to 10^4.9(±0.7) times: under steady-state acclimation, a compound stoichiometrically identical to carbohydrates or nucleic acids, is 10^3.2 to 10^4.9 times faster aerobically degraded than a compound marginally similar. Our new method, simulating (contribution by) the state of acclimation, supplements existing structure-biodegradation and kinetic models for predicting biodegradation in wastewater and surface water. The accuracy of prediction may increase when characterizing nutrients/co-metabolites in terms of, e.g., elemental analysis. We discuss strengths and limitations of our approach by comparison to empirical and mechanism-based methods.

Protein cost minimization promotes the emergence of coenzyme redundancy

Metabolism relies on a small class of molecules (coenzymes) that serve as universal donors and acceptors of key chemical groups and electrons. Although metabolic networks crucially depend on structurally redundant coenzymes [e.g., NAD(H) and NADP(H)] associated with different enzymes, the criteria that led to the emergence of this redundancy remain poorly understood. Our combination of modeling and structural and sequence analysis indicates that coenzyme redundancy may not be essential for metabolism but could rather constitute an evolved strategy promoting efficient usage of enzymes when biochemical reactions are near equilibrium. Our work suggests that early metabolism may have operated with fewer coenzymes and that adaptation for metabolic efficiency may have driven the rise of coenzyme diversity in living systems.

Coenzymes distribute a variety of chemical moieties throughout cellular metabolism, participating in group (e.g., phosphate and acyl) and electron transfer. For a variety of reactions requiring acceptors or donors of specific resources, there often exist degenerate sets of molecules [e.g., NAD(H) and NADP(H)] that carry out similar functions. Although the physiological roles of various coenzyme systems are well established, it is unclear what selective pressures may have driven the emergence of coenzyme redundancy. Here, we use genome-wide metabolic modeling approaches to decompose the selective pressures driving enzymatic specificity for either NAD(H) or NADP(H) in the metabolic network of Escherichia coli. We found that few enzymes are thermodynamically constrained to using a single coenzyme, and in principle a metabolic network relying on only NAD(H) is feasible. However, structural and sequence analyses revealed widespread conservation of residues that retain selectivity for either NAD(H) or NADP(H), suggesting that additional forces may shape specificity. Using a model accounting for the cost of oxidoreductase enzyme expression, we found that coenzyme redundancy universally reduces the minimal amount of protein required to catalyze coenzyme-coupled reactions, inducing individual reactions to strongly prefer one coenzyme over another when reactions are near thermodynamic equilibrium. We propose that protein minimization generically promotes coenzyme redundancy and that coenzymes typically thought to exist in a single pool (e.g., coenzyme A [CoA]) may exist in more than one form (e.g., dephospho-CoA).

eQuilibrator 3.0: a database solution for thermodynamic constant estimation

eQuilibrator (equilibrator.weizmann.ac.il) is a database of biochemical equilibrium constants and Gibbs free energies, originally designed as a web-based interface. While the website now counts around 1,000 distinct monthly users, its design could not accommodate larger compound databases and it lacked a scalable Application Programming Interface (API) for integration into other tools developed by the systems biology community. Here, we report on the recent updates to the database as well as the addition of a new Python-based interface to eQuilibrator that adds many new features such as a 100-fold larger compound database, the ability to add novel compounds, improvements in speed and memory use, and correction for Mg²⁺ ion concentrations. Moreover, the new interface can compute the covariance matrix of the uncertainty between estimates, for which we show the advantages and describe the application in metabolic modelling. We foresee that these improvements will make thermodynamic modelling more accessible and facilitate the integration of eQuilibrator into other software platforms.

Sepsis: Evidence-based pathogenesis and treatment

Sepsis can develop during the body’s response to a critical illness leading to multiple organ failure, irreversible shock, and death. Sepsis has been vexing health care providers for centuries due to its insidious onset, generalized metabolic dysfunction, and lack of specific therapy. A common factor underlying sepsis is the characteristic hypermetabolic response as the body ramps up every physiological system in its fight against the underlying critical illness. A hypermetabolic response requires supraphysiological amounts of energy, which is mostly supplied via oxidative phosphorylation generated ATP. A by-product of oxidative phosphorylation is hydrogen peroxide (H₂O₂), a toxic, membrane-permeable oxidizing agent that is produced in far greater amounts during a hypermetabolic state. Continued production of mitochondrial H₂O₂ can overwhelm cellular reductive (antioxidant) capacity leading to a build-up within cells and eventual diffusion into the bloodstream. H₂O₂ is a metabolic poison that can inhibit enzyme systems leading to organ failure, microangiopathic dysfunction, and irreversible septic shock. The toxic effects of H₂O₂ mirror the clinical and laboratory abnormalities observed in sepsis, and toxic levels of blood H₂O₂ have been reported in patients with septic shock. This review provides evidence to support a causal role for H₂O₂ in the pathogenesis of sepsis, and an evidence-based therapeutic intervention to reduce H₂O₂ levels in the body and restore redox homeostasis, which is necessary for normal organ function and vascular responsiveness.

A Computational Protocol Combining DFT and Cheminformatics for Prediction of pH-Dependent Redox Potentials

Discovering new materials for energy storage requires reliable and efficient protocols for predicting key properties of unknown compounds. In the context of the search for new organic electrolytes for redox flow batteries, we present and validate a robust procedure to calculate the redox potentials of organic molecules at any pH value, using widely available quantum chemistry and cheminformatics methods. Using a consistent experimental data set for validation, we explore and compare a few different methods for calculating reaction free energies, the treatment of solvation, and the effect of pH on redox potentials. We find that the B3LYP hybrid functional with the COSMO solvation method, in conjunction with thermal contributions evaluated from BLYP gas-phase harmonic frequencies, yields a good prediction of pH = 0 redox potentials at a moderate computational cost. To predict how the potentials are affected by pH, we propose an improved version of the Alberty-Legendre transform that allows the construction of a more realistic Pourbaix diagram by taking into account how the protonation state changes with pH.

Quantum Mechanical Methods Predict Accurate Thermodynamics of Biochemical Reactions

Thermodynamics plays a crucial role in regulating the metabolic processes in all living organisms. Accurate determination of biochemical and biophysical properties is important to understand, analyze, and synthetically design such metabolic processes for engineered systems. In this work, we extensively performed first-principles quantum mechanical calculations to assess its accuracy in estimating free energy of biochemical reactions and developed automated quantum-chemistry (QC) pipeline (https://appdev.kbase.us/narrative/45710) for the prediction of thermodynamics parameters of biochemical reactions. We benchmark the QC methods based on density functional theory (DFT) against different basis sets, solvation models, pH, and exchange-correlation functionals using the known thermodynamic properties from the NIST database. Our results show that QC calculations when combined with simple calibration yield a mean absolute error in the range of 1.60-2.27 kcal/mol for different exchange-correlation functionals, which is comparable to the error in the experimental measurements. This accuracy over a diverse set of metabolic reactions is unprecedented and near the benchmark chemical accuracy of 1 kcal/mol that is usually desired from DFT calculations.

A chemically consistent graph architecture for massive reaction networks applied to solid-electrolyte interphase formation

Modeling reactivity with chemical reaction networks could yield fundamental mechanistic understanding that would expedite the development of processes and technologies for energy storage, medicine, catalysis, and more. Thus far, reaction networks have been limited in size by chemically inconsistent graph representations of multi-reactant reactions (e.g. A + B → C) that cannot enforce stoichiometric constraints, precluding the use of optimized shortest-path algorithms. Here, we report a chemically consistent graph architecture that overcomes these limitations using a novel multi-reactant representation and iterative cost-solving procedure. Our approach enables the identification of all low-cost pathways to desired products in massive reaction networks containing reactions of any stoichiometry, allowing for the investigation of vastly more complex systems than previously possible. Leveraging our architecture, we construct the first ever electrochemical reaction network from first-principles thermodynamic calculations to describe the formation of the Li-ion solid electrolyte interphase (SEI), which is critical for passivation of the negative electrode. Using this network comprised of nearly 6000 species and 4.5 million reactions, we interrogate the formation of a key SEI component, lithium ethylene dicarbonate. We automatically identify previously proposed mechanisms as well as multiple novel pathways containing counter-intuitive reactions that have not, to our knowledge, been reported in the literature. We envision that our framework and data-driven methodology will facilitate efforts to engineer the composition-related properties of the SEI - or of any complex chemical process - through selective control of reactivity.

A thermodynamic atlas of carbon redox chemical space

Carbon redox chemistry plays a fundamental role in biology. However, the thermodynamic and physicochemical principles underlying the rise of metabolites involved in redox biochemistry remain poorly understood. Our work introduces the theory and techniques that allow us to quantify and understand the global energy landscape of carbon redox biochemistry. We analyze the space of all possible oxidation states of linear-chain molecules with two to five carbon atoms and generate a detailed atlas of the thermodynamic stability of metabolites in comparison to nonbiological molecules. Although the emergence of life required the underlying chemistry to bootstrap itself out of equilibrium, a quantitative understanding of the environment-dependent thermodynamic landscape of prebiotic molecules will be extremely valuable for future origins of life models.

Redox biochemistry plays a key role in the transduction of chemical energy in living systems. However, the compounds observed in metabolic redox reactions are a minuscule fraction of chemical space. It is not clear whether compounds that ended up being selected as metabolites display specific properties that distinguish them from nonbiological compounds. Here, we introduce a systematic approach for comparing the chemical space of all possible redox states of linear-chain carbon molecules to the corresponding metabolites that appear in biology. Using cheminformatics and quantum chemistry, we analyze the physicochemical and thermodynamic properties of the biological and nonbiological compounds. We find that, among all compounds, aldose sugars have the highest possible number of redox connections to other molecules. Metabolites are enriched in carboxylic acid functional groups and depleted of ketones and aldehydes and have higher solubility than nonbiological compounds. Upon constructing the energy landscape for the full chemical space as a function of pH and electron-donor potential, we find that metabolites tend to have lower Gibbs energies than nonbiological molecules. Finally, we generate Pourbaix phase diagrams that serve as a thermodynamic atlas to indicate which compounds are energy minima in redox chemical space across a set of pH values and electron-donor potentials. While escape from thermodynamic equilibrium toward kinetically driven states is a hallmark of life and its origin, we envision that a deeper quantitative understanding of the environment-dependent thermodynamic landscape of putative prebiotic molecules will provide a crucial reference for future origins-of-life models.

Recent advances in constraint and machine learning-based metabolic modeling by leveraging stoichiometric balances, thermodynamic feasibility and kinetic law formalisms

Understanding the governing principles behind organisms' metabolism and growth underpins their effective deployment as bioproduction chassis. A central objective of metabolic modeling is predicting how metabolism and growth are affected by both external environmental factors and internal genotypic perturbations. The fundamental concepts of reaction stoichiometry, thermodynamics, and mass action kinetics have emerged as the foundational principles of many modeling frameworks designed to describe how and why organisms allocate resources towards both growth and bioproduction. This review focuses on the latest algorithmic advancements that have integrated these foundational principles into increasingly sophisticated quantitative frameworks.

Thermodynamic Favorability of End Products of Anaerobic Glucose Metabolism

The eQuilibrator component contribution method allows calculation of the overall Gibbs energy changes for conversion of glucose to a wide range of final products in the absence of other oxidants. Values are presented for all possible combinations of products with up to three carbons and selected others. The most negative Gibbs energy change is for the formation of graphite and water (-499 kJ mol-1) followed by CH4 and CO2 (-430 kJ mol-1), the observed final products of anaerobic digestion. Other favored products (with various combinations having Gibbs energy changes between -300 and -367 kJ mol-1) are short-chain alkanes, fatty acids, dicarboxylic acids, and even hexane and benzene. The most familiar products, lactate and ethanol + CO2, are less favored (Gibbs energy changes of -206 and -265 kJ mol-1 respectively). The values presented offer an interesting perspective on observed metabolism and its evolutionary origins as well as on cells engineered for biotechnological purposes.

Two for the price of one: Attacking the energetic-metabolic hub of mycobacteria to produce new chemotherapeutic agents

Cellular bioenergetics is an area showing promise for the development of new antimicrobials, antimalarials and cancer therapy. Enzymes involved in central carbon metabolism and energy generation are essential mediators of bacterial physiology, persistence and pathogenicity, lending themselves natural interest for drug discovery. In particular, succinate and malate are two major focal points in both the central carbon metabolism and the respiratory chain of Mycobacterium tuberculosis. Both serve as direct links between the citric acid cycle and the respiratory chain due to the quinone-linked reactions of succinate dehydrogenase, fumarate reductase and malate:quinone oxidoreductase. Inhibitors against these enzymes therefore hold the promise of disrupting two distinct, but essential, cellular processes at the same time. In this review, we discuss the roles and unique adaptations of these enzymes and critically evaluate the role that future inhibitors of these complexes could play in the bioenergetics target space.

A Mixed Quantum Chemistry/Machine Learning Approach for the Fast and Accurate Prediction of Biochemical Redox Potentials and Its Large-Scale Application to 315 000 Redox Reactions

A quantitative understanding of the thermodynamics of biochemical reactions is essential for accurately modeling metabolism. The group contribution method (GCM) is one of the most widely used approaches to estimate standard Gibbs energies and redox potentials of reactions for which no experimental measurements exist. Previous work has shown that quantum chemical predictions of biochemical thermodynamics are a promising approach to overcome the limitations of GCM. However, the quantum chemistry approach is significantly more expensive. Here, we use a combination of quantum chemistry and machine learning to obtain a fast and accurate method for predicting the thermodynamics of biochemical redox reactions. We focus on predicting the redox potentials of carbonyl functional group reductions to alcohols and amines, two of the most ubiquitous carbon redox transformations in biology. Our method relies on semiempirical quantum chemistry calculations calibrated with Gaussian process (GP) regression against available experimental data and results in higher predictive power than the GCM at low computational cost. Direct calibration of GCM and fingerprint-based predictions (without quantum chemistry) with GP regression also results in significant improvements in prediction accuracy, demonstrating the versatility of the approach. We design and implement a network expansion algorithm that iteratively reduces and oxidizes a set of natural seed metabolites and demonstrate the high-throughput applicability of our method by predicting the standard potentials of more than 315 000 redox reactions involving approximately 70 000 compounds. Additionally, we developed a novel fingerprint-based framework for detecting molecular environment motifs that are enriched or depleted across different regions of the redox potential landscape. We provide open access to all source code and data generated.