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One-carbon (C1) feedstocks, such as carbon monoxide (CO), formate (HCO 2 H), methanol (CH 3 OH), and methane (CH 4 ), can be obtained either through stepwise electrochemical reduction of CO 2 with renewable electricity or via processing of organic side streams. These C1 substrates are increasingly investigated in biotechnology as they can contribute to a circular carbon economy. In recent years, noncanonical redox cofactors (NCRCs) emerged as a tool to generate synthetic electron circuits in cell factories to maximize electron transfer within a pathway of interest. Here, we argue that expanding the use of NCRCs in the context of C1-driven bioprocesses will boost product yields and facilitate challenging redox transactions that are typically out of the scope of natural cofactors due to inherent thermodynamic constraints., Competing Interests: Declaration of Competing Interest Nothing declared., (Copyright © 2024 The Authors. Published by Elsevier Ltd.. All rights reserved.)

The expression of metabolic proteins is controlled by genetic circuits, matching metabolic demands and changing environmental conditions. Ideally, this regulation brings about a competitive level of metabolic fitness. Understanding how cells can achieve a robust (close-to-optimal) functioning of metabolism by appropriate control of gene expression aids synthetic biology by providing design criteria of synthetic circuits for biotechnological purposes. It also extends our understanding of the designs of genetic circuitry found in nature such as metabolite control of transcription factor activity, promoter architectures and transcription factor dependencies, and operon composition (in bacteria). Here, we review, explain and illustrate an approach that allows for the inference and design of genetic circuitry that steers metabolic networks to achieve a maximal flux per unit invested protein across dynamic conditions. We discuss how this approach and its understanding can be used to rationalize Escherichia coli's strategy to regulate the expression of its ribosomes and infer the design of circuitry controlling gene expression of amino-acid biosynthesis enzymes. The inferred regulation indeed resembles E. coli's circuits, suggesting that these have evolved to maximize amino-acid production fluxes per unit invested protein. We end by an outlook of the use of this approach in metabolic engineering applications., (© 2024 The Author(s).)

Microbial systems biology has made enormous advances in relating microbial physiology to the underlying biochemistry and molecular biology. By meticulously studying model microorganisms, in particular Escherichia coli and Saccharomyces cerevisiae, increasingly comprehensive computational models predict metabolic fluxes, protein expression, and growth. The modeling rationale is that cells are constrained by a limited pool of resources that they allocate optimally to maximize fitness. As a consequence, the expression of particular proteins is at the expense of others, causing trade-offs between cellular objectives such as instantaneous growth, stress tolerance, and capacity to adapt to new environments. While current computational models are remarkably predictive for E. coli and S. cerevisiae when grown in laboratory environments, this may not hold for other growth conditions and other microorganisms. In this contribution, we therefore discuss the relationship between the instantaneous growth rate, limited resources, and long-term fitness. We discuss uses and limitations of current computational models, in particular for rapidly changing and adverse environments, and propose to classify microbial growth strategies based on Grimes's CSR framework., (© 2023 The Authors. BioEssays published by Wiley Periodicals LLC.)

Across all kingdoms of life, gene regulatory mechanisms underlie cellular adaptation to ever-changing environments. Regulation of gene expression adjusts protein synthesis and, in turn, cellular growth. Messenger RNAs are key molecules in the process of gene expression. Our ability to quantitatively measure mRNA expression in single cells has improved tremendously over the past decades. This revealed an unexpected coordination between the steps that control the life of an mRNA, from transcription to degradation. Here, we provide an overview of the state-of-the-art imaging approaches for measurement and quantitative understanding of gene expression, starting from the early visualizations of single genes by electron microscopy to current fluorescence-based approaches in single cells, including live-cell RNA-imaging approaches to FISH-based spatial transcriptomics across model organisms. We also highlight how these methods have shaped our current understanding of the spatiotemporal coupling between transcriptional and post-transcriptional events in prokaryotes. We conclude by discussing future challenges of this multidisciplinary field. Abbreviations: mRNA: messenger RNA; rRNA: ribosomal rDNA; tRNA: transfer RNA; sRNA: small RNA; FISH: fluorescence in situ hybridization; RNP: ribonucleoprotein; smFISH: single RNA molecule FISH; smiFISH: single molecule inexpensive FISH; HCR-FISH: Hybridization Chain-Reaction-FISH; RCA: Rolling Circle Amplification; seqFISH: Sequential FISH; MERFISH: Multiplexed error robust FISH; UTR: Untranslated region; RBP: RNA binding protein; FP: fluorescent protein; eGFP: enhanced GFP, MCP: MS2 coat protein; PCP: PP7 coat protein; MB: Molecular beacons; sgRNA: single guide RNA.

Microbes in the wild face highly variable and unpredictable environments and are naturally selected for their average growth rate across environments. Apart from using sensory regulatory systems to adapt in a targeted manner to changing environments, microbes employ bet-hedging strategies where cells in an isogenic population switch stochastically between alternative phenotypes. Yet, bet-hedging suffers from a fundamental trade-off: Increasing the phenotype-switching rate increases the rate at which maladapted cells explore alternative phenotypes but also increases the rate at which cells switch out of a well-adapted state. Consequently, it is currently believed that bet-hedging strategies are effective only when the number of possible phenotypes is limited and when environments last for sufficiently many generations. However, recent experimental results show that gene expression noise generally decreases with growth rate, suggesting that phenotype-switching rates may systematically decrease with growth rate. Such growth rate dependent stability (GRDS) causes cells to be more explorative when maladapted and more phenotypically stable when well-adapted, and we show that GRDS can almost completely overcome the trade-off that limits bet-hedging, allowing for effective adaptation even when environments are diverse and change rapidly. We further show that even a small decrease in switching rates of faster-growing phenotypes can substantially increase long-term fitness of bet-hedging strategies. Together, our results suggest that stochastic strategies may play an even bigger role for microbial adaptation than hitherto appreciated.

Microbial populations often contain persister cells, which reduce the extinction risk upon sudden stresses. Persister cell formation is deeply intertwined with physiology. Due to this complexity, it cannot be satisfactorily understood by focusing only on mechanistic, physiological or evolutionary aspects. In this review, we take an integrative biology perspective to identify common principles of persister cell formation, which might be applicable across evolutionary-distinct microbes. Persister cells probably evolved to cope with a fundamental trade-off between cellular stress and growth tasks, as any biosynthetic resource investment in growth-supporting proteins is at the expense of stress tasks and vice versa. Natural selection probably favours persister cell subpopulation formation over a single-phenotype strategy, where each cell is prepared for growth and stress to a suboptimal extent, since persister cells can withstand harsher environments and their coexistence with growing cells leads to a higher fitness. The formation of coexisting phenotypes requires bistable molecular circuitry. Bistability probably emerges from growth-modulated, positive feedback loops in the cell's growth versus stress control network, involving interactions between sigma factors, guanosine pentaphosphate and toxin-antitoxin (TA) systems. We conclude that persister cell formation is most likely a response to a sudden reduction in growth rate, which can be achieved by antibiotic addition, nutrient starvation, sudden stresses, nutrient transitions or activation of a TA system.

Fitness-enhancing adaptations of protein expression and its regulation are an important aspect of bacterial evolution. A key question is whether evolution has led to optimal protein expression that maximizes immediate growth rate (short-term fitness) in a robust manner (consistently across diverse conditions). Alternatively, they could display suboptimal short-term fitness, because they cannot do better or because they instead strive for long-term fitness maximization by, for instance, preparing for future conditions. To address this question, we focus on the ATP-producing enzyme F 1 F 0 H + -ATPase, which is an abundant enzyme and ubiquitously expressed across conditions. Its expression is highly regulated and dependent on growth rate and nutrient conditions. For instance, during growth on sugars, when metabolism is overflowing acetate, glycolysis supplies most ATP, while H + -ATPase is the main source of ATP synthesis during growth on acetate. We tested the optimality of H + -ATPase expression in Escherichia coli across different nutrient conditions. In all tested conditions, wild-type E. coli expresses its H + -ATPase remarkably close (within a few per cent) to optimal concentrations that maximize immediate growth rate. This work indicates that bacteria can indeed achieve robust optimal protein expression for immediate growth-rate maximization., (© 2022 The Authors. The FEBS Journal published by John Wiley & Sons Ltd on behalf of Federation of European Biochemical Societies.)

Kinases play key roles in signaling networks that are activated by G-protein-coupled receptors (GPCRs). Kinase activities are generally inferred from cell lysates, hiding cell-to-cell variability. To study the dynamics and heterogeneity of ERK and Akt proteins, we employed high-content biosensor imaging with kinase translocation reporters. The kinases were activated with GPCR ligands. We observed ligand concentration-dependent response kinetics to histamine, α2-adrenergic and S1P receptor stimulation. By using G-protein inhibitors, we observed that Gq mediated the ERK and Akt responses to histamine. In contrast, Gi was necessary for ERK and Akt activation in response to α2-adrenergic receptor activation. ERK and Akt were also strongly activated by S1P, showing high heterogeneity at the single-cell level, especially for ERK. Cluster analysis of time series derived from 68,000 cells obtained under the different conditions revealed several distinct populations of cells that display similar response dynamics. ERK response dynamics to S1P showed high heterogeneity, which was reduced by the inhibition of Gi. To conclude, we have set up an imaging and analysis strategy that reveals substantial cell-to-cell heterogeneity in kinase activity driven by GPCRs., Competing Interests: Competing interests The authors declare no competing or financial interests., (© 2022. Published by The Company of Biologists Ltd.)

When conditions change, unicellular organisms rewire their metabolism to sustain cell maintenance and cellular growth. Such rewiring may be understood as resource re-allocation under cellular constraints. Eukaryal cells contain metabolically active organelles such as mitochondria, competing for cytosolic space and resources, and the nature of the relevant cellular constraints remain to be determined for such cells. Here, we present a comprehensive metabolic model of the yeast cell, based on its full metabolic reaction network extended with protein synthesis and degradation reactions. The model predicts metabolic fluxes and corresponding protein expression by constraining compartment-specific protein pools and maximising growth rate. Comparing model predictions with quantitative experimental data suggests that under glucose limitation, a mitochondrial constraint limits growth at the onset of ethanol formation-known as the Crabtree effect. Under sugar excess, however, a constraint on total cytosolic volume dictates overflow metabolism. Our comprehensive model thus identifies condition-dependent and compartment-specific constraints that can explain metabolic strategies and protein expression profiles from growth rate optimisation, providing a framework to understand metabolic adaptation in eukaryal cells., (© 2022. The Author(s).)

Overflow metabolism is ubiquitous in nature, and it is often considered inefficient because it leads to a relatively low biomass yield per consumed carbon. This metabolic strategy has been described as advantageous because it supports high growth rates during nutrient competition. Here, we experimentally evolved bacteria without nutrient competition by repeatedly growing and mixing millions of parallel batch cultures of Escherichia coli. Each culture originated from a water-in-oil emulsion droplet seeded with a single cell. Unexpectedly we found that overflow metabolism (acetate production) did not change. Instead, the numerical cell yield during the consumption of the accumulated acetate increased as a consequence of a reduction in cell size. Our experiments and a mathematical model show that fast growth and overflow metabolism, followed by the consumption of the overflow metabolite, can lead to a higher numerical cell yield and therefore a higher fitness compared with full respiration of the substrate. This provides an evolutionary scenario where overflow metabolism can be favorable even in the absence of nutrient competition., (© The Author(s) 2021. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.)

How do you define homeostasis, and what experimental observations are necessary to discover homeostatic mechanisms in the biological system you study?, (Copyright © 2021. Published by Elsevier Inc.)

The cAMP-PKA signaling cascade in budding yeast regulates adaptation to changing environments. We developed yEPAC, a FRET-based biosensor for cAMP measurements in yeast. We used this sensor with flow cytometry for high-throughput single cell-level quantification during dynamic changes in response to sudden nutrient transitions. We found that the characteristic cAMP peak differentiates between different carbon source transitions and is rather homogenous among single cells, especially for transitions to glucose. The peaks are mediated by a combination of extracellular sensing and intracellular metabolism. Moreover, the cAMP peak follows the Weber-Fechner law; its height scales with the relative, and not the absolute, change in glucose. Last, our results suggest that the cAMP peak height conveys information about prospective growth rates. In conclusion, our yEPAC-sensor makes possible new avenues for understanding yeast physiology, signaling, and metabolic adaptation.

The metabolic capabilities of cells determine their biotechnological potential, fitness in ecosystems, pathogenic threat levels, and function in multicellular organisms. Their comprehensive experimental characterization is generally not feasible, particularly for unculturable organisms. In principle, the full range of metabolic capabilities can be computed from an organism's annotated genome using metabolic network reconstruction. However, current computational methods cannot deal with genome-scale metabolic networks. Part of the problem is that these methods aim to enumerate all metabolic pathways, while computation of all (elementally balanced) conversions between nutrients and products would suffice. Indeed, the elementary conversion modes (ECMs, defined by Urbanczik and Wagner) capture the full metabolic capabilities of a network, but the use of ECMs has not been accessible until now. We explain and extend the theory of ECMs, implement their enumeration in ecmtool, and illustrate their applicability. This work contributes to the elucidation of the full metabolic footprint of any cell., Competing Interests: The authors declare no competing interests., (© 2020 The Authors.)

A recent article in Nature Physics unified key results from thermodynamics, statistics, and information theory. The unification arose from a general equation for the rate of change in the information content of a system. The general equation describes the change in the moments of an observable quantity over a probability distribution. One term in the equation describes the change in the probability distribution. The other term describes the change in the observable values for a given state. We show the equivalence of this general equation for moment dynamics with the widely known Price equation from evolutionary theory, named after George Price. We introduce the Price equation from its biological roots, review a mathematically abstract form of the equation, and discuss the potential for this equation to unify diverse mathematical theories from different disciplines. The new work in Nature Physics and many applications in biology show that this equation also provides the basis for deriving many novel theoretical results within each discipline.

Why do evolutionarily distinct microorganisms display similar physiological behaviours? Why are transitions from high-ATP yield to low(er)-ATP yield metabolisms so widespread across species? Why is fast growth generally accompanied with low stress tolerance? Do these regularities occur because most microbial species are subject to the same selective pressures and physicochemical constraints? If so, a broadly-applicable theory might be developed that predicts common microbiological behaviours. Microbial systems biologists have been working out the contours of this theory for the last two decades, guided by experimental data. At its foundations lie basic principles from evolutionary biology, enzyme biochemistry, metabolism, cell composition and steady-state growth. The theory makes predictions about fitness costs and benefits of protein expression, physicochemical constraints on cell growth and characteristics of optimal metabolisms that maximise growth rate. Comparisons of the theory with experimental data indicates that microorganisms often aim for maximisation of growth rate, also in the presence of stresses; they often express optimal metabolisms and metabolic proteins at optimal concentrations. This review explains the current status of the theory for microbiologists; its roots, predictions, experimental evidence and future directions., (© The Author(s) 2020. Published by Oxford University Press on behalf of FEMS.)

The growth rate of single bacterial cells is continuously disturbed by random fluctuations in biosynthesis rates and by deterministic cell-cycle events, such as division, genome duplication, and septum formation. It is not understood whether, and how, bacteria reject these growth-rate disturbances. Here, we quantified growth and constitutive protein expression dynamics of single Bacillus subtilis cells as a function of cell-cycle progression. We found that, even though growth at the population level is exponential, close inspection of the cell cycle of thousands of single Bacillus subtilis cells reveals systematic deviations from exponential growth. Newborn cells display varying growth rates that depend on their size. When they divide, growth-rate variation has decreased, and growth rates have become birth size independent. Thus, cells indeed compensate for growth-rate disturbances and achieve growth-rate homeostasis. Protein synthesis and growth of single cells displayed correlated, biphasic dynamics from cell birth to division. During a first phase of variable duration, the absolute rates were approximately constant and cells behaved as sizers. In the second phase, rates increased, and growth behavior exhibited characteristics of a timer strategy. These findings demonstrate that, just like size homeostasis, growth-rate homeostasis is an inherent property of single cells that is achieved by cell-cycle-dependent rate adjustments of biosynthesis and growth., Competing Interests: Declaration of Interests The authors declare no competing interests., (Copyright © 2020 The Author(s). Published by Elsevier Inc. All rights reserved.)

Living cells can express different metabolic pathways that support growth. The criteria that determine which pathways are selected in which environment remain unclear. One recurrent selection is overflow metabolism: the simultaneous usage of an ATP-efficient and -inefficient pathway, shown for example in Escherichia coli, Saccharomyces cerevisiae and cancer cells. Many models, based on different assumptions, can reproduce this observation. Therefore, they provide no conclusive evidence which mechanism is causing overflow metabolism. We compare the mathematical structure of these models. Although ranging from flux balance analyses to self-fabricating metabolism and expression models, we can rewrite all models into one standard form. We conclude that all models predict overflow metabolism when two, model-specific, growth-limiting constraints are hit. This is consistent with recent theory. Thus, identifying these two constraints is essential for understanding overflow metabolism. We list all imposed constraints by these models, so that they can hopefully be tested in future experiments.

In this paper we try to describe all possible molecular states (phenotypes) for a cell that fabricates itself at a constant rate, given its enzyme kinetics and the stoichiometry of all reactions. For this, we must understand the process of cellular growth: steady-state self-fabrication requires a cell to synthesize all of its components, including metabolites, enzymes and ribosomes, in proportions that match its own composition. Simultaneously, the concentrations of these components affect the rates of metabolism and biosynthesis, and hence the growth rate. We here derive a theory that describes all phenotypes that solve this circular problem. All phenotypes can be described as a combination of minimal building blocks, which we call Elementary Growth Modes (EGMs). EGMs can be used as the theoretical basis for all models that explicitly model self-fabrication, such as the currently popular Metabolism and Expression models. We then use our theory to make concrete biological predictions. We find that natural selection for maximal growth rate drives microorganisms to states of minimal phenotypic complexity: only one EGM will be active when growth rate is maximised. The phenotype of a cell is only extended with one more EGM whenever growth becomes limited by an additional biophysical constraint, such as a limited solvent capacity of a cellular compartment. The theory presented here extends recent results on Elementary Flux Modes: the minimal building blocks of cellular growth models that lack the self-fabrication aspect. Our theory starts from basic biochemical and evolutionary considerations, and describes unicellular life, both in growth-promoting and in stress-inducing environments, in terms of EGMs., Competing Interests: The authors have declared that no competing interests exist.

The physical biology of G protein-coupled receptor (GPCR) signalling can be inferred from imaging of single molecules and single living cells. In this opinion paper, we highlight recent developments in technologies to study GPCR signalling in vitro and in cyto. We start from mobility and localisation characteristics of single receptors in membranes. Subsequently, we discuss the kinetics of shifts in receptor-conformation equilibrium due to allosteric binding events and G protein activation. We continue with recent insights into downstream signalling and the role of delayed negative feedback to suppress GPCR signalling. Finally, we discuss new strategies to reveal how the multiplex signalling responses of cells to ligand mixtures, mediated by their entire receptor arsenal, can be disentangled, using single-cell data., (Copyright © 2019. Published by Elsevier Ltd.)

Growth rate is a near-universal selective pressure across microbial species. High growth rates require hundreds of metabolic enzymes, each with different nonlinear kinetics, to be precisely tuned within the bounds set by physicochemical constraints. Yet, the metabolic behaviour of many species is characterized by simple relations between growth rate, enzyme expression levels and metabolic rates. We asked if this simplicity could be the outcome of optimisation by evolution. Indeed, when the growth rate is maximized-in a static environment under mass-conservation and enzyme expression constraints-we prove mathematically that the resulting optimal metabolic flux distribution is described by a limited number of subnetworks, known as Elementary Flux Modes (EFMs). We show that, because EFMs are the minimal subnetworks leading to growth, a small active number automatically leads to the simple relations that are measured. We find that the maximal number of flux-carrying EFMs is determined only by the number of imposed constraints on enzyme expression, not by the size, kinetics or topology of the network. This minimal-EFM extremum principle is illustrated in a graphical framework, which explains qualitative changes in microbial behaviours, such as overflow metabolism and co-consumption, and provides a method for identification of the enzyme expression constraints that limit growth under the prevalent conditions. The extremum principle applies to all microorganisms that are selected for maximal growth rates under protein concentration constraints, for example the solvent capacities of cytosol, membrane or periplasmic space., Competing Interests: The authors have declared that no competing interests exist.

Background: A central theme in (micro)biology is understanding the molecular basis of fitness i.e. which strategies are successful under which conditions; how do organisms implement such strategies at the molecular level; and which constraints shape the trade-offs between alternative strategies. Highly standardized microbial laboratory evolution experiments are ideally suited to approach these questions. For example, prolonged chemostats provide a constant environment in which the growth rate can be set, and the adaptive process of the organism to such environment can be subsequently characterized., Results: We performed parallel laboratory evolution of Lactococcus lactis in chemostats varying the quantitative value of the selective pressure by imposing two different growth rates. A mutation in one specific amino acid residue of the global transcriptional regulator of carbon metabolism, CcpA, was selected in all of the evolution experiments performed. We subsequently showed that this mutation confers predictable fitness improvements at other glucose-limited growth rates as well. In silico protein structural analysis of wild type and evolved CcpA, as well as biochemical and phenotypic assays, provided the underpinning molecular mechanisms that resulted in the specific reprogramming favored in constant environments., Conclusion: This study provides a comprehensive understanding of a case of microbial evolution and hints at the wide dynamic range that a single fitness-enhancing mutation may display. It demonstrates how the modulation of a pleiotropic regulator can be used by cells to improve one trait while simultaneously work around other limiting constraints, by fine-tuning the expression of a wide range of cellular processes.

One of the marvels of biology is the phenotypic plasticity of microorganisms. It allows them to maintain high growth rates across conditions. Studies suggest that cells can express metabolic enzymes at tuned concentrations through adjustment of gene expression. The associated transcription factors are often regulated by intracellular metabolites. Here we study metabolite-mediated regulation of metabolic-gene expression that maximises metabolic fluxes across conditions. We developed an adaptive control theory, qORAC (for 'Specific Flux (q) Optimization by Robust Adaptive Control'), and illustrate it with several examples of metabolic pathways. The key feature of the theory is that it does not require knowledge of the regulatory network, only of the metabolic part. We derive that maximal metabolic flux can be maintained in the face of varying N environmental parameters only if the number of transcription-factor binding metabolites is at least equal to N. The controlling circuits appear to require simple biochemical kinetics. We conclude that microorganisms likely can achieve maximal rates in metabolic pathways, in the face of environmental changes., Competing Interests: The authors have declared that no competing interests exist.

Yeast glycolysis has been the focus of research for decades, yet a number of dynamical aspects of yeast glycolysis remain poorly understood at present. If nutrients are scarce, yeast will provide its catabolic and energetic needs with other pathways, but the enzymes catalysing upper glycolytic fluxes are still expressed. We conjecture that this overexpression facilitates the rapid transition to glycolysis in case of a sudden increase in nutrient concentration. However, if starved yeast is presented with abundant glucose, it can enter into an imbalanced state where glycolytic intermediates keep accumulating, leading to arrested growth and cell death. The bistability between regularly functioning and imbalanced phenotypes has been shown to depend on redox balance. We shed new light on these phenomena with a mathematical analysis of an ordinary differential equation model, including NADH to account for the redox balance. In order to gain qualitative insight, most of the analysis is parameter-free, i.e., without assigning a numerical value to any of the parameters. The model has a subtle bifurcation at the switch between an inviable equilibrium state and stable flux through glycolysis. This switch occurs if the ratio between the flux through upper glycolysis and ATP consumption rate of the cell exceeds a fixed threshold. If the enzymes of upper glycolysis would be barely expressed, our model predicts that there will be no glycolytic flux, even if external glucose would be at growth-permissable levels. The existence of the imbalanced state can be found for certain parameter conditions independent of the mentioned bifurcation. The parameter-free analysis proved too complex to directly gain insight into the imbalanced states, but the starting point of a branch of imbalanced states can be shown to exist in detail. Moreover, the analysis offers the key ingredients necessary for successful numerical continuation, which highlight the existence of this bistability and the influence of the redox balance., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Microbes may maximize the number of daughter cells per time or per amount of nutrients consumed. These two strategies correspond, respectively, to the use of enzyme-efficient or substrate-efficient metabolic pathways. In reality, fast growth is often associated with wasteful, yield-inefficient metabolism, and a general thermodynamic trade-off between growth rate and biomass yield has been proposed to explain this. We studied growth rate/yield trade-offs by using a novel modeling framework, Enzyme-Flux Cost Minimization (EFCM) and by assuming that the growth rate depends directly on the enzyme investment per rate of biomass production. In a comprehensive mathematical model of core metabolism in E. coli, we screened all elementary flux modes leading to cell synthesis, characterized them by the growth rates and yields they provide, and studied the shape of the resulting rate/yield Pareto front. By varying the model parameters, we found that the rate/yield trade-off is not universal, but depends on metabolic kinetics and environmental conditions. A prominent trade-off emerges under oxygen-limited growth, where yield-inefficient pathways support a 2-to-3 times higher growth rate than yield-efficient pathways. EFCM can be widely used to predict optimal metabolic states and growth rates under varying nutrient levels, perturbations of enzyme parameters, and single or multiple gene knockouts.

The inherent stochasticity of molecular reactions prevents us from predicting the exact state of single-cells in a population. However, when a population grows at steady-state, the probability to observe a cell with particular combinations of properties is fixed. Here we validate and exploit existing theory on the statistics of single-cell growth in order to predict the probability of phenotypic characteristics such as cell-cycle times, volumes, accuracy of division and cell-age distributions, using real-time imaging data for Bacillus subtilis and Escherichia coli. Our results show that single-cell growth-statistics can accurately be predicted from a few basic measurements. These equations relate different phenotypic characteristics, and can therefore be used in consistency tests of experimental single-cell growth data and prediction of single-cell statistics. We also exploit these statistical relations in the development of a fast stochastic-simulation algorithm of single-cell growth and protein expression. This algorithm greatly reduces computational burden, by recovering the statistics of growing cell-populations from the simulation of only one of its lineages. Our approach is validated by comparison of simulations and experimental data. This work illustrates a methodology for the prediction, analysis and tests of consistency of single-cell growth and protein expression data from a few basic statistical principles.

Protein expression in a single cell depends on its global physiological state. Moreover, genetically-identical cells exhibit variability (noise) in protein expression, arising from the stochastic nature of biochemical processes, cell growth and division. While it is well understood how cellular growth rate influences mean protein expression, little is known about the relationship between growth rate and noise in protein expression. Here we quantify this relationship in Bacillus subtilis by a novel combination of experiments and theory. We measure the effects of promoter activity and growth rate on the expression of a fluorescent protein in single cells. We disentangle the observed protein expression noise into protein-specific and systemic contributions, using theory and variance decomposition. We find that noise in protein expression depends solely on mean expression levels, regardless of whether expression is set by promoter activity or growth rate, and that noise increases linearly with growth rate. Our results can aid studies of (synthetic) gene circuits of single cells and their condition dependence.

Natural selection has shaped the strategies for survival and growth of microorganisms. The success of microorganisms depends not only on slow evolutionary tuning but also on the ability to adapt to unpredictable changes in their environment. In principle, adaptive strategies range from purely deterministic mechanisms to those that exploit the randomness intrinsic to many cellular and molecular processes. Depending on the environment and selective pressures, particular strategies can lie somewhere along this continuum. In recent years, non-genetic cell-to-cell differences have received a lot of attention, not least because of their potential impact on the ability of microbial populations to survive in dynamic environments. Using several examples, we describe the origins of spontaneous and induced mechanisms of phenotypic adaptation. We identify some of the commonalities of these examples and consider the potential role of chance and constraints in microbial phenotypic adaptation., (© 2017 The Author(s).)

An important challenge in microbial ecology is to infer metabolic-exchange fluxes between growing microbial species from community-level data, concerning species abundances and metabolite concentrations. Here we apply a model-based approach to integrate such experimental data and thereby infer metabolic-exchange fluxes. We designed a synthetic anaerobic co-culture of Clostridium acetobutylicum and Wolinella succinogenes that interact via interspecies hydrogen transfer and applied different environmental conditions for which we expected the metabolic-exchange rates to change. We used stoichiometric models of the metabolism of the two microorganisms that represents our current physiological understanding and found that this understanding - the model - is sufficient to infer the identity and magnitude of the metabolic-exchange fluxes and it suggested unexpected interactions. Where the model could not fit all experimental data, it indicates specific requirement for further physiological studies. We show that the nitrogen source influences the rate of interspecies hydrogen transfer in the co-culture. Additionally, the model can predict the intracellular fluxes and optimal metabolic exchange rates, which can point to engineering strategies. This study therefore offers a realistic illustration of the strengths and weaknesses of model-based integration of heterogenous data that makes inference of metabolic-exchange fluxes possible from community-level experimental data.

Microbial communities are ubiquitously found in Nature and have direct implications for the environment, human health and biotechnology. The species composition and overall function of microbial communities are largely shaped by metabolic interactions such as competition for resources and cross-feeding. Although considerable scientific progress has been made towards mapping and modelling species-level metabolism, elucidating the metabolic exchanges between microorganisms and steering the community dynamics remain an enormous scientific challenge. In view of the complexity, computational models of microbial communities are essential to obtain systems-level understanding of ecosystem functioning. This review discusses the applications and limitations of constraint-based stoichiometric modelling tools, and in particular flux balance analysis (FBA). We explain this approach from first principles and identify the challenges one faces when extending it to communities, and discuss the approaches used in the field in view of these challenges. We distinguish between steady-state and dynamic FBA approaches extended to communities. We conclude that much progress has been made, but many of the challenges are still open., (© 2016 The Authors.)

Protein expression is shaped by evolutionary processes that tune microbial fitness. The limited biosynthetic capacity of a cell constrains protein expression and forces the cell to carefully manage its protein economy. In a chemostat, the physiology of the cell feeds back on the growth conditions, hindering intuitive understanding of how changes in protein concentration affect fitness. Here, we aim to provide a theoretical framework that addresses the selective pressures and optimal evolutionary-strategies in the chemostat. We show that the optimal enzyme levels are the result of a trade-off between the cost of their production and the benefit of their catalytic function. We also show that deviations from optimal enzyme levels are directly related to selection coefficients. The maximal fitness strategy for an organism in the chemostat is to express a well-defined metabolic subsystem known as an elementary flux mode. Using a coarse-grained, kinetic model of Saccharomyces cerevisiae's metabolism and growth, we illustrate that the dynamics and outcome of evolution in a chemostat can be very counter-intuitive: Strictly-respiring and strictly-fermenting strains can evolve from a common ancestor. This work provides a theoretical framework that relates a kinetic, mechanistic view on metabolism with cellular physiology and evolutionary dynamics in the chemostat.

Microbial growth can be characterized by a limited set of macroscopic parameters such as growth rate, biomass yield and substrate affinity. Different culturing protocols for laboratory evolution have been developed to select mutant strains that have one specific macroscopic growth parameter improved. Some of those mutant strains display tradeoffs between growth parameters and changed metabolic strategies, for example, a shift from respiration to fermentation. Here we discuss recent studies suggesting that metabolic strategies and growth parameter tradeoffs originate from a common set of physicochemical and cellular constraints, associated with the allocation of intracellular resources over biosynthetic processes, mostly protein synthesis. This knowledge will give insight in ecological and biological concepts and can be used for metabolic and evolutionary engineering strategies., (Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.)

The signal-transduction network of a mammalian cell integrates internal and external cues to initiate adaptive responses. Among the cell-surface receptors are the G protein-coupled receptors (GPCRs), which have remarkable signal-integrating capabilities. Binding of extracellular signals stabilizes intracellular-domain conformations that selectively activate intracellular proteins. Hereby, multiple signaling routes are activated simultaneously to degrees that are signal-combination dependent. Systems-biology studies indicate that signaling networks have emergent processing capabilities that go far beyond those of single proteins. Such networks are spatiotemporally organized and capable of gradual, oscillatory, all-or-none, and subpopulation-generating responses. Protein-protein interactions, generating feedback and feedforward circuitry, are generally required for these spatiotemporal phenomena. Understanding of information processing by signaling networks therefore requires network theories in addition to biochemical and biophysical concepts. Here we review some of the key signaling systems behaviors that have been discovered recurrently across signaling networks. We emphasize the role of GPCRs, so far underappreciated receptors in systems-biology research., (Copyright © 2015 by The American Society for Pharmacology and Experimental Therapeutics.)

Metabolism is generally required for cellular maintenance and for the generation of offspring under conditions that support growth. The rates, yields (efficiencies), adaptation time and robustness of metabolism are therefore key determinants of cellular fitness. For biotechnological applications and our understanding of the evolution of metabolism, it is necessary to figure out how the functional system properties of metabolism can be optimized, via adjustments of the kinetics and expression of enzymes, and by rewiring metabolism. The trade-offs that can occur during such optimizations then indicate fundamental limits to evolutionary innovations and bioengineering. In this paper, we review several theoretical and experimental findings about mechanisms for metabolic optimization.

Microorganisms rely on binding-protein assisted, active transport systems to scavenge for scarce nutrients. Several advantages of using binding proteins in such uptake systems have been proposed. However, a systematic, rigorous and quantitative analysis of the function of binding proteins is lacking. By combining knowledge of selection pressure and physiochemical constraints, we derive kinetic, thermodynamic, and stoichiometric properties of binding-protein dependent transport systems that enable a maximal import activity per amount of transporter. Under the hypothesis that this maximal specific activity of the transport complex is the selection objective, binding protein concentrations should exceed the concentration of both the scarce nutrient and the transporter. This increases the encounter rate of transporter with loaded binding protein at low substrate concentrations, thereby enhancing the affinity and specific uptake rate. These predictions are experimentally testable, and a number of observations confirm them., (© 2015 FEBS.)

Maximization of growth rate is an important fitness strategy for bacteria. Bacteria can achieve this by expressing proteins at optimal concentrations, such that resources are not wasted. This is exemplified for Escherichia coli by the increase of its ribosomal protein-fraction with growth rate, which precisely matches the increased protein synthesis demand. These findings and others have led to the hypothesis that E. coli aims to maximize its growth rate in environments that support growth. However, what kind of regulatory strategy is required for a robust, optimal adjustment of the ribosome concentration to the prevailing condition is still an open question. In the present study, we analyze the ppGpp-controlled mechanism of ribosome expression used by E. coli and show that this mechanism maintains the ribosomes saturated with its substrates. In this manner, overexpression of the highly abundant ribosomal proteins is prevented, and limited resources can be redirected to the synthesis of other growth-promoting enzymes. It turns out that the kinetic conditions for robust, optimal protein-partitioning, which are required for growth rate maximization across conditions, can be achieved with basic biochemical interactions. We show that inactive ribosomes are the most suitable 'signal' for tracking the intracellular nutritional state and for adjusting gene expression accordingly, as small deviations from optimal ribosome concentration cause a huge fractional change in ribosome inactivity. We expect to find this control logic implemented across fast-growing microbial species because growth rate maximization is a common selective pressure, ribosomes are typically highly abundant and thus costly, and the required control can be implemented by a small, simple network., (© 2015 The Authors FEBS Journal published by John Wiley & Sons Ltd on behalf of FEBS.)

Flux balance analysis (FBA) is one of the most often applied methods on genome-scale metabolic networks. Although FBA uniquely determines the optimal yield, the pathway that achieves this is usually not unique. The analysis of the optimal-yield flux space has been an open challenge. Flux variability analysis is only capturing some properties of the flux space, while elementary mode analysis is intractable due to the enormous number of elementary modes. However, it has been found by Kelk et al. (2012) that the space of optimal-yield fluxes decomposes into flux modules. These decompositions allow a much easier but still comprehensive analysis of the optimal-yield flux space. Using the mathematical definition of module introduced by Müller and Bockmayr (2013b), we discovered useful connections to matroid theory, through which efficient algorithms enable us to compute the decomposition into modules in a few seconds for genome-scale networks. Using that every module can be represented by one reaction that represents its function, in this article, we also present a method that uses this decomposition to visualize the interplay of modules. We expect the new method to replace flux variability analysis in the pipelines for metabolic networks.

Activation of eukaryotic transcription is an intricate process that relies on a multitude of regulatory proteins forming complexes on chromatin. Chromatin modifications appear to play a guiding role in protein-complex assembly on chromatin. Together, these processes give rise to stochastic, often bursting, transcriptional activity. Here we present a model of eukaryotic transcription that aims to integrate those mechanisms. We use stochastic and ordinary-differential-equation modeling frameworks to examine various possible mechanisms of gene regulation by multiple transcription factors. We find that the assembly of large transcription factor complexes on chromatin via equilibrium-binding mechanisms is highly inefficient and insensitive to concentration changes of single regulatory proteins. An alternative model that lacks these limitations is a cyclic ratchet mechanism. In this mechanism, small protein complexes assemble sequentially on the promoter. Chromatin modifications mark the completion of a protein complex assembly, and sensitize the local chromatin for the assembly of the next protein complex. In this manner, a strict order of protein complex assemblies is attained. Even though the individual assembly steps are highly stochastic in duration, a sequence of them gives rise to a remarkable precision of the transcription cycle duration. This mechanism explains how transcription activation cycles, lasting for tens of minutes, derive from regulatory proteins residing on chromatin for only tens of seconds. Transcriptional bursts are an inherent feature of such transcription activation cycles. Bursting transcription can cause individual cells to remain in synchrony transiently, offering an explanation of transcriptional cycling as observed in cell populations, both on promoter chromatin status and mRNA levels.

High-throughput data generation and genome-scale stoichiometric models have greatly facilitated the comprehensive study of metabolic networks. The computation of all feasible metabolic routes with these models, given stoichiometric, thermodynamic, and steady-state constraints, provides important insights into the metabolic capacities of a cell. How the feasible metabolic routes emerge from the interplay between flux constraints, optimality objectives, and the entire metabolic network of a cell is, however, only partially understood. We show how optimal metabolic routes, resulting from flux balance analysis computations, arise out of elementary flux modes, constraints, and optimization objectives. We illustrate our findings with a genome-scale stoichiometric model of Escherichia coli metabolism. In the case of one flux constraint, all feasible optimal flux routes can be derived from elementary flux modes alone. We found up to 120 million of such optimal elementary flux modes. We introduce a new computational method to compute the corner points of the optimal solution space fast and efficiently. Optimal flux routes no longer depend exclusively on elementary flux modes when we impose additional constraints; new optimal metabolic routes arise out of combinations of elementary flux modes. The solution space of feasible metabolic routes shrinks enormously when additional objectives---e.g. those related to pathway expression costs or pathway length---are introduced. In many cases, only a single metabolic route remains that is both feasible and optimal. This paper contributes to reaching a complete topological understanding of the metabolic capacity of organisms in terms of metabolic flux routes, one that is most natural to biochemists and biotechnologists studying and engineering metabolism.

Microbial communities play important roles in health, industrial applications and earth's ecosystems. With current molecular techniques we can characterize these systems in unprecedented detail. However, such methods provide little mechanistic insight into how the genetic properties and the dynamic couplings between individual microorganisms give rise to their dynamic activities. Neither do they give insight into what we call "the community state", that is the fluxes and concentrations of nutrients within the community. This knowledge is a prerequisite for rational control and intervention in microbial communities. Therefore, the inference of the community structure from experimental data is a major current challenge. We will argue that this inference problem requires mathematical models that can integrate heterogeneous experimental data with existing knowledge. We propose that two types of models are needed. Firstly, mathematical models that integrate existing genomic, physiological, and physicochemical information with metagenomics data so as to maximize information content and predictive power. This can be achieved with the use of constraint-based genome-scale stoichiometric modeling of community metabolism which is ideally suited for this purpose. Next, we propose a simpler coarse-grained model, which is tailored to solve the inference problem from the experimental data. This model unambiguously relate to the more detailed genome-scale stoichiometric models which act as heterogeneous data integrators. The simpler inference models are, in our opinion, key to understanding microbial ecosystems, yet until now, have received remarkably little attention. This has led to the situation where the modeling of microbial communities, using only genome-scale models is currently more a computational, theoretical exercise than a method useful to the experimentalist.