An upper limit on Gibbs energy dissipation governs cellular metabolism

Decoupled respiration in electro-active bacteria

Studies on electron-transfer pathways in certain bacterial strains have revealed that the degree of coupling of electron transfer to proton translocation along the respiratory chain can be regulated according to metabolic demands. This first line of metabolic response, based on the existence of energy dissipation mechanisms, has not been demonstrated to be a general pattern across the bacterial kingdom, let alone to be operative in electro-active bacteria. In this study, we hypothesized that electro-active cells should respond to over-polarization by also triggering energy decoupling mechanisms to prevent metabolic overloads. Based on electrochemical analyses, we propose that the recently discovered inner-membrane cytochrome CbcBA - used by electro-active Geobacter sulfurreducens bacteria for cellular respiration near the thermodynamic energetic limit - can also act as an energy dissipation gate when the metabolism is demanded, contributing to regulate the energy balance of the cell by decoupling carbon assimilation from electrode respiration.

Enhanced Stability and Chaotic Condensates in Multispecies Nonreciprocal Mixtures

Random nonreciprocal interactions between a large number of conserved densities are shown to enhance the stability of the system toward pattern formation. The enhanced stability is an exact result when the number of species approaches infinity and is confirmed numerically by simulations of the multispecies nonreciprocal Cahn-Hilliard model. Furthermore, the diversity in dynamical patterns increases with an increasing number of components, and novel steady states such as pulsating or spatiotemporally chaotic condensates are observed. Our results may help to unravel the mechanisms by which living systems self-organize via metabolism.

Exploring the Evolution-Coupling Hypothesis: Do Enzymes' Performance Gains Correlate with Increased Dissipation?

The research literature presents divergent opinions regarding the role of dissipation in living systems, with views ranging from it being useless to it being essential for driving life. The implications of universal thermodynamic evolution are often overlooked or considered controversial. A higher rate of entropy production indicates faster thermodynamic evolution. We calculated enzyme-associated dissipation under steady-state conditions using minimalistic models of enzyme kinetics when all microscopic rate constants are known. We found that dissipation is roughly proportional to the turnover number, and a log-log power-law relationship exists between dissipation and the catalytic efficiency of enzymes. "Perfect" specialized enzymes exhibit the highest dissipation levels and represent the pinnacle of biological evolution. The examples that we analyzed suggested two key points: (a) more evolved enzymes excel in free-energy dissipation, and (b) the proposed evolutionary trajectory from generalist to specialized enzymes should involve increased dissipation for the latter. Introducing stochastic noise in the kinetics of individual enzymes may lead to optimal performance parameters that exceed the observed values. Our findings indicate that biological evolution has opened new channels for dissipation through specialized enzymes. We also discuss the implications of our results concerning scaling laws and the seamless coupling between thermodynamic and biological evolution in living systems immersed in out-of-equilibrium environments.

The rate of glucose metabolism sets the cell morphology across yeast strains and species

Yeasts are a diverse group of unicellular fungi that have developed a wide array of phenotypes and traits over 400 million years of evolution. However, we still lack an understanding of the biological principles governing the range of cell morphologies, metabolic modes, and reproductive strategies yeasts display. In this study, we explored the relationship between cell morphology and metabolism in sixteen yeast strains across eleven species. We performed a quantitative analysis of the physiology and morphology of these strains and discovered a strong correlation between the glucose uptake rate (GUR) and the surface-area-to-volume ratio. 14C-glucose uptake experiments demonstrated that the GUR for a given strain is governed either by glucose transport capacity or glycolytic rate, indicating that it is rather the rate of glucose metabolism in general that correlates with cell morphology. Furthermore, perturbations in glucose metabolism influenced cell sizes, whereas manipulating cell size did not affect GUR, suggesting that glucose metabolism determines cell size rather than the reverse. Across the strains tested, we also found that the rate of glucose metabolism influenced ethanol production rate, biomass yield, and carbon dioxide transfer rate. Overall, our findings demonstrate that the rate of glucose metabolism is a key factor shaping yeast cell morphology and physiology, offering new insights into the fundamental principles of yeast biology.

Impact of Ligand-Induced Oligomer Dissociation on Enzyme Diffusion, Directly Observed at the Single-Molecule Level

The existence of the phenomenon of enhanced enzyme diffusion (EED) has been a topic of debate in recent literature. One proposed mechanism to explain the origin of EED is oligomeric enzyme dissociation. We used mass photometry (MP), a label-free single-molecule technique, to investigate the dependence of the oligomeric states of several enzymes on their ligands. The studied enzymes of interest are catalase, aldolase, alkaline phosphatase, and vanillyl-alcohol oxidase (VAO). We compared the ratios of oligomeric states in the presence and absence of the substrate as well as different substrate and inhibitor concentrations. Catalase and aldolase were found to dissociate into smaller oligomers in the presence of their substrates, independently of inhibition, while for alkaline phosphatase and VAO, different behaviors were observed. Thus, we have identified a possible mechanism which explains the previously observed diffusion enhancement in vitro. This enhancement may occur due to the dissociation of oligomers through ligand binding.

(R)evolution of Viruses: Introduction to biothermodynamics of viruses

As of 26 April 2024, the International Committee on Taxonomy of Viruses has registered 14690 virus species. Of these, only several dozen have been chemically and thermodynamically characterized. Every virus species is characterized by a specific empirical formula and thermodynamic properties - enthalpy, entropy and Gibbs energy. These physical properties are used in a mechanistic model of virus-host interactions at the cell membrane and in the cytoplasm. This review article presents empirical formulas and Gibbs energies for all major variants of SARS-CoV-2. This article also reports and suggests a mechanistic model of evolutionary changes, with the example of time evolution of SARS-CoV-2 from 2019 to 2024.

The physiology of an engineered Saccharomyces cerevisiae strain that carries both an improved glycerol-3-phosphate and the synthetic dihydroxyacetone pathway for glycerol utilization

Our laboratory previously established variants of the Saccharomyces cerevisiae strain CEN.PK113-1A able to grow in synthetic glycerol medium. One approach focused on improving the endogenous l-glycerol-3-phosphate (G3P) pathway, while a second approach aimed to replace the endogenous pathway with the dihydroxyacetone (DHA) pathway. The latter approach led to a significantly higher maximum specific growth rate (µmax) of 0.26 h-1 compared to 0.14 h-1. The current study focused on combining all genetic modifications in one strain. Apart from the so-called "TWO pathway strain" (CEN TWOPW), two isogenic control strains, CEN G3PPW and CEN DHAPW, were constructed. The µmax of CEN TWOPW (∼0.24 h-1) was virtually identical to that of CEN DHAPW. Remarkable characteristics of the strain CEN TWOPW compared to CEN DHAPW include a higher specific glycerol consumption rate, the capacity to deplete glycerol completely, and a much higher ethanol and lower biomass formation during oxygen-limited shake flask cultivations. The results obtained with different alleles of the GUT1 gene, encoding for glycerol kinase, suggest that the phenotype of the strain CEN TWOPW is at least partly attributed to the particular point mutation in the GUT1 allele used from the strain JL1, which was previously generated through adaptive laboratory evolution.

Neural differentiation in perspective: mitochondria as early programmers

Neural differentiation during development of the nervous system has been extensively studied for decades. These efforts have culminated in the generation of a detailed map of developmental events that appear to be associated with emergence of committed cells in the nervous system. In this review the landscape of neural differentiation is revisited by focusing on abiotic signals that play a role in induction of neural differentiation. Evidence is presented regarding a chimeric landscape whereby abiotic signals generated by mitochondria orchestrate early events during neural differentiation. This early stage, characterised by mitochondrial hyperactivity, in turn triggers a late stage of differentiation by reprogramming the activity of biotic signals.

The galactokinase enzyme of yeast senses metabolic flux to stabilize galactose pathway regulation

Nutrient sensors allow cells to adapt their metabolisms to match nutrient availability by regulating metabolic pathway expression. Many such sensors are cytosolic receptors that measure intracellular nutrient concentrations. One might expect that inducing the metabolic pathway that degrades a nutrient would reduce intracellular nutrient levels, destabilizing induction. However, in the galactose-responsive (GAL) pathway of Saccharomyces cerevisiae, we find that induction is stabilized by flux sensing. Previously proposed mechanisms for flux sensing postulate the existence of metabolites whose concentrations correlate with flux. The GAL pathway flux sensor uses a different principle: the galactokinase Gal1p both performs the first step in GAL metabolism and reports on flux by signalling to the GAL repressor, Gal80p. Both Gal1p catalysis and Gal1p signalling depend on the concentration of the Gal1p-GAL complex and are therefore directly correlated. Given the simplicity of this mechanism, flux sensing is probably a general feature throughout metabolic regulation.

Thermodynamic tools for more efficient biotechnological processes: an example in poly-(3-hydroxybutyrate) production from carbon monoxide

Modern biotechnology requires the integration of several disciplines, with thermodynamics being a crucial one. Experimental approaches frequently used in biotechnology, such as rewiring of metabolic networks or culturing of micro-organisms in engineered environments, can benefit from the application of thermodynamic tools. In this paper, we provide an overview of several thermodynamic tools that are useful for the design and optimization of biotechnological processes, and we demonstrate their potential application in the production of poly-(3-hydroxybutyrate) (PHB) from carbon monoxide (CO). We discuss how these tools can aid in the design of metabolic engineering strategies, the calculation of expected yields, the assessment of the thermodynamic feasibility of the targeted conversions, the identification of potential thermodynamic bottlenecks, and the selection of genetic engineering targets. Although we illustrate these tools using the specific example of PHB production from CO, they can be applied to other substrates and products.

Flux balance analysis of metabolic networks for efficient engineering of microbial cell factories

Metabolic engineering principles have long been applied to explore the metabolic networks of complex microbial cell factories under a variety of environmental constraints for effective deployment of the microorganisms in the optimal production of biochemicals like biofuels, polymers, amino acids, recombinant proteins. One of the methodologies used for analyzing microbial metabolic networks is the Flux Balance Analysis (FBA), which employs applications of optimization techniques for forecasting biomass growth and metabolic flux distribution of industrially important products under specified environmental conditions. The in silico flux simulations are instrumental for designing the production-specific microbial cell factories. However, FBA has some inherent limitations. The present review emphasizes how the incorporation of additional kinetic, thermodynamic, expression and regulatory constraints and integration of omics data into the classical FBA platform improve the prediction accuracy of FBA. A programmed comparison of the simulated data with the experimental observations is presented for supporting the claim. The review further accounts for the successful implementation of classical FBA in biotechnological applications and identifies areas in which classical FBA fails to make correct predictions. The analysis of the predictive capabilities of the different FBA strategies presented here is expected to help researchers in finding new avenues in engineering highly efficient microbial metabolic pathways and identify the key metabolic bottlenecks during the process. Based on the appropriate metabolic network design, fermentation engineers will be able to effectively design the bioreactors and optimize large-scale biochemical production through suitable pathway modifications.

Free-energy transduction mechanisms shape the flux space of metabolic networks

The transduction of free energy in metabolic networks represents a thermodynamic mechanism by which the free energy derived from nutrients is converted to drive nonspontaneous, energy-requiring metabolic reactions. This transduction is typically observed in processes that generate energy-rich molecules such as ATP and NAD(P)H, which, in turn, power specific reactions, particularly biosynthetic reactions. This property establishes a pivotal connection between the intricate topology of metabolic networks and their ability to redirect energy for functional purposes. The present study proposes a dedicated framework aimed at exploring the relationship between free-energy dissipation, network topology, and metabolic objectives. The starting point is that, regardless of the network topology, nonequilibrium chemostatting conditions impose stringent thermodynamic constraints on the feasible flux steady states to satisfy energy and entropy balances. An analysis of randomly sampled reaction networks shows that the network topology imposes additional constraints that restrict the accessible flux solution space, depending on key structural features such as the reaction's molecularity, reaction cycles, and conservation laws. Notably, topologies featuring multimolecular reactions that implement free-energy transduction mechanisms tend to extend the accessible flux domains, facilitating the achievement of metabolic objectives such as anabolic flux maximization or flux rerouting capacity. This approach is applied to a coarse-grained model of carbohydrate metabolism, highlighting the structural requirements for optimal biomass yield.

The brain-body energy conservation model of aging

Aging involves seemingly paradoxical changes in energy metabolism. Molecular damage accumulation increases cellular energy expenditure, yet whole-body energy expenditure remains stable or decreases with age. We resolve this apparent contradiction by positioning the brain as the mediator and broker in the organismal energy economy. As somatic tissues accumulate damage over time, costly intracellular stress responses are activated, causing aging or senescent cells to secrete cytokines that convey increased cellular energy demand (hypermetabolism) to the brain. To conserve energy in the face of a shrinking energy budget, the brain deploys energy conservation responses, which suppress low-priority processes, producing fatigue, physical inactivity, blunted sensory capacities, immune alterations and endocrine 'deficits'. We term this cascade the brain-body energy conservation (BEC) model of aging. The BEC outlines (1) the energetic cost of cellular aging, (2) how brain perception of senescence-associated hypermetabolism may drive the phenotypic manifestations of aging and (3) energetic principles underlying the modifiability of aging trajectories by stressors and geroscience interventions.

Mitochondrial ATP generation is more proteome efficient than glycolysis

Metabolic efficiency profoundly influences organismal fitness. Nonphotosynthetic organisms, from yeast to mammals, derive usable energy primarily through glycolysis and respiration. Although respiration is more energy efficient, some cells favor glycolysis even when oxygen is available (aerobic glycolysis, Warburg effect). A leading explanation is that glycolysis is more efficient in terms of ATP production per unit mass of protein (that is, faster). Through quantitative flux analysis and proteomics, we find, however, that mitochondrial respiration is actually more proteome efficient than aerobic glycolysis. This is shown across yeast strains, T cells, cancer cells, and tissues and tumors in vivo. Instead of aerobic glycolysis being valuable for fast ATP production, it correlates with high glycolytic protein expression, which promotes hypoxic growth. Aerobic glycolytic yeasts do not excel at aerobic growth but outgrow respiratory cells during oxygen limitation. We accordingly propose that aerobic glycolysis emerges from cells maintaining a proteome conducive to both aerobic and hypoxic growth.

Anomalous Fluctuations in a Droplet of Chemically Active Colloids or Enzymes

Chemically active colloids or enzymes cluster into dense droplets driven by their phoretic response to collectively generated chemical gradients. Employing Brownian dynamics simulation techniques, our study of the dynamics of such a chemically active droplet uncovers a rich variety of structures and dynamical properties, including the full range of fluidlike to solidlike behavior, and non-Gaussian positional fluctuations. Our work sheds light on the complex dynamics of the active constituents of metabolic clusters, which are the main drivers of nonequilibrium activity in living systems.

Emergence of Orchestrated and Dynamic Metabolism of Saccharomyces cerevisiae

Microbial metabolism is a fundamental cellular process that involves many biochemical events and is distinguished by its emergent properties. While the molecular details of individual reactions have been increasingly elucidated, it is not well understood how these reactions are quantitatively orchestrated to produce collective cellular behaviors. Here we developed a coarse-grained, systems, and dynamic mathematical framework, which integrates metabolic reactions with signal transduction and gene regulation to dissect the emergent metabolic traits of Saccharomyces cerevisiae. Our framework mechanistically captures a set of characteristic cellular behaviors, including the Crabtree effect, diauxic shift, diauxic lag time, and differential growth under nutrient-altered environments. It also allows modular expansion for zooming in on specific pathways for detailed metabolic profiles. This study provides a systems mathematical framework for yeast metabolic behaviors, providing insights into yeast physiology and metabolic engineering.

Living Cell as a Self-Synchronized Chemical Reactor

Thermal fluctuations power all processes inside living cells. Therefore, these processes are inherently random. However, myriad multistep chemical reactions act in concerto inside a cell, finally leading to this chemical reactor's self-replication. We speculate that an underlying mechanism in nature must exist that allows all of these reactions to synchronize at multiple time and length scales, overcoming in this way the random nature of any single process in a cell. This Perspective discusses what type of research is needed to understand this undiscovered synchronization law.

Calcium oscillations optimize the energetic efficiency of mitochondrial metabolism

Energy transduction is central to living organisms, but the impact of enzyme regulation and signaling on its thermodynamic efficiency is generally overlooked. Here, we analyze the efficiency of ATP production by the tricarboxylic acid cycle and oxidative phosphorylation, which generate most of the chemical energy in eukaryotes. Calcium signaling regulates this pathway and can affect its energetic output, but the concrete energetic impact of this cross-talk remains elusive. Calcium enhances ATP production by activating key enzymes of the tricarboxylic acid cycle while calcium homeostasis is ATP-dependent. We propose a detailed kinetic model describing the calcium-mitochondria cross-talk and analyze it using nonequilibrium thermodynamics: after identifying the effective reactions driving mitochondrial metabolism out of equilibrium, we quantify the mitochondrial thermodynamic efficiency for different conditions. Calcium oscillations, triggered by extracellular stimulation or energy deficiency, boost the thermodynamic efficiency of mitochondrial metabolism, suggesting a compensatory role of calcium signaling in mitochondrial bioenergetics.

The minimum energy required to build a cell

Understanding the energy requirements for cell synthesis accurately and comprehensively has been a longstanding challenge. We introduce a computational model that estimates the minimum energy necessary to build any cell from its constituent parts. This method combines omics and internal cell compositions from various sources to calculate the Gibbs Free Energy of biosynthesis independently of specific metabolic pathways. Our public tool, Synercell, can be used with other models for minumum species-specific energy estimations in any well-sequenced species. The energy for synthesising the genome, transcriptome, proteome, and lipid bilayer of four cell types: Escherichia coli, Saccharomyces cerevisiae, an average mammalian cell and JCVI-syn3A were estimated. Their modelled minimum synthesis energies at 298 K were 9.54 × 10 - 11 J/cell, 4.99 × 10 - 9 J/cell, 3.71 × 10 - 7 J/cell and 3.69 × 10 - 12 respectively. Gram-for-gram synthesis of lipid bilayers requires the most energy, followed by the proteome, genome, and transcriptome. The average per gram cost of biomass synthesis is in the 300s of J/g for all four cells. Implications for the generalisability of cell construction and applications to biogeosciences, cellular biology, biotechnology, and astrobiology are discussed.

Microbial Pathway Thermodynamics: Stoichiometric Models Unveil Anabolic and Catabolic Processes

The biotechnological exploitation of microorganisms enables the use of metabolism for the production of economically valuable substances, such as drugs or food. It is, thus, unsurprising that the investigation of microbial metabolism and its regulation has been an active research field for many decades. As a result, several theories and techniques were developed that allow for the prediction of metabolic fluxes and yields as biotechnologically relevant output parameters. One important approach is to derive macrochemical equations that describe the overall metabolic conversion of an organism and basically treat microbial metabolism as a black box. The opposite approach is to include all known metabolic reactions of an organism to assemble a genome-scale metabolic model. Interestingly, both approaches are rather successful at characterizing and predicting the expected product yield. Over the years, macrochemical equations especially have been extensively characterized in terms of their thermodynamic properties. However, a common challenge when characterizing microbial metabolism by a single equation is to split this equation into two, describing the two modes of metabolism, anabolism and catabolism. Here, we present strategies to systematically identify separate equations for anabolism and catabolism. Based on metabolic models, we systematically identify all theoretically possible catabolic routes and determine their thermodynamic efficiency. We then show how anabolic routes can be derived, and we use these to approximate biomass yield. Finally, we challenge the view of metabolism as a linear energy converter, in which the free energy gradient of catabolism drives the anabolic reactions.

Predicting microbial interactions with approaches based on flux balance analysis: an evaluation

BACKGROUND

Given a genome-scale metabolic model (GEM) of a microorganism and criteria for optimization, flux balance analysis (FBA) predicts the optimal growth rate and its corresponding flux distribution for a specific medium. FBA has been extended to microbial consortia and thus can be used to predict interactions by comparing in-silico growth rates for co- and monocultures. Although FBA-based methods for microbial interaction prediction are becoming popular, a systematic evaluation of their accuracy has not yet been performed.

RESULTS

Here, we evaluate the accuracy of FBA-based predictions of human and mouse gut bacterial interactions using growth data from the literature. For this, we collected 26 GEMs from the semi-curated AGORA database as well as four previously published curated GEMs. We tested the accuracy of three tools (COMETS, Microbiome Modeling Toolbox and MICOM) by comparing growth rates predicted in mono- and co-culture to growth rates extracted from the literature and also investigated the impact of different tool settings and media. We found that except for curated GEMs, predicted growth rates and their ratios (i.e. interaction strengths) do not correlate with growth rates and interaction strengths obtained from in vitro data.

CONCLUSIONS

Prediction of growth rates with FBA using semi-curated GEMs is currently not sufficiently accurate to predict interaction strengths reliably.

Performance and robustness analysis reveals phenotypic trade-offs in yeast

To design strains that can function efficiently in complex industrial settings, it is crucial to consider their robustness, that is, the stability of their performance when faced with perturbations. In the present study, we cultivated 24 Saccharomyces cerevisiae strains under conditions that simulated perturbations encountered during lignocellulosic bioethanol production, and assessed the performance and robustness of multiple phenotypes simultaneously. The observed negative correlations confirmed a trade-off between performance and robustness of ethanol yield, biomass yield, and cell dry weight. Conversely, the specific growth rate performance positively correlated with the robustness, presumably because of evolutionary selection for robust, fast-growing cells. The Ethanol Red strain exhibited both high performance and robustness, making it a good candidate for bioproduction in the tested perturbation space. Our results experimentally map the robustness-performance trade-offs, previously demonstrated mainly by single-phenotype and computational studies.

Four ways of implementing robustness quantification in strain characterisation

BACKGROUND

In industrial bioprocesses, microorganisms are generally selected based on performance, whereas robustness, i.e., the ability of a system to maintain a stable performance, has been overlooked due to the challenges in its quantification and implementation into routine experimental procedures. This work presents four ways of implementing robustness quantification during strain characterisation. One Saccharomyces cerevisiae laboratory strain (CEN.PK113-7D) and two industrial strains (Ethanol Red and PE2) grown in seven different lignocellulosic hydrolysates were assessed for growth-related functions (specific growth rate, product yields, etc.) and eight intracellular parameters (using fluorescent biosensors).

RESULTS

Using flasks and high-throughput experimental setups, robustness was quantified in relation to: (i) stability of growth functions in response to the seven hydrolysates; (ii) stability of growth functions across different strains to establish the impact of perturbations on yeast metabolism; (iii) stability of intracellular parameters over time; (iv) stability of intracellular parameters within a cell population to indirectly quantify population heterogeneity. Ethanol Red was the best-performing strain under all tested conditions, achieving the highest growth function robustness. PE2 displayed the highest population heterogeneity. Moreover, the intracellular environment varied in response to non-woody or woody lignocellulosic hydrolysates, manifesting increased oxidative stress and unfolded protein response, respectively.

CONCLUSIONS

Robustness quantification is a powerful tool for strain characterisation as it offers novel information on physiological and biochemical parameters. Owing to the flexibility of the robustness quantification method, its implementation was successfully validated at single-cell as well as high-throughput levels, showcasing its versatility and potential for several applications.

Inferring mitochondrial and cytosolic metabolism by coupling isotope tracing and deconvolution

The inability to inspect metabolic activities within distinct subcellular compartments has been a major barrier to our understanding of eukaryotic cell metabolism. Previous work addressed this challenge by analyzing metabolism in isolated organelles, which grossly bias metabolic activity. Here, we describe a method for inferring physiological metabolic fluxes and metabolite concentrations in mitochondria and cytosol based on isotope tracing experiments performed with intact cells. This is made possible by computational deconvolution of metabolite isotopic labeling patterns and concentrations into cytosolic and mitochondrial counterparts, coupled with metabolic and thermodynamic modelling. Our approach lowers the uncertainty regarding compartmentalized fluxes and concentrations by one and three orders of magnitude compared to existing modelling approaches, respectively. We derive a quantitative view of mitochondrial and cytosolic metabolic activities in central carbon metabolism across cultured cell lines without performing cell fractionation, finding major variability in compartmentalized malate-aspartate shuttle fluxes. We expect our approach for inferring metabolism at a subcellular resolution to be instrumental for a variety of studies of metabolic dysfunction in human disease and for bioengineering.

Modeling cell populations metabolism and competition under maximum power constraints

Ecological interactions are fundamental at the cellular scale, addressing the possibility of a description of cellular systems that uses language and principles of ecology. In this work, we use a minimal ecological approach that encompasses growth, adaptation and survival of cell populations to model cell metabolisms and competition under energetic constraints. As a proof-of-concept, we apply this general formulation to study the dynamics of the onset of a specific blood cancer-called Multiple Myeloma. We show that a minimal model describing antagonist cell populations competing for limited resources, as regulated by microenvironmental factors and internal cellular structures, reproduces patterns of Multiple Myeloma evolution, due to the uncontrolled proliferation of cancerous plasma cells within the bone marrow. The model is characterized by a class of regime shifts to more dissipative states for selectively advantaged malignant plasma cells, reflecting a breakdown of self-regulation in the bone marrow. The transition times obtained from the simulations range from years to decades consistently with clinical observations of survival times of patients. This irreversible dynamical behavior represents a possible description of the incurable nature of myelomas based on the ecological interactions between plasma cells and the microenvironment, embedded in a larger complex system. The use of ATP equivalent energy units in defining stocks and flows is a key to constructing an ecological model which reproduces the onset of myelomas as transitions between states of a system which reflects the energetics of plasma cells. This work provides a basis to construct more complex models representing myelomas, which can be compared with model ecosystems.

Model-driven insights into the effects of temperature on metabolism

Temperature affects cellular processes at different spatiotemporal scales, and identifying the genetic and molecular mechanisms underlying temperature responses paves the way to develop approaches for mitigating the effects of future climate scenarios. A systems view of the effects of temperature on cellular physiology can be obtained by focusing on metabolism since: (i) its functions depend on transcription and translation and (ii) its outcomes support organisms' development, growth, and reproduction. Here we provide a systematic review of modelling efforts directed at investigating temperature effects on properties of single biochemical reactions, system-level traits, metabolic subsystems, and whole-cell metabolism across different prokaryotes and eukaryotes. We compare and contrast computational approaches and theories that facilitate modelling of temperature effects on key properties of enzymes and their consideration in constraint-based as well as kinetic models of metabolism. In addition, we provide a summary of insights from computational approaches, facilitating integration of omics data from temperature-modulated experiments with models of metabolic networks, and review the resulting biotechnological applications. Lastly, we provide a perspective on how different types of metabolic modelling can profit from developments in machine learning and models of different cellular layers to improve model-driven insights into the effects of temperature relevant for biotechnological applications.

Brain mitochondrial diversity and network organization predict anxiety-like behavior in male mice

The brain and behavior are under energetic constraints, limited by mitochondrial energy transformation capacity. However, the mitochondria-behavior relationship has not been systematically studied at a brain-wide scale. Here we examined the association between multiple features of mitochondrial respiratory chain capacity and stress-related behaviors in male mice with diverse behavioral phenotypes. Miniaturized assays of mitochondrial respiratory chain enzyme activities and mitochondrial DNA (mtDNA) content were deployed on 571 samples across 17 brain areas, defining specific patterns of mito-behavior associations. By applying multi-slice network analysis to our brain-wide mitochondrial dataset, we identified three large-scale networks of brain areas with shared mitochondrial signatures. A major network composed of cortico-striatal areas exhibited the strongest mitochondria-behavior correlations, accounting for up to 50% of animal-to-animal behavioral differences, suggesting that this mito-based network is functionally significant. The mito-based brain networks also overlapped with regional gene expression and structural connectivity, and exhibited distinct molecular mitochondrial phenotype signatures. This work provides convergent multimodal evidence anchored in enzyme activities, gene expression, and animal behavior that distinct, behaviorally-relevant mitochondrial phenotypes exist across the male mouse brain.

Linear Response Theory of Evolved Metabolic Systems

Predicting cellular metabolic states is a central problem in biophysics. Conventional approaches, however, sensitively depend on the microscopic details of individual metabolic systems. In this Letter, we derived a universal linear relationship between the metabolic responses against nutrient conditions and metabolic inhibition, with the aid of a microeconomic theory. The relationship holds in arbitrary metabolic systems as long as the law of mass conservation stands, as supported by extensive numerical calculations. It offers quantitative predictions without prior knowledge of systems.

Optimal evaluation of energy yield and driving force in microbial metabolic pathway variants

This work presents a methodology to evaluate the bioenergetic feasibility of alternative metabolic pathways for a given microbial conversion, optimising their energy yield and driving forces as a function of the concentration of metabolic intermediates. The tool, based on thermodynamic principles and multi-objective optimisation, accounts for pathway variants in terms of different electron carriers, as well as energy conservation (proton translocating) reactions within the pathway. The method also accommodates other constraints, some of them non-linear, such as the balance of conserved moieties. The approach involves the transformation of the maximum energy yield problem into a multi-objective mixed-integer linear optimisation problem which is then subsequently solved using the epsilon-constraint method, highlighting the trade-off between yield and rate in metabolic reactions. The methodology is applied to analyse several pathway alternatives occurring during propionate oxidation in anaerobic fermentation processes, as well as to the reverse TCA cycle pathway occurring during autotrophic microbial CO2 fixation. The results obtained using the developed methodology match previously reported literature and bring about insights into the studied pathways.

Probing Single-Cell Fermentation Fluxes and Exchange Networks via pH-Sensing Hybrid Nanofibers

The homeostatic control of their environment is an essential task of living cells. It has been hypothesized that, when microenvironmental pH inhomogeneities are induced by high cellular metabolic activity, diffusing protons act as signaling molecules, driving the establishment of exchange networks sustained by the cell-to-cell shuttling of overflow products such as lactate. Despite their fundamental role, the extent and dynamics of such networks is largely unknown due to the lack of methods in single-cell flux analysis. In this study, we provide direct experimental characterization of such exchange networks. We devise a method to quantify single-cell fermentation fluxes over time by integrating high-resolution pH microenvironment sensing via ratiometric nanofibers with constraint-based inverse modeling. We apply our method to cell cultures with mixed populations of cancer cells and fibroblasts. We find that the proton trafficking underlying bulk acidification is strongly heterogeneous, with maximal single-cell fluxes exceeding typical values by up to 3 orders of magnitude. In addition, a crossover in time from a networked phase sustained by densely connected "hubs" (corresponding to cells with high activity) to a sparse phase dominated by isolated dipolar motifs (i.e., by pairwise cell-to-cell exchanges) is uncovered, which parallels the time course of bulk acidification. Our method addresses issues ranging from the homeostatic function of proton exchange to the metabolic coupling of cells with different energetic demands, allowing for real-time noninvasive single-cell metabolic flux analysis.

Temporal segregation of biosynthetic processes is responsible for metabolic oscillations during the budding yeast cell cycle

Many cell biological and biochemical mechanisms controlling the fundamental process of eukaryotic cell division have been identified; however, the temporal dynamics of biosynthetic processes during the cell division cycle are still elusive. Here, we show that key biosynthetic processes are temporally segregated along the cell cycle. Using budding yeast as a model and single-cell methods to dynamically measure metabolic activity, we observe two peaks in protein synthesis, in the G1 and S/G2/M phase, whereas lipid and polysaccharide synthesis peaks only once, during the S/G2/M phase. Integrating the inferred biosynthetic rates into a thermodynamic-stoichiometric metabolic model, we find that this temporal segregation in biosynthetic processes causes flux changes in primary metabolism, with an acceleration of glucose-uptake flux in G1 and phase-shifted oscillations of oxygen and carbon dioxide exchanges. Through experimental validation of the model predictions, we demonstrate that primary metabolism oscillates with cell-cycle periodicity to satisfy the changing demands of biosynthetic processes exhibiting unexpected dynamics during the cell cycle.

Whole-cell energy modeling reveals quantitative changes of predicted energy flows in RAS mutant cancer cell lines

Cellular utilization of available energy flows to drive a multitude of forms of cellular "work" is a major biological constraint. Cells steer metabolism to address changing phenotypic states but little is known as to how bioenergetics couples to the richness of processes in a cell as a whole. Here, we outline a whole-cell energy framework that is informed by proteomic analysis and an energetics-based gene ontology. We separate analysis of metabolic supply and the capacity to generate high-energy phosphates from a representation of demand that is built on the relative abundance of ATPases and GTPases that deliver cellular work. We employed mouse embryonic fibroblast cell lines that express wild-type KRAS or oncogenic mutations and with distinct phenotypes. We observe shifts between energy-requiring processes. Calibrating against Seahorse analysis, we have created a whole-cell energy budget with apparent predictive power, for instance in relation to protein synthesis.

Biothermodynamics of Viruses from Absolute Zero (1950) to Virothermodynamics (2022)

Biothermodynamics of viruses is among the youngest but most rapidly developing scientific disciplines. During the COVID-19 pandemic, it closely followed the results published by molecular biologists. Empirical formulas were published for 50 viruses and thermodynamic properties for multiple viruses and virus variants, including all variants of concern of SARS-CoV-2, SARS-CoV, MERS-CoV, Ebola virus, Vaccinia and Monkeypox virus. A review of the development of biothermodynamics of viruses during the last several decades and intense development during the last 3 years is described in this paper.

Engineering proton-coupled hexose uptake in Saccharomyces cerevisiae for improved ethanol yield

Background

In the yeast Saccharomyces cerevisiae, which is widely applied for industrial bioethanol production, uptake of hexoses is mediated by transporters with a facilitated diffusion mechanism. In anaerobic cultures, a higher ethanol yield can be achieved when transport of hexoses is proton-coupled, because of the lower net ATP yield of sugar dissimilation. In this study, the facilitated diffusion transport system for hexose sugars of S. cerevisiae was replaced by hexose–proton symport.

Results

Introduction of heterologous glucose– or fructose–proton symporters in an hxt⁰ yeast background strain (derived from CEN.PK2-1C) restored growth on the corresponding sugar under aerobic conditions. After applying an evolutionary engineering strategy to enable anaerobic growth, the hexose–proton symporter-expressing strains were grown in anaerobic, hexose-limited chemostats on synthetic defined medium, which showed that the biomass yield of the resulting strains was decreased by 44.0-47.6%, whereas the ethanol yield had increased by up to 17.2% (from 1.51 to 1.77 mol mol hexose⁻¹) compared to an isogenic strain expressing the hexose uniporter HXT5. To apply this strategy to increase the ethanol yield on sucrose, we constructed a platform strain in which all genes encoding hexose transporters, disaccharide transporters and disaccharide hydrolases were deleted, after which a combination of a glucose–proton symporter, fructose–proton symporter and extracellular invertase (SUC2) were introduced. After evolution, the resulting strain exhibited a 16.6% increased anaerobic ethanol yield (from 1.51 to 1.76 mol mol hexose equivalent⁻¹) and 46.6% decreased biomass yield on sucrose.

Conclusions

This study provides a proof-of-concept for the replacement of the endogenous hexose transporters of S. cerevisiae by hexose-proton symport, and the concomitant decrease in ATP yield, to greatly improve the anaerobic yield of ethanol on sugar. Moreover, the sugar-negative platform strain constructed in this study acts as a valuable starting point for future studies on sugar transport or development of cell factories requiring specific sugar transport mechanisms.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13068-022-02145-7.

The energetic cost of allostasis and allostatic load

Chronic psychosocial stress increases disease risk and mortality, but the underlying mechanisms remain largely unclear. Here we outline an energy-based model for the transduction of chronic stress into disease over time. The energetic model of allostatic load (EMAL) emphasizes the energetic cost of allostasis and allostatic load, where the "load" is the additional energetic burden required to support allostasis and stress-induced energy needs. Living organisms have a limited capacity to consume energy. Overconsumption of energy by allostatic brain-body processes leads to hypermetabolism, defined as excess energy expenditure above the organism's optimum. In turn, hypermetabolism accelerates physiological decline in cells, laboratory animals, and humans, and may drive biological aging. Therefore, we propose that the transition from adaptive allostasis to maladaptive allostatic states, allostatic load, and allostatic overload arises when the added energetic cost of stress competes with longevity-promoting growth, maintenance, and repair. Mechanistically, the energetic restriction of growth, maintenance and repair processes leads to the progressive wear-and-tear of molecular and organ systems. The proposed model makes testable predictions around the physiological, cellular, and sub-cellular energetic mechanisms that transduce chronic stress into disease risk and mortality. We also highlight new avenues to quantify allostatic load and its link to health across the lifespan, via the integration of systemic and cellular energy expenditure measurements together with classic allostatic load biomarkers.

The choice of the objective function in flux balance analysis is crucial for predicting replicative lifespans in yeast

Flux balance analysis (FBA) is a powerful tool to study genome-scale models of the cellular metabolism, based on finding the optimal flux distributions over the network. While the objective function is crucial for the outcome, its choice, even though motivated by evolutionary arguments, has not been directly connected to related measures. Here, we used an available multi-scale mathematical model of yeast replicative ageing, integrating cellular metabolism, nutrient sensing and damage accumulation, to systematically test the effect of commonly used objective functions on features of replicative ageing in budding yeast, such as the number of cell divisions and the corresponding time between divisions. The simulations confirmed that assuming maximal growth is essential for reaching realistic lifespans. The usage of the parsimonious solution or the additional maximisation of a growth-independent energy cost can improve lifespan predictions, explained by either increased respiratory activity using resources otherwise allocated to cellular growth or by enhancing antioxidative activity, specifically in early life. Our work provides a new perspective on choosing the objective function in FBA by connecting it to replicative ageing.

Catalysis-Induced Phase Separation and Autoregulation of Enzymatic Activity

We present a thermodynamically consistent model describing the dynamics of a multicomponent mixture where one enzyme component catalyzes a reaction between other components. We find that the catalytic activity alone can induce phase separation for sufficiently active systems and large enzymes, without any equilibrium interactions between components. In the limit of fast reaction rates, binodal lines can be calculated using a mapping to an effective free energy. We also explain how this catalysis-induced phase separation can act to autoregulate the enzymatic activity, which points at the biological relevance of this phenomenon.

Thermodynamic limitations of PHB production from formate and fructose in Cupriavidus necator

The chemolithotroph Cupriavidus necator H16 is known as a natural producer of the bioplastic-polymer PHB, as well as for its metabolic versatility to utilize different substrates, including formate as the sole carbon and energy source. Depending on the entry point of the substrate, this versatility requires adjustment of the thermodynamic landscape to maintain sufficiently high driving forces for biological processes. Here we employed a model of the core metabolism of C. necator H16 to analyze the thermodynamic driving forces and PHB yields from formate for different metabolic engineering strategies. For this, we enumerated elementary flux modes (EFMs) of the network and evaluated their PHB yields as well as thermodynamics via Max-min driving force (MDF) analysis and random sampling of driving forces. A heterologous ATP:citrate lyase reaction was predicted to increase driving force for producing acetyl-CoA. A heterologous phosphoketolase reaction was predicted to increase maximal PHB yields as well as driving forces. These enzymes were then verified experimentally to enhance PHB titers between 60 and 300% in select conditions. The EFM analysis also revealed that PHB production from formate may be limited by low driving forces through citrate lyase and aconitase, as well as cofactor balancing, and identified additional reactions associated with low and high PHB yield. Proteomics analysis of the engineered strains confirmed an increased abundance of aconitase and cofactor balancing. The findings of this study aid in understanding metabolic adaptation. Furthermore, the outlined approach will be useful in designing metabolic engineering strategies in other non-model bacteria.

Free-Energy Transduction in Chemical Reaction Networks: from Enzymes to Metabolism

We provide a rigorous definition of free-energy transduction and its efficiency in arbitrary---linear or nonlinear---open chemical reaction networks (CRNs) operating at steady state. Our method is based on the knowledge of the stoichiometric matrix and of the chemostatted species (i.e. the species maintained at constant concentration by the environment) to identify the fundamental currents and forces contributing to the entropy production. Transduction occurs when the current of a stoichiometrically balanced process is driven against its spontaneous direction (set by its force) thanks to other processes flowing along their spontaneous direction. In these regimes, open CRNs operate as thermodynamic machines. After exemplifying these general ideas using toy models, we analyze central energy metabolism. We relate the fundamental currents to metabolic pathways and discuss the efficiency with which they are able to transduce free energy.

Mechanisms and mathematical modelling of ROS production by the mitochondrial electron transport chain

Reactive oxygen species (ROS) are recognised both as damaging molecules and intracellular signalling entities. In addition to its role in ATP generation, the mitochondrial electron transport chain (ETC) constitutes a relevant source of mitochondrial ROS, in particular during pathological conditions. Mitochondrial ROS homeostasis depends on species- and site-dependent ROS production, their bioreactivity, diffusion, and scavenging. However, our quantitative understanding of mitochondrial ROS homeostasis has thus far been hampered by technical limitations, including lack of truly site- and/or ROS-specific reporter molecules. In this context, the use of computational models is of great value to complement and interpret empirical data, as well as to predict variables that are difficult to assess experimentally. During the last decades, various mechanistic models of ETC-mediated ROS production have been developed. Although these often-complex models have generated novel insights, their parameterisation, analysis, and integration with other computational models is not straightforward. In contrast, phenomenological (sometimes termed "minimal") models use a relatively small set of equations to describe empirical relationship(s) between ROS-related and other parameters, and generally aim to explore system behaviour and generate hypotheses for experimental validation. In this review, we first discuss ETC-linked ROS homeostasis and introduce various detailed mechanistic models. Next, we present how bioenergetic parameters (e.g. NADH/NAD⁺ ratio, mitochondrial membrane potential) relate to site-specific ROS production within the ETC and how these relationships can be used to design minimal models of ROS homeostasis. Finally, we illustrate how minimal models have been applied to explore pathophysiological aspects of ROS.

Notch ankyrin domain: evolutionary rise of a thermodynamic sensor

Notch signalling pathway plays a key role in metazoan biology by contributing to resolution of binary decisions in the life cycle of cells during development. Outcomes such as proliferation/differentiation dichotomy are resolved by transcriptional remodelling that follows a switch from Notch^on to Notch^off state, characterised by dissociation of Notch intracellular domain (NICD) from DNA-bound RBPJ. Here we provide evidence that transitioning to the Notch^off state is regulated by heat flux, a phenomenon that aligns resolution of fate dichotomies to mitochondrial activity. A combination of phylogenetic analysis and computational biochemistry was utilised to disclose structural adaptations of Notch1 ankyrin domain that enabled function as a sensor of heat flux. We then employed DNA-based micro-thermography to measure heat flux during brain development, followed by analysis in vitro of the temperature-dependent behaviour of Notch1 in mouse neural progenitor cells. The structural capacity of NICD to operate as a thermodynamic sensor in metazoans stems from characteristic enrichment of charged acidic amino acids in β-hairpins of the ankyrin domain that amplify destabilising inter-residue electrostatic interactions and render the domain thermolabile. The instability emerges upon mitochondrial activity which raises the perinuclear and nuclear temperatures to 50 °C and 39 °C, respectively, leading to destabilization of Notch1 transcriptional complex and transitioning to the Notch^off state. Notch1 functions a metazoan thermodynamic sensor that is switched on by intercellular contacts, inputs heat flux as a proxy for mitochondrial activity in the Notch^on state via the ankyrin domain and is eventually switched off in a temperature-dependent manner.

Perspective: a stirring role for metabolism in cells

Based on recent findings indicating that metabolism might be governed by a limit on the rate at which cells can dissipate Gibbs energy, in this Perspective, we propose a new mechanism of how metabolic activity could globally regulate biomolecular processes in a cell. Specifically, we postulate that Gibbs energy released in metabolic reactions is used to perform work, allowing enzymes to self-propel or to break free from supramolecular structures. This catalysis-induced enzyme movement will result in increased intracellular motion, which in turn can compromise biomolecular functions. Once the increased intracellular motion has a detrimental effect on regulatory mechanisms, this will establish a feedback mechanism on metabolic activity, and result in the observed thermodynamic limit. While this proposed explanation for the identified upper rate limit on cellular Gibbs energy dissipation rate awaits experimental validation, it offers an intriguing perspective of how metabolic activity can globally affect biomolecular functions and will hopefully spark new research.

Developmental energetics: Energy expenditure, budgets and metabolism during animal embryogenesis

Developing embryos are metabolically active, open systems that constantly exchange matter and energy with their environment. They function out of thermodynamic equilibrium and continuously use metabolic pathways to obtain energy from maternal nutrients, in order to fulfill the energetic requirements of growth and development. While an increasing number of studies highlight the role of metabolism in different developmental contexts, the physicochemical basis of embryogenesis, or how cellular processes use energy and matter to act together and transform a zygote into an adult organism, remains unknown. As we obtain a better understanding of metabolism, and benefit from current technology development, it is a promising time to revisit the energetic cost of development and how energetic principles may govern embryogenesis. Here, we review recent advances in methodology to measure and infer energetic parameters in developing embryos. We highlight a potential common pattern in embryonic energy expenditure and metabolic strategy across animal embryogenesis, and discuss challenges and open questions in developmental energetics.

On the design principles of metabolic flux sensing

Metabolism is precisely coordinated, with the goal of balancing fluxes to maintain robust growth. However, coordinating fluxes requires information about rates, which can only be inferred through concentrations. While flux-sensitive metabolites have been reported, the design principles underlying such sensing have not been clearly elucidated. Here we use kinetic modeling to show that substrate concentrations of thermodynamically constrained reactions reflect upstream flux and therefore carry information about rates. Then we use untargeted multi-omic data from Escherichia coli and Saccharomyces cerevisiae to show that the concentrations of some metabolites in central carbon metabolism reflect fluxes as a result of thermodynamic constraints. We then establish, using 37 real concentration-flux relationships across both organisms, that in vivo ΔG∘≥-4 kJ/mol is the threshold above which substrates are likely to be sensitive to upstream flux(es).

Vitreoscilla Haemoglobin: A Tool to Reduce Overflow Metabolism

Overflow metabolism is a phenomenon extended in nature, ranging from microbial to cancer cells. Accumulation of overflow metabolites pose a challenge for large-scale bioprocesses. Yet, the causes of overflow metabolism are not fully clarified. In this work, the underlying mechanisms, reasons and consequences of overflow metabolism in different organisms have been summarized. The reported effect of aerobic expression of Vitreoscilla haemoglobin (VHb) in different organisms are revised. The use of VHb to reduce overflow metabolism is proposed and studied through flux balance analysis in E. coli at a fixed maximum substrate and oxygen uptake rates. Simulations showed that the presence of VHb increases the growth rate, while decreasing acetate production, in line with the experimental measurements. Therefore, aerobic VHb expression is considered a potential tool to reduce overflow metabolism in cells.

Thermodynamic constraints on the assembly and diversity of microbial ecosystems are different near to and far from equilibrium

Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. However, most of this interest has focused on developing coarse ecosystem-level maximisation principles, providing little insight into underlying mechanisms that lead to such emergent constraints. Microbial communities are a natural system to decipher this mechanistic basis because their interactions in the form of substrate consumption, metabolite production, and cross-feeding can be described explicitly in thermodynamic terms. Previous work has considered how thermodynamic constraints impact competition between pairs of species, but restrained from analysing how this manifests in complex dynamical systems. To address this gap, we develop a thermodynamic microbial community model with fully reversible reaction kinetics, which allows direct consideration of free-energy dissipation. This also allows species to interact via products rather than just substrates, increasing the dynamical complexity, and allowing a more nuanced classification of interaction types to emerge. Using this model, we find that community diversity increases with substrate lability, because greater free-energy availability allows for faster generation of niches. Thus, more niches are generated in the time frame of community establishment, leading to higher final species diversity. We also find that allowing species to make use of near-to-equilibrium reactions increases diversity in a low free-energy regime. In such a regime, two new thermodynamic interaction types that we identify here reach comparable strengths to the conventional (competition and facilitation) types, emphasising the key role that thermodynamics plays in community dynamics. Our results suggest that accounting for realistic thermodynamic constraints is vital for understanding the dynamics of real-world microbial communities.

There is a growing interest in microbial communities due to their important role in biogeochemical cycling as well as plant and animal health. Although our understanding of thermodynamic constraints on individual cells is rapidly improving, the impact of these constraints on complex microbial communities remains largely unexplored theoretically and empirically. Here, we develop a new microbial community model which allows thermodynamic efficiency and entropy production to be calculated directly. We find that availability of substrates with greater free-energy allows for a faster rate of niche generation, leading to higher final species diversity. We also show that when the free-energy availability is low, species with reactions close to thermodynamic equilibrium are favoured, leading to more diverse and efficient communities. In addition to the conventional interaction types (competition and facilitation), our model reveals the existence of two novel interaction types mediated by products rather than substrates. Though the conventional interactions are generally the strongest, the novel interaction types are significant when free-energy availability is low. Our results suggest that non-equilibrium thermodynamics need to be considered when studying microbial community dynamics.

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.

Energetic scaling in microbial growth

Microbial growth is a clear example of organization and structure arising in nonequilibrium conditions. Due to the complexity of the microbial metabolic network, elucidating the fundamental principles governing microbial growth remains a challenge. Here, we present a systematic analysis of microbial growth thermodynamics, leveraging an extensive dataset on energy-limited monoculture growth. A consistent thermodynamic framework based on reaction stoichiometry allows us to quantify how much of the available energy microbes can efficiently convert into new biomass while dissipating the remaining energy into the environment and producing entropy. We show that dissipation mechanisms can be linked to the electron donor uptake rate, a fact leading to the central result that the thermodynamic efficiency is related to the electron donor uptake rate by the scaling law [Formula: see text] and to the growth yield by [Formula: see text] These findings allow us to rederive the Pirt equation from a thermodynamic perspective, providing a means to compute its coefficients, as well as a deeper understanding of the relationship between growth rate and yield. Our results provide rather general insights into the relation between mass and energy conversion in microbial growth with potentially wide application, especially in ecology and biotechnology.

Modeling aging and its impact on cellular function and organismal behavior

Aging is a complex phenomenon of functional decay in a biological organism. Although the effects of aging are readily recognizable in a wide range of organisms, the cause(s) of aging are ill defined and poorly understood. Experimental methods on model organisms have driven significant insight into aging as a process, but have not provided a complete model of aging. Computational biology offers a unique opportunity to resolve this gap in our knowledge by generating extensive and testable models that can help us understand the fundamental nature of aging, identify the presence and characteristics of unaccounted aging factor(s), demonstrate the mechanics of particular factor(s) in driving aging, and understand the secondary effects of aging on biological function. In this review, we will address each of the above roles for computational biology in aging research. Concurrently, we will explore the different applications of computational biology to aging in single-celled versus multicellular organisms. Given the long history of computational biogerontological research on lower eukaryotes, we emphasize the key future goals of gradually integrating prior models into a holistic map of aging and translating successful models to higher-complexity organisms.

Microeconomics of Metabolism: The Warburg Effect as Giffen Behaviour

Metabolic behaviours of proliferating cells are often explained as a consequence of rational optimization of cellular growth rate, whereas microeconomics formulates consumption behaviours as optimization problems. Here, we pushed beyond the analogy to precisely map metabolism onto the theory of consumer choice. We thereby revealed the correspondence between long-standing mysteries in both fields: the Warburg effect, a seemingly wasteful but ubiquitous strategy where cells favour aerobic glycolysis over more energetically efficient oxidative phosphorylation, and Giffen behaviour, the unexpected consumer behaviour where a good is demanded more as its price rises. We identified the minimal, universal requirements for the Warburg effect: a trade-off between oxidative phosphorylation and aerobic glycolysis and complementarity, i.e. impossibility of substitution for different metabolites. Thus, various hypotheses for the Warburg effect are integrated into an identical optimization problem with the same universal structure. Besides, the correspondence between the Warburg effect and Giffen behaviour implies that oxidative phosphorylation is counter-intuitively stimulated when its efficiency is decreased by metabolic perturbations such as drug administration or mitochondrial dysfunction; the concept of Giffen behaviour bridges the Warburg effect and the reverse Warburg effect. This highlights that the application of microeconomics to metabolism can offer new predictions and paradigms for both biology and economics.