Effective bet-hedging through growth rate dependent stability.

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.

Trade-offs between the instantaneous growth rate and long-term fitness: Consequences for microbial physiology and predictive computational models.

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.

Single-cell imaging of ERK and Akt activation dynamics and heterogeneity induced by G-protein-coupled receptors.

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.

Population-level transcription cycles derive from stochastic timing of single-cell transcription.

Eukaryotic transcription is a dynamic process relying on a large number of proteins. By measuring the cycling expression of the pyruvate dehydrogenase kinase 4 gene in human cells, we constructed a detailed stochastic model for single-gene transcription at the molecular level using realistic kinetics for diffusion and protein complex dynamics. We observed that gene induction caused an approximate 60 min periodicity of several transcription related processes: first, the covalent histone modifications and presence of many regulatory proteins at the transcription start site; second, RNA polymerase II activity; third, chromatin loop formation; and fourth, mRNA accumulation. Our model can predict the precise timing of single-gene activity leading to transcriptional cycling on the cell population level when we take into account the sequential and irreversible multistep nature of transcriptional initiation. We propose that the cyclic nature of population gene expression is primarily based on the intrinsic periodicity of the transcription process itself.

Selection for Cell Yield Does Not Reduce Overflow Metabolism in Escherichia coli.

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.

Elementary Growth Modes provide a molecular description of cellular self-fabrication.

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.

The common message of constraint-based optimization approaches: overflow metabolism is caused by two growth-limiting constraints.

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.

The number of active metabolic pathways is bounded by the number of cellular constraints at maximal metabolic rates.

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.

The Fundamental Equations of Change in Statistical Ensembles and Biological Populations.

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.

Adaption to glucose limitation is modulated by the pleotropic regulator CcpA, independent of selection pressure strength.

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.

Metabolic enzyme cost explains variable trade-offs between microbial growth rate and yield.

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.

Maintaining maximal metabolic flux by gene expression control.

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.

Multi-tasking of biosynthetic and energetic functions of glycolysis explained by supply and demand logic.

After more than a century of research on glycolysis, we have detailed descriptions of its molecular organization, but despite this wealth of knowledge, linking the enzyme properties to metabolic pathway behavior remains challenging. These challenges arise from multi-layered regulation and the context and time dependence of component functions. However, when viewed as a system that functions according to the principles of supply and demand, a simplifying theoretical framework can be applied to study its regulation logic and to assess the coherence of experimental interpretations. These principles are universally applicable, as they emphasize the common metabolic tasks of glycolysis: the provision of free-energy carriers, and precursors for biosynthesis and stress-related compounds. Here we will review the regulation of multi-tasking by glycolysis and consider how an understanding of this central metabolic pathway can be pursued using general principles, rather than focusing on the biochemical details of constituent components.

Tracing the molecular basis of transcriptional dynamics in noisy data by using an experiment-based mathematical model.

Changes in transcription factor levels, epigenetic status, splicing kinetics and mRNA degradation can each contribute to changes in the mRNA dynamics of a gene. We present a novel method to identify which of these processes is changed in cells in response to external signals or as a result of a diseased state. The method employs a mathematical model, for which the kinetics of gene regulation, splicing, elongation and mRNA degradation were estimated from experimental data of transcriptional dynamics. The time-dependent dynamics of several species of adipose differentiation-related protein (ADRP) mRNA were measured in response to ligand activation of the transcription factor peroxisome proliferator-activated receptor δ (PPARδ). We validated the method by monitoring the mRNA dynamics upon gene activation in the presence of a splicing inhibitor. Our mathematical model correctly identifies splicing as the inhibitor target, despite the noise in the data.

Interplay between constraints, objectives, and optimality for genome-scale stoichiometric models.

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.

Multiplex Eukaryotic Transcription (In)activation: Timing, Bursting and Cycling of a Ratchet Clock Mechanism.

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.

A data integration and visualization resource for the metabolic network of Synechocystis sp. PCC 6803.

Data integration is a central activity in systems biology. The integration of genomic, transcript, protein, metabolite, flux, and computational data yields unprecedented information about the system level functioning of organisms. Often, data integration is done purely computationally, leaving the user with little insight in addition to statistical information. In this article, we present a visualization tool for the metabolic network of Synechocystis sp. PCC 6803, an important model cyanobacterium for sustainable biofuel production. We illustrate how this metabolic map can be used to integrate experimental and computational data for Synechocystis sp. PCC 6803 systems biology and metabolic engineering studies. Additionally, we discuss how this map, and the software infrastructure that we supply with it, can be used in the development of other organism-specific metabolic network visualizations. In addition to the Python console package VoNDA (http://vonda.sf.net), we provide a working demonstration of the interactive metabolic map and the associated Synechocystis sp. PCC 6803 genome-scale stoichiometric model, as well as various ready-to-visualize microarray data sets, at http://f-a-m-e.org/synechocytis.

Contributions of cell growth and biochemical reactions to nongenetic variability of cells.

Cell-to-cell variability in the molecular composition of isogenic, steady-state growing cells arises spontaneously from the inherent stochasticity of intracellular biochemical reactions and cell growth. Here, we present a general decomposition of the total variance in the copy number per cell of a particular molecule. It quantifies the individual contributions made by processes associated with cell growth, biochemical reactions, and their control. We decompose the growth contribution further into variance contributions of random partitioning of molecules at cell division, mother-cell heterogeneity, and variation in cell-cycle progression. The contribution made by biochemical reactions is expressed in variance generated by molecule synthesis, degradation, and their regulation. We use this theory to study the influence of different growth and reaction-related processes, such as DNA replication, variable molecule-partitioning probability, and synthesis bursts, on stochastic cell-to-cell variability. Using simulations, we characterize the impact of noise in the generation-time on cell-to-cell variability. This article offers a widely-applicable theory on the influence of biochemical reactions and cellular growth on the phenotypic variability of growing, isogenic cells. The theory aids the design and interpretation of experiments involving single-molecule counting or real-time imaging of fluorescent reporter constructs.

Understanding and computational design of genetic circuits of metabolic networks.

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.

Harnessing noncanonical redox cofactors to advance synthetic assimilation of one-carbon feedstocks.

One-carbon (C1) feedstocks, such as carbon monoxide (CO), formate (HCO2H), methanol (CH3OH), and methane (CH4), can be obtained either through stepwise electrochemical reduction of CO2 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.