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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., Nature Communications, 14 (1), ISSN:2041-1723

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.

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.

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., Nature Communications, 13 (1), ISSN:2041-1723

Bacteria allocate their proteome to cellular functions differently in different growth conditions. It is largely unknown how such allocation arises from known mechanisms of gene regulation while constrained by limited translation capacity and fixed protein density. Here, we performed absolute transcriptomic and proteomic analysis forE. coliacross many conditions, obtaining a plethora of results on promoters and mRNAs characteristics that clash with conventional expectations: the majority of mRNAs exhibit similar translational efficiencies, while the promoter strengths are vastly different across genes. These characteristics prescribe two principles of gene regulation guiding bacteria to attain the desired protein allocation under global constraints: Total transcriptional output is tightly coordinated with ribosomal activity, and the concentrations of individual proteins are largely set by transcription. These two principles lead to a quantitative formulation of Central Dogma which unravels the complex relationship between gene regulatory activities and mRNA/protein concentrations across conditions. The knowledge obtained will be invaluable for accurately inferring gene regulatory interactions from ‘omics data, as well as for guiding the design of genetic circuits for synthetic biology applications inE. coliand other organisms.

Significance Motility is one of the most striking bacterial behaviors common among many species. Motile bacteria can expand rapidly into previously unoccupied habitats, thus increasing fitness. Fast expansion is fostered by the sensing of gradients which the bacteria generate themselves and is further boosted by cell growth. Here we analyze the integrated dynamics of these processes mathematically. The relations obtained provide an analytical description of the expansion process and its dependence on core bacterial and environmental characteristics, like the growth rate, the abundance of chemical attractants in the surroundings, and the detection limit of the attractants., 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.

International audience; Bacterial chemotaxis, the directed movement of cells along gradients of chemoattractants, is among the best-characterized subjects in molecular biology1,2,3,4,5,6,7,8,9,10, 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 situations12,13,14,15,16. 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.

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.

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.

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.

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.

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 long-standing problem in molecular biology is the determination of a complete functional conformational landscape of proteins. This includes not only proteins' native structures, but also all their respective functional states, including functionally important intermediates. Here, we reveal a signature of functionally important states in several protein families, using direct coupling analysis, which detects residue pair coevolution of protein sequence composition. This signature is exploited in a protein structure-based model to uncover conformational diversity, including hidden functional configurations. We uncovered, with high resolution (mean ~1.9 Å rmsd for nonapo structures), different functional structural states for medium to large proteins (200-450 aa) belonging to several distinct families. The combination of direct coupling analysis and the structure-based model also predicts several intermediates or hidden states that are of functional importance. This enhanced sampling is broadly applicable and has direct implications in protein structure determination and the design of ligands or drugs to trap intermediate states.

Bacterial growth is crucially dependent on protein synthesis and thus on the cellular abundance of ribosomes and related proteins. Here, we show that the slow diffusion of the bulky tRNA complexes in the crowded cytoplasm imposes a physical limit on the speed of translation, which ultimately limits the rate of cell growth. To study the required allocation of ancillary translational proteins to alleviate the effect of molecular crowding, we develop a model for cell growth based on a coarse-grained partitioning of the proteome. We find that coregulation of ribosome- and tRNA-affiliated proteins is consistent with measured growth-rate dependencies and results in near-optimal allocation over a broad range of growth rates. The analysis further resolves a long-standing controversy in bacterial growth physiology concerning the growth-rate dependence of translation speed and serves as a caution against premature identification of phenomenological parameters with mechanistic processes.

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.

Theory of Growth Control Although quantitative studies of growth in bacterial cultures have been made for over 50 years, the relationship between cell proliferation and gene expression has not been clear. Scott et al. (p. 1099 ; see the Perspective by Lerman and Palsson ) have revealed that mass per cell exponentially increased with linear increases in growth rate and that ribosome abundance increased linearly with growth rate depending on the rate of translation. Hence, the systems properties of the biological processes involved in growth can be derived without any molecular understanding of their basis and can be used to establish fundamental properties for the design of biotechnological procedures.

Bacteria use two-component signal transduction systems (TCS) extensively to sense and react to external stimuli. In these, a membrane-bound sensor histidine kinase (SK) autophosphorylates in response to an environmental stimulus and transfers the phosphoryl group to a transcription factor/response regulator (RR) that mediates the cellular response. The complex between these two proteins is ruled by transient interactions, which provides a challenge to experimental structure determination techniques. The functional and structural homolog of an SK/RR pair Spo0B/Spo0F, however, has been structurally resolved. Here, we describe a method capable of generating structural models of such transient protein complexes. By using existing structures of the individual proteins, our method combines bioinformatically derived contact residue information with molecular dynamics simulations. We find crystal resolution accuracy with existing crystallographic data when reconstituting the known system Spo0B/Spo0F. Using this approach, we introduce a complex structure of TM0853/TM0468 as an exemplary SK/RR TCS, consistent with all experimentally available data.

Microorganisms employ a wealth of gene regulatory mechanisms to adjust their growth programs to variations in the environment. It was pointed out long ago [Savageau M (1977) Proc Natl Acad Sci USA 74 : 5647–5651] that the particular mode of gene regulation employed may be correlated with the “demand” on the regulated gene, i.e., how frequently the gene product is needed in its natural habitat. An evolutionary “use-it-or-lose-it” principle was proposed to govern the choice of gene regulatory strategies. Here, we examine quantitatively the forces selecting for and against two opposing modes of gene regulation, in the context of an evolutionary model that takes genetic drift, mutation, and time-dependent selection into account. We consider the effect of time-dependent selection, with periods of strong selection alternating with periods of neutral evolution. Using a variety of analytical methods, we find the effective population size and the typical time scale of environmental variations to be key parameters determining the fitness advantage of the different modes of regulation. Our results support Savageau's use-it-or-lose-it principle for small populations with long time scales of environmental variations and support a complementary “wear-and-tear” principle for the opposite situation.

In fast growing bacteria, ribosomal RNA (rRNA) is required to be transcribed at very high rates to sustain the high cellular demand on ribosome synthesis. This results in dense traffic of RNA polymerases (RNAP). We developed a stochastic model, integrating results of single-molecule and quantitative in vivo studies of E. coli, to evaluate the quantitative effect of pausing, termination, and antitermination on rRNA transcription. Our calculations reveal that in dense RNAP traffic, spontaneous pausing of RNAP can lead to severe "traffic jams", as manifested in the broad distribution of inter-RNAP distances and can be a major factor limiting transcription and hence growth. Our results suggest the suppression of these pauses by the ribosomal antitermination complex to be essential at fast growth. Moreover, unsuppressed pausing by even a few non-antiterminated RNAPs can already reduce transcription drastically under dense traffic. However, the termination factor Rho can remove the non-antiterminated RNAPs and restore fast transcription. The results thus suggest an intriguing role by Rho to enhance rather than attenuate rRNA transcription., includes Supporting Information

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.

Cells receive a wide variety of cellular and environmental signals, which are often processed combinatorially to generate specific genetic responses. Here we explore theoretically the potentials and limitations of combinatorial signal integration at the level of cis-regulatory transcription control. Our analysis suggests that many complex transcription-control functions of the type encountered in higher eukaryotes are already implementable within the much simpler bacterial transcription system. Using a quantitative model of bacterial transcription and invoking only specific protein–DNA interaction and weak glue-like interaction between regulatory proteins, we show explicit schemes to implement regulatory logic functions of increasing complexity by appropriately selecting the strengths and arranging the relative positions of the relevant protein-binding DNA sequences in the cis-regulatory region. The architectures that emerge are naturally modular and evolvable. Our results suggest that the transcription regulatory apparatus is a “programmable” computing machine, belonging formally to the class of Boltzmann machines. Crucial to our results is the ability to regulate gene expression at a distance. In bacteria, this can be achieved for isolated genes via DNA looping controlled by the dimerization of DNA-bound proteins. However, if adopted extensively in the genome, long-distance interaction can cause unintentional intergenic cross talk, a detrimental side effect difficult to overcome by the known bacterial transcription-regulation systems. This may be a key factor limiting the genome-wide adoption of complex transcription control in bacteria. Implications of our findings for combinatorial transcription control in eukaryotes are discussed.

Introduction Understanding how bacteria harboring antibiotic resistance grow in the presence of antibiotics is critical for predicting the spread and evolution of drug resistance. Because drugs inhibit cell growth and a cell’s growth state globally influences its gene expression, the expression of drug resistance is subject to an innate, growth-mediated feedback, leading to complex behaviors that affect both the characterization and the prevention of antibiotic resistance. We characterized the consequences of this feedback for the growth of antibiotic-resistant bacteria. Methods We studied the growth of Escherichia coli strains expressing resistance to translation-inhibiting antibiotics, by using both bulk and single-cell techniques. The growth of each strain was quantified in a broad range of drug concentrations by using time-lapse microscopy (to track the responses of individual cells to antibiotics inside a microfluidic chemostat) and by the enrichment of batch cultures for nongrowing cells. We formulated a quantitative phenomenological model to predict the growth rates of drug-resistant strains in the presence of drugs, based on the well-characterized biochemistry of drug and drug-resistance interactions and on bacterial growth laws that dictate relations between cell growth and gene expression. We tested the model predictions for various drugs and resistance mechanisms by constructing strains that constitutively express varying degrees of drug resistance. Results In strains expressing a moderate degree of drug resistance, growth rates dropped abruptly above a critical drug concentration, the minimum inhibitory concentration (MIC), whose value increased linearly with the basal level of resistance expression (see figure below, panel A). Cells exhibited growth bistability over a broad range of drug concentrations below the MIC: Isogenic cells expressing drug resistance coexisted in growing and nongrowing states in a homogeneous environment (panel B). Our model accurately predicted the range of drug concentrations in which growth bistability occurred, as well as the growth rates of the growing subpopulation, without any ad hoc fitting parameters. These findings reveal a plateau-like fitness landscape (panel A), which can be used to study the evolution of drug resistance in environments with varying drug concentrations. Discussion The broad occurrence of growth bistability in drug-resistant bacteria challenges the common notions and measures of drug efficacy and resistance. And because growth bistability can arise without complex regulation when gene expression is coupled to the state of cell growth, similar physiological links may underlie the growth bistability implicated in causing bacterial persistence. The availability of quantitative, predictive models will facilitate the formulation of strategies to limit the efficacy and evolvability of drug resistance.

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.

The rapid emergence of bacterial strains resistant to multiple antibiotics is posing a growing public health risk. The mechanisms underlying the rapid evolution of drug resistance are, however, poorly understood. The heterogeneity of the environments in which bacteria encounter antibiotic drugs could play an important role. E.g., in the highly compartmentalized human body, drug levels can vary substantially between different organs and tissues. It has been proposed that this could facilitate the selection of resistant mutants, and recent experiments support this. To study the role of spatial heterogeneity in the evolution of drug resistance, we present a quantitative model describing an environment subdivided into relatively isolated compartments with various antibiotic concentrations, in which bacteria evolve under the stochastic processes of proliferation, migration, mutation and death. Analytical and numerical results demonstrate that concentration gradients can foster a mode of adaptation that is impossible in uniform environments. It allows resistant mutants to evade competition and circumvent the slow process of fixation by invading compartments with higher drug concentrations, where less resistant strains cannot subsist. The speed of this process increases sharply with the sensitivity of the growth rate to the antibiotic concentration, which we argue to be generic. Comparable adaptation rates in uniform environments would require a high selection coefficient ( s > 0.1) for each forward mutation. Similar processes can occur if the heterogeneity is more complex than just a linear gradient. The model may also be applicable to other adaptive processes involving environmental heterogeneity and range expansion.

Periodic stripe patterns are ubiquitous in living organisms, yet the underlying developmental processes are complex and difficult to disentangle. We describe a synthetic genetic circuit that couples cell density and motility. This system enabled programmed Escherichia coli cells to form periodic stripes of high and low cell densities sequentially and autonomously. Theoretical and experimental analyses reveal that the spatial structure arises from a recurrent aggregation process at the front of the continuously expanding cell population. The number of stripes formed could be tuned by modulating the basal expression of a single gene. The results establish motility control as a simple route to establishing recurrent structures without requiring an extrinsic pacemaker.

Sequence–function relations for small RNA (sRNA)-mediated gene silencing were quantified for the sRNA RyhB and some of its mRNA targets in Escherichia coli . Numerous mutants of RyhB and its targets were generated and their in vivo functions characterized at various levels of target and RyhB expression. Although a core complementary region is required for repression by RyhB, variations in the complementary sequences of the core region gave rise to a continuum of repression strengths, correlated exponentially with the computed free energy of RyhB-target duplex formation. Moreover, sequence variations in the linker region known to interact with the RNA chaperone Hfq also gave rise to a continuum of repression strengths, correlated exponentially with the computed energy cost of keeping the linker region open. These results support the applicability of the thermodynamic model in predicting sRNA–mRNA interaction and suggest that sequences at these locations may be used to fine-tune the degree of repression. Surprisingly, a truncated RyhB without the Hfq-binding region is found to repress multiple targets of the wild-type RyhB effectively, both in the presence and absence of Hfq, even though the former is required for the activity of wild-type RyhB itself. These findings challenge the commonly accepted model concerning the function of Hfq in gene silencing—both in providing stability to the sRNAs and in catalyzing the target mRNAs to take on active conformations—and raise the intriguing question of why many endogenous sRNAs subject their functions to Hfq-dependences.

The similarity in the three-dimensional structures of homologous proteins imposes strong constraints on their sequence variability. It has long been suggested that the resulting correlations among amino acid compositions at different sequence positions can be exploited to infer spatial contacts within the tertiary protein structure. Crucial to this inference is the ability to disentangle direct and indirect correlations, as accomplished by the recently introduced Direct Coupling Analysis (DCA) (Weigt et al. (2009) Proc Natl Acad Sci 106:67). Here we develop a computationally efficient implementation of DCA, which allows us to evaluate the accuracy of contact prediction by DCA for a large number of protein domains, based purely on sequence information. DCA is shown to yield a large number of correctly predicted contacts, recapitulating the global structure of the contact map for the majority of the protein domains examined. Furthermore, our analysis captures clear signals beyond intra- domain residue contacts, arising, e.g., from alternative protein conformations, ligand- mediated residue couplings, and inter-domain interactions in protein oligomers. Our findings suggest that contacts predicted by DCA can be used as a reliable guide to facilitate computational predictions of alternative protein conformations, protein complex formation, and even the de novo prediction of protein domain structures, provided the existence of a large number of homologous sequences which are being rapidly made available due to advances in genome sequencing., 28 pages, 7 figures, to appear in PNAS

Understanding the molecular determinants of specificity in protein-protein interaction is an outstanding challenge of postgenome biology. The availability of large protein databases generated from sequences of hundreds of bacterial genomes enables various statistical approaches to this problem. In this context covariance-based methods have been used to identify correlation between amino acid positions in interacting proteins. However, these methods have an important shortcoming, in that they cannot distinguish between directly and indirectly correlated residues. We developed a method that combines covariance analysis with global inference analysis, adopted from use in statistical physics. Applied to a set of >2,500 representatives of the bacterial two-component signal transduction system, the combination of covariance with global inference successfully and robustly identified residue pairs that are proximal in space without resorting to ad hoc tuning parameters, both for heterointeractions between sensor kinase (SK) and response regulator (RR) proteins and for homointeractions between RR proteins. The spectacular success of this approach illustrates the effectiveness of the global inference approach in identifying direct interaction based on sequence information alone. We expect this method to be applicable soon to interaction surfaces between proteins present in only 1 copy per genome as the number of sequenced genomes continues to expand. Use of this method could significantly increase the potential targets for therapeutic intervention, shed light on the mechanism of protein-protein interaction, and establish the foundation for the accurate prediction of interacting protein partners., Supplementary information available on http://www.pnas.org/content/106/1/67.abstract

Physiological changes which result in changes in bacterial gene expression are often accompanied by changes in the growth rate for fast adapting enteric bacteria. Since the availability of RNA polymerase (RNAP) in cells is dependent on the growth rate, transcriptional control involves not only the regulation of promoters, but also depends on the available (or free) RNAP concentration which is difficult to quantify directly. Here we develop a simple physical model describing the partitioning of cellular RNAP into different classes: RNAPs transcribing mRNA and ribosomal RNA (rRNA), RNAPs non-specifically bound to DNA, free RNAP, and immature RNAP. Available experimental data for E. coli allow us to determine the two unknown parameters of the model and hence deduce the free RNAP concentration at different growth rates. The results allow us to predict the growth-rate dependence of the activities of constitutive (unregulated) promoters, and to disentangle the growth-rate dependent regulation of promoters (e.g., the promoters of rRNA operons) from changes in transcription due to changes in the free RNAP concentration at different growth rates. Our model can quantitatively account for the observed changes in gene expression patterns in mutant E. coli strains with altered levels of RNAP expression without invoking additional parameters. Applying our model to the case of the stringent response following amino acid starvation, we can evaluate the plausibility of various scenarios of passive transcriptional control proposed to account for the observed changes in the expression of rRNA and biosynthetic operons., Comment: includes supporting information

During mitosis, the condensed chromosomes undergo a series of spectacular oscillations after they are captured in an end-on manner by kinetochore microtubules (KMT) emanating from the spindle poles. Such oscillations are commonly attributed to tug-of-war-like mechanisms, where the mechanical force imbalance alone drives the chromosome movement. However, a large portion of the force imbalance upon the chromosome is absorbed by the kinetochore and may not drive chromosome movement directly. Mounting evidence suggests that such resistance by the kinetochores regulates the chemical reactions of KMT plus-end growth and shrinkage, which have been shown as the determinant of the chromosome antipoleward (AP) and poleward movements. Here we incorporate this important regulatory feature, propose a mechanobiochemical feedback mechanism, and apply it to the monooriented chromosome oscillation, the early stage of the series of observed chromosome oscillations. In this model, the mechanical movement of the chromosome and the local biochemical reactions at the attached kinetochore region form a feedback loop that drives the oscillation. The force imbalance exerted on the chromosomes provides a bias (via mechanically sensitive proteins) on the local biochemical reactions controlling the KMT plus-end dynamics, and the movement of the chromosome in turn changes the forces exerted on it through the experimentally supported gradient in AP force. The proposed feedback mechanism can generate oscillatory behavior that depends on the topology of the feedback loop but is largely independent of the detailed molecular mechanism. We suggest potential molecular players, whose perturbation may allow direct experimental tests of the model.

Fluctuations in the abundance of molecules in the living cell may affect its growth and well being. For regulatory molecules (e.g., signaling proteins or transcription factors), fluctuations in their expression can affect the levels of downstream targets in a network. Here, we develop an analytic framework to investigate the phenomenon of noise correlation in molecular networks. Specifically, we focus on the metabolic network, which is highly interlinked, and noise properties may constrain its structure and function. Motivated by the analogy between the dynamics of a linear metabolic pathway and that of the exactly soluble linear queuing network or, alternatively, a mass transfer system, we derive a plethora of results concerning fluctuations in the abundance of intermediate metabolites in various common motifs of the metabolic network. For all but one case examined, we find the steady-state fluctuation in different nodes of the pathways to be effectively uncorrelated. Consequently, fluctuations in enzyme levels only affect local properties and do not propagate elsewhere into metabolic networks, and intermediate metabolites can be freely shared by different reactions. Our approach may be applicable to study metabolic networks with more complex topologies or protein signaling networks that are governed by similar biochemical reactions. Possible implications for bioinformatic analysis of metabolomic data are discussed.

For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of deterministic rate equation models. Unfortunately, there are few analytic methods for examining the qualitative behavior of stochastic systems. Here we describe such a method that extends deterministic analysis to include leading-order corrections due to the molecular noise. The method allows the steady-state behavior of the stochastic model to be easily computed, facilitates the mapping of stability phase diagrams that include stochastic effects and reveals how model parameters affect noise susceptibility, in a manner not accessible to numerical simulation. By way of illustration we consider two genetic circuits: a bistable positive-feedback loop and a negative-feedback oscillator. We find in the positive feedback circuit that translational activation leads to a far more stable system than transcriptional control. Conversely, in a negative-feedback loop triggered by a positive-feedback switch, the stochasticity of transcriptional control is harnessed to generate reproducible oscillations., Comment: 6 pages (Supplementary Information is appended)

The goal of systems biology is to understand the behavior of the whole in terms of knowledge of the parts. This is hard to achieve in many cases due to the difficulty of characterizing the many constituents involved in a biological system and their complex web of interactions. The lac promoter of Escherichia coli offers the possibility of confronting “system-level” properties of transcriptional regulation with the known biochemistry of the molecular constituents and their mutual interactions. Such confrontations can reveal previously unknown constituents and interactions, as well as offer insight into how the components work together as a whole. Here we study the combinatorial control of the lac promoter by the regulators Lac repressor (LacR) and cAMP-receptor protein (CRP). A previous in vivo study [Setty Y, Mayo AE, Surette MG, Alon U (2003) Proc Natl Acad Sci USA 100:7702–7707] found gross disagreement between the observed promoter activities and the expected behavior based on the known molecular mechanisms. We repeated the study by identifying and removing several extraneous factors that significantly modulated the expression of the lac promoter. Through quantitative, systematic characterization of promoter activity for a number of key mutants and guided by the thermodynamic model of transcriptional regulation, we were able to account for the combinatorial control of the lac promoter quantitatively, in terms of a cooperative interaction between CRP and LacR-mediated DNA looping. Specifically, our analysis indicates that the sensitivity of the inducer response results from LacR-mediated DNA looping, which is significantly enhanced by CRP.

The functions of most genetic circuits require sufficient degrees of cooperativity in the circuit components. While mechanisms of cooperativity have been studied most extensively in the context of transcriptional initiation control, cooperativity from other processes involved in the operation of the circuits can also play important roles. In this study, we examine a simple kinetic source of cooperativity stemming from the nonlinear degradation of multimeric proteins. Ample experimental evidence suggests that protein subunits can degrade less rapidly when associated in multimeric complexes, an effect we refer to as cooperative stability. For dimeric transcription factors, this effect leads to a concentration-dependence in the degradation rate because monomers, which are predominant at low concentrations, will be more rapidly degraded. Thus cooperative stability can effectively widen the accessible range of protein levels in vivo. Through theoretical analysis of two exemplary genetic circuits in bacteria, we show that such an increased range is important for the robust operation of genetic circuits as well as their evolvability. Our calculations demonstrate that a few-fold difference between the degradation rate of monomers and dimers can already enhance the function of these circuits substantially. These results suggest that cooperative stability needs to be considered explicitly and characterized quantitatively in any systematic experimental or theoretical study of gene circuits., Comment: 42 pages, 10 figures

We study the thermodynamic and dynamic behaviors of twist-induced denaturation bubbles in a long, stretched random sequence of DNA. The small bubbles associated with weak twist are delocalized. Above a threshold torque, the bubbles of several tens of bases or larger become preferentially localized to \AT-rich segments. In the localized regime, the bubbles exhibit ``aging'' and move around sub-diffusively with continuously varying dynamic exponents. These properties are derived using results of large-deviation theory together with scaling arguments, and are verified by Monte-Carlo simulations., TeX file with postscript figures

We study theoretical ``design principles'' for transcription factor-DNA interaction in bacteria, focusing particularly on the statistical interaction of the transcription factors (TF's) with the genomic background (i.e., the genome without the target sites). We introduce and motivate the concept of `programmability', i.e. the ability to set the threshold concentration for TF binding over a wide range merely by mutating the binding sequence of a target site. This functional demand, together with physical constraints arising from the thermodynamics and kinetics of TF-DNA interaction, leads us to a narrow range of ``optimal'' interaction parameters. We find that this parameter set agrees well with experimental data for the interaction parameters of a few exemplary prokaryotic TF's. This indicates that TF-DNA interaction is indeed programmable. We suggest further experiments to test whether this is a general feature for a large class of TF's., 9 pages, 4 figures; revised version as published in PNAS

MEMBRANES composed of bilayers of amphiphiles such as phospholipids generally exhibit two-dimensional liquid-like structure within the layers. When the constituent molecules of such a membrane are permanently cross-linked to each other, the membrane becomes less flexible, forming a two-dimensional solid. Solid membranes are expected to exhibit very different behaviour from their liquid counterparts1–3, including transitions between a two-dimensional flat phase, a crumpled phase of fractal dimension 2.5 and a compact, three-dimensional phase. Experimental evidence for the crumpled phase has, however, been lacking. As this phase was not observed in computer simulations4–6, it has been suggested that it may always be absent for self-avoiding (and therefore all real) membranes4–6. To the contrary, we report here the experimental observation of the crumpled conformation in an aqueous suspension of graphite oxide membranes. Static light scattering measurements indicate the presence of membrane conformations with a fractal dimension of 2.54 ±0.05. As the intra-membrane affinity is enhanced by changing the composition of the solvent, the membranes collapse to a compact configuration.

A micro-mechanical oscillator has been used, for the first time, to measure the dynamics of individual magnetic vortices threading a superconductor crystal. Predicting the behaviour of single vortex lines requires using a ‘1+1’-dimensional model from statistical mechanics — a tool that has wide applications, ranging from quantum mechanics to sequence alignment in genomics.

A Genetic Switch Third Edition, Phage Lambda Revisited. by Mark Ptashne. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, 2004. 168 pp. Paper, $39, £24.99. ISBN 0-87969-716-4. This revision includes a new chapter that considers discoveries such as interactions among proteins that bind to widely separated sites on DNA.