Dynamic coexistence driven by physiological transitions in microbial communities

Microbial ecosystems are commonly modeled by fixed interactions between species in steady exponential growth states. However, microbes often modify their environments so strongly that they are forced out of the exponential state into stressed or non-growing states. Such dynamics are typical of ecological succession in nature and serial-dilution cycles in the laboratory. Here, we introduce a phenomenological model, the Community State model, to gain insight into the dynamic coexistence of microbes due to changes in their physiological states. Our model bypasses specific interactions (e.g., nutrient starvation, stress, aggregation) that lead to different combinations of physiological states, referred to collectively as "community states", and modeled by specifying the growth preference of each species along a global ecological coordinate, taken here to be the total community biomass density. We identify three key features of such dynamical communities that contrast starkly with steady-state communities: increased tolerance of community diversity to fast growth rates of species dominating different community states, enhanced community stability through staggered dominance of different species in different community states, and increased requirement on growth dominance for the inclusion of late-growing species. These features, derived explicitly for simplified models, are proposed here to be principles aiding the understanding of complex dynamical communities. Our model shifts the focus of ecosystem dynamics from bottom-up studies based on idealized inter-species interaction to top-down studies based on accessible macroscopic observables such as growth rates and total biomass density, enabling quantitative examination of community-wide characteristics.

Dynamic coexistence driven by physiological transitions in microbial communities

Microbial ecosystems are commonly modeled by fixed interactions between species in steady exponential growth states. However, microbes often modify their environments so strongly that they are forced out of the exponential state into stressed or non-growing states. Such dynamics are typical of ecological succession in nature and serial-dilution cycles in the laboratory. Here, we introduce a phenomenological model, the Community State model, to gain insight into the dynamic coexistence of microbes due to changes in their physiological states. Our model bypasses specific interactions (e.g., nutrient starvation, stress, aggregation) that lead to different combinations of physiological states, referred to collectively as "community states", and modeled by specifying the growth preference of each species along a global ecological coordinate, taken here to be the total community biomass density. We identify three key features of such dynamical communities that contrast starkly with steady-state communities: increased tolerance of community diversity to fast growth rates of species dominating different community states, enhanced community stability through staggered dominance of different species in different community states, and increased requirement on growth dominance for the inclusion of late-growing species. These features, derived explicitly for simplified models, are proposed here to be principles aiding the understanding of complex dynamical communities. Our model shifts the focus of ecosystem dynamics from bottom-up studies based on idealized inter-species interaction to top-down studies based on accessible macroscopic observables such as growth rates and total biomass density, enabling quantitative examination of community-wide characteristics.

Inherited chitinases enable sustained growth and rapid dispersal of bacteria from chitin particles

Many biogeochemical functions involve bacteria utilizing solid substrates. However, little is known about the coordination of bacterial growth with the kinetics of attachment to and detachment from such substrates. In this quantitative study of Vibrio sp. 1A01 growing on chitin particles, we reveal the heterogeneous nature of the exponentially growing culture comprising two co-existing subpopulations: a minority replicating on chitin particles and a non-replicating majority which was planktonic. This partition resulted from a high rate of cell detachment from particles. Despite high detachment, sustained exponential growth of cells on particles was enabled by the enrichment of extracellular chitinases excreted and left behind by detached cells. The 'inheritance' of these chitinases sustains the colonizing subpopulation despite its reduced density. This simple mechanism helps to circumvent a trade-off between growth and dispersal, allowing particle-associated marine heterotrophs to explore new habitats without compromising their fitness on the habitat they have already colonized.

Functional decomposition of metabolism allows a system-level quantification of fluxes and protein allocation towards specific metabolic functions

Quantifying the contribution of individual molecular components to complex cellular processes is a grand challenge in systems biology. Here we establish a general theoretical framework (Functional Decomposition of Metabolism, FDM) to quantify the contribution of every metabolic reaction to metabolic functions, e.g. the synthesis of biomass building blocks. FDM allowed for a detailed quantification of the energy and biosynthesis budget for growing Escherichia coli cells. Surprisingly, the ATP generated during the biosynthesis of building blocks from glucose almost balances the demand from protein synthesis, the largest energy expenditure known for growing cells. This leaves the bulk of the energy generated by fermentation and respiration unaccounted for, thus challenging the common notion that energy is a key growth-limiting resource. Moreover, FDM together with proteomics enables the quantification of enzymes contributing towards each metabolic function, allowing for a first-principle formulation of a coarse-grained model of global protein allocation based on the structure of the metabolic network.

Stress-induced metabolic exchanges between complementary bacterial types underly a dynamic mechanism of inter-species stress resistance

Metabolic cross-feeding plays vital roles in promoting ecological diversity. While some microbes depend on exchanges of essential nutrients for growth, the forces driving the extensive cross-feeding needed to support the coexistence of free-living microbes are poorly understood. Here we characterize bacterial physiology under self-acidification and establish that extensive excretion of key metabolites following growth arrest provides a collaborative, inter-species mechanism of stress resistance. This collaboration occurs not only between species isolated from the same community, but also between unrelated species with complementary (glycolytic vs. gluconeogenic) modes of metabolism. Cultures of such communities progress through distinct phases of growth-dilution cycles, comprising of exponential growth, acidification-triggered growth arrest, collaborative deacidification, and growth recovery, with each phase involving different combinations of physiological states of individual species. Our findings challenge the steady-state view of ecosystems commonly portrayed in ecological models, offering an alternative dynamical view based on growth advantages of complementary species in different phases.

Shaping bacterial gene expression by physiological and proteome allocation constraints

Networks of molecular regulators are often the primary objects of focus in the study of gene regulation, with the machinery of protein synthesis tacitly relegated to the background. Shifting focus to the constraints imposed by the allocation of protein synthesis flux reveals surprising ways in which the actions of molecular regulators are shaped by physiological demands. Using carbon catabolite repression as a case study, we describe how physiological constraints are sensed through metabolic fluxes and how flux-controlled regulation gives rise to simple empirical relations between protein levels and the rate of cell growth.

Enzyme expression kinetics by Escherichia coli during transition from rich to minimal media depends on proteome reserves

Bacterial fitness depends on adaptability to changing environments. In rich growth medium, which is replete with amino acids, Escherichia coli primarily expresses protein synthesis machineries, which comprise ~40% of cellular proteins and are required for rapid growth. Upon transition to minimal medium, which lacks amino acids, biosynthetic enzymes are synthesized, eventually reaching ~15% of cellular proteins when growth fully resumes. We applied quantitative proteomics to analyse the timing of enzyme expression during such transitions, and established a simple positive relation between the onset time of enzyme synthesis and the fractional enzyme 'reserve' maintained by E. coli while growing in rich media. We devised and validated a coarse-grained kinetic model that quantitatively captures the enzyme recovery kinetics in different pathways, solely on the basis of proteomes immediately preceding the transition and well after its completion. Our model enables us to infer regulatory strategies underlying the 'as-needed' gene expression programme adopted by E. coli.

Principles of gene regulation quantitatively connect DNA to RNA and proteins in bacteria

Protein concentrations are set by a complex interplay between gene-specific regulatory processes and systemic factors, including cell volume and shared gene expression machineries. Elucidating this interplay is crucial for discerning and designing gene regulatory systems. We quantitatively characterized gene-specific and systemic factors that affect transcription and translation genome-wide for Escherichia coli across many conditions. The results revealed two design principles that make regulation of gene expression insulated from concentrations of shared machineries: RNA polymerase activity is fine-tuned to match translational output, and translational characteristics are similar across most messenger RNAs (mRNAs). Consequently, in bacteria, protein concentration is set primarily at the promoter level. A simple mathematical formula relates promoter activities and protein concentrations across growth conditions, enabling quantitative inference of gene regulation from omics data.

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.

Microbes contribute to setting the ocean carbon flux by altering the fate of sinking particulates

Sinking particulate organic carbon out of the surface ocean sequesters carbon on decadal to millennial timescales. Predicting the particulate carbon flux is therefore critical for understanding both global carbon cycling and the future climate. Microbes play a crucial role in particulate organic carbon degradation, but the impact of depth-dependent microbial dynamics on ocean-scale particulate carbon fluxes is poorly understood. Here we scale-up essential features of particle-associated microbial dynamics to understand the large-scale vertical carbon flux in the ocean. Our model provides mechanistic insight into the microbial contribution to the particulate organic carbon flux profile. We show that the enhanced transfer of carbon to depth can result from populations struggling to establish colonies on sinking particles due to diffusive nutrient loss, cell detachment, and mortality. These dynamics are controlled by the interaction between multiple biotic and abiotic factors. Accurately capturing particle-microbe interactions is essential for predicting variability in large-scale carbon cycling.

Micro-scale microbial community dynamics can substantially alter the fate of sinking particulates in the ocean thus playing a key role in setting the vertical flux of particulate carbon in the ocean.

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.

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.

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 (K_m). 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.

This study shows that in E. coli, the cellular mass of each metabolite approximately equals the combined mass of the free enzymes waiting to consume it; this simple relationship arises from the optimal utilization of cellular dry mass, and quantitatively describes available experimental data.

Hierarchical and simultaneous utilization of carbon substrates: mechanistic insights, physiological roles, and ecological consequences

Bacteria grown on a mixture of carbon substrates exhibit two utilization patterns: hierarchical utilization (HU) and simultaneous utilization (SU). How and why cells adopt these different behaviors remains poorly understood despite decades of research. Recent studies address various open questions from multiple viewpoints. From a mechanistic perspective, it was found that flux sensors play a central role in the regulation of substrate utilization, accounting for the known dependences on single-substrate growth rates, substrate concentrations, and the point where the substrate enters central metabolism. From a physiological perspective, several recent studies suggested HU or SU as growth-optimizing strategies through efficient allocation of essential proteome resources. However, other studies demonstrate that a significant fraction of the proteome is dedicated to functions apparently unnecessary for growth, casting doubt on explanations based on slight efficiency gains. From an ecological perspective, recent theoretical studies suggest that HU can help increase species diversity in bacterial communities.

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.

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.

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

The rate of cell growth is crucial for bacterial fitness and a main driver of proteome allocation^1,2, but it is unclear what ultimately determines growth rates in different environmental conditions. Increasing evidence suggests that other objectives also play key roles^3–7, such as the rate of physiological adaptation to changing environments^8,9. The challenge for cells is that these objectives often cannot be independently optimized, and maximizing one often reduces another. Many such tradeoffs have indeed been hypothesized, based on qualitative correlative studies^8–11. Here we report the occurrence of a tradeoff between steady-state growth rate and physiological adaptability for Escherichia coli, upon abruptly shifting a growing culture from a preferred carbon source to fermentation products such as acetate. Such transitions, common for enteric bacteria, are often accompanied by multi-hour lags before growth resumes. Metabolomic analysis revealed that the long lags resulted from the depletion of key metabolites due to the sudden reversal of central carbon flux imposed by these nutrient shifts. A model of sequential flux limitation not only explained the observed universal tradeoff between growth and adaptability, but also generated quantitative predictions that were validated experimentally. The observed trade-off reflects the opposing enzyme requirements for glycolysis versus gluconeogenesis.

Disruption of transcription-translation coordination in Escherichia coli leads to premature transcriptional termination

Tight coordination between transcription and translation is crucial to maintaining the integrity of gene expression in bacteria, yet how bacteria manage to coordinate these two processes remains unclear. Possible direct physical coupling between the RNA polymerase and ribosome has been thoroughly investigated in recent years. Here, we quantitatively characterize the transcriptional kinetics of Escherichia coli under different growth conditions. Transcriptional and translational elongation remain coordinated under various nutrient conditions, as previously reported. However, transcriptional elongation was not affected under antibiotics that slowed down translational elongation. This result was also found by introducing nonsense mutation that completely dissociated transcription from translation. Our data thus provide direct evidence that translation is not required to maintain the speed of transcriptional elongation. In cases where transcription and translation are dissociated, our study provides quantitative characterization of the resulting process of premature transcriptional termination (PTT). PTT-mediated polarity caused by translation-targeting antibiotics substantially affected the coordinated expression of genes in several long operons, contributing to the key physiological effects of these antibiotics. Our results also suggest a model in which the coordination between transcriptional and translational elongation under normal growth conditions is implemented by guanosine tetraphosphate.

Spatiotemporal establishment of dense bacterial colonies growing on hard agar

The physical interactions of growing bacterial cells with each other and with their surroundings significantly affect the structure and dynamics of biofilms. Here a 3D agent-based model is formulated to describe the establishment of simple bacterial colonies expanding by the physical force of their growth. With a single set of parameters, the model captures key dynamical features of colony growth by non-motile, non EPS-producing E. coli cells on hard agar. The model, supported by experiment on colony growth in different types and concentrations of nutrients, suggests that radial colony expansion is not limited by nutrients as commonly believed, but by mechanical forces. Nutrient penetration instead governs vertical colony growth, through thin layers of vertically oriented cells lifting up their ancestors from the bottom. Overall, the model provides a versatile platform to investigate the influences of metabolic and environmental factors on the growth and morphology of bacterial colonies.

Bacterial growth, flow, and mixing shape human gut microbiota density and composition

The human gut microbiota is highly dynamic, and host physiology and diet exert major influences on its composition. In our recent study, we integrated new quantitative measurements on bacterial growth physiology with a reanalysis of published data on human physiology to build a comprehensive modeling framework. This can generate predictions of how changes in different host factors influence microbiota composition. For instance, hydrodynamic forces in the colon, along with colonic water absorption that manifests as transit time, exert a major impact on microbiota density and composition. This can be mechanistically explained by their effect on colonic pH which directly affects microbiota competition for food. In this addendum, we describe the underlying analysis in more detail. In particular, we discuss the mixing dynamics of luminal content by wall contractions and its implications for bacterial growth and density, as well as the broader implications of our insights for the field of gut microbiota research.

Quantifying the benefit of a proteome reserve in fluctuating environments

The overexpression of proteins is a major burden for fast-growing bacteria. Paradoxically, recent characterization of the proteome of Escherichia coli found many proteins expressed in excess of what appears to be optimal for exponential growth. Here, we quantitatively investigate the possibility that this overexpression constitutes a strategic reserve kept by starving cells to quickly meet demand upon sudden improvement in growth conditions. For cells exposed to repeated famine-and-feast cycles, we derive a simple relation between the duration of feast and the allocation of the ribosomal protein reserve to maximize the overall gain in biomass during the feast.

Fast-growing bacteria produce many proteins in excess of what seems optimal for exponential growth. Here, the authors present a mathematical model and experimental evidence supporting that this overexpression serves as a strategic reserve to quickly meet demand upon sudden improvement in growth conditions.

Reduction of translating ribosomes enables Escherichia coli to maintain elongation rates during slow growth

Bacteria growing under different conditions experience a broad range of demand on the rate of protein synthesis, which profoundly affects cellular resource allocation. During fast growth, protein synthesis has long been known to be modulated by adjusting the ribosome content, with the vast majority of ribosomes engaged at a near-maximal rate of elongation. Here, we systematically characterize protein synthesis by Escherichia coli, focusing on slow-growth conditions. We establish that the translational elongation rate decreases as growth slows, exhibiting a Michaelis-Menten dependence on the abundance of the cellular translational apparatus. However, an appreciable elongation rate is maintained even towards zero growth, including the stationary phase. This maintenance, critical for timely protein synthesis in harsh environments, is accompanied by a drastic reduction in the fraction of active ribosomes. Interestingly, well-known antibiotics such as chloramphenicol also cause a substantial reduction in the pool of active ribosomes, instead of slowing down translational elongation as commonly thought.

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.

The intracellular protein levels of exponentially growing bacteria are known to vary strongly with growth conditions, as described by quantitative “growth laws”. This work introduces a computational genome-scale framework (Constrained Allocation Flux Balance Analysis, CAFBA) which incorporates growth laws into canonical Flux Balance Analysis. Upon introducing 3 parameters based on established growth laws for E. coli, CAFBA accurately reproduces empirical results on the growth-rate dependent rate of carbon overflow and growth yield, and generates testable predictions about cellular energetic strategies and protein expression levels. CAFBA therefore provides a simple, quantitative approach to balancing the trade-off between growth and its associated biosynthetic costs at genome-scale, without the burden of tuning many inaccessible parameters.

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 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 mysterious despite decades of research. Here we study metabolic overflow in E. 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 behaviors and accurately predict responses to novel 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.

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.

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.

Quantitative proteomic analysis reveals a simple strategy of global resource allocation in bacteria

A central aim of cell biology was to understand the strategy of gene expression in response to the environment. Here, we study gene expression response to metabolic challenges in exponentially growing Escherichia coli using mass spectrometry. Despite enormous complexity in the details of the underlying regulatory network, we find that the proteome partitions into several coarse-grained sectors, with each sector's total mass abundance exhibiting positive or negative linear relations with the growth rate. The growth rate-dependent components of the proteome fractions comprise about half of the proteome by mass, and their mutual dependencies can be characterized by a simple flux model involving only two effective parameters. The success and apparent generality of this model arises from tight coordination between proteome partition and metabolism, suggesting a principle for resource allocation in proteome economy of the cell. This strategy of global gene regulation should serve as a basis for future studies on gene expression and constructing synthetic biological circuits. Coarse graining may be an effective approach to derive predictive phenomenological models for other ‘omics’ studies.

Emergence of robust growth laws from optimal regulation of ribosome synthesis

Bacteria must constantly adapt their growth to changes in nutrient availability; yet despite large-scale changes in protein expression associated with sensing, adaptation, and processing different environmental nutrients, simple growth laws connect the ribosome abundance and the growth rate. Here, we investigate the origin of these growth laws by analyzing the features of ribosomal regulation that coordinate proteome-wide expression changes with cell growth in a variety of nutrient conditions in the model organism Escherichia coli. We identify supply-driven feedforward activation of ribosomal protein synthesis as the key regulatory motif maximizing amino acid flux, and autonomously guiding a cell to achieve optimal growth in different environments. The growth laws emerge naturally from the robust regulatory strategy underlying growth rate control, irrespective of the details of the molecular implementation. The study highlights the interplay between phenomenological modeling and molecular mechanisms in uncovering fundamental operating constraints, with implications for endogenous and synthetic design of microorganisms.

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.

Bacterial growth: global effects on gene expression, growth feedback and proteome partition

The function of endogenous as well as synthetic genetic circuits is generically coupled to the physiological state of the cell. For exponentially growing bacteria, a key characteristic of the state of the cell is the growth rate and thus gene expression is often growth-rate dependent. Here we review recent results on growth-rate dependent gene expression. We distinguish different types of growth-rate dependencies by the mechanisms of regulation involved and the presence or absence of an effect of the gene product on growth. The latter can lead to growth feedback, feedback mediated by changes of the global state of the cell. Moreover, we discuss how growth rate dependence can be used as a guide to study the molecular implementation of physiological regulation.

Direct coupling analysis for protein contact prediction

During evolution, structure, and function of proteins are remarkably conserved, whereas amino-acid sequences vary strongly between homologous proteins. Structural conservation constrains sequence variability and forces different residues to coevolve, i.e., to show correlated patterns of amino-acid occurrences. However, residue correlation may result from direct coupling, e.g., by a contact in the folded protein, or be induced indirectly via intermediate residues. To use empirically observed correlations for predicting residue-residue contacts, direct and indirect effects have to be disentangled. Here we present mechanistic details on how to achieve this using a methodology called Direct Coupling Analysis (DCA). DCA has been shown to produce highly accurate estimates of amino-acid pairs that have direct reciprocal constraints in evolution. Specifically, we provide instructions and protocols on how to use the algorithmic implementations of DCA starting from data extraction to predicted-contact visualization in contact maps or representative protein structures.

The innate growth bistability and fitness landscapes of antibiotic-resistant bacteria

To predict the emergence of antibiotic resistance, quantitative relations must be established between the fitness of drug-resistant organisms and the molecular mechanisms conferring resistance. These relations are often unknown and may depend on the state of bacterial growth. To bridge this gap, we have investigated Escherichia coli strains expressing resistance to translation-inhibiting antibiotics. We show that resistance expression and drug inhibition are linked in a positive feedback loop arising from an innate, global effect of drug-inhibited growth on gene expression. A quantitative model of bacterial growth based on this innate feedback accurately predicts the rich phenomena observed: a plateau-shaped fitness landscape, with an abrupt drop in the growth rates of cultures at a threshold drug concentration, and the coexistence of growing and nongrowing populations, that is, growth bistability, below the threshold.

Stripe formation in bacterial systems with density-suppressed motility

Engineered bacteria in which motility is reduced by local cell density generate periodic stripes of high and low density when spotted on agar plates. We study theoretically the origin and mechanism of this process in a kinetic model that includes growth and density-suppressed motility of the cells. The spreading of a region of immotile cells into an initially cell-free region is analyzed. From the calculated front profile we provide an analytic ansatz to determine the phase boundary between the stripe and the no-stripe phases. The influence of various parameters on the phase boundary is discussed.

Stripe formation in bacterial systems with density-suppressed motility

Engineered bacteria in which motility is reduced by local cell density generate periodic stripes of high and low density when spotted on agar plates. We study theoretically the origin and mechanism of this process in a kinetic model that includes growth and density-suppressed motility of the cells. The spreading of a region of immotile cells into an initially cell-free region is analyzed. From the calculated front profile we provide an analytic ansatz to determine the phase boundary between the stripe and the no-stripe phases. The influence of various parameters on the phase boundary is discussed.

Need-based activation of ammonium uptake in Escherichia coli

The efficient sequestration of nutrients is vital for the growth and survival of microorganisms. Some nutrients, such as CO2 and NH3, are readily diffusible across the cell membrane. The large membrane permeability of these nutrients obviates the need of transporters when the ambient level is high. When the ambient level is low, however, maintaining a high intracellular nutrient level against passive back diffusion is both challenging and costly. Here, we study the delicate management of ammonium (NH4+/NH3) sequestration by E. coli cells using microfluidic chemostats. We find that as the ambient ammonium concentration is reduced, E. coli cells first maximize their ability to assimilate the gaseous NH3 diffusing into the cytoplasm and then abruptly activate ammonium transport. The onset of transport varies under different growth conditions, but always occurring just as needed to maintain growth. Quantitative modeling of known interactions reveals an integral feedback mechanism by which this need-based uptake strategy is implemented. This novel strategy ensures that the expensive cost of upholding the internal ammonium concentration against back diffusion is kept at a minimum.

Speed, sensitivity, and bistability in auto-activating signaling circuits

Cells employ a myriad of signaling circuits to detect environmental signals and drive specific gene expression responses. A common motif in these circuits is inducible auto-activation: a transcription factor that activates its own transcription upon activation by a ligand or by post-transcriptional modification. Examples range from the two-component signaling systems in bacteria and plants to the genetic circuits of animal viruses such as HIV. We here present a theoretical study of such circuits, based on analytical calculations, numerical computations, and simulation. Our results reveal several surprising characteristics. They show that auto-activation can drastically enhance the sensitivity of the circuit's response to input signals: even without molecular cooperativity, an ultra-sensitive threshold response can be obtained. However, the increased sensitivity comes at a cost: auto-activation tends to severely slow down the speed of induction, a stochastic effect that was strongly underestimated by earlier deterministic models. This slow-induction effect again requires no molecular cooperativity and is intimately related to the bimodality recently observed in non-cooperative auto-activation circuits. These phenomena pose strong constraints on the use of auto-activation in signaling networks. To achieve both a high sensitivity and a rapid induction, an inducible auto-activation circuit is predicted to acquire low cooperativity and low fold-induction. Examples from Escherichia coli's two-component signaling systems support these predictions.

Different times call for different measures. Therefore, cells adjust their protein levels depending on their environment. Upon the detection of certain environmental signals, transcription factors are activated, which activate or inhibit the production of specific sets of proteins. As it turns out, these transcription factors often also stimulate their own production. Indeed, such self-regulation is a common motif in signal–response systems of many organisms, including bacteria, animals, plants and viruses–but its function is not well understood. We have used mathematical models to study its benefits and drawbacks. On the one hand, calculations show that self-regulation can be a very useful tool if the cell needs to respond in a sensitive way to changes in its environment, or if it is supposed to respond only if the signal exceeds a threshold level. On the other hand, these benefits come at a cost: self-regulation severely slows down the cell's response to changes in the environment. We have analyzed how the cell can benefit from the advantages of self-regulation, while mitigating the drawbacks. This leads to strict design constraints that examples from the bacterium E. coli indeed seem to obey.

Bacterial growth laws and their applications

Quantitative empirical relationships between cell composition and growth rate played an important role in the early days of microbiology. Gradually, the focus of the field began to shift from growth physiology to the ever more elaborate molecular mechanisms of regulation employed by the organisms. Advances in systems biology and biotechnology have renewed interest in the physiology of the cell as a whole. Furthermore, gene expression is known to be intimately coupled to the growth state of the cell. Here, we review recent efforts in characterizing such couplings, particularly the quantitative phenomenological approaches exploiting bacterial 'growth laws.' These approaches point toward underlying design principles that can guide the predictive manipulation of cell behavior in the absence of molecular details.

Dissecting the specificity of protein-protein interaction in bacterial two-component signaling: orphans and crosstalks

Predictive understanding of the myriads of signal transduction pathways in a cell is an outstanding challenge of systems biology. Such pathways are primarily mediated by specific but transient protein-protein interactions, which are difficult to study experimentally. In this study, we dissect the specificity of protein-protein interactions governing two-component signaling (TCS) systems ubiquitously used in bacteria. Exploiting the large number of sequenced bacterial genomes and an operon structure which packages many pairs of interacting TCS proteins together, we developed a computational approach to extract a molecular interaction code capturing the preferences of a small but critical number of directly interacting residue pairs. This code is found to reflect physical interaction mechanisms, with the strongest signal coming from charged amino acids. It is used to predict the specificity of TCS interaction: Our results compare favorably to most available experimental results, including the prediction of 7 (out of 8 known) interaction partners of orphan signaling proteins in Caulobacter crescentus. Surveying among the available bacterial genomes, our results suggest 15∼25% of the TCS proteins could participate in out-of-operon “crosstalks”. Additionally, we predict clusters of crosstalking candidates, expanding from the anecdotally known examples in model organisms. The tools and results presented here can be used to guide experimental studies towards a system-level understanding of two-component signaling.

Interdependence of cell growth and gene expression: origins and consequences

In bacteria, the rate of cell proliferation and the level of gene expression are intimately intertwined. Elucidating these relations is important both for understanding the physiological functions of endogenous genetic circuits and for designing robust synthetic systems. We describe a phenomenological study that reveals intrinsic constraints governing the allocation of resources toward protein synthesis and other aspects of cell growth. A theory incorporating these constraints can accurately predict how cell proliferation and gene expression affect one another, quantitatively accounting for the effect of translation-inhibiting antibiotics on gene expression and the effect of gratuitous protein expression on cell growth. The use of such empirical relations, analogous to phenomenological laws, may facilitate our understanding and manipulation of complex biological systems before underlying regulatory circuits are elucidated.

Sources and sinks: a stochastic model of evolution in heterogeneous environments

We study evolution driven by spatial heterogeneity in a stochastic model of source-sink ecologies. A sink is a habitat where mortality exceeds reproduction so that a local population persists only due to immigration from a source. Immigrants can, however, adapt to conditions in the sink by mutation. To characterize the adaptation rate, we derive expressions for the first arrival time of adapted mutants. The joint effects of migration, mutation, birth, and death result in two distinct parameter regimes. These results may pertain to the rapid evolution of drug-resistant pathogens and insects.

Reversible adenylylation of glutamine synthetase is dynamically counterbalanced during steady-state growth of Escherichia coli

Glutamine synthetase (GS) is the central enzyme for nitrogen assimilation in Escherichia coli and is subject to reversible adenylylation (inactivation) by a bifunctional GS adenylyltransferase/adenylyl-removing enzyme (ATase). In vitro, both of the opposing activities of ATase are regulated by small effectors, most notably glutamine and 2-oxoglutarate. In vivo, adenylyltransferase (AT) activity is critical for growth adaptation when cells are shifted from nitrogen-limiting to nitrogen-excess conditions and a rapid decrease of GS activity by adenylylation is needed. Here, we show that the adenylyl-removing (AR) activity of ATase is required to counterbalance its AT activity during steady-state growth under both nitrogen-excess and nitrogen-limiting conditions. This conclusion was established by studying AR(-)/AT(+) mutants, which surprisingly displayed steady-state growth defects in nitrogen-excess conditions due to excessive GS adenylylation. Moreover, GS was abnormally adenylylated in the AR(-) mutants even under nitrogen-limiting conditions, whereas there was little GS adenylylation in wild-type strains. Despite the importance of AR activity, we establish that AT activity is significantly regulated in vivo, mainly by the cellular glutamine concentration. There is good general agreement between quantitative estimates of AT regulation in vivo and results derived from previous in vitro studies except at very low AT activities. We propose additional mechanisms for the low AT activities in vivo. The results suggest that dynamic counterbalance by reversible covalent modification may be a general strategy for controlling the activity of enzymes such as GS, whose physiological output allows adaptation to environmental fluctuations.

Computational modeling of phosphotransfer complexes in two-component signaling

Two-component signal transduction systems enable cells in bacteria, fungi, and plants to react to extracellular stimuli. A sensor histidine kinase (SK) detects such stimuli with its sensor domains and transduces the input signals to a response regulator (RR) by trans-phosphorylation. This trans-phosphorylation reaction requires the formation of a complex formed by the two interacting proteins. The complex is stabilized by transient interactions. The nature of the transient interactions makes it challenging for experimental techniques to gain structural information. X-ray crystallography requires stable crystals, which are difficult to grow and stabilize. Similarly, the mere size of these systems proves problematic for NMR. Theoretical methods can, however, complement existing data. The statistical direct coupling analysis presented in the previous chapter reveals the interacting residues at the contact interface of the SK/RR pair. This information can be combined with the structures of the individual proteins in molecular dynamical simulation to generate structural models of the complex. The general approach, referred to as MAGMA, was tested on the sporulation phosphorelay phosphotransfer complex, the Spo0B/Spo0F pair, delivering crystal resolution accuracy. The MAGMA method is described here in a step-by-step explanation. The developed parameters are transferrable to other SK/RR 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).

Traffic patrol in the transcription of ribosomal RNA

Synthesis of ribosomal RNA (rRNA) is essential for fast cell growth and rRNA transcription is typically characterized by dense traffic of RNA polymerases along the rRNA genes. However, dense traffic is susceptible to traffic jams which may arise inevitably due to stochastic pausing of the polymerases. Based on recent theoretical and experimental results, we suggest that the "traffic viewpoint" provides a unique perspective towards understanding the control of ribosome synthesis in both bacterial and eukaryotic cells.

Small RNAs establish gene expression thresholds

The central role of small RNAs in regulating bacterial gene expression has been elucidated in the past years. Typically, small RNAs act via specific basepairing with target mRNAs, leading to modulation of translation initiation and mRNA stability. Quantitative studies suggest that small RNA regulation is characterized by unique features, which allow it to complement regulation at the transcriptional level. In particular, small RNAs are shown to establish a threshold for the expression of their target, providing safety mechanism against random fluctuations and transient signals. The threshold level is set by the transcription rate of the small RNA and can thus be modulated dynamically to reflect changing environmental conditions.

An integrated mechanobiochemical feedback mechanism describes chromosome motility from prometaphase to anaphase in mitosis

During mitosis, chromosomes undergo a series of movements while being end-on attached to the kinetochore microtubules (KMTs) from spindle poles. The mechanism underlying such movements and their physiological functions remains elusive. We describe a mechanobiochemical feedback model of chromosome motility. The key ingredient is a feedback mechanism between the local chemical reactions that control the dynamics of KMTs and the mechanical state of the chromosome via tension-sensitive proteins localized at the kinetochores. This model can recapitulate all of the essential and distinct features of chromosome motilities from prometaphase to anaphase in a coherent manner. We further show that this feedback mechanism provides robust and precise means of guiding the chromosome to the cell equator regardless of the initial conditions and uncertainty in velocity. Predictions of our model can be tested experimentally.

Co-evolving motions at protein-protein interfaces of two-component signaling systems identified by covariance analysis

Short-lived protein interactions determine signal transduction specificity among genetically amplified, structurally identical two-component signaling systems. Interacting protein pairs evolve recognition precision by varying residues at specific positions in the interaction surface consistent with constraints of charge, size, and chemical properties. Such positions can be detected by covariance analyses of two-component protein databases. Here, covariance is shown to identify a cluster of co-evolving dynamic residues in two-component proteins. NMR dynamics and structural studies of both wild-type and mutant proteins in this cluster suggest that motions serve to precisely arrange the site of phosphoryl transfer within the complex.