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.
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.
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.
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.
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.
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.
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.
The chemotaxis system in the bacterium Escherichia coli is remarkably sensitive to small relative changes in the concentrations of multiple chemical signals over a broad range of ambient concentrations. 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. Precise adaptation relies on methylation and demethylation of chemoreceptors by the enzymes CheR and CheB, respectively. Experiments indicate that when transiently bound to one receptor, these enzymes act on small assistance neighborhoods (AN) of five to seven receptor homodimers. In this paper, we model a strongly coupled complex of receptors including dynamic CheR and CheB acting on ANs. The model yields sensitive response and precise adaptation over several orders of magnitude of attractant concentrations and accounts for different responses to aspartate and serine. Within the model, we explore how the precision of adaptation is limited by small AN size as well as by CheR and CheB kinetics (including dwell times, saturation, and kinetic differences among modification sites) and how these kinetics contribute to noise in complex activity. The robustness of our dynamic model for precise adaptation is demonstrated by randomly varying biochemical parameters.
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.
There is increasing experimental evidence that cells can utilize biochemical noise to switch probabilistically between distinct gene-expression states. In this paper, we demonstrate that such noise-driven switching is dominated by tails of probability distributions and is therefore exponentially sensitive to changes in physiological parameters such as transcription and translation rates. Exponential sensitivity limits the robustness of noise-driven switching, suggesting cells may use other mechanisms in order to switch reliably. We discuss our results in the context of competence in the bacterium Bacillus subtilis.
Our goal is to develop accurate electrostatic models that can be implemented in current computational protein design protocols. To this end, we improve upon a previously reported pairwise decomposable, finite difference Poisson-Boltzmann (FDPB) model for protein design (Marshall et al., Protein Sci 2005, 14, 1293). The improvement involves placing generic sidechains at positions with unknown amino acid identity and explicitly capturing two-body perturbations to the dielectric environment. We compare the original and improved FDPB methods to standard FDPB calculations in which the dielectric environment is completely determined by protein atoms. The generic sidechain approach yields a two to threefold increase in accuracy per residue or residue pair over the original pairwise FDPB implementation, with no additional computational cost. Distance dependent dielectric and solvent-exclusion models were also compared with standard FDPB energies. The accuracy of the new pairwise FDPB method is shown to be superior to these models, even after reparameterization of the solvent-exclusion model.
Although many proteins are known to localize in bacterial cells, for the most part our understanding of how such localization takes place is limited. Recent evidence that the phospholipid cardiolipin localizes to the poles of rod-shaped bacteria suggests that targeting of some proteins may rely on the heterogeneous distribution of membrane lipids. Membrane curvature has been proposed as a factor in the polar localization of high-intrinsic-curvature lipids, but the small size of lipids compared to the dimensions of the cell means that single molecules cannot stably localize. At the other extreme, phase separation of the membrane energetically favors a single domain of such lipids at one pole. We have proposed a physical mechanism in which osmotic pinning of the membrane to the cell wall naturally produces microphase separation, i.e., lipid domains of finite size, whose aggregate sensitivity to cell curvature can support spontaneous and stable localization to both poles. Here, we demonstrate that variations in the strength of pinning of the membrane to the cell wall can also act as a strong localization mechanism, in agreement with observations of cardiolipin relocalization from the poles to the septum during sporulation in the bacterium Bacillus subtilis. In addition, we rigorously determine the relationship between localization and the domain-size distribution including the effects of entropy, and quantify the strength of domain-domain interactions. Our model predicts a critical concentration of cardiolipin below which domains will not form and hence polar localization will not take place. This observation is consistent with recent experiments showing that in Escherichia coli cells with reduced cardiolipin concentrations, cardiolipin and the osmoregulatory protein ProP fail to localize to the poles.
Like many sensory receptors, bacterial chemotaxis receptors form clusters. In bacteria, large-scale clusters are subdivided into signaling teams that act as 'antennas' allowing detection of ligands with remarkable sensitivity. The range of sensitivity is greatly extended by adaptation of receptors to changes in concentrations through covalent modification. However, surprisingly little is known about the sizes of receptor signaling teams. Here, we combine measurements of the signaling response, obtained from in vivo fluorescence resonance energy transfer, with the statistical method of principal component analysis, to quantify the size of signaling teams within the framework of the previously successful Monod-Wyman-Changeux model. We find that size of signaling teams increases 2- to 3-fold with receptor modification, indicating an additional, previously unrecognized level of adaptation of the chemotaxis network. This variation of signaling-team size shows that receptor cooperativity is dynamic and likely optimized for sensing noisy ligand concentrations.
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.
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.
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.
Small non-coding RNAs (sRNAs) have important functions as genetic regulators in prokaryotes. sRNAs act post-transcriptionally through complementary pairing with target mRNAs to regulate protein expression. We use a quantitative approach to compare and contrast sRNAs with conventional transcription factors (TFs) to better understand the advantages of each form of regulation. In particular, we calculate the steady-state behavior, noise properties, frequency-dependent gain (amplification), and dynamical response to large input signals of both forms of regulation. Although the mean steady-state behavior of sRNA-regulated proteins exhibits a distinctive tunable threshold linear behavior, our analysis shows that transcriptional bursting leads to significantly higher intrinsic noise in sRNA-based regulation than in TF-based regulation in a large range of expression levels and limits the ability of sRNAs to perform quantitative signaling. Nonetheless, we find that sRNAs are better than TFs at filtering noise in input signals. Additionally, we find that sRNAs allow cells to respond rapidly to large changes in input signals. These features suggest a 'niche' for sRNAs in allowing cells to transition quickly yet reliably between distinct states. This functional niche is consistent with the widespread appearance of sRNAs in stress response and quasi-developmental networks in prokaryotes.
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.
Product-feedback inhibition is a ubiquitous regulatory scheme for maintaining homeostasis in living cells. Individual metabolic pathways with product-feedback inhibition are stable as long as one pathway step is rate limiting. However, pathways are often coupled both by the use of a common substrate and by stoichiometric utilization of their products for cell growth. We show that such a coupled network with product-feedback inhibition may exhibit limit-cycle oscillations which arise via a Hopf bifurcation. Our results highlight novel evolutionary constraints on the architecture of metabolism.