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CTP Synthetase (CtpS) is a universally conserved and essential metabolic enzyme. While many enzymes form small oligomers, CtpS forms large-scale filamentous structures of unknown function in prokaryotes and eukaryotes. By simultaneously monitoring CtpS polymerization and enzymatic activity, we show that polymerization inhibits activity, and CtpS's product, CTP, induces assembly. To understand how assembly inhibits activity, we used electron microscopy to define the structure of CtpS polymers. This structure suggests that polymerization sterically hinders a conformational change necessary for CtpS activity. Structure-guided mutagenesis and mathematical modeling further indicate that coupling activity to polymerization promotes cooperative catalytic regulation. This previously uncharacterized regulatory mechanism is important for cellular function since a mutant that disrupts CtpS polymerization disrupts E. coli growth and metabolic regulation without reducing CTP levels. We propose that regulation by large-scale polymerization enables ultrasensitive control of enzymatic activity while storing an enzyme subpopulation in a conformationally restricted form that is readily activatable., (Copyright © 2014, Barry et al.)

The ParABS system mediates chromosome segregation and plasmid partitioning in many bacteria. As part of the partitioning mechanism, ParB proteins form a nucleoprotein complex at parS sites. The biophysical basis underlying ParB-DNA complex formation and localization remains elusive. Specifically, it is unclear whether ParB spreads in 1D along DNA or assembles into a 3D protein-DNA complex. We show that a combination of 1D spreading bonds and a single 3D bridging bond between ParB proteins constitutes a minimal model for a condensed ParB-DNA complex. This model implies a scaling behavior for ParB-mediated silencing of parS-flanking genes, which we confirm to be satisfied by experimental data from P1 plasmids. Furthermore, this model is consistent with experiments on the effects of DNA roadblocks on ParB localization. Finally, we show experimentally that a single parS site is necessary and sufficient for ParB-DNA complex formation in vivo. Together with our model, this suggests that ParB binding to parS triggers a conformational switch in ParB that overcomes a nucleation barrier. Conceptually, the combination of spreading and bridging bonds in our model provides a surface tension ensuring the condensation of the ParB-DNA complex, with analogies to liquid-like compartments such as nucleoli in eukaryotes.

Adaptability is an essential property of many sensory systems, enabling maintenance of a sensitive response over a range of background stimulus levels. In bacterial chemotaxis, adaptation to the preset level of pathway activity is achieved through an integral feedback mechanism based on activity-dependent methylation of chemoreceptors. It has been argued that this architecture ensures precise and robust adaptation regardless of the ambient ligand concentration, making perfect adaptation a celebrated property of the chemotaxis system. However, possible deviations from such ideal adaptive behavior and its consequences for chemotaxis have not been explored in detail. Here we show that the chemotaxis pathway in Escherichia coli shows increasingly imprecise adaptation to higher concentrations of attractants, with a clear correlation between the time of adaptation to a step-like stimulus and the extent of imprecision. Our analysis suggests that this imprecision results from a gradual saturation of receptor methylation sites at high levels of stimulation, which prevents full recovery of the pathway activity by violating the conditions required for precise adaptation. We further use computer simulations to show that limited imprecision of adaptation has little effect on the rate of chemotactic drift of a bacterial population in gradients, but hinders precise accumulation at the peak of the gradient. Finally, we show that for two major chemoeffectors, serine and cysteine, failure of adaptation at concentrations above 1 mM might prevent bacteria from accumulating at toxic concentrations of these amino acids.

Bacteria frequently live in densely populated surface-bound communities, termed biofilms [1-4]. Biofilm-dwelling cells rely on secretion of extracellular substances to construct their communities and to capture nutrients from the environment [5]. Some secreted factors behave as cooperative public goods: they can be exploited by nonproducing cells [6-11]. The means by which public-good-producing bacteria avert exploitation in biofilm environments are largely unknown. Using experiments with Vibrio cholerae, which secretes extracellular enzymes to digest its primary food source, the solid polymer chitin, we show that the public goods dilemma may be solved by two very different mechanisms: cells can produce thick biofilms that confine the goods to producers, or fluid flow can remove soluble products of chitin digestion, denying access to nonproducers. Both processes are unified by limiting the distance over which enzyme-secreting cells provide benefits to neighbors, resulting in preferential benefit to nearby clonemates and allowing kin selection to favor public good production. Our results demonstrate new mechanisms by which the physical conditions of natural habitats can interact with bacterial physiology to promote the evolution of cooperation., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

The essential outer membrane β-barrel protein BamA forms a complex with four lipoprotein partners BamBCDE that assembles β-barrel proteins into the outer membrane of Escherichia coli. Detailed genetic studies have shown that BamA cycles through multiple conformations during substrate assembly, suggesting that a complex network of residues may be involved in coordinating conformational changes and lipoprotein partner function. While genetic analysis of BamA has been informative, it has also been slow in the absence of a straightforward selection for mutants. Here we take a bioinformatic approach to identify candidate residues for mutagenesis using direct coupling analysis. Starting with the BamA paralog FhaC, we show that direct coupling analysis works well for large β-barrel proteins, identifying pairs of residues in close proximity in tertiary structure with a true positive rate of 0.64 over the top 50 predictions. To reduce the effects of noise, we designed and incorporated a novel structured prior into the empirical correlation matrix, dramatically increasing the FhaC true positive rate from 0.64 to 0.88 over the top 50 predictions. Our direct coupling analysis of BamA implicates residues R661 and D740 in a functional interaction. We find that the substitutions R661G and D740G each confer OM permeability defects and destabilize the BamA β-barrel. We also identify synthetic phenotypes and cross-suppressors that suggest R661 and D740 function in a similar process and may interact directly. We expect that the direct coupling analysis approach to informed mutagenesis will be particularly useful in systems lacking adequate selections and for dynamic proteins with multiple conformations.

Cooperativity arising from local interactions in equilibrium receptor systems provides gain, but does not increase sensory performance, as measured by the signal-to-noise ratio (SNR) due to a fundamental tradeoff between gain and intrinsic noise. Here we allow sensing to be a nonequilibrium process and show that energy dissipation cannot circumvent the fundamental tradeoff, so that the SNR is still optimal for independent receptors. For systems requiring high gain, nonequilibrium 2D-coupled receptors maximize the SNR, revealing a new design principle for biological sensors.

Many cellular populations cooperate through the secretion of diffusible extracellular resources, such as digestive enzymes or virulence factors. Diffusion of these resources leads to long-range intercellular interactions, creating the possibility of cooperation but also the risk of exploitation by non-producing neighbors. In the past, considerable attention has been given to game-theoretic lattice models of intercellular cooperation. In these models, coexistence is commonly observed between cooperators (corresponding to resource producers) and cheaters (corresponding to nonproducers). However, these models consider only interactions between direct competitors. We find that when individuals are allowed to interact non-locally through the diffusion of a shared resource coexistence between cooperators and cheaters is lost. Instead, we find population dynamics similar to simple competition, either neutral or biased, with no balancing selection that would favor coexistence. Our results highlight the importance of an accurate treatment of diffusion of shared resources and argue against the generality of the conclusions of game-theoretic lattice models.

The bacterial cytoskeleton guides the synthesis of cell wall and thus regulates cell shape. Because spatial patterning of the bacterial cytoskeleton is critical to the proper control of cell shape, it is important to ask how the cytoskeleton spatially self-organizes in the first place. In this work, we develop a quantitative model to account for the various spatial patterns adopted by bacterial cytoskeletal proteins, especially the orientation and length of cytoskeletal filaments such as FtsZ and MreB in rod-shaped cells. We show that the combined mechanical energy of membrane bending, membrane pinning, and filament bending of a membrane-attached cytoskeletal filament can be sufficient to prescribe orientation, e.g., circumferential for FtsZ or helical for MreB, with the accuracy of orientation increasing with the length of the cytoskeletal filament. Moreover, the mechanical energy can compete with the chemical energy of cytoskeletal polymerization to regulate filament length. Notably, we predict a conformational transition with increasing polymer length from smoothly curved to end-bent polymers. Finally, the mechanical energy also results in a mutual attraction among polymers on the same membrane, which could facilitate tight polymer spacing or bundling. The predictions of the model can be verified through genetic, microscopic, and microfluidic approaches., (Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Chemotaxis allows bacteria to follow gradients of nutrients and other environmental stimuli. The bacterium Escherichia coli performs chemotaxis via a run-and-tumble strategy in which sensitive temporal comparisons lead to a biased random walk, with longer runs in the preferred gradient direction. The chemotaxis network of E. coli has developed over the years into one of the most thoroughly studied model systems for signal transduction and behavior, yielding general insights into such properties of cellular networks as signal amplification, signal integration, and robustness. Despite its relative simplicity, the operation of the E. coli chemotaxis network is highly refined and evolutionarily optimized at many levels. For example, recent studies revealed that the network adjusts its signaling properties dependent on the extracellular environment, apparently to optimize chemotaxis under particular conditions. The network can even utilize potentially detrimental stochastic fluctuations in protein levels and reaction rates to maximize the chemotactic performance of the population., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Motile eukaryotic cells migrate with directional persistence by alternating left and right turns, even in the absence of external cues. For example, Dictyostelium discoideum cells crawl by extending distinct pseudopods in an alternating right-left pattern. The mechanisms underlying this zig-zag behavior, however, remain unknown. Here we propose a new Excitable Cortex and Memory (EC&M) model for understanding the alternating, zig-zag extension of pseudopods. Incorporating elements of previous models, we consider the cell cortex as an excitable system and include global inhibition of new pseudopods while a pseudopod is active. With the novel hypothesis that pseudopod activity makes the local cortex temporarily more excitable--thus creating a memory of previous pseudopod locations--the model reproduces experimentally observed zig-zag behavior. Furthermore, the EC&M model makes four new predictions concerning pseudopod dynamics. To test these predictions we develop an algorithm that detects pseudopods via hierarchical clustering of individual membrane extensions. Data from cell-tracking experiments agrees with all four predictions of the model, revealing that pseudopod placement is a non-Markovian process affected by the dynamics of previous pseudopods. The model is also compatible with known limits of chemotactic sensitivity. In addition to providing a predictive approach to studying eukaryotic cell motion, the EC&M model provides a general framework for future models, and suggests directions for new research regarding the molecular mechanisms underlying directional persistence.

Many cytoskeletal biopolymers are "active," consuming energy in large quantities. In this Letter, we identify a fundamental difference between active polymers and passive, equilibrium polymers: for equal mean lengths, active polymers can reorganize faster than equilibrium polymers. We show that equilibrium polymers are intrinsically limited to linear scaling between mean lifetime (or mean first-passage time, or MFPT) and mean length, MFPT∼, by analogy to 1D Potts models. By contrast, we present a simple active-polymer model that improves upon this scaling, such that MFPT∼(1/2). Since, to be biologically useful, structural biopolymers must typically be many monomers long yet respond dynamically to the needs of the cell, the difference in reorganization kinetics may help to justify the active polymers' greater energy cost.

Cooperative interactions among sensory receptors provide a general mechanism to increase the sensitivity of signal transduction. In particular, bacterial chemotaxis receptors interact cooperatively to produce an ultrasensitive response to chemoeffector concentrations. However, cooperativity between receptors in large macromolecular complexes is necessarily based on local interactions and consequently is fundamentally connected to slowing of receptor-conformational dynamics, which increases intrinsic noise. Therefore, it is not clear whether or under what conditions cooperativity actually increases the precision of the concentration measurement. We explicitly calculate the signal-to-noise ratio (SNR) for sensing a concentration change using a simple, Ising-type model of receptor-receptor interactions, generalized via scaling arguments, and find that the optimal SNR is always achieved by independent receptors., (© 2011 American Physical Society)

Microbes survive in a variety of nutrient environments by modulating their intracellular metabolism. Balanced growth requires coordinated uptake of carbon and nitrogen, the primary substrates for biomass production. Yet the mechanisms that balance carbon and nitrogen uptake are poorly understood. We find in Escherichia coli that a sudden increase in nitrogen availability results in an almost immediate increase in glucose uptake. The concentrations of glycolytic intermediates and known regulators, however, remain homeostatic. Instead, we find that α-ketoglutarate, which accumulates in nitrogen limitation, directly blocks glucose uptake by inhibiting enzyme I, the first step of the sugar-phosphoenolpyruvate phosphotransferase system (PTS). This inhibition enables rapid modulation of glycolytic flux without marked changes in the concentrations of glycolytic intermediates by simultaneously altering import of glucose and consumption of the terminal glycolytic intermediate phosphoenolpyruvate. Quantitative modeling shows that this previously unidentified regulatory connection is, in principle, sufficient to coordinate carbon and nitrogen utilization.

Bacterial cells possess multiple cytoskeletal proteins involved in a wide range of cellular processes. These cytoskeletal proteins are dynamic, but the driving forces and cellular functions of these dynamics remain poorly understood. Eukaryotic cytoskeletal dynamics are often driven by motor proteins, but in bacteria no motors that drive cytoskeletal motion have been identified to date. Here, we quantitatively study the dynamics of the Escherichia coli actin homolog MreB, which is essential for the maintenance of rod-like cell shape in bacteria. We find that MreB rotates around the long axis of the cell in a persistent manner. Whereas previous studies have suggested that MreB dynamics are driven by its own polymerization, we show that MreB rotation does not depend on its own polymerization but rather requires the assembly of the peptidoglycan cell wall. The cell-wall synthesis machinery thus either constitutes a novel type of extracellular motor that exerts force on cytoplasmic MreB, or is indirectly required for an as-yet-unidentified motor. Biophysical simulations suggest that one function of MreB rotation is to ensure a uniform distribution of new peptidoglycan insertion sites, a necessary condition to maintain rod shape during growth. These findings both broaden the view of cytoskeletal motors and deepen our understanding of the physical basis of bacterial morphogenesis.

Chromosome segregation is fundamental to all cells, but the force-generating mechanisms underlying chromosome translocation in bacteria remain mysterious. Caulobacter crescentus utilizes a depolymerization-driven process in which a ParA protein structure elongates from the new cell pole, binds to a ParB-decorated chromosome, and then retracts via disassembly, pulling the chromosome across the cell. This poses the question of how a depolymerizing structure can robustly pull the chromosome that disassembles it. We perform Brownian dynamics simulations with a simple, physically consistent model of the ParABS system. The simulations suggest that the mechanism of translocation is "self-diffusiophoretic": by disassembling ParA, ParB generates a ParA concentration gradient so that the ParA concentration is higher in front of the chromosome than behind it. Since the chromosome is attracted to ParA via ParB, it moves up the ParA gradient and across the cell. We find that translocation is most robust when ParB binds side-on to ParA filaments. In this case, robust translocation occurs over a wide parameter range and is controlled by a single dimensionless quantity: the product of the rate of ParA disassembly and a characteristic relaxation time of the chromosome. This time scale measures the time it takes for the chromosome to recover its average shape after it is has been pulled. Our results suggest explanations for observed phenomena such as segregation failure, filament-length-dependent translocation velocity, and chromosomal compaction.

For the rod-shaped Gram-negative bacterium Escherichia coli, changes in cell shape have critical consequences for motility, immune system evasion, proliferation and adhesion. For most bacteria, the peptidoglycan cell wall is both necessary and sufficient to determine cell shape. However, how the synthesis machinery assembles a peptidoglycan network with a robustly maintained micron-scale shape has remained elusive. To explore shape maintenance, we have quantified the robustness of cell shape in three Gram-negative bacteria in different genetic backgrounds and in the presence of an antibiotic that inhibits division. Building on previous modelling suggesting a prominent role for mechanical forces in shape regulation, we introduce a biophysical model for the growth dynamics of rod-shaped cells to investigate the roles of spatial regulation of peptidoglycan synthesis, glycan-strand biochemistry and mechanical stretching during insertion. Our studies reveal that rod-shape maintenance requires insertion to be insensitive to fluctuations in cell-wall density and stress, and even a simple helical pattern of insertion is sufficient for over sixfold elongation without significant loss in shape. In addition, we demonstrate that both the length and pre-stretching of newly inserted strands regulate cell width. In sum, we show that simple physical rules can allow bacteria to achieve robust, shape-preserving cell-wall growth., (© 2011 Blackwell Publishing Ltd.)

Although many of the core components of the embryonic cell-cycle network have been elucidated, the question of how embryos achieve robust, synchronous cellular divisions post-fertilization remains unexplored. What are the different schemes that could be implemented by the embryo to achieve synchronization? By extending a cell-cycle model previously developed for embryos of the frog Xenopus laevis to include the spatial dimensions of the embryo, we establish a novel role for the rapid, fertilization-initiated calcium wave that triggers cell-cycle oscillations. Specifically, in our simulations a fast calcium wave results in synchronized cell cycles, while a slow wave results in full-blown spatio-temporal chaos. We show that such chaos would ultimately lead to an unpredictable patchwork of cell divisions across the embryo. Given this potential for chaos, our results indicate a novel design principle whereby the fast calcium-wave trigger following embryo fertilization synchronizes cell divisions.

Gene expression is stochastic, and noise that arises from the stochastic nature of biochemical reactions propagates through active regulatory links. Thus, correlations in gene-expression noise can provide information about regulatory links. We present what to our knowledge is a new approach to measure and interpret such correlated fluctuations at the level of single microcolonies, which derive from single cells. We demonstrated this approach mathematically using stochastic modeling, and applied it to experimental time-lapse fluorescence microscopy data. Specifically, we investigated the relationships among LuxO, LuxR, and the small regulatory RNA qrr4 in the model quorum-sensing bacterium Vibrio harveyi. Our results show that LuxR positively regulates the qrr4 promoter. Under our conditions, we find that qrr regulation weakly depends on total LuxO levels and that LuxO autorepression is saturated. We also find evidence that the fluctuations in LuxO levels are dominated by intrinsic noise. We furthermore propose LuxO and LuxR interact at all autoinducer levels via an unknown mechanism. Of importance, our new method of evaluating correlations at the microcolony level is unaffected by partition noise at cell division. Moreover, the method is first-order accurate and requires less effort for data analysis than single-cell-based approaches. This new correlation approach can be applied to other systems to aid analysis of gene regulatory circuits., (Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Quorum sensing is a chemical signaling mechanism used by bacteria to communicate and orchestrate group behaviors. Multiple feedback loops exist in the quorum-sensing circuit of the model bacterium Vibrio harveyi. Using fluorescence microscopy of individual cells, we assayed the activity of the quorum-sensing circuit, with a focus on defining the functions of the feedback loops. We quantitatively investigated the signaling input-output relation both in cells with all feedback loops present as well as in mutants with specific feedback loops disrupted. We found that one of the feedback loops regulates receptor ratios to control the integration of multiple signals. Together, the feedback loops affect the input-output dynamic range of signal transmission and the noise in the output. We conclude that V. harveyi employs multiple feedback loops to simultaneously control quorum-sensing signal integration and to ensure signal transmission fidelity.

Temperature is a global factor that affects the performance of all intracellular networks. Robustness against temperature variations is thus expected to be an essential network property, particularly in organisms without inherent temperature control. Here, we combine experimental analyses with computational modeling to investigate thermal robustness of signaling in chemotaxis of Escherichia coli, a relatively simple and well-established model for systems biology. We show that steady-state and kinetic pathway parameters that are essential for chemotactic performance are indeed temperature-compensated in the entire physiological range. Thermal robustness of steady-state pathway output is ensured at several levels by mutual compensation of temperature effects on activities of individual pathway components. Moreover, the effect of temperature on adaptation kinetics is counterbalanced by preprogrammed temperature dependence of enzyme synthesis and stability to achieve nearly optimal performance at the growth temperature. Similar compensatory mechanisms are expected to ensure thermal robustness in other systems., (Copyright © 2011 Elsevier Inc. All rights reserved.)

The bacterial cell wall is a network of sugar strands crosslinked by peptides that serve as the primary structure for bearing osmotic stress. Despite its importance in cellular survival, the robustness of the cell wall to network defects has been relatively unexplored. Treatment of the gram-negative bacterium Escherichia coli with the antibiotic vancomycin, which disrupts the crosslinking of new material during growth, leads to the development of pronounced bulges and eventually of cell lysis. Here, we model the mechanics of the bulging of the cytoplasmic membrane through pores in the cell wall. We find that the membrane undergoes a transition between a nearly flat state and a spherical bulge at a critical pore radius of ~20 nm. This critical pore size is large compared to the typical distance between neighboring peptides and glycan strands, and hence pore size acts as a constraint on network integrity. We also discuss the general implications of our model to membrane deformations in eukaryotic blebbing and vesiculation in red blood cells., (©2011 American Physical Society)

By analyzing 30 min, high-resolution recordings of single Escherichia coli flagellar motors in the physiological regime, we show that two main properties of motor switching-the mean clockwise and mean counter-clockwise interval durations-vary significantly. When we represent these quantities on a two-dimensional plot for several cells, the data do not fall on a one-dimensional curve, as expected with a single control parameter, but instead spread in two dimensions, pointing to motor individuality. The largest variations are in the mean counter-clockwise interval, and are attributable to variations in the concentration of the internal signaling molecule CheY-P. In contrast, variations in the mean clockwise interval are interpreted in terms of motor individuality. We argue that the sensitivity of the mean counter-clockwise interval to fluctuations in CheY-P is consistent with an optimal strategy of run and tumble. The concomittent variability in mean run length may allow populations of cells to better survive in rapidly changing environments by 'hedging their bets'.

Competing Interests: The authors have declared that no competing interests exist.

Recently, a novel approach has been developed to study gene expression in single cells with high time resolution using RNA Fluorescent In Situ Hybridization (FISH). The technique allows individual mRNAs to be counted with high accuracy in wild-type cells, but requires cells to be fixed; thus, each cell provides only a "snapshot" of gene expression. Here we show how and when RNA FISH data on pairs of genes can be used to reconstruct real-time dynamics from a collection of such snapshots. Using maximum-likelihood parameter estimation on synthetically generated, noisy FISH data, we show that dynamical programs of gene expression, such as cycles (e.g., the cell cycle) or switches between discrete states, can be accurately reconstructed. In the limit that mRNAs are produced in short-lived bursts, binary thresholding of the FISH data provides a robust way of reconstructing dynamics. In this regime, prior knowledge of the type of dynamics--cycle versus switch--is generally required and additional constraints, e.g., from triplet FISH measurements, may also be needed to fully constrain all parameters. As a demonstration, we apply the thresholding method to RNA FISH data obtained from single, unsynchronized cells of Saccharomyces cerevisiae. Our results support the existence of metabolic cycles and provide an estimate of global gene-expression noise. The approach to FISH data presented here can be applied in general to reconstruct dynamics from snapshots of pairs of correlated quantities including, for example, protein concentrations obtained from immunofluorescence assays.

The chemotaxis network of the bacterium Escherichia coli is perhaps the most studied model for adaptation of a signaling system to persistent stimuli. Although adaptation in this system is generally considered to be precise, there has been little effort to quantify this precision, or to understand how and when precision fails. Using a Förster resonance energy transfer-based reporter of signaling activity, we undertook a systematic study of adaptation kinetics and precision in E. coli cells expressing a single type of chemoreceptor (Tar). Quantifiable loss of precision of adaptation was observed at levels of the attractant MeAsp as low 10 μM, with pronounced differences in both kinetics and precision of adaptation between addition and removal of attractant. Quantitative modeling of the kinetic data suggests that loss of precise adaptation is due to a slowing of receptor methylation as available modification sites become scarce. Moreover, the observed kinetics of adaptation imply large cell-to-cell variation in adaptation rates-potentially providing genetically identical cells with the ability to "hedge their bets" by pursuing distinct chemotactic strategies., (Copyright © 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

In chemotaxis of Escherichia coli and other bacteria, extracellular stimuli are perceived by transmembrane receptors that bind their ligands either directly, or indirectly through periplasmic-binding proteins (BPs). As BPs are also involved in ligand uptake, they provide a link between chemotaxis and nutrient utilization by cells. However, signalling by indirectly binding ligands remains much less understood than signalling by directly binding ligands. Here, we compared intracellular responses mediated by both types of ligands and developed a new mathematical model for signalling by indirectly binding ligands. We show that indirect binding allows cells to better control sensitivity to specific ligands in response to their nutrient environment and to coordinate chemotaxis with ligand transport, but at the cost of the dynamic range being much narrower than for directly binding ligands. We further demonstrate that signal integration by the chemosensory complexes does not depend on the type of ligand. Overall, our data suggest that the distinction between signalling by directly and indirectly binding ligands is more physiologically important than the traditional distinction between high- and low-abundance receptors.

The chemotaxis system of Escherichia coli is sensitive to small relative changes in ambient chemoattractant concentrations over a broad range. Interactions among receptors are crucial to this sensitivity, as is precise adaptation, the return of chemoreceptor activity to prestimulus levels in a constant chemoeffector environment through methylation and demethylation of receptors. Signal integration and cooperativity have been attributed to strongly coupled, mixed teams of receptors, but receptors become individually methylated according to their ligand occupancy states. Here, we present a model of dynamic signaling teams that reconciles strong coupling among receptors with receptor-specific methylation. Receptor trimers of dimers couple to form a honeycomb lattice, consistent with cryo-electron microscopy (cryoEM) tomography, within which the boundaries of signaling teams change rapidly. Our model helps explain the inferred increase in signaling team size with receptor modification, and indicates that active trimers couple more strongly than inactive trimers.

Berg and Purcell [Biophys. J. 20, 193 (1977)] calculated how the accuracy of concentration sensing by single-celled organisms is limited by noise from the small number of counted molecules. Here we generalize their results to the sensing of concentration ramps, which is often the biologically relevant situation (e.g., during bacterial chemotaxis). We calculate lower bounds on the uncertainty of ramp sensing by three measurement devices: a single receptor, an absorbing sphere, and a monitoring sphere. We contrast two strategies, simple linear regression of the input signal versus maximum likelihood estimation, and show that the latter can be twice as accurate as the former. Finally, we consider biological implementations of these two strategies, and identify possible signatures that maximum likelihood estimation is implemented by real biological systems.

Recent evidence suggests that the metabolism of some organisms, such as Escherichia coli, is remarkably efficient, producing close to the maximum amount of biomass per unit of nutrient consumed. This observation raises the question of what regulatory mechanisms enable such efficiency. Here, we propose that simple product-feedback inhibition by itself is capable of leading to such optimality. We analyze several representative metabolic modules--starting from a linear pathway and advancing to a bidirectional pathway and metabolic cycle, and finally to integration of two different nutrient inputs. In each case, our mathematical analysis shows that product-feedback inhibition is not only homeostatic but also, with appropriate feedback connections, can minimize futile cycling and optimize fluxes. However, the effectiveness of simple product-feedback inhibition comes at the cost of high levels of some metabolite pools, potentially associated with toxicity and osmotic imbalance. These large metabolite pool sizes can be restricted if feedback inhibition is ultrasensitive. Indeed, the multi-layer regulation of metabolism by control of enzyme expression, enzyme covalent modification, and allostery is expected to result in such ultrasensitive feedbacks. To experimentally test whether the qualitative predictions from our analysis of feedback inhibition apply to metabolic modules beyond linear pathways, we examine the case of nitrogen assimilation in E. coli, which involves both nutrient integration and a metabolic cycle. We find that the feedback regulation scheme suggested by our mathematical analysis closely aligns with the actual regulation of the network and is sufficient to explain much of the dynamical behavior of relevant metabolite pool sizes in nutrient-switching experiments.

Quorum-sensing is the mechanism by which bacteria communicate and synchronize group behaviors. Quantitative information on parameters such as the copy number of particular quorum-sensing proteins should contribute strongly to understanding how the quorum-sensing network functions. Here, we show that the copy number of the master regulator protein LuxR in Vibrio harveyi can be determined in vivo by exploiting small-number fluctuations of the protein distribution when cells undergo division. When a cell divides, both its volume and LuxR protein copy number, N, are partitioned with slight asymmetries. We measured the distribution functions describing the partitioning of the protein fluorescence and the cell volume. The fluorescence distribution is found to narrow systematically as the LuxR population increases, whereas the volume partitioning is unchanged. Analyzing these changes statistically, we determined that N = 80-135 dimers at low cell density and 575 dimers at high cell density. In addition, we measured the static distribution of LuxR over a large (3000) clonal population. Combining the static and time-lapse experiments, we determine the magnitude of the Fano factor of the distribution. This technique has broad applicability as a general in vivo technique for measuring protein copy number and burst size., (Copyright (c) 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Bacterial histidine kinases transduce extracellular signals into the cytoplasm. Most stimuli are chemically undefined; therefore, despite intensive study, signal recognition mechanisms remain mysterious. We exploit the fact that quorum-sensing signals are known molecules to identify mutants in the Vibrio cholerae quorum-sensing receptor CqsS that display altered responses to natural and synthetic ligands. Using this chemical-genetics approach, we assign particular amino acids of the CqsS sensor to particular roles in recognition of the native ligand, CAI-1 (S-3 hydroxytridecan-4-one) as well as ligand analogues. Amino acids W104 and S107 dictate receptor preference for the carbon-3 moiety. Residues F162 and C170 specify ligand head size and tail length, respectively. By combining mutations, we can build CqsS receptors responsive to ligand analogues altered at both the head and tail. We suggest that rationally designed ligands can be employed to study, and ultimately to control, histidine kinase activity.

Quorum-sensing (QS) bacteria assess population density through secretion and detection of molecules called autoinducers (AIs). We identify and characterize two Vibrio harveyi negative feedback loops that facilitate precise transitions between low-cell-density (LCD) and high-cell-density (HCD) states. The QS central regulator LuxO autorepresses its own transcription, and the Qrr small regulatory RNAs (sRNAs) posttranscriptionally repress luxO. Disrupting feedback increases the concentration of AIs required for cells to transit from LCD to HCD QS modes. Thus, the two cooperative negative feedback loops determine the point at which V. harveyi has reached a quorum and control the range of AIs over which the transition occurs. Negative feedback regulation also constrains the range of QS output by preventing sRNA levels from becoming too high and preventing luxO mRNA levels from reaching zero. We suggest that sRNA-mediated feedback regulation is a network design feature that permits fine-tuning of gene regulation and maintenance of homeostasis., (Copyright 2010 Elsevier Inc. All rights reserved.)

Methylation of specific histone residues is capable of both gene activation and silencing. Despite vast work on the function of methylation, most studies either present a static snapshot of methylation or fail to assign kinetic information to specific residues. Using liquid chromatography-tandem mass spectrometry on a high-resolution mass spectrometer and heavy methyl-SILAC labeling, we studied site-specific histone lysine and arginine methylation dynamics. The detection of labeled intermediates within a methylation state revealed that mono-, di-, and trimethylated residues generally have progressively slower rates of formation. Furthermore, methylations associated with active genes have faster rates than methylations associated with silent genes. Finally, the presence of both an active and silencing mark on the same peptide results in a slower rate of methylation than the presence of either mark alone. Here we show that quantitative proteomic approaches such as this can determine the dynamics of multiple methylated residues, an understudied portion of histone biology.

In the bacterium Escherichia coli, the enzyme glutamine synthetase (GS) converts ammonium into the amino acid glutamine. GS is principally active when the cell is experiencing nitrogen limitation, and its activity is regulated by a bicyclic covalent modification cascade. The advantages of this bicyclic-cascade architecture are poorly understood. We analyze a simple model of the GS cascade in comparison to other regulatory schemes and conclude that the bicyclic cascade is suboptimal for maintaining metabolic homeostasis of the free glutamine pool. Instead, we argue that the lag inherent in the covalent modification of GS slows the response to an ammonium shock and thereby allows GS to transiently detoxify the cell, while maintaining homeostasis over longer times.

We present a minimal physical model for the flagellar motor that enables bacteria to swim. Our model explains the experimentally measured torque-speed relationship of the proton-driven E. coli motor at various pH and temperature conditions. In particular, the dramatic drop of torque at high rotation speeds (the "knee") is shown to arise from saturation of the proton flux. Moreover, we show that shot noise in the proton current dominates the diffusion of motor rotation at low loads. This suggests a new way to probe the discreteness of the energy source, analogous to measurements of charge quantization in superconducting tunnel junctions.

Bacterial cells come in a variety of shapes, determined by the stress-bearing cell wall. Though many molecular details about the cell wall are known, our understanding of how a particular shape is produced during cell growth is at its infancy. Experiments on curved Escherichia coli grown in microtraps, and on naturally curved Caulobacter crescentus, reveal different modes of growth: one preserving arc length and the other preserving radius of curvature. We present a simple model for curved cell growth that relates these two growth modes to distinct but related growth rules--"hooplike growth" and "self-similar growth"--and discuss the implications for microscopic growth mechanisms.

The accuracy by which biological cells sense chemical concentration is ultimately limited by the random arrival of particles at the receptors by diffusion. This fundamental physical limit is generally considered to be the Berg-Purcell limit [Biophys. J. 20, 193 (1977)]. Here we derive a lower limit by applying maximum likelihood to the time series of receptor occupancy. The increased accuracy stems from solely considering the unoccupied time intervals--disregarding the occupied time intervals as these do not contain any information about the external particle concentration, and only decrease the accuracy of the concentration estimate. Receptors which minimize the bound time intervals achieve the highest possible accuracy. We discuss how a cell could implement such an optimal sensing strategy by absorbing or degrading bound particles.

The bacterial flagellar motor is a highly efficient rotary machine used by many bacteria to propel themselves. It has recently been shown that at low speeds its rotation proceeds in steps. Here we propose a simple physical model, based on the storage of energy in protein springs, that accounts for this stepping behavior as a random walk in a tilted corrugated potential that combines torque and contact forces. We argue that the absolute angular position of the rotor is crucial for understanding step properties and show this hypothesis to be consistent with the available data, in particular the observation that backward steps are smaller on average than forward steps. We also predict a sublinear speed versus torque relationship for fixed load at low torque, and a peak in rotor diffusion as a function of torque. Our model provides a comprehensive framework for understanding and analyzing stepping behavior in the bacterial flagellar motor and proposes novel, testable predictions. More broadly, the storage of energy in protein springs by the flagellar motor may provide useful general insights into the design of highly efficient molecular machines.

Chemotactic cells of eukaryotic organisms are able to accurately sense shallow chemical concentration gradients using cell-surface receptors. This sensing ability is remarkable as cells must be able to spatially resolve small fractional differences in the numbers of particles randomly arriving at cell-surface receptors by diffusion. An additional challenge and source of uncertainty is that particles, once bound and released, may rebind the same or a different receptor, which adds to noise without providing any new information about the environment. We recently derived the fundamental physical limits of gradient sensing using a simple spherical-cell model, but not including explicit particle-receptor kinetics. Here, we use a method based on the fluctuation-dissipation theorem (FDT) to calculate the accuracy of gradient sensing by realistic receptors. We derive analytical results for two receptors, as well as two coaxial rings of receptors, e.g. one at each cell pole. For realistic receptors, we find that particle rebinding lowers the accuracy of gradient sensing, in line with our previous results.

The Escherichia coli chemotaxis network is a model system for biological signal processing. In E. coli, transmembrane receptors responsible for signal transduction assemble into large clusters containing several thousand proteins. These sensory clusters have been observed at cell poles and future division sites. Despite extensive study, it remains unclear how chemotaxis clusters form, what controls cluster size and density, and how the cellular location of clusters is robustly maintained in growing and dividing cells. Here, we use photoactivated localization microscopy (PALM) to map the cellular locations of three proteins central to bacterial chemotaxis (the Tar receptor, CheY, and CheW) with a precision of 15 nm. We find that cluster sizes are approximately exponentially distributed, with no characteristic cluster size. One-third of Tar receptors are part of smaller lateral clusters and not of the large polar clusters. Analysis of the relative cellular locations of 1.1 million individual proteins (from 326 cells) suggests that clusters form via stochastic self-assembly. The super-resolution PALM maps of E. coli receptors support the notion that stochastic self-assembly can create and maintain approximately periodic structures in biological membranes, without direct cytoskeletal involvement or active transport., Competing Interests: The authors declare competing financial interests. EB and Harald Hess (Janelia Farm) have licensed the PALM technology to Carl Zeiss Microimaging, GmbH.

It is generally assumed that amino acid mutations in the surface protein, hemagglutinin (HA), of influenza viruses allow these viruses to circumvent neutralization by antibodies induced during infection. However, empirical data on circulating influenza viruses show that certain amino acid changes to HA actually increase the efficiency of neutralization of the mutated virus by antibodies raised against the parent virus. Here, we suggest that this surprising increase in neutralization efficiency after HA mutation could reflect steric interference between antibodies. Specifically, if there is a steric competition for binding to HA by antibodies with different neutralization efficiencies, then a mutation that reduces the binding of antibodies with low neutralization efficiencies could increase overall viral neutralization. We use a mathematical model of virus-antibody interaction to elucidate the conditions under which amino acid mutations to HA could lead to an increase in viral neutralization. Using insights gained from the model, together with genetic and structural data, we predict that amino acid mutations to epitopes C and E of the HA of influenza A/H3N2 viruses could lead on average to an increase in the neutralization of the mutated viruses. We present data supporting this prediction and discuss the implications for the design of more effective vaccines against influenza viruses and other pathogens.

Cell-to-cell communication in bacteria is a process known as quorum sensing that relies on the production, detection, and response to the extracellular accumulation of signaling molecules called autoinducers. Often, bacteria use multiple autoinducers to obtain information about the vicinal cell density. However, how cells integrate and interpret the information contained within multiple autoinducers remains a mystery. Using single-cell fluorescence microscopy, we quantified the signaling responses to and analyzed the integration of multiple autoinducers by the model quorum-sensing bacterium Vibrio harveyi. Our results revealed that signals from two distinct autoinducers, AI-1 and AI-2, are combined strictly additively in a shared phosphorelay pathway, with each autoinducer contributing nearly equally to the total response. We found a coherent response across the population with little cell-to-cell variation, indicating that the entire population of cells can reliably distinguish several distinct conditions of external autoinducer concentration. We speculate that the use of multiple autoinducers allows a growing population of cells to synchronize gene expression during a series of distinct developmental stages., Competing Interests: Competing interests. The authors have declared that no competing interests exist.

Despite extensive study of individual enzymes and their organization into pathways, the means by which enzyme networks control metabolite concentrations and fluxes in cells remains incompletely understood. Here, we examine the integrated regulation of central nitrogen metabolism in Escherichia coli through metabolomics and ordinary-differential-equation-based modeling. Metabolome changes triggered by modulating extracellular ammonium centered around two key intermediates in nitrogen assimilation, alpha-ketoglutarate and glutamine. Many other compounds retained concentration homeostasis, indicating isolation of concentration changes within a subset of the metabolome closely linked to the nutrient perturbation. In contrast to the view that saturated enzymes are insensitive to substrate concentration, competition for the active sites of saturated enzymes was found to be a key determinant of enzyme fluxes. Combined with covalent modification reactions controlling glutamine synthetase activity, such active-site competition was sufficient to explain and predict the complex dynamic response patterns of central nitrogen metabolites.

Bacteria communicate using secreted chemical signaling molecules called autoinducers in a process known as quorum sensing. The quorum-sensing network of the marine bacterium Vibrio harveyi uses three autoinducers, each known to encode distinct ecological information. Yet how cells integrate and interpret the information contained within these three autoinducer signals remains a mystery. Here, we develop a new framework for analyzing signal integration on the basis of information theory and use it to analyze quorum sensing in V. harveyi. We quantify how much the cells can learn about individual autoinducers and explain the experimentally observed input-output relation of the V. harveyi quorum-sensing circuit. Our results suggest that the need to limit interference between input signals places strong constraints on the architecture of bacterial signal-integration networks, and that bacteria probably have evolved active strategies for minimizing this interference. Here, we analyze two such strategies: manipulation of autoinducer production and feedback on receptor number ratios.

In bacterial cells, the peptidoglycan cell wall is the stress-bearing structure that dictates cell shape. Although many molecular details of the composition and assembly of cell-wall components are known, how the network of peptidoglycan subunits is organized to give the cell shape during normal growth and how it is reorganized in response to damage or environmental forces have been relatively unexplored. In this work, we introduce a quantitative physical model of the bacterial cell wall that predicts the mechanical response of cell shape to peptidoglycan damage and perturbation in the rod-shaped Gram-negative bacterium Escherichia coli. To test these predictions, we use time-lapse imaging experiments to show that damage often manifests as a bulge on the sidewall, coupled to large-scale bending of the cylindrical cell wall around the bulge. Our physical model also suggests a surprising robustness of cell shape to peptidoglycan defects, helping explain the observed porosity of the cell wall and the ability of cells to grow and maintain their shape even under conditions that limit peptide crosslinking. Finally, we show that many common bacterial cell shapes can be realized within the same model via simple spatial patterning of peptidoglycan defects, suggesting that minor patterning changes could underlie the great diversity of shapes observed in the bacterial kingdom.

Chemotaxis receptors in E. coli form clusters at the cell poles and also laterally along the cell body, and this clustering plays an important role in signal transduction. Recently, experiments using fluorescence imaging have shown that, during cell growth, lateral clusters form at positions approximately periodically spaced along the cell body. In this Letter, we demonstrate within a lattice model that such spatial organization could arise spontaneously from a stochastic nucleation mechanism. The same mechanism may explain the recent observation of periodic aggregates of misfolded proteins in E. coli.

Live-cell imaging by light microscopy has demonstrated that all cells are spatially and temporally organized. Quantitative, computational image analysis is an important part of cellular imaging, providing both enriched information about individual cell properties and the ability to analyze large datasets. However, such studies are often limited by the small size and variable shape of objects of interest. Here, we address two outstanding problems in bacterial cell division by developing a generally applicable, standardized, and modular software suite termed Projected System of Internal Coordinates from Interpolated Contours (PSICIC) that solves common problems in image quantitation. PSICIC implements interpolated-contour analysis for accurate and precise determination of cell borders and automatically generates internal coordinate systems that are superimposable regardless of cell geometry. We have used PSICIC to establish that the cell-fate determinant, SpoIIE, is asymmetrically localized during Bacillus subtilis sporulation, thereby demonstrating the ability of PSICIC to discern protein localization features at sub-pixel scales. We also used PSICIC to examine the accuracy of cell division in Esherichia coli and found a new role for the Min system in regulating division-site placement throughout the cell length, but only prior to the initiation of cell constriction. These results extend our understanding of the regulation of both asymmetry and accuracy in bacterial division while demonstrating the general applicability of PSICIC as a computational approach for quantitative, high-throughput analysis of cellular images.

Many types of cells are able to accurately sense shallow gradients of chemicals across their diameters, allowing the cells to move toward or away from chemical sources. This chemotactic ability relies on the remarkable capacity of cells to infer gradients from particles randomly arriving at cell-surface receptors by diffusion. Whereas the physical limits of concentration sensing by cells have been explored, there is no theory for the physical limits of gradient sensing. Here, we derive such a theory, using as models a perfectly absorbing sphere and a perfectly monitoring sphere, which, respectively, infer gradients from the absorbed surface particle density or the positions of freely diffusing particles inside a spherical volume. We find that the perfectly absorbing sphere is superior to the perfectly monitoring sphere, both for concentration and gradient sensing, because previously observed particles are never remeasured. The superiority of the absorbing sphere helps explain the presence at the surfaces of cells of signal-degrading enzymes, such as PDE for cAMP in Dictyostelium discoideum (Dicty) and BAR1 for mating factor alpha in Saccharomyces cerevisiae (budding yeast). Quantitatively, our theory compares favorably with recent measurements of Dicty moving up a cAMP gradient, suggesting these cells operate near the physical limits of gradient detection.

Quorum sensing is the process of cell-to-cell communication by which bacteria communicate via secreted signal molecules called autoinducers. As cell population density increases, the accumulation of autoinducers leads to co-ordinated changes in gene expression across the bacterial community. The marine bacterium, Vibrio harveyi, uses three autoinducers to achieve intra-species, intra-genera and inter-species cell-cell communication. The detection of these autoinducers ultimately leads to the production of LuxR, the quorum-sensing master regulator that controls expression of the genes in the quorum-sensing regulon. LuxR is a member of the TetR protein superfamily; however, unlike other TetR repressors that typically repress their own gene expression and that of an adjacent operon, LuxR is capable of activating and repressing a large number of genes. Here, we used protein binding microarrays and a two-layered bioinformatics approach to show that LuxR binds a 21 bp consensus operator with dyad symmetry. In vitro and in vivo analyses of two promoters directly regulated by LuxR allowed us to identify those bases that are critical for LuxR binding. Together, the in silico and biochemical results enabled us to scan the genome and identify novel targets of LuxR in V. harveyi and thus expand the understanding of the quorum-sensing regulon.

Quorum sensing, a process of bacterial cell-cell communication, relies on production, detection, and response to autoinducer signaling molecules. LuxN, a nine-transmembrane domain protein from Vibrio harveyi, is the founding example of membrane-bound receptors for acyl-homoserine lactone (AHL) autoinducers. We used mutagenesis and suppressor analyses to identify the AHL-binding domain of LuxN and discovered LuxN mutants that confer both decreased and increased AHL sensitivity. Our analysis of dose-response curves of multiple LuxN mutants pins these inverse phenotypes on quantifiable opposing shifts in the free-energy bias of LuxN for occupying its kinase and phosphatase states. To understand receptor activation and to characterize the pathway signaling parameters, we exploited a strong LuxN antagonist, one of fifteen small-molecule antagonists we identified. We find that quorum-sensing-mediated communication can be manipulated positively and negatively to control bacterial behavior and, more broadly, that signaling parameters can be deduced from in vivo data.