A universal trade-off between growth and lag in fluctuating environments.

The rate of cell growth is crucial for bacterial fitness and drives the allocation of bacterial resources, affecting, for example, the expression levels of proteins dedicated to metabolism and biosynthesis1,2. It is unclear, however, what ultimately determines growth rates in different environmental conditions. Moreover, increasing evidence suggests that other objectives are also important3-7, such as the rate of physiological adaptation to changing environments8,9. A common challenge for cells is that these objectives cannot be independently optimized, and maximizing one often reduces another. Many such trade-offs have indeed been hypothesized on the basis of qualitative correlative studies8-11. Here we report a trade-off between steady-state growth rate and physiological adaptability in Escherichia coli, observed when a growing culture is abruptly shifted from a preferred carbon source such as glucose to fermentation products such as acetate. These metabolic transitions, common for enteric bacteria, are often accompanied by multi-hour lags before growth resumes. Metabolomic analysis reveals that long lags result from the depletion of key metabolites that follows the sudden reversal in the central carbon flux owing to the imposed nutrient shifts. A model of sequential flux limitation not only explains the observed trade-off between growth and adaptability, but also allows quantitative predictions regarding the universal occurrence of such tradeoffs, based on the opposing enzyme requirements of glycolysis versus gluconeogenesis. We validate these predictions experimentally for many different nutrient shifts in E. coli, as well as for other respiro-fermentative microorganisms, including Bacillus subtilis and Saccharomyces cerevisiae.

Chemotaxis as a navigation strategy to boost range expansion.

Bacterial chemotaxis, the directed movement of cells along gradients of chemoattractants, is among the best-characterized subjects in molecular biology1-10, but much less is known about its physiological roles11. It is commonly seen as a starvation response when nutrients run out, or as an escape response from harmful situations12-16. Here we identify an alternative role of chemotaxis by systematically examining the spatiotemporal dynamics of Escherichia coli in soft agar12,17,18. Chemotaxis in nutrient-replete conditions promotes the expansion of bacterial populations into unoccupied territories well before nutrients run out in the current environment. Low levels of chemoattractants act as aroma-like cues in this process, establishing the direction and enhancing the speed of population movement along the self-generated attractant gradients. This process of navigated range expansion spreads faster and yields larger population gains than unguided expansion following the canonical Fisher-Kolmogorov dynamics19,20 and is therefore a general strategy to promote population growth in spatially extended, nutrient-replete environments.

An evolutionarily stable strategy to colonize spatially extended habitats.

The ability of a species to colonize newly available habitats is crucial to its overall fitness1-3. In general, motility and fast expansion are expected to be beneficial for colonization and hence for the fitness of an organism4-7. Here we apply an evolution protocol to investigate phenotypical requirements for colonizing habitats of different sizes during range expansion by chemotaxing bacteria8. Contrary to the intuitive expectation that faster is better, we show that there is an optimal expansion speed for a given habitat size. Our analysis showed that this effect arises from interactions among pioneering cells at the front of the expanding population, and revealed a simple, evolutionarily stable strategy for colonizing a habitat of a specific size: to expand at a speed given by the product of the growth rate and the habitat size. These results illustrate stability-to-invasion as a powerful principle for the selection of phenotypes in complex ecological processes.

Cellular perception of growth rate and the mechanistic origin of bacterial growth law.

Many cellular activities in bacteria are organized according to their growth rate. The notion that ppGpp measures the cell's growth rate is well accepted in the field of bacterial physiology. However, despite decades of interrogation and the identification of multiple molecular interactions that connects ppGpp to some aspects of cell growth, we lack a system-level, quantitative picture of how this alleged "measurement" is performed. Through quantitative experiments, we show that the ppGpp pool responds inversely to the rate of translational elongation in Escherichia coli. Together with its roles in inhibiting ribosome biogenesis and activity, ppGpp closes a key regulatory circuit that enables the cell to perceive and control the rate of its growth across conditions. The celebrated linear growth law relating the ribosome content and growth rate emerges as a consequence of keeping a supply of ribosome reserves while maintaining elongation rate in slow growth conditions. Further analysis suggests the elongation rate itself is detected by sensing the ratio of dwelling and translocating ribosomes, a strategy employed to collapse the complex, high-dimensional dynamics of the molecular processes underlying cell growth to perceive the physiological state of the whole.

Coordination of gene expression with cell size enables Escherichia coli to efficiently maintain motility across conditions.

To swim and navigate, motile bacteria synthesize a complex motility machinery involving flagella, motors, and a sensory system. A myriad of studies has elucidated the molecular processes involved, but less is known about the coordination of motility expression with cellular physiology: In Escherichia coli, motility genes are strongly up-regulated in nutrient-poor conditions compared to nutrient-replete conditions; yet a quantitative link to cellular motility has not been developed. Here, we systematically investigated gene expression, swimming behavior, cell growth, and available proteomics data across a broad spectrum of exponential growth conditions. Our results suggest that cells up-regulate the expression of motility genes at slow growth to compensate for reduction in cell size, such that the number of flagella per cell is maintained across conditions. The observed four or five flagella per cell is the minimum number needed to keep the majority of cells motile. This simple regulatory objective allows E. coli cells to remain motile across a broad range of growth conditions, while keeping the biosynthetic and energetic demands to establish and drive the motility machinery at the minimum needed. Given the strong reduction in flagella synthesis resulting from cell size increases at fast growth, our findings also provide a different physiological perspective on bacterial cell size control: A larger cell size at fast growth is an efficient strategy to increase the allocation of cellular resources to the synthesis of those proteins required for biomass synthesis and growth, while maintaining processes such as motility that are only needed on a per-cell basis.

On the optimality of the enzyme-substrate relationship in bacteria.

Much recent progress has been made to understand the impact of proteome allocation on bacterial growth; much less is known about the relationship between the abundances of the enzymes and their substrates, which jointly determine metabolic fluxes. Here, we report a correlation between the concentrations of enzymes and their substrates in Escherichia coli. We suggest this relationship to be a consequence of optimal resource allocation, subject to an overall constraint on the biomass density: For a cellular reaction network composed of effectively irreversible reactions, maximal reaction flux is achieved when the dry mass allocated to each substrate is equal to the dry mass of the unsaturated (or "free") enzymes waiting to consume it. Calculations based on this optimality principle successfully predict the quantitative relationship between the observed enzyme and metabolite abundances, parameterized only by molecular masses and enzyme-substrate dissociation constants (Km). The corresponding organizing principle provides a fundamental rationale for cellular investment into different types of molecules, which may aid in the design of more efficient synthetic cellular systems.

Growth rate-dependent global effects on gene expression in bacteria.

Bacterial gene expression depends not only on specific regulatory mechanisms, but also on bacterial growth, because important global parameters such as the abundance of RNA polymerases and ribosomes are all growth-rate dependent. Understanding of these global effects is necessary for a quantitative understanding of gene regulation and for the design of synthetic genetic circuits. We find that the observed growth-rate dependence of constitutive gene expression can be explained by a simple model using the measured growth-rate dependence of the relevant cellular parameters. More complex growth dependencies for genetic circuits involving activators, repressors, and feedback control were analyzed and verified experimentally with synthetic circuits. Additional results suggest a feedback mechanism mediated by general growth-dependent effects that does not require explicit gene regulation if the expressed protein affects cell growth. This mechanism can lead to growth bistability and promote the acquisition of important physiological functions such as antibiotic resistance and tolerance (persistence).

A traveling-wave solution for bacterial chemotaxis with growth.

Bacterial cells navigate their environment by directing their movement along chemical gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial populations into previously unoccupied territories. However, despite numerous experimental and theoretical studies on this classical topic, chemotaxis-driven population expansion is not understood in quantitative terms. Building on recent experimental progress, we here present a detailed analytical study that provides a quantitative understanding of how chemotaxis and cell growth lead to rapid and stable expansion of bacterial populations. We provide analytical relations that accurately describe the dependence of the expansion speed and density profile of the expanding population on important molecular, cellular, and environmental parameters. In particular, expansion speeds can be boosted by orders of magnitude when the environmental availability of chemicals relative to the cellular limits of chemical sensing is high. Analytical understanding of such complex spatiotemporal dynamic processes is rare. Our analytical results and the methods employed to attain them provide a mathematical framework for investigations of the roles of taxis in diverse ecological contexts across broad parameter regimes.

A global resource allocation strategy governs growth transition kinetics of Escherichia coli.

A grand challenge of systems biology is to predict the kinetic responses of living systems to perturbations starting from the underlying molecular interactions. Changes in the nutrient environment have long been used to study regulation and adaptation phenomena in microorganisms and they remain a topic of active investigation. Although much is known about the molecular interactions that govern the regulation of key metabolic processes in response to applied perturbations, they are insufficiently quantified for predictive bottom-up modelling. Here we develop a top-down approach, expanding the recently established coarse-grained proteome allocation models from steady-state growth into the kinetic regime. Using only qualitative knowledge of the underlying regulatory processes and imposing the condition of flux balance, we derive a quantitative model of bacterial growth transitions that is independent of inaccessible kinetic parameters. The resulting flux-controlled regulation model accurately predicts the time course of gene expression and biomass accumulation in response to carbon upshifts and downshifts (for example, diauxic shifts) without adjustable parameters. As predicted by the model and validated by quantitative proteomics, cells exhibit suboptimal recovery kinetics in response to nutrient shifts owing to a rigid strategy of protein synthesis allocation, which is not directed towards alleviating specific metabolic bottlenecks. Our approach does not rely on kinetic parameters, and therefore points to a theoretical framework for describing a broad range of such kinetic processes without detailed knowledge of the underlying biochemical reactions.

Global coordination of metabolic pathways in Escherichia coli by active and passive regulation.

Microorganisms adjust metabolic activity to cope with diverse environments. While many studies have provided insights into how individual pathways are regulated, the mechanisms that give rise to coordinated metabolic responses are poorly understood. Here, we identify the regulatory mechanisms that coordinate catabolism and anabolism in Escherichia coli. Integrating protein, metabolite, and flux changes in genetically implemented catabolic or anabolic limitations, we show that combined global and local mechanisms coordinate the response to metabolic limitations. To allocate proteomic resources between catabolism and anabolism, E. coli uses a simple global gene regulatory program. Surprisingly, this program is largely implemented by a single transcription factor, Crp, which directly activates the expression of catabolic enzymes and indirectly reduces the expression of anabolic enzymes by passively sequestering cellular resources needed for their synthesis. However, metabolic fluxes are not controlled by this regulatory program alone; instead, fluxes are adjusted mostly through passive changes in the local metabolite concentrations. These mechanisms constitute a simple but effective global regulatory program that coarsely partitions resources between different parts of metabolism while ensuring robust coordination of individual metabolic reactions.

Suboptimal resource allocation in changing environments constrains response and growth in bacteria.

To respond to fluctuating conditions, microbes typically need to synthesize novel proteins. As this synthesis relies on sufficient biosynthetic precursors, microbes must devise effective response strategies to manage depleting precursors. To better understand these strategies, we investigate the active response of Escherichia coli to changes in nutrient conditions, connecting transient gene expression to growth phenotypes. By synthetically modifying gene expression during changing conditions, we show how the competition by genes for the limited protein synthesis capacity constrains cellular response. Despite this constraint cells substantially express genes that are not required, trapping them in states where precursor levels are low and the genes needed to replenish the precursors are outcompeted. Contrary to common modeling assumptions, our findings highlight that cells do not optimize growth under changing environments but rather exhibit hardwired response strategies that may have evolved to promote fitness in their native environment. The constraint and the suboptimality of the cellular response uncovered provide a conceptual framework relevant for many research applications, from the prediction of evolution to the improvement of gene circuits in biotechnology.

From coarse to fine: the absolute Escherichia coli proteome under diverse growth conditions.

Accurate measurements of cellular protein concentrations are invaluable to quantitative studies of gene expression and physiology in living cells. Here, we developed a versatile mass spectrometric workflow based on data-independent acquisition proteomics (DIA/SWATH) together with a novel protein inference algorithm (xTop). We used this workflow to accurately quantify absolute protein abundances in Escherichia coli for > 2,000 proteins over > 60 growth conditions, including nutrient limitations, non-metabolic stresses, and non-planktonic states. The resulting high-quality dataset of protein mass fractions allowed us to characterize proteome responses from a coarse (groups of related proteins) to a fine (individual) protein level. Hereby, a plethora of novel biological findings could be elucidated, including the generic upregulation of low-abundant proteins under various metabolic limitations, the non-specificity of catabolic enzymes upregulated under carbon limitation, the lack of large-scale proteome reallocation under stress compared to nutrient limitations, as well as surprising strain-dependent effects important for biofilm formation. These results present valuable resources for the systems biology community and can be used for future multi-omics studies of gene regulation and metabolic control in E. coli.

Overflow metabolism in Escherichia coli results from efficient proteome allocation.

Overflow metabolism refers to the seemingly wasteful strategy in which cells use fermentation instead of the more efficient respiration to generate energy, despite the availability of oxygen. Known as the Warburg effect in the context of cancer growth, this phenomenon occurs ubiquitously for fast-growing cells, including bacteria, fungi and mammalian cells, but its origin has remained unclear despite decades of research. Here we study metabolic overflow in Escherichia coli, and show that it is a global physiological response used to cope with changing proteomic demands of energy biogenesis and biomass synthesis under different growth conditions. A simple model of proteomic resource allocation can quantitatively account for all of the observed behaviours, and accurately predict responses to new perturbations. The key hypothesis of the model, that the proteome cost of energy biogenesis by respiration exceeds that by fermentation, is quantitatively confirmed by direct measurement of protein abundances via quantitative mass spectrometry.

Effect of water flow and chemical environment on microbiota growth and composition in the human colon.

The human gut harbors a dynamic microbial community whose composition bears great importance for the health of the host. Here, we investigate how colonic physiology impacts bacterial growth, which ultimately dictates microbiota composition. Combining measurements of bacterial physiology with analysis of published data on human physiology into a quantitative, comprehensive modeling framework, we show how water flow in the colon, in concert with other physiological factors, determine the abundances of the major bacterial phyla. Mechanistically, our model shows that local pH values in the lumen, which differentially affect the growth of different bacteria, drive changes in microbiota composition. It identifies key factors influencing the delicate regulation of colonic pH, including epithelial water absorption, nutrient inflow, and luminal buffering capacity, and generates testable predictions on their effects. Our findings show that a predictive and mechanistic understanding of microbial ecology in the gut is possible. Such predictive understanding is needed for the rational design of intervention strategies to actively control the microbiota.

Coordination of bacterial proteome with metabolism by cyclic AMP signalling.

The cyclic AMP (cAMP)-dependent catabolite repression effect in Escherichia coli is among the most intensely studied regulatory processes in biology. However, the physiological function(s) of cAMP signalling and its molecular triggers remain elusive. Here we use a quantitative physiological approach to show that cAMP signalling tightly coordinates the expression of catabolic proteins with biosynthetic and ribosomal proteins, in accordance with the cellular metabolic needs during exponential growth. The expression of carbon catabolic genes increased linearly with decreasing growth rates upon limitation of carbon influx, but decreased linearly with decreasing growth rate upon limitation of nitrogen or sulphur influx. In contrast, the expression of biosynthetic genes showed the opposite linear growth-rate dependence as the catabolic genes. A coarse-grained mathematical model provides a quantitative framework for understanding and predicting gene expression responses to catabolic and anabolic limitations. A scheme of integral feedback control featuring the inhibition of cAMP signalling by metabolic precursors is proposed and validated. These results reveal a key physiological role of cAMP-dependent catabolite repression: to ensure that proteomic resources are spent on distinct metabolic sectors as needed in different nutrient environments. Our findings underscore the power of quantitative physiology in unravelling the underlying functions of complex molecular signalling networks.

Effect of flow and peristaltic mixing on bacterial growth in a gut-like channel.

The ecology of microbes in the gut has been shown to play important roles in the health of the host. To better understand microbial growth and population dynamics in the proximal colon, the primary region of bacterial growth in the gut, we built and applied a fluidic channel that we call the "minigut." This is a channel with an array of membrane valves along its length, which allows mimicking active contractions of the colonic wall. Repeated contraction is shown to be crucial in maintaining a steady-state bacterial population in the device despite strong flow along the channel that would otherwise cause bacterial washout. Depending on the flow rate and the frequency of contractions, the bacterial density profile exhibits varying spatial dependencies. For a synthetic cross-feeding community, the species abundance ratio is also strongly affected by mixing and flow along the length of the device. Complex mixing dynamics due to contractions is described well by an effective diffusion term. Bacterial dynamics is captured by a simple reaction-diffusion model without adjustable parameters. Our results suggest that flow and mixing play a major role in shaping the microbiota of the colon.

Constrained Allocation Flux Balance Analysis.

New experimental results on bacterial growth inspire a novel top-down approach to study cell metabolism, combining mass balance and proteomic constraints to extend and complement Flux Balance Analysis. We introduce here Constrained Allocation Flux Balance Analysis, CAFBA, in which the biosynthetic costs associated to growth are accounted for in an effective way through a single additional genome-wide constraint. Its roots lie in the experimentally observed pattern of proteome allocation for metabolic functions, allowing to bridge regulation and metabolism in a transparent way under the principle of growth-rate maximization. We provide a simple method to solve CAFBA efficiently and propose an "ensemble averaging" procedure to account for unknown protein costs. Applying this approach to modeling E. coli metabolism, we find that, as the growth rate increases, CAFBA solutions cross over from respiratory, growth-yield maximizing states (preferred at slow growth) to fermentative states with carbon overflow (preferred at fast growth). In addition, CAFBA allows for quantitatively accurate predictions on the rate of acetate excretion and growth yield based on only 3 parameters determined by empirical growth laws.

Predicting the spatiotemporal dynamics of hair follicle patterns in the developing mouse.

Reaction-diffusion models have been used as a paradigm for describing the de novo emergence of biological patterns such as stripes and spots. In many organisms, these initial patterns are typically refined and elaborated over the subsequent course of development. Here we study the formation of secondary hair follicle patterns in the skin of developing mouse embryos. We used the expression of sex-determining region Y box 2 to identify and distinguish the primary and secondary hair follicles and to infer the spatiotemporal dynamics of the follicle formation process. Quantitative analysis of the specific follicle patterns observed reveals a simple geometrical rule governing the formation of secondary follicles, and motivates an expansion-induction (EI) model in which new follicle formation is driven by the physical growth of the embryo. The EI model requires only one diffusible morphogen and provides quantitative, accurate predictions on the relative positions and timing of secondary follicle formation, using only the observed configuration of primary follicles as input. The same model accurately describes the positions of additional follicles that emerge from skin explants treated with an activator. Thus, the EI model provides a simple and robust mechanism for predicting secondary space-filling patterns in growing embryos.

A growth-rate composition formula for the growth of E.coli on co-utilized carbon substrates.

When bacteria are cultured in medium with multiple carbon substrates, they frequently consume these substrates simultaneously. Building on recent advances in the understanding of metabolic coordination exhibited by Escherichia coli cells through cAMP-Crp signaling, we show that this signaling system responds to the total carbon-uptake flux when substrates are co-utilized and derive a mathematical formula that accurately predicts the resulting growth rate, based only on the growth rates on individual substrates.

Inflating bacterial cells by increased protein synthesis.

Understanding how the homeostasis of cellular size and composition is accomplished by different organisms is an outstanding challenge in biology. For exponentially growing Escherichia coli cells, it is long known that the size of cells exhibits a strong positive relation with their growth rates in different nutrient conditions. Here, we characterized cell sizes in a set of orthogonal growth limitations. We report that cell size and mass exhibit positive or negative dependences with growth rate depending on the growth limitation applied. In particular, synthesizing large amounts of "useless" proteins led to an inversion of the canonical, positive relation, with slow growing cells enlarged 7- to 8-fold compared to cells growing at similar rates under nutrient limitation. Strikingly, this increase in cell size was accompanied by a 3- to 4-fold increase in cellular DNA content at slow growth, reaching up to an amount equivalent to ~8 chromosomes per cell. Despite drastic changes in cell mass and macromolecular composition, cellular dry mass density remained constant. Our findings reveal an important role of protein synthesis in cell division control.