An allosteric model for transmembrane signaling in bacterial chemotaxis

SpoVAF and FigP assemble into oligomeric ion channels that enhance spore germination

Bacterial spores can remain dormant for decades yet rapidly germinate and resume growth in response to nutrients. GerA family receptors that sense and respond to these signals have recently been shown to oligomerize into nutrient-gated ion channels. Ion release initiates exit from dormancy. Here, we report that a distinct ion channel, composed of SpoVAF (5AF) and its newly discovered partner protein, YqhR (FigP), amplifies the response. At high germinant concentrations, 5AF/FigP accelerate germination; at low concentrations, this complex becomes critical for exit from dormancy. 5AF is homologous to the channel-forming subunit of GerA family receptors and is predicted to oligomerize around a central pore. 5AF mutations predicted to widen the channel cause constitutive germination during spore formation and membrane depolarization in vegetative cells. Narrow-channel mutants are impaired in germination. A screen for suppressors of a constitutively germinating 5AF mutant identified FigP as an essential cofactor of 5AF activity. We demonstrate that 5AF and FigP interact and colocalize with GerA family receptors in spores. Finally, we show that 5AF/FigP accelerate germination in B. subtilis spores that have nutrient receptors from another species. Our data support a model in which nutrient-triggered ion release by GerA family receptors activates 5AF/FigP ion release, amplifying the response to germinant signals.

Peptide-Metal Organic Framework Swimmers that Direct the Motion toward Chemical Targets

Highly efficient and robust chemical motors are expected for the application in microbots that can selectively swim toward targets and accomplish their tasks in sensing, labeling, and delivering. However, one of major issues for such development is that current artificial swimmers have difficulty controlling their directional motion toward targets like bacterial chemotaxis. To program synthetic motors with sensing capability for the target-directed motion, we need to develop swimmers whose motions are sensitive to chemical gradients in environments. Here we create a new intelligent biochemical swimmer by integrating metal organic frameworks (MOFs) and peptides that can sense toxic heavy metals in solution and swim toward the targets. With the aid of Pb-binding enzymes, the peptide-MOF motor can directionally swim toward PbSe quantum dots (QD) by sensing pH gradient and eventually complete the motion as the swimmer reaches the highest gradient point at the target position in solution. This type of technology could be evolved to miniaturize chemical robotic systems that sense target chemicals and swim toward target locations.

Excitation and adaptation in bacteria-a model signal transduction system that controls taxis and spatial pattern formation

The machinery for transduction of chemotactic stimuli in the bacterium E. coli is one of the most completely characterized signal transduction systems, and because of its relative simplicity, quantitative analysis of this system is possible. Here we discuss models which reproduce many of the important behaviors of the system. The important characteristics of the signal transduction system are excitation and adaptation, and the latter implies that the transduction system can function as a "derivative sensor" with respect to the ligand concentration in that the DC component of a signal is ultimately ignored if it is not too large. This temporal sensing mechanism provides the bacterium with a memory of its passage through spatially- or temporally-varying signal fields, and adaptation is essential for successful chemotaxis. We also discuss some of the spatial patterns observed in populations and indicate how cell-level behavior can be embedded in population-level descriptions.

Quantitative modeling of bacterial chemotaxis: signal amplification and accurate adaptation

We review the recent developments in understanding the bacterial chemotaxis signaling pathway by using quantitative modeling methods. The models developed are based on structural information of the signaling complex and the dynamics of the underlying biochemical network. We focus on two important functions of the bacterial chemotaxis signaling pathway: signal amplification and adaptation. We describe in detail the structure and the dynamics of the mathematical models and how they compare with existing experiments, emphasizing the predictability of the models. Finally, we outline future directions for developing the modeling approach to better understand the bacterial chemosensory system.

The relation of signal transduction to the sensitivity and dynamic range of bacterial chemotaxis

Complex networks of interacting molecular components of living cells are responsible for many important processes, such as signal processing and transduction. An important challenge is to understand how the individual properties of these molecular interactions and biochemical transformations determine the system-level properties of biological functions. Here, we address the issue of the accuracy of signal transduction performed by a bacterial chemotaxis system. The chemotaxis sensitivity of bacteria to a chemoattractant gradient has been measured experimentally from bacterial aggregation in a chemoattractant-containing capillary. The observed precision of the chemotaxis depended on environmental conditions such as the concentration and molecular makeup of the chemoattractant. In a quantitative model, we derived the chemotactic response function, which is essential to describing the signal transduction process involved in bacterial chemotaxis. In the presence of a gradient, an analytical solution is derived that reveals connections between the chemotaxis sensitivity and the characteristics of the signaling system, such as reaction rates. These biochemical parameters are integrated into two system-level parameters: one characterizes the efficiency of gradient sensing, and the other is related to the dynamic range of chemotaxis. Thus, our approach explains how a particular signal transduction property affects the system-level performance of bacterial chemotaxis. We further show that the two parameters can be derived from published experimental data from a capillary assay, which successfully characterizes the performance of bacterial chemotaxis.

Characterization of the adaptation module of the signaling network in bacterial chemotaxis by measurement of step responses

The bacterial chemotaxis network features robust adaptation implemented by negative integral feedback. Here, we show that the adaptation module can be characterized by measurement of the response to simple step-addition and removal of a chemoattractant. The method does not rely on a particular form of the receptor module, and thus can be used to characterize other integral feedback networks.

A "trimer of dimers"-based model for the chemotactic signal transduction network in bacterial chemotaxis

The network that controls chemotaxis in Escherichia coli is one of the most completely characterized signal transduction systems to date. Receptor clustering accounts for characteristics such as high sensitivity, precise adaptation over a wide dynamic range of ligand concentrations, and robustness to variations in the amounts of intracellular proteins. To gain insights into the structure-function relationship of receptor clusters and understand the mechanism behind the high-performance signaling, we develop and analyze a model for a single trimer of dimers. This new model extends an earlier model (Spiro et al. in Proc. Natl. Acad. Sci. 94:7263-7268, 1997) to incorporate the recent experimental findings that the core structure of receptor clusters is the trimer of receptor dimers. We show that the model can reproduce most of the experimentally-observed behaviors, including excitation, adaptation, high sensitivity, and robustness to parameter variations. In addition, the model makes a number of new predictions as to how the adaptation time varies with the expression level of various proteins involved in signal transduction. Our results provide a more mechanistically-based description of the structure-function relationship for the signaling system, and show the key role of the interaction among dimer members of the trimer in the chemotactic response of cells.

Site-specific methylation in Bacillus subtilis chemotaxis: effect of covalent modifications to the chemotaxis receptor McpB

The Bacillus subtilis chemotaxis pathway employs a receptor methylation system that functions differently from the one in the canonical Escherichia coli pathway. Previously, we hypothesized that B. subtilis employs a site-specific methylation system for adaptation where methyl groups are added and removed at different sites. This study investigated how covalent modifications to the adaptation region of the chemotaxis receptor McpB altered its apparent affinity for its cognate ligand, asparagine, and also its ability to activate the CheA kinase. This receptor has three closely spaced adaptation sites located at residues Gln371, Glu630 and Glu637. We found that amidation, a putative methylation mimic, of site 371 increased the receptor's apparent affinity for asparagine and its ability to activate the CheA kinase. Conversely, amidation of sites 630 and 637 reduced the receptor's ability to activate the kinase but did not affect the apparent affinity for asparagine, suggesting that activity and sensitivity are independently controlled in B. subtilis. We also examined how electrostatic interactions may underlie this behaviour, using homology models. These findings further our understanding of the site-specific methylation system in B. subtilis by demonstrating how the modification of specific sites can have varying effects on receptor function.

An agent-based model of signal transduction in bacterial chemotaxis

We report the application of agent-based modeling to examine the signal transduction network and receptor arrays for chemotaxis in Escherichia coli, which are responsible for regulating swimming behavior in response to environmental stimuli. Agent-based modeling is a stochastic and bottom-up approach, where individual components of the modeled system are explicitly represented, and bulk properties emerge from their movement and interactions. We present the Chemoscape model: a collection of agents representing both fixed membrane-embedded and mobile cytoplasmic proteins, each governed by a set of rules representing knowledge or hypotheses about their function. When the agents were placed in a simulated cellular space and then allowed to move and interact stochastically, the model exhibited many properties similar to the biological system including adaptation, high signal gain, and wide dynamic range. We found the agent based modeling approach to be both powerful and intuitive for testing hypotheses about biological properties such as self-assembly, the non-linear dynamics that occur through cooperative protein interactions, and non-uniform distributions of proteins in the cell. We applied the model to explore the role of receptor type, geometry and cooperativity in the signal gain and dynamic range of the chemotactic response to environmental stimuli. The model provided substantial qualitative evidence that the dynamic range of chemotactic response can be traced to both the heterogeneity of receptor types present, and the modulation of their cooperativity by their methylation state.

Signal amplification in a lattice of coupled protein kinases

The bacterium Escherichia coli detects chemical attractants and repellents by means of a cluster of transmembrane receptors and associated molecules. Experiments have shown that this cluster amplifies the signal about 35-fold and current models attribute this amplification to cooperative interactions between neighbouring receptors. However, when applied to the mixed population of receptors of wild-type E. coli, these models lead to indiscriminate methylation of all receptor types rather than the selective methylation observed experimentally. In this paper, we propose that cooperative interactions occur not between receptors but in the underlying lattice of CheA molecules. In our model, each CheA molecule is stimulated by its neighbours via their flexible P1 domains and modulated by the ligand binding and methylation states of associated receptors. We test this idea with detailed, molecular-based stochastic simulations and show that it gives an accurate reproduction of signalling in this system, including ligand-specific adaptation.

Differential affinity and catalytic activity of CheZ in E. coli chemotaxis

Push–pull networks, in which two antagonistic enzymes control the activity of a messenger protein, are ubiquitous in signal transduction pathways. A classical example is the chemotaxis system of the bacterium Escherichia coli, in which the kinase CheA and the phosphatase CheZ regulate the phosphorylation level of the messenger protein CheY. Recent experiments suggest that both the kinase and the phosphatase are localized at the receptor cluster, and Vaknin and Berg recently demonstrated that the spatial distribution of the phosphatase can markedly affect the dose–response curves. We argue, using mathematical modeling, that the canonical model of the chemotaxis network cannot explain the experimental observations of Vaknin and Berg. We present a new model, in which a small fraction of the phosphatase is localized at the receptor cluster, while the remainder freely diffuses in the cytoplasm; moreover, the phosphatase at the cluster has a higher binding affinity for the messenger protein and a higher catalytic activity than the phosphatase in the cytoplasm. This model is consistent with a large body of experimental data and can explain many of the experimental observations of Vaknin and Berg. More generally, the combination of differential affinity and catalytic activity provides a generic mechanism for amplifying signals that could be exploited in other two-component signaling systems. If this model is correct, then a number of recent modeling studies, which aim to explain the chemotactic gain in terms of the activity of the receptor cluster, should be reconsidered.

In both prokaryotes and eukaryotes, extra- and intracellular signals are often processed by biochemical networks in which two enzymes together control the activity of a messenger protein via opposite modification reactions. A well-known example is the chemotaxis network of Escherichia coli that controls the swimming behavior of the bacterium in response to chemical stimuli. Recent experiments suggest that the two counteracting enzymes in this network are colocalized at the receptor cluster, while experiments by Vaknin and Berg indicate that the spatial distribution of the enzymes by itself can markedly affect the response of the network. We argue using mathematical modeling that the most widely used model of the chemotaxis network is inconsistent with these experimental observations. We then present an alternative model in which part of one enzyme is colocalized with the other enzyme at the receptor cluster, while the remainder freely diffuses in the cytoplasm; moreover, the fraction at the cluster both binds more strongly to the messenger protein and modifies it faster. This model is consistent with a large number of experimental observations and provides a generic mechanism for amplifying signals.

Modeling the chemotactic response of Escherichia coli to time-varying stimuli

In their natural environment, cells need to extract useful information from complex temporal signals that vary over a wide range of intensities and time scales. Here, we study how such signals are processed by Escherichia coli during chemotaxis by developing a general theoretical model based on receptor adaptation and receptor-receptor cooperativity. Measured responses to various monotonic, oscillatory, and impulsive stimuli are all explained consistently by the underlying adaptation kinetics within this model. For exponential ramp signals, an analytical solution is discovered that reveals a remarkable connection between the dependence of kinase activity on the exponential ramp rate and the receptor methylation rate function. For exponentiated sine-wave signals, spectral analysis shows that the chemotaxis pathway acts as a lowpass filter for the derivative of the signal with the cutoff frequency determined by an intrinsic adaptation time scale. For large step stimuli, we find that the recovery time is determined by the constant maximum methylation rate, which provides a natural explanation for the observed recovery time additivity. Our model provides a quantitative system-level description of the chemotaxis signaling pathway and can be used to predict E. coli chemotaxis responses to arbitrary temporal signals. This model of the receptor system reveals the molecular origin of Weber's law in bacterial chemotaxis. We further identify additional constraints required to account for the related observation that the output of this pathway is constant under exponential ramp stimuli, a feature that we call "logarithmic tracking."

Effects of adaptation in maintaining high sensitivity over a wide range of backgrounds for Escherichia coli chemotaxis

An allosteric model is developed to study the cooperative kinase response of wild-type (wt) Escherichia coli cells to the chemoattractant MeAsp in different ambient MeAsp concentrations. The model, together with wt dose response data, reveals the underlying mechanism for E. coli's ability to maintain high sensitivity over a wide range of backgrounds. We find: 1), Adaptation tunes the system to the steepest part of the dose response curve, where the sensitivity to a given type of stimulus is amplified by the number of corresponding receptors in the (mixed) functional receptor complex. A lower bound on the number of Tar receptor dimers (Na) in the complex Na>approximately 6 is obtained from the measured sensitivity. 2), Accurate adaptation synchronizes the kinase activities from different (uncoupled) receptor complexes in a single cell and is crucial in maintaining the high Hill coefficient in the (population averaged) kinase response curve. 3), The wide dynamic range of the high sensitivity can be explained in our model by either having a very small ratio between ligand dissociation constants of the inactive and the active receptors C=0.006, Na=6, and a (methylation level independent) dissociation constant for the inactive Tar receptor K=18.2 microM or by having K and/or Na increase with receptor methylation level together with a larger value of C>0.01. Specific experiments are suggested to distinguish these two scenarios. 4), The receptor occupancy in a wt cell should also adapt and exhibit a slow (approximately logarithmic) dependence on the ligand concentration in the adapted state; this general prediction can be tested experimentally to verify/falsify our model.

In vivo measurement by FRET of pathway activity in bacterial chemotaxis

The two-component pathway in Escherichia coli chemotaxis has become a paradigm for bacterial signal processing. Genetics and biochemistry of the pathway as well as physiological responses have been studied in detail. Despite its relative simplicity, the chemotaxis pathway is renowned for its ability to amplify and integrate weak signals and for its robustness against various kinds of perturbations. All this information inspired multiple attempts at mathematical analysis and computer modeling, but a quantitative understanding of the pathway was hampered by our inability to follow the signal processing in vivo. To address this problem, we developed assays based on fluorescence resonance energy transfer (FRET) and bioluminescence resonance energy transfer (BRET) that enabled us to monitor activity-dependent protein interactions in real time directly in living cells. Here, we describe quantitative applications of these assays in cell populations and on a single-cell level to study the interaction of the phosphorylated response regulator CheY with its phosphatase CheZ. Since this interaction defines the rate of CheY dephosphorylation, which at steady state equals the rate of CheY phosphorylation, it can be used to characterize intracellular kinase activity and thus to analyze properties of the chemotaxis signaling network.

Physical responses of bacterial chemoreceptors

Chemoreceptors of the bacterium Escherichia coli are thought to form trimers of homodimers that undergo conformational changes upon ligand binding and thereby signal a cytoplasmic kinase. We monitored the physical responses of trimers in living cells lacking other chemotaxis proteins by fluorescently tagging receptors and measuring changes in fluorescence anisotropy. These changes were traced to changes in energy transfer between fluorophores on different dimers of a trimer: attractants move these fluorophores farther apart, and repellents move them closer together. These measurements allowed us to define the responses of bare receptor oligomers to ligand binding and compare them to the corresponding response in kinase activity. Receptor responses could be fit by a simple "two-state" model in which receptor dimers are in either active or inactive conformations, from which energy bias and dissociation constants could be estimated. Comparison with responses in kinase-activity indicated that higher-order interactions are dominant in receptor clusters.

Reconstruction of the chemotaxis receptor–kinase assembly

In bacterial chemotaxis, an assembly of transmembrane receptors, the CheA histidine kinase and the adaptor protein CheW processes environmental stimuli to regulate motility. The structure of a Thermotoga maritima receptor cytoplasmic domain defines CheA interaction regions and metal ion-coordinating charge centers that undergo chemical modification to tune receptor response. Dimeric CheA-CheW, defined by crystallography and pulsed ESR, positions two CheWs to form a cleft that is lined with residues important for receptor interactions and sized to clamp one receptor dimer. CheW residues involved in kinase activation map to interfaces that orient the CheW clamps. CheA regulatory domains associate in crystals through conserved hydrophobic surfaces. Such CheA self-contacts align the CheW receptor clamps for binding receptor tips. Linking layers of ternary complexes with close-packed receptors generates a lattice with reasonable component ratios, cooperative interactions among receptors and accessible sites for modification enzymes.

Receptor-receptor coupling in bacterial chemotaxis: evidence for strongly coupled clusters

Receptor coupling is believed to explain the high sensitivity of the Escherichia coli chemotaxis network to small changes in levels of chemoattractant. We compare in detail the activity response of coupled two-state receptors for different models of receptor coupling: weakly-coupled extended one-dimensional and two-dimensional lattice models and the Monod-Wyman-Changeux model of isolated strongly-coupled clusters. We identify features in recent data that distinguish between the models. Specifically, researchers have measured the receptor activity response to steps of chemoattractant for a variety of engineered E. coli strains using in vivo fluorescence resonance energy transfer. We find that the fluorescence resonance energy transfer results for wild-type and for a low-activity mutant are inconsistent with the lattice models of receptor coupling, but consistent with the Monod-Wyman-Changeux model of receptor coupling, suggesting that receptors form isolated strongly-coupled clusters.

An allosteric model for heterogeneous receptor complexes: understanding bacterial chemotaxis responses to multiple stimuli

The classical Monod-Wyman-Changeux model for homogeneous allosteric protein complex is generalized in this article to model the responses of heterogeneous receptor complexes to multiple types of ligand stimulus. We show that the recent in vivo experimental data of Escherichia coli chemotaxis responses for mutant strains with different expression levels of the chemo-receptors to different types of stimulus [Sourjik, V. & Berg, H. C. (2004) Nature 428, 437-441] all can be explained consistently within this generalized Monod-Wyman-Changeux model. Based on the model and the existing data, responses of all of the strains (studied in this article) to the presence of any combinations of ligand (Ser and MeAsp) concentrations are predicted quantitatively for future experimental verification. Through modeling the in vivo response data, our study reveals important information about the properties of different types of individual receptors, as well as the composition of the cluster. The energetic contribution of the nonligand binding, cytoplasmic parts of the cluster, such as CheA and CheW, is also discussed. The generalized allosteric model provides a consistent framework in understanding signal integration and differentiation in bacterial chemotaxis. It should also be useful for studying the functions of other heterogeneous receptor complexes.

Adaptational assistance in clusters of bacterial chemoreceptors

Sensory adaptation of low-abundance chemoreceptors in Escherichia coli requires assistance from high-abundance receptors, because only high-abundance receptors carry the carboxyl-terminal pentapeptide sequence NWETF that enhances adaptational covalent modification. Using membrane vesicles containing both high-abundance receptor Tar and low-abundance receptor Trg, we observed effective assistance in vitro for all three adaptational modifications: methylation, demethylation and deamidation. These results demonstrated that adaptational assistance involves not only the previously documented assistance for methylation but also assistance for the two CheB-catalysed reactions. We determined rates of assisted methylation and demethylation at many ratios of assisting to assisted receptor. Analysis by a model of assistance indicated one Tar dimer could assist seven Trg dimers in methylation or five in demethylation, defining assistance neighbourhoods. These neighbourhoods were larger than a trimer of homodimers, required only receptors and were minimally affected by formation of signalling complexes. Time courses of assisted Trg methylation in membranes with low amounts of Tar showed that assisting receptors did not diffuse beyond initial neighbourhoods for at least two hours. Taken together, these observations indicate that chemoreceptors can form stable neighbourhoods larger than trimers in the absence of other chemotaxis proteins. Such interactions are likely to occur in natural receptor clusters in vivo.