Variable sizes of Escherichia coli chemoreceptor signaling teams

Potassium-mediated bacterial chemotactic response

Bacteria in biofilms secrete potassium ions to attract free swimming cells. However, the basis of chemotaxis to potassium remains poorly understood. Here, using a microfluidic device, we found that Escherichia coli can rapidly accumulate in regions of high potassium concentration on the order of millimoles. Using a bead assay, we measured the dynamic response of individual flagellar motors to stepwise changes in potassium concentration, finding that the response resulted from the chemotaxis signaling pathway. To characterize the chemotactic response to potassium, we measured the dose-response curve and adaptation kinetics via an Förster resonance energy transfer (FRET) assay, finding that the chemotaxis pathway exhibited a sensitive response and fast adaptation to potassium. We further found that the two major chemoreceptors Tar and Tsr respond differently to potassium. Tar receptors exhibit a biphasic response, whereas Tsr receptors respond to potassium as an attractant. These different responses were consistent with the responses of the two receptors to intracellular pH changes. The sensitive response and fast adaptation allow bacteria to sense and localize small changes in potassium concentration. The differential responses of Tar and Tsr receptors to potassium suggest that cells at different growth stages respond differently to potassium and may have different requirements for potassium.

Signal integration in chemoreceptor complexes

Motile bacteria use large receptor arrays to detect chemical and physical stimuli in their environment, process this complex information, and accordingly bias their swimming in a direction they deem favorable. The chemoreceptor molecules form tripod-like trimers of receptor dimers through direct contacts between their cytoplasmic tips. A pair of trimers, together with a dedicated kinase enzyme, form a core signaling complex. Hundreds of core complexes network to form extended arrays. While considerable progress has been made in revealing the hierarchical structure of the array, the molecular properties underlying signal processing in these structures remain largely unclear. Here we analyzed the signaling properties of nonnetworked core complexes in live cells by following both conformational and kinase control responses to attractant stimuli and to output-biasing lesions at various locations in the receptor molecule. Contrary to the prevailing view that individual receptors are binary two-state devices, we demonstrate that conformational coupling between the ligand binding and the kinase-control receptor domains is, in fact, only moderate. In addition, we demonstrate communication between neighboring receptors through their trimer-contact domains that biases them to adopt similar signaling states. Taken together, these data suggest a view of signaling in receptor trimers that allows significant signal integration to occur within individual core complexes.

A Mathematical Description of Bacterial Chemotaxis in Response to Two Stimuli

Bacteria are often exposed to multiple stimuli in complex environments, and their efficient chemotactic decisions are critical to survive and grow in their native environments. Bacterial responses to the environmental stimuli depend on the ratio of their corresponding chemoreceptors. By incorporating the signaling machinery of individual cells, we analyze the collective motion of a population of Escherichia coli bacteria in response to two stimuli, mainly serine and methyl-aspartate (MeAsp), in a one-dimensional and a two-dimensional environment, which is inspired by experimental results in Y. Kalinin et al., J. Bacteriol. 192(7):1796-1800, 2010. Under suitable conditions, we show that if the ratio of the main chemoreceptors of individual cells, namely Tar/Tsr, is less than a specific threshold, the bacteria move to the gradient of serine, and if the ratio is greater than the threshold, the group of bacteria moves toward the gradient of MeAsp. Finally, we examine the theory with Monte Carlo agent-based simulations and verify that our results qualitatively agree well with the experimental results in Y. Kalinin et al. (2010).

Effect of receptor clustering on chemotactic performance of E. coli: Sensing versus adaptation

We show how the competition between sensing and adaptation can result in a performance peak in Escherichia coli chemotaxis using extensive numerical simulations in a detailed theoretical model. Receptor clustering amplifies the input signal coming from ligand binding which enhances chemotactic efficiency. But large clusters also induce large fluctuations in total activity since the number of clusters goes down. The activity and hence the run-tumble motility now gets controlled by methylation levels which are part of adaptation module rather than ligand binding. This reduces chemotactic efficiency.

Connection between the Bacterial Chemotactic Network and Optimal Filtering

The chemotactic network of Escherichia coli has been studied extensively both biophysically and information theoretically. Nevertheless, connection between these two aspects is still elusive. In this work, we report such a connection. We derive an optimal filtering dynamics under the assumption that E. coli's sensory system optimally infers the binary information whether it is swimming up or down along an exponential ligand gradient from noisy sensory signals. Then we show that a standard biochemical model of the chemotactic network is mathematically equivalent to this information-theoretically optimal dynamics. Moreover, we demonstrate that an experimentally observed nonlinear response relation can be reproduced from the optimal dynamics. These results suggest that the biochemical network of E. coli chemotaxis is designed to optimally extract the binary information along an exponential gradient in a noisy condition.

Numerous Post-translational Modifications of RNA Polymerase II Subunit Rpb4/7 Link Transcription to Post-transcriptional Mechanisms

Rpb4/7 binds RNA polymerase II (RNA Pol II) transcripts co-transcriptionally and accompanies them throughout their lives. By virtue of its capacity to interact with key regulators (e.g., RNA Pol II, eIF3, and Pat1) temporally and spatially, Rpb4/7 regulates the major stages of the mRNA life cycle. Here we show that Rpb4/7 can undergo more than 100 combinations of post-translational modifications (PTMs). Remarkably, the Rpb4/7 PTM repertoire changes as the mRNA/Rpb4/7 complex progresses from one stage to the next. These temporal PTMs regulate Rpb4 interactions with key regulators of gene expression that control transcriptional and post-transcriptional stages. Moreover, one mutant type specifically affects mRNA synthesis, whereas the other affects mRNA synthesis and decay; both types disrupt the balance between mRNA synthesis and decay ("mRNA buffering") and the cell's capacity to respond to the environment. We propose that temporal Rpb4/7 PTMs mediate the cross-talk among the various stages of the mRNA life cycle.

Adaptive tuning of cell sensory diversity without changes in gene expression

In the face of uncertainty, cell populations tend to diversify to enhance survival and growth. Previous studies established that cells can optimize such bet hedging upon environmental change by modulating gene expression to adapt both the average and diversity of phenotypes. Here, we demonstrate that cells can tune phenotypic diversity also using posttranslational modifications. In the chemotaxis network of Escherichia coli, we find, for both major chemoreceptors Tar and Tsr, that cell-to-cell variation in response sensitivity is dynamically modulated depending on the presence or absence of their cognate chemoeffector ligands in the environment. Combining experiments with mathematical modeling, we show that this diversity tuning requires only the environment-dependent covalent modification of chemoreceptors and a standing cell-to-cell variation in their allosteric coupling. Thus, when environmental cues are unavailable, phenotypic diversity enhances the population's readiness for many signals. However, once a signal is perceived, the population focuses on tracking that signal.

Maximal information transmission is compatible with ultrasensitive biological pathways

Cells are often considered input-output devices that maximize the transmission of information by converting extracellular stimuli (input) via signaling pathways (communication channel) to cell behavior (output). However, in biological systems outputs might feed back into inputs due to cell motility, and the biological channel can change by mutations during evolution. Here, we show that the conventional channel capacity obtained by optimizing the input distribution for a fixed channel may not reflect the global optimum. In a new approach we analytically identify both input distributions and input-output curves that optimally transmit information, given constraints from noise and the dynamic range of the channel. We find a universal optimal input distribution only depending on the input noise, and we generalize our formalism to multiple outputs (or inputs). Applying our formalism to Escherichia coli chemotaxis, we find that its pathway is compatible with optimal information transmission despite the ultrasensitive rotary motors.

Conformational shifts in a chemoreceptor helical hairpin control kinase signaling in Escherichia coli

Motile bacteria use chemoreceptor signaling arrays to track chemical gradients with high precision. The Escherichia coli chemotaxis system offers an ideal model for probing the molecular mechanisms of transmembrane and intracellular signaling. In this study, we characterized the signaling properties of mutant E. coli receptors that had amino acid replacements in residues that form a salt-bridge connection between the cytoplasmic tips of receptor molecules. The mutant signaling defects suggested that the chemoreceptor tip operates as a two-state device with discrete active and inactive conformations and that the level of output activity modulates connections between receptor signaling units that produce highly cooperative responses to attractant stimuli. These findings shed important light on the nature and control of receptor signaling states.

Motile Escherichia coli cells use chemoreceptor signaling arrays to track chemical gradients with exquisite precision. Highly conserved residues in the cytoplasmic hairpin tip of chemoreceptor molecules promote assembly of trimer-based signaling complexes and modulate the activity of their CheA kinase partners. To explore hairpin tip output states in the serine receptor Tsr, we characterized the signaling consequences of amino acid replacements at the salt-bridge residue pair E385-R388. All mutant receptors assembled trimers and signaling complexes, but most failed to support serine chemotaxis in soft agar assays. Small side-chain replacements at either residue produced OFF- or ON-shifted outputs that responded to serine stimuli in wild-type fashion, suggesting that these receptors, like the wild-type, operate as two-state signaling devices. Larger aliphatic or aromatic side chains caused slow or partial kinase control responses that proved dependent on the connections between core signaling units that promote array cooperativity. In a mutant lacking one of two key adapter-kinase contacts (interface 2), those mutant receptors exhibited more wild-type behaviors. Lastly, mutant receptors with charged amino acid replacements assembled signaling complexes that were locked in kinase-ON (E385K|R) or kinase-OFF (R388D|E) output. The hairpin tips of mutant receptors with these more aberrant signaling properties probably have nonnative structures or dynamic behaviors. Our results suggest that chemoeffector stimuli and adaptational modifications influence the cooperative connections between core signaling units. This array remodeling process may involve activity-dependent changes in the relative strengths of interface 1 and 2 interactions between the CheW and CheA.P5 components of receptor core signaling complexes.

Blue Light Is a Universal Signal for Escherichia coli Chemoreceptors

Blue light has been shown to elicit a tumbling response in Escherichia coli, a nonphototrophic bacterium. The exact mechanism of this phototactic response is still unknown. Here, we quantify phototaxis in E. coli by analyzing single-cell trajectories in populations of free-swimming bacteria before and after light exposure. Bacterial strains expressing only one type of chemoreceptor reveal that all five E. coli receptors (Aer, Tar, Tsr, Tap, and Trg) are capable of mediating responses to light. In particular, light exposure elicits a running response in the Tap-only strain, the opposite of the tumbling responses observed for all other strains. Therefore, light emerges as a universal stimulus for all E. coli chemoreceptors. We also show that blue light exposure causes a reversible decrease in swimming velocity, a proxy for proton motive force. This result is consistent with a previously proposed hypothesis that, rather than sensing light directly, chemoreceptors sense light-induced perturbations in proton motive force, although other factors are also likely to contribute.IMPORTANCE Our findings provide new insights into the mechanism of E. coli phototaxis, showing that all five chemoreceptor types respond to light and their interactions play an important role in cell behavior. Our results also open up new avenues for examining and manipulating E. coli taxis. Since light is a universal stimulus, it may provide a way to quantify interactions among different types of receptors. Because light is easier to control spatially and temporally than chemicals, it may be used to study swimming behavior in complex environments. Since phototaxis can cause migration of E. coli bacteria in light gradients, light may be used to control bacterial density for studying density-dependent processes in bacteria.

Inverted signaling by bacterial chemotaxis receptors

Microorganisms use transmembrane sensory receptors to perceive a wide range of environmental factors. It is unclear how rapidly the sensory properties of these receptors can be modified when microorganisms adapt to novel environments. Here, we demonstrate experimentally that the response of an Escherichia coli chemotaxis receptor to its chemical ligands can be easily inverted by mutations at several sites along receptor sequence. We also perform molecular dynamics simulations to shed light on the mechanism of the transmembrane signaling by E. coli chemoreceptors. Finally, we use receptors with inverted signaling to map determinants that enable the same receptor to sense multiple environmental factors, including metal ions, aromatic compounds, osmotic pressure, and salt ions. Our findings demonstrate high plasticity of signaling and provide further insights into the mechanisms of stimulus sensing and processing by bacterial chemoreceptors.

Bacteria use chemotaxis receptors to perceive environmental factors. Here, the authors show that mutations in a chemotaxis receptor can invert the sensory response, e.g. from attractant to repellent, and use these mutants to map regions that enable the receptor to sense multiple environmental factors.

Dynamics of Bacterial Gene Regulatory Networks

The ability of bacterial cells to adjust their gene expression program in response to environmental perturbation is often critical for their survival. Recent experimental advances allowing us to quantitatively record gene expression dynamics in single cells and in populations coupled with mathematical modeling enable mechanistic understanding on how these responses are shaped by the underlying regulatory networks. Here, we review how the combination of local and global factors affect dynamical responses of gene regulatory networks. Our goal is to discuss the general principles that allow extrapolation from a few model bacteria to less understood microbes. We emphasize that, in addition to well-studied effects of network architecture, network dynamics are shaped by global pleiotropic effects and cell physiology.

Mathematical Analysis of the Escherichia coli Chemotaxis Signalling Pathway

We undertake a detailed mathematical analysis of a recent nonlinear ordinary differential equation (ODE) model describing the chemotactic signalling cascade within an Escherichia coli cell. The model includes a detailed description of the cell signalling cascade and an average approximation of the receptor activity. A steady-state stability analysis reveals the system exhibits one positive real steady state which is shown to be asymptotically stable. Given the occurrence of a negative feedback between phosphorylated CheB (CheB-P) and the receptor state, we ask under what conditions the system may exhibit oscillatory-type behaviour. A detailed analysis of parameter space reveals that whilst variation in kinetic rate parameters within known biological limits is unlikely to lead to such behaviour, changes in the total concentration of the signalling proteins do. We postulate that experimentally observed overshoot behaviour can actually be described by damped oscillatory dynamics and consider the relationship between overshoot amplitude, total cell protein concentration and the magnitude of the external ligand stimulus. Model reductions in the full ODE model allow us to understand the link between phosphorylation events and the negative feedback between CheB-P and receptor methylation, as well as elucidate why some mathematical models exhibit overshoot and others do not. Our paper closes by discussing intercell variability of total protein concentration as a means of ensuring the overall survival of a population as cells are subjected to different environments.

FRET Analysis of the Chemotaxis Pathway Response

Most motile bacteria follow spatial gradients of chemical and physical stimuli in their environment. In Escherichia coli and other bacteria, the best characterized chemotaxis is in gradients of amino acids or sugars, but other physiological stimuli such as pH, osmolarity, redox potentials, and temperature are also known to elicit tactic responses. These multiple environmental stimuli are integrated and processed within a highly sophisticated chemotaxis network to generate coordinated chemotaxis behavior, which features high sensitivity, a wide dynamic range, and robustness against variations in background stimulation, protein levels, and temperature. Although early studies relied on behavioral analyses to characterize chemotactic responses in vivo, or on biochemical assays to study the pathway in vitro, we describe here a method to directly measure the intracellular pathway response using Förster resonance energy transfer (FRET). In E. coli, the most commonly used form of the FRET assay relies on the interaction between the phosphorylated response regulator CheY and its phosphatase CheZ to quantify activity of the histidine kinase CheA. We further describe a FRET assay for Bacillus subtilis, which employs CheY and the motor-associated phosphatase FliY as a FRET pair. In particular, we highlight the use of FRET to quantify pathway properties, including signal amplification, dynamic range, and kinetics of adaptation.

Bacterial Chemoreceptor Imaging at High Spatiotemporal Resolution Using Photoconvertible Fluorescent Proteins

We describe two methods for high-resolution fluorescence imaging of the positioning and mobility of E. coli chemoreceptors fused to photoconvertible fluorescent proteins. Chemoreceptors such as Tar and Tsr are transmembrane proteins expressed at high levels (thousands of copies per cell). Together with their cognate cytosolic signaling proteins, they form clusters on the plasma membrane. Theoretical models imply that the size of these clusters is an important parameter for signaling, and recent PALM imaging has revealed a broad distribution of cluster sizes. We describe experimental setups and protocols for PALM imaging in fixed cells with ~10 nm spatial precision, which allows analysis of cluster-size distributions, and localized-photoactivation single-particle tracking (LPA-SPT) in live cells at ~10 ms temporal resolution, which allows for analysis of cluster mobility.

Transmembrane region of bacterial chemoreceptor is capable of promoting protein clustering

Many membrane proteins are known to form higher-order oligomers, but the degree to which membrane regions could facilitate protein complex assembly remains largely unclear. Clusters of chemotaxis receptors are among the most prominent structures in the bacterial cell membrane, and they play important functions in processing of chemotactic signals. Although much work has been done to elucidate mechanisms of cluster formation, it almost exclusively focused on cytoplasmic interactions among receptors and other chemotaxis proteins, whereas involvement of membrane-mediated interactions was only hypothesized. Here we used imaging of constructs composed of only a fluorescent protein and the TM helices of Tar to demonstrate that interactions between the lipid bilayer and transmembrane (TM) helices of Escherichia coli chemoreceptors alone are sufficient to mediate clustering. We found that the ability to cluster depends on the sequence or length of the TM helices, implying that certain conformations of these helices facilitate clustering, whereas others do not. Notably, observed sequence specificity was apparently consistent with differences in clustering between native E. coli receptors, with the TM sequence of better-clustering high-abundance receptors being more efficient in promoting membrane-mediated complex formation. These results indicate that being more than just membrane anchors, TM helices could play an important role in the clustering and organization of membrane proteins in bacteria.

Multiple sources of slow activity fluctuations in a bacterial chemosensory network

Cellular networks are intrinsically subject to stochastic fluctuations, but analysis of the resulting noise remained largely limited to gene expression. The pathway controlling chemotaxis of Escherichia coli provides one example where posttranslational signaling noise has been deduced from cellular behavior. This noise was proposed to result from stochasticity in chemoreceptor methylation, and it is believed to enhance environment exploration by bacteria. Here we combined single-cell FRET measurements with analysis based on the fluctuation-dissipation theorem (FDT) to characterize origins of activity fluctuations within the chemotaxis pathway. We observed surprisingly large methylation-independent thermal fluctuations of receptor activity, which contribute to noise comparably to the energy-consuming methylation dynamics. Interactions between clustered receptors involved in amplification of chemotactic signals are also necessary to produce the observed large activity fluctuations. Our work thus shows that the high response sensitivity of this cellular pathway also increases its susceptibility to noise, from thermal and out-of-equilibrium processes.

Mechanism of bidirectional thermotaxis in Escherichia coli

In bacteria various tactic responses are mediated by the same cellular pathway, but sensing of physical stimuli remains poorly understood. Here, we combine an in-vivo analysis of the pathway activity with a microfluidic taxis assay and mathematical modeling to investigate the thermotactic response of Escherichia coli. We show that in the absence of chemical attractants E. coli exhibits a steady thermophilic response, the magnitude of which decreases at higher temperatures. Adaptation of wild-type cells to high levels of chemoattractants sensed by only one of the major chemoreceptors leads to inversion of the thermotactic response at intermediate temperatures and bidirectional cell accumulation in a thermal gradient. A mathematical model can explain this behavior based on the saturation-dependent kinetics of adaptive receptor methylation. Lastly, we find that the preferred accumulation temperature corresponds to optimal growth in the presence of the chemoattractant serine, pointing to a physiological relevance of the observed thermotactic behavior.

Many bacteria can move towards or away from chemicals, heat and other stimuli in their environment. The ability of bacteria to move in response to nutrients and other chemicals, known as chemotaxis, is the best understood of these phenomena. Bacteria generally swim in a fairly random way and frequently change direction. During chemotaxis, however, the bacteria sense changes in the concentrations of a chemical in their surroundings and this biases the direction in which they swim so that they spend more time swimming towards or away from the source of the chemical. The bacteria have various receptor proteins that can detect different chemicals. For example, the Tar and Tsr receptors can recognize chemicals called aspartate and serine, respectively, which are – amongst other things – nutrients that are used to build proteins.

Tar and Tsr are also involved in the response to temperature, referred to as thermotaxis. At low temperatures, a bacterium Escherichia coli will move towards sources of heat. Yet when the bacteria detect both serine and aspartate they may reverse the response and move towards colder areas instead. However, it was not clear why the bacteria do this, and what roles Tar and Tsr play in this response.

Paulick et al. have now combined approaches that directly visualise signalling inside living bacteria and that track the movements of individual bacterial cellswith mathematical modelling to investigate thermotaxis in E. coli. The experiments show that the bacteria’s behaviour could be explained by interplay between the responses mediated by Tar and Tsr. In the absence of both serine and aspartate, both receptors stimulate heat-seeking responses, causing the bacteria to move towards hotter areas. When only aspartate is present, Tsr continues to stimulate the heat-seeking response, but the aspartate causes Tar to switch to promoting a cold-seeking response instead. This leads to the bacteria accumulating in areas of intermediate temperature. In the presence of serine only, the bacteria behave in a similar way because the receptors swap roles so that Tsr stimulates the cold-seeking response, while Tar promotes the heat-seeking one.

The intermediate temperature at which the bacteria accumulate in response to serine is also around the optimal temperature for E.coli growth in presence of this chemical, suggesting that thermotaxis might play an important role in allowing bacteria to survive and grow in many different environments, including in the human body. Thus, understanding how chemotaxis and thermotaxis are regulated may lead to new ways to control how bacteria behave in patients and natural environments.

Resonance in the response of the bacterial flagellar motor to thermal oscillations

We have studied the dynamics of the Escherichia coli flagellar motor's angular velocity in response to thermal oscillations. We find that the oscillations' amplitude of the motor's angular velocity exhibits resonance when the temperature is oscillated at frequencies around 4 Hz. This resonance appears to be due to the existence of a natural mode of oscillation in the state of the motor, specifically in the torque generated by the motor. Natural modes of oscillation in torque generation cannot result from random fluctuations in the state of the motor. Their presence points to the existence of a coupling mechanism between the magnitude of the torque generated by the motor and the rates of transition between the different states of the motor components responsible for torque generation. The results presented here show resonance response in torque generation to external perturbations. They are explained with a simple phenomenological model, which can help future studies identify the source of the feedback mechanism between the torque and the interactions responsible for its generation. It can also help us to quantitatively estimate the strength of these interactions and how they are affected by the magnitude of the torque they generate.

Information processing in bacteria: memory, computation, and statistical physics: a key issues review

Living systems have to constantly sense their external environment and adjust their internal state in order to survive and reproduce. Biological systems, from as complex as the brain to a single E. coli cell, have to process these data in order to make appropriate decisions. How do biological systems sense external signals? How do they process the information? How do they respond to signals? Through years of intense study by biologists, many key molecular players and their interactions have been identified in different biological machineries that carry out these signaling functions. However, an integrated, quantitative understanding of the whole system is still lacking for most cellular signaling pathways, not to say the more complicated neural circuits. To study signaling processes in biology, the key thing to measure is the input-output relationship. The input is the signal itself, such as chemical concentration, external temperature, light (intensity and frequency), and more complex signals such as the face of a cat. The output can be protein conformational changes and covalent modifications (phosphorylation, methylation, etc), gene expression, cell growth and motility, as well as more complex output such as neuron firing patterns and behaviors of higher animals. Due to the inherent noise in biological systems, the measured input-output dependence is often noisy. These noisy data can be analysed by using powerful tools and concepts from information theory such as mutual information, channel capacity, and the maximum entropy hypothesis. This information theory approach has been successfully used to reveal the underlying correlations between key components of biological networks, to set bounds for network performance, and to understand possible network architecture in generating observed correlations. Although the information theory approach provides a general tool in analysing noisy biological data and may be used to suggest possible network architectures in preserving information, it does not reveal the underlying mechanism that leads to the observed input-output relationship, nor does it tell us much about which information is important for the organism and how biological systems use information to carry out specific functions. To do that, we need to develop models of the biological machineries, e.g. biochemical networks and neural networks, to understand the dynamics of biological information processes. This is a much more difficult task. It requires deep knowledge of the underlying biological network-the main players (nodes) and their interactions (links)-in sufficient detail to build a model with predictive power, as well as quantitative input-output measurements of the system under different perturbations (both genetic variations and different external conditions) to test the model predictions to guide further development of the model. Due to the recent growth of biological knowledge thanks in part to high throughput methods (sequencing, gene expression microarray, etc) and development of quantitative in vivo techniques such as various florescence technology, these requirements are starting to be realized in different biological systems. The possible close interaction between quantitative experimentation and theoretical modeling has made systems biology an attractive field for physicists interested in quantitative biology. In this review, we describe some of the recent work in developing a quantitative predictive model of bacterial chemotaxis, which can be considered as the hydrogen atom of systems biology. Using statistical physics approaches, such as the Ising model and Langevin equation, we study how bacteria, such as E. coli, sense and amplify external signals, how they keep a working memory of the stimuli, and how they use these data to compute the chemical gradient. In particular, we will describe how E. coli cells avoid cross-talk in a heterogeneous receptor cluster to keep a ligand-specific memory. We will also study the thermodynamic costs of adaptation for cells to maintain an accurate memory. The statistical physics based approach described here should be useful in understanding design principles for cellular biochemical circuits in general.

The source of high signal cooperativity in bacterial chemosensory arrays

The Escherichia coli chemosensory system consists of large arrays of transmembrane chemoreceptors associated with a dedicated histidine kinase, CheA, and a linker protein, CheW, that couples CheA activity to receptor control. The kinase activity responses to receptor ligand occupancy changes can be highly cooperative, reflecting allosteric coupling of multiple CheA and receptor molecules. Recent structural and functional studies have led to a working model in which receptor core complexes, the minimal units of signaling, are linked into hexagonal arrays through a unique interface 2 interaction between CheW and the P5 domain of CheA. To test this array model, we constructed and characterized CheA and CheW mutants with amino acid replacements at key interface 2 residues. The mutant proteins proved defective in interface 2-specific in vivo cross-linking assays, and formed signaling complexes that were dispersed around the cell membrane rather than clustered at the cell poles as in wild type chemosensory arrays. Interface 2 mutants down-regulated CheA activity in response to attractant stimuli in vivo, but with much less cooperativity than the wild type. Moreover, mutant cells containing fluorophore-tagged receptors exhibited greater basal anisotropy that changed rapidly in response to attractant stimuli, consistent with facile changes in loosely packed receptors. We conclude that interface 2 lesions disrupt important network connections between core complexes, preventing receptors from operating in large, allosteric teams. This work confirms the critical role of interface 2 in organizing the chemosensory array, in directing the clustered array to the cell poles, and in producing its highly cooperative signaling properties.

Fundamental constraints on the abundances of chemotaxis proteins

Flagellated bacteria, such as Escherichia coli, perform directed motion in gradients of concentration of attractants and repellents in a process called chemotaxis. The E. coli chemotaxis signaling pathway is a model for signal transduction, but it has unique features. We demonstrate that the need for fast signaling necessitates high abundances of the proteins involved in this pathway. We show that further constraints on the abundances of chemotaxis proteins arise from the requirements of self-assembly both of flagellar motors and of chemoreceptor arrays. All these constraints are specific to chemotaxis, and published data confirm that chemotaxis proteins tend to be more highly expressed than their homologs in other pathways. Employing a chemotaxis pathway model, we show that the gain of the pathway at the level of the response regulator CheY increases with overall chemotaxis protein abundances. This may explain why, at least in one E. coli strain, the abundance of all chemotaxis proteins is higher in media with lower nutrient content. We also demonstrate that the E. coli chemotaxis pathway is particularly robust to abundance variations of the motor protein FliM.

Importance of Multiple Methylation Sites in Escherichia coli Chemotaxis

Bacteria navigate within inhomogeneous environments by temporally comparing concentrations of chemoeffectors over the course of a few seconds and biasing their rate of reorientations accordingly, thereby drifting towards more favorable conditions. This navigation requires a short-term memory achieved through the sequential methylations and demethylations of several specific glutamate residues on the chemotaxis receptors, which progressively adjusts the receptors' activity to track the levels of stimulation encountered by the cell with a delay. Such adaptation also tunes the receptors' sensitivity according to the background ligand concentration, enabling the cells to respond to fractional rather than absolute concentration changes, i.e. to perform logarithmic sensing. Despite the adaptation system being principally well understood, the need for a specific number of methylation sites remains relatively unclear. Here we systematically substituted the four glutamate residues of the Tar receptor of Escherichia coli by non-methylated alanine, creating a set of 16 modified receptors with a varying number of available methylation sites and explored the effect of these substitutions on the performance of the chemotaxis system. Alanine substitutions were found to desensitize the receptors, similarly but to a lesser extent than glutamate methylation, and to affect the methylation and demethylation rates of the remaining sites in a site-specific manner. Each substitution reduces the dynamic range of chemotaxis, by one order of magnitude on average. The substitution of up to two sites could be partly compensated by the adaptation system, but the full set of methylation sites was necessary to achieve efficient logarithmic sensing.

Protein Connectivity in Chemotaxis Receptor Complexes

The chemotaxis sensory system allows bacteria such as Escherichia coli to swim towards nutrients and away from repellents. The underlying pathway is remarkably sensitive in detecting chemical gradients over a wide range of ambient concentrations. Interactions among receptors, which are predominantly clustered at the cell poles, are crucial to this sensitivity. Although it has been suggested that the kinase CheA and the adapter protein CheW are integral for receptor connectivity, the exact coupling mechanism remains unclear. Here, we present a statistical-mechanics approach to model the receptor linkage mechanism itself, building on nanodisc and electron cryotomography experiments. Specifically, we investigate how the sensing behavior of mixed receptor clusters is affected by variations in the expression levels of CheA and CheW at a constant receptor density in the membrane. Our model compares favorably with dose-response curves from in vivo Förster resonance energy transfer (FRET) measurements, demonstrating that the receptor-methylation level has only minor effects on receptor cooperativity. Importantly, our model provides an explanation for the non-intuitive conclusion that the receptor cooperativity decreases with increasing levels of CheA, a core signaling protein associated with the receptors, whereas the receptor cooperativity increases with increasing levels of CheW, a key adapter protein. Finally, we propose an evolutionary advantage as explanation for the recently suggested CheW-only linker structures.

Receptor clusters of the bacterial chemotaxis sensory system act as antennae to amplify tiny changes in concentrations in the chemical environment of the cell, ultimately steering the cell towards nutrients and away from toxins. Despite bacterial chemotaxis being the most widely studied sensory pathway, the exact architecture of the receptor clusters remains speculative, with understanding suffering from a number of paradoxical observations. To address these issues with respect to the protein arrangement in the linkers connecting receptors, we present a statistical-mechanics model that combines insights from electron cryotomography on the linker architecture with results from fluorescence imaging of signaling in living cells. Although the signaling data for different expression levels of key molecular components in the linkers seems contradictory at first, our model reconciles these predictions with structural and biochemical data. Finally, we provide an evolutionary explanation for the observation that some of the incorporated linkers do not seem to transmit signals from the receptors.

Universal response-adaptation relation in bacterial chemotaxis

The bacterial strategy of chemotaxis relies on temporal comparisons of chemical concentrations, where the probability of maintaining the current direction of swimming is modulated by changes in stimulation experienced during the recent past. A short-term memory required for such comparisons is provided by the adaptation system, which operates through the activity-dependent methylation of chemotaxis receptors. Previous theoretical studies have suggested that efficient navigation in gradients requires a well-defined adaptation rate, because the memory time scale needs to match the duration of straight runs made by bacteria. Here we demonstrate that the chemotaxis pathway of Escherichia coli does indeed exhibit a universal relation between the response magnitude and adaptation time which does not depend on the type of chemical ligand. Our results suggest that this alignment of adaptation rates for different ligands is achieved through cooperative interactions among chemoreceptors rather than through fine-tuning of methylation rates for individual receptors. This observation illustrates a yet-unrecognized function of receptor clustering in bacterial chemotaxis.

Predicting chemical environments of bacteria from receptor signaling

Sensory systems have evolved to respond to input stimuli of certain statistical properties, and to reliably transmit this information through biochemical pathways. Hence, for an experimentally well-characterized sensory system, one ought to be able to extract valuable information about the statistics of the stimuli. Based on dose-response curves from in vivo fluorescence resonance energy transfer (FRET) experiments of the bacterial chemotaxis sensory system, we predict the chemical gradients chemotactic Escherichia coli cells typically encounter in their natural environment. To predict average gradients cells experience, we revaluate the phenomenological Weber's law and its generalizations to the Weber-Fechner law and fold-change detection. To obtain full distributions of gradients we use information theory and simulations, considering limitations of information transmission from both cell-external and internal noise. We identify broad distributions of exponential gradients, which lead to log-normal stimuli and maximal drift velocity. Our results thus provide a first step towards deciphering the chemical nature of complex, experimentally inaccessible cellular microenvironments, such as the human intestine.

Outside the laboratory, bacteria live in complex microenvironments characterized by competition for space and available nutrients. Although often inaccessible by experiments, understanding the spatio-temporal dynamics of bacterial microenvironments is biomedically important. For instance, the chemical environment that symbiotic Escherichia coli encounter in the human gut relates to health of the gastrointestinal tract, gut metabolism, immune response, and tissue homeostasis. Other complex microenvironments include soil and biofilms. Assuming that bacterial sensory systems have evolved to optimally sense typical gradients, we treat signaling data, the signaling pathway with its architecture and reaction rates, and computer simulations of swimming bacteria in different gradients as “prior knowledge” to “reverse engineer” E. coli's habitat. Our identified gradients are exponentially shaped with wide-ranging rate values. These microenvironments most likely stem from local fluctuating nutrient sources and degradation by competing species, in which bacteria have evolved to swim with optimal performance.

Functional suppression of HAMP domain signaling defects in the E. coli serine chemoreceptor

HAMP domains play key signaling roles in many bacterial receptor proteins. The four-helix HAMP bundle of the homodimeric Escherichia coli serine chemoreceptor (Tsr) interacts with an adjoining four-helix sensory adaptation bundle to regulate the histidine autokinase CheA bound to the cytoplasmic tip of the Tsr molecule. The adaptation helices undergo reversible covalent modifications that tune the stimulus-responsive range of the receptor: unmodified E residues promote kinase-off output, and methylated E residues or Q replacements at modification sites promote kinase-on output. We used mutationally imposed adaptational modification states and cells with various combinations of the sensory adaptation enzymes, CheR and CheB, to characterize the signaling properties of mutant Tsr receptors that had amino acid replacements in packing layer 3 of the HAMP bundle and followed in vivo CheA activity with an assay based on Förster resonance energy transfer. We found that an alanine or a serine replacement at HAMP residue I229 effectively locked Tsr output in a kinase-on state, abrogating chemotactic responses. A second amino acid replacement in the same HAMP packing layer alleviated the I229A and I229S signaling defects. Receptors with the suppressor changes alone mediated chemotaxis in adaptation-proficient cells but exhibited altered sensitivity to serine stimuli. Two of the suppressors (S255E and S255A) shifted Tsr output toward the kinase-off state, but two others (S255G and L256F) shifted output toward a kinase-on state. The alleviation of locked-on defects by on-shifted suppressors implies that Tsr-HAMP has several conformationally distinct kinase-active output states and that HAMP signaling might involve dynamic shifts over a range of bundle conformations.

Fold-change detection in a whole-pathway model of Escherichia coli chemotaxis

There has been recent interest in sensory systems that are able to display a response which is proportional to a fold change in stimulus concentration, a feature referred to as fold-change detection (FCD). Here, we demonstrate FCD in a recent whole-pathway mathematical model of Escherichia coli chemotaxis. FCD is shown to hold for each protein in the signalling cascade and to be robust to kinetic rate and protein concentration variation. Using a sensitivity analysis, we find that only variations in the number of receptors within a signalling team lead to the model not exhibiting FCD. We also discuss the ability of a cell with multiple receptor types to display FCD and explain how a particular receptor configuration may be used to elucidate the two experimentally determined regimes of FCD behaviour. All findings are discussed in respect of the experimental literature.

Defining a key receptor-CheA kinase contact and elucidating its function in the membrane-bound bacterial chemosensory array: a disulfide mapping and TAM-IDS Study

The three core components of the ubiquitous bacterial chemosensory array - the transmembrane chemoreceptor, the histidine kinase CheA, and the adaptor protein CheW - assemble to form a membrane-bound, hexagonal lattice in which receptor transmembrane signals regulate kinase activity. Both the regulatory domain of the kinase and the adaptor protein bind to overlapping sites on the cytoplasmic tip of the receptor (termed the protein interaction region). Notably, the kinase regulatory domain and the adaptor protein share the same fold constructed of two SH3-like domains. The present study focuses on the structural interface between the receptor and the kinase regulatory domain. Two models have been proposed for this interface: Model 1 is based on the crystal structure of a homologous Thermotoga complex between a receptor fragment and the CheW adaptor protein. This model has been used in current models of chemosensory array architecture to build the receptor-CheA kinase interface. Model 2 is based on a newly determined crystal structure of a homologous Thermotoga complex between a receptor fragment and the CheA kinase regulatory domain. Both models present unique strengths and weaknesses, and current evidence is unable to resolve which model best describes contacts in the native chemosensory arrays of Escherichia coli, Salmonella typhimurium, and other bacteria. Here we employ disulfide mapping and tryptophan and alanine mutation to identify docking sites (TAM-IDS) to test Models 1 and 2 in well-characterized membrane-bound arrays formed from E. coli and S. typhimurium components. The results reveal that the native array interface between the receptor protein interaction region and the kinase regulatory domain is accurately described by Model 2, but not by Model 1. In addition, the results show that the interface possesses both a structural function that contributes to stable CheA kinase binding in the array and a regulatory function central to transmission of the activation signal from receptor to CheA kinase. On-off switching alters the disulfide formation rates of specific Cys pairs at the interface, but not most Cys pairs, indicating that signaling perturbs localized regions of the interface. The findings suggest a simple model for the rearrangement of the interface triggered by the attractant signal and for longer range transmission of the signal in the chemosensory array.

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.

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.

Chemotactic signaling via carbohydrate phosphotransferase systems in Escherichia coli

Chemotaxis allows bacteria to follow gradients of nutrients, environmental stimuli, and signaling molecules, optimizing bacterial growth and survival. Escherichia coli has long served as a model of bacterial chemotaxis, and the signal processing by the core of its chemotaxis pathway is well understood. However, most of the research so far has focused on one branch of chemotactic signaling, in which ligands bind to periplasmic sensory domains of transmembrane chemoreceptors and induce a conformational change that is transduced across the membrane to regulate activity of the receptor-associated kinase CheA. Here we quantitatively characterize another, receptor-independent branch of chemotactic signaling that is linked to the sugar uptake through a large family of phosphotransferase systems (PTSs). Using in vivo characterization of intracellular signaling and protein interactions, we demonstrate that signals from cytoplasmic PTS components are transmitted directly to the sensory complexes formed by chemoreceptors, CheA and an adapter protein CheW. We further conclude that despite different modes of sensing, the PTS- and receptor-mediated signals have similar regulatory effects on the conformation of the sensory complexes. As a consequence, both types of signals become integrated and undergo common downstream processing including methylation-dependent adaptation. We propose that such mode of signaling is essential for efficient chemotaxis to PTS substrates and may be common to most bacteria.

Theoretical insights into bacterial chemotaxis

Research into understanding bacterial chemotactic systems has become a paradigm for Systems Biology. Experimental and theoretical researchers have worked hand-in-hand for over 40 years to understand the intricate behavior driving bacterial species, in particular how such small creatures, usually not more than 5 µm in length, detect and respond to small changes in their extracellular environment. In this review we highlight the importance that theoretical modeling has played in providing new insight and understanding into bacterial chemotaxis. We begin with an overview of the bacterial chemotaxis sensory response, before reviewing the role of theoretical modeling in understanding elements of the system on the single cell scale and features underpinning multiscale extensions to population models.

Effects of receptor modification and temperature on dynamics of sensory complexes in Escherichia coli chemotaxis

BACKGROUND

Extracellular stimuli in chemotaxis of Escherichia coli and other bacteria are processed by large clusters of sensory complexes. The stable core of these clusters is formed by transmembrane receptors, a kinase CheA, and an adaptor CheW, whereas adaptation enzymes CheR and CheB dynamically associate with the clusters via interactions with receptors and/or CheA. Several biochemical studies have indicated the dependence of the sensory complex stability on the adaptive modification state of receptors and/or on temperature, which may potentially allow environment-dependent tuning of its signalling properties. However, the extent of such regulation in vivo and its significance for chemotaxis remained unclear.

RESULTS

Here we used fluorescence recovery after photobleaching (FRAP) to confirm in vivo that the exchange of CheA and CheW shows a modest dependency on the level of receptor modification/activity. An even more dramatic effect was observed for the exchange kinetics of CheR and CheB, indicating that their association with clusters may depend on the ability to bind substrate sites on receptors and on the regulatory phosphorylation of CheB. In contrast, environmental temperature did not have a discernible effect on stability of the cluster core. Strain-specific loss of E. coli chemotaxis at high temperature could instead be explained by a heat-induced reduction in the chemotaxis protein levels. Nevertheless, high basal levels of chemotaxis and flagellar proteins in common wild type strains MG1655 and W3110 enabled these strains to maintain their chemotactic ability up to 42°C.

CONCLUSIONS

Our results confirmed that clusters formed by less modified receptors are more dynamic, which can explain the previously observed adjustment of the chemotaxis response sensitivity according to the level of background stimulation. We further propose that the dependency of CheR exchange on the availability of unmethylated sites on receptors is important to improve the overall chemotaxis efficiency by suppressing molecular noise under conditions of high ligand concentrations. Moreover, the observed stability of the cluster core at high temperature is in line with the overall thermal robustness of the chemotaxis pathway and allows maintenance of chemotaxis up to 42°C in the common wild type strains of E. coli.

Response rescaling in bacterial chemotaxis

Sensory systems rescale their response sensitivity upon adaptation according to simple strategies that recur in processes as diverse as single-cell signaling, neural network responses, and whole-organism perception. Here, we study response rescaling in Escherichia coli chemotaxis, where adaptation dynamically tunes the cells' motile response during searches for nutrients. Using in vivo fluorescence resonance energy transfer (FRET) measurements on immobilized cells, we demonstrate that the design of this prokaryotic signaling network follows the fold-change detection (FCD) strategy, responding faithfully to the shape of the input profile irrespective of its absolute intensity. Using a microfluidics-based assay for free swimming cells, we confirm intensity-independent gradient responses at the behavioral level. By theoretical analysis, we identify a set of sufficient conditions for FCD in E. coli chemotaxis, which leads to the prediction that the adaptation timescale is invariant with respect to the background input level. Additional FRET experiments confirm that the adaptation timescale is invariant over an ∼10,000-fold range of background concentrations. These observations in a highly optimized bacterial system support the concept that FCD represents a robust sensing strategy for spatial searches. To our knowledge, these experiments provide a unique demonstration of FCD in any biological sensory system.

Thermal robustness of signaling in bacterial chemotaxis

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.

Core unit of chemotaxis signaling complexes

Bacterial chemoreceptors, histidine kinase CheA, and coupling protein CheW form clusters of chemotaxis signaling complexes. In signaling complexes kinase activity is enhanced several hundredfold and placed under receptor control. Activation is necessary to poise enzyme activity such that receptor control has physiologically relevant effects. Thus kinase activation can be considered the underlying core activity of signaling complexes. We defined the minimal physical unit that generates this activity using chemoreceptor Tar from Escherichia coli rendered water soluble by insertion into nanodiscs to (i) measure saturable binding of CheA and CheW to the smallest kinase-activating groups of receptor dimers and (ii) purify and characterize core units of signaling complexes. Purified complexes activated kinase almost as well as signaling complexes formed on arrays of receptors in isolated native membrane. Purified complexes contained two receptor trimers of dimers and two CheW for each CheA dimer, consistent with the approximately 1:1 CheACheW ratio determined by binding measurements. The 2:2:1 stoichiometry implied that CheA dimers, the enzymatically active form, connect two chemoreceptor trimers of dimers by interaction of one CheA protomer and a CheW with each trimer, an organization for which specific molecular interactions have previously been identified. The core unit associates six receptor dimers with a CheA dimer, providing sufficient capacity to account for much of the cooperativity and interdimer influence observed experimentally. We conclude that the 221 organization is the core structural and functional unit of chemotaxis signaling complexes and postulate that hexagonal arrays characteristic of signaling complexes are built from this unit.

Optimal receptor-cluster size determined by intrinsic and extrinsic noise

Biological cells sense external chemical stimuli in their environment using cell-surface receptors. To increase the sensitivity of sensing, receptors often cluster. This process occurs most noticeably in bacterial chemotaxis, a paradigm for sensing and signaling in general. While amplification of weak stimuli is useful in the absence of noise, its usefulness is less clear in the presence of extrinsic input noise and intrinsic signaling noise. Here, exemplified in a bacterial chemotaxis system, we combine the allosteric Monod-Wyman-Changeux model for signal amplification by receptor complexes with calculations of noise to study their interconnectedness. Importantly, we calculate the signal-to-noise ratio, describing the balance of beneficial and detrimental effects of clustering for the cell. Interestingly, we find that there is no advantage for the cell to build receptor complexes for noisy input stimuli in the absence of intrinsic signaling noise. However, with intrinsic noise, an optimal complex size arises in line with estimates of the size of chemoreceptor complexes in bacteria and protein aggregates in lipid rafts of eukaryotic cells.

Precision and kinetics of adaptation in bacterial chemotaxis

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.

Chemotaxis kinase CheA is activated by three neighbouring chemoreceptor dimers as effectively as by receptor clusters

Chemoreceptors are central to bacterial chemotaxis. These transmembrane homodimers form trimers of dimers. Trimers form clusters of a few to thousands of receptors. A crucial receptor function is 100-fold activation, in signalling complexes, of sensory histidine kinase CheA. Significant activation has been shown to require more than one receptor dimer but the number required for full activation was unknown. We investigated this issue using Nanodiscs, soluble, nanoscale (∼10 nm diameter) plugs of lipid bilayer, to limit the number of neighbouring receptors contributing to activation. Utilizing size-exclusion chromatography, we separated primary preparations of receptor-containing Nanodiscs, otherwise heterogeneous for number and orientation of inserted receptors, into fractions enriched for specific numbers of dimers per disc. Fractionated, clarified Nanodiscs carrying approximately five dimers per disc were as effective in activating kinase as native membrane vesicles containing many neighbouring dimers. At five independently inserted dimers per disc, every disc would have at least three dimers oriented in parallel and thus able act together as they would in native membrane. We conclude full kinase activation involves interaction of CheA with groups of three receptor dimers, presumably as a trimer of dimers, and that more extensive interactions among receptors are not necessary for full kinase activation.

A modular gradient-sensing network for chemotaxis in Escherichia coli revealed by responses to time-varying stimuli

Combining in vivo FRET with time-varying stimuli, such as steps, ramps, and sinusoids allowed deduction of the molecular mechanisms underlying cellular signal processing.

The bacterial chemotaxis pathway can be described as a two-module feedback circuit, the transfer functions of which we have characterized quantitatively by experiment. Model-driven experimental design allowed the use of a single FRET pair for measurements of both transfer functions of the pathway.

The adaptation module's transfer function revealed that feedback near steady state is weak, consistent with high sensitivity to shallow gradients, but also strong steady-state fluctuations in pathway output.

The measured response to oscillatory stimuli defines the frequency band over which the chemotaxis system can compute time derivatives.

In searching for better environments, bacteria sample their surroundings by random motility, and make temporal comparisons of experienced sensory cues to bias their movement toward favorable directions (Berg and Brown, 1972). Thus, the problem of sensing spatial gradients is reduced to time-derivative computations, carried out by a signaling pathway that is well characterized at the molecular level in Escherichia coli. Here, we study the physiology of this signal processing system in vivo by fluorescence resonance energy transfer (FRET) experiments in which live cells are stimulated by time-varying chemoeffector signals. By measuring FRET between the active response regulator of the pathway CheY-P and its phosphatase CheZ, each labeled with GFP variants, we obtain a readout that is directly proportional to pathway activity (Sourjik et al, 2007). We analyze the measured response functions in terms of mechanistic models of signaling, and discuss functional consequences of the observed quantitative characteristics.

Experiments are guided by a coarse-grained modular model (Tu et al, 2008) of the sensory network (Figure 1), in which we identify two important ‘transfer functions': one corresponding to the receptor–kinase complex, which responds to changes in input ligand concentration on a fast time scale, and another corresponding to the adaptation system, which provides negative feedback, opposing the effect of ligand on a slower time scale. For the receptor module, we calibrate an allosteric MWC-type model of the receptor–kinase complex by FRET measurements of the ‘open-loop' transfer function G([L],m) using step stimuli. This calibration provides a basis for using the same FRET readout (between CheY-P and CheZ) to further study properties of the adaptation module.

It is well known that adaptation in E. coli's chemotaxis system uses integral feedback, which guarantees exact restoration of the baseline activity after transient responses to step stimuli (Barkai and Leibler, 1997; Yi et al, 2000). However, the output of time-derivative computations during smoothly varying stimuli depends not only on the presence of integral feedback, but also on what is being integrated. As this integrand can in general be any function of the output, we represent it by a black-box function F(a) in our model, and set out to determine its shape by experiments with time-varying stimuli.

We first apply exponential ramp stimuli—waveforms in which the logarithm of the stimulus level varies linearly with time, at a fixed rate r. It was shown many years ago that during such a stimulus, the kinase output of the pathway changes to a new constant value, a_c that is dependent on the applied ramp rate, r (Block et al, 1983). A plot of a_c versus r (Figure 5A) can thus be considered as an output of time-derivative computations by the network, and could also be used to study the ‘gradient sensitivity' of bacteria traveling at constant speeds.

To obtain the feedback transfer function, F(a), we apply a simple coordinate transformation, identified using our model, to the same ramp-response data (Figure 5B). This function reveals how the temporal rate of change of the feedback signal m depends on the current output signal a. The shape of this function is analyzed using a biochemical reaction scheme, from which in vivo kinetic parameters of the feedback enzymes, CheR and CheB, are extracted. The fitted Michaelis constants for these enzymatic reactions are small compared with the steady-state abundance of their substrates, thus indicating that these enzymes operate close to saturation in vivo. The slope of the function near steady state can be used to assess the strength of feedback, and to compute the relaxation time of the system, τ_m. Relaxation is found to be slow (i.e. large τ_m), consistent with large fluctuations about the steady-state activity caused by the near-saturation kinetics of the feedback enzymes (Emonet and Cluzel, 2008).

Finally, exponential sine-wave stimuli are used to map out the system's frequency response (Figure 5C). The measured data points for both the amplitude and phase of the response are found to be in excellent agreement with model predictions based on parameters from the independently measured step and ramp responses. No curve fitting was required to obtain this agreement. Although the amplitude response as a function of frequency resembles a first-order high-pass filter with a well-defined cutoff frequency, ν_m, we point out that the chemotaxis pathway is actually a low-pass filter if the time derivative of the input is viewed as the input signal. In this latter perspective, ν_m defines an upper bound for the frequency band over which time-derivative computations can be carried out.

The two types of measurements yield complementary information regarding time-derivative computations by E. coli. The ramp-responses characterize the asymptotically constant output when a temporal gradient is held fixed over extended periods. Interestingly, the ramp responses do not depend on receptor cooperativity, but only on properties of the adaptation system, and thus can be used to reveal the in vivo adaptation kinetics, even outside the linear regime of the kinase response. The frequency response is highly relevant in considering spatial searches in the real world, in which experienced gradients are not held fixed in time. The characteristic cutoff frequency ν_m is found by working within the linear regime of the kinase response, and depends on parameters from both modules (it increases with both cooperativity in the receptor module, and the strength of feedback in the adaptation module).

Both ramp responses and sine-wave responses were measured at two different temperatures (22 and 32°C), and found to differ significantly. Both the slope of F(a) near steady state, from ramp experiments, and the characteristic cutoff frequency, from sine-wave experiments, were higher by a factor of ∼3 at 32°C. Fits of the enzymatic model to F(a) suggest that temperature affects the maximal velocity (V_max) more strongly than the Michaelis constants (K_m) for CheR and CheB.

Successful application of inter-molecular FRET in live cells using GFP variants always requires some degree of serendipity. Genetic fusions to these bulky fluorophores can impair the function of the original proteins, and even when fusions are functional, efficient FRET still requires the fused fluorophores to come within the small (<10 nm) Förster radius on interactions between the labeled proteins. Thus, when a successful FRET pair is identified, it is desirable to make the most of it. We have shown here that combined with careful temporal control of input stimuli, and appropriately calibrated models, a single FRET pair can be used to study the structure of multiple transfer functions within a signaling network.

The Escherichia coli chemotaxis-signaling pathway computes time derivatives of chemoeffector concentrations. This network features modules for signal reception/amplification and robust adaptation, with sensing of chemoeffector gradients determined by the way in which these modules are coupled in vivo. We characterized these modules and their coupling by using fluorescence resonance energy transfer to measure intracellular responses to time-varying stimuli. Receptor sensitivity was characterized by step stimuli, the gradient sensitivity by exponential ramp stimuli, and the frequency response by exponential sine-wave stimuli. Analysis of these data revealed the structure of the feedback transfer function linking the amplification and adaptation modules. Feedback near steady state was found to be weak, consistent with strong fluctuations and slow recovery from small perturbations. Gradient sensitivity and frequency response both depended strongly on temperature. We found that time derivatives can be computed by the chemotaxis system for input frequencies below 0.006 Hz at 22°C and below 0.018 Hz at 32°C. Our results show how dynamic input–output measurements, time honored in physiology, can serve as powerful tools in deciphering cell-signaling mechanisms.

Bistability in apoptosis by receptor clustering

Apoptosis is a highly regulated cell death mechanism involved in many physiological processes. A key component of extrinsically activated apoptosis is the death receptor Fas which, on binding to its cognate ligand FasL, oligomerize to form the death-inducing signaling complex. Motivated by recent experimental data, we propose a mathematical model of death ligand-receptor dynamics where FasL acts as a clustering agent for Fas, which form locally stable signaling platforms through proximity-induced receptor interactions. Significantly, the model exhibits hysteresis, providing an upstream mechanism for bistability and robustness. At low receptor concentrations, the bistability is contingent on the trimerism of FasL. Moreover, irreversible bistability, representing a committed cell death decision, emerges at high concentrations which may be achieved through receptor pre-association or localization onto membrane lipid rafts. Thus, our model provides a novel theory for these observed biological phenomena within the unified context of bistability. Importantly, as Fas interactions initiate the extrinsic apoptotic pathway, our model also suggests a mechanism by which cells may function as bistable life/death switches independently of any such dynamics in their downstream components. Our results highlight the role of death receptors in deciding cell fate and add to the signal processing capabilities attributed to receptor clustering.

Many prominent diseases, most notably cancer, arise from an imbalance between the rates of cell growth and death in the body. This is often due to mutations that disrupt a cell death program called apoptosis. Here, we focus on the extrinsic pathway of apoptotic activation which is initiated upon detection of an external death signal, encoded by a death ligand, by its corresponding death receptor. Through the tools of mathematical analysis, we find that a novel model of death ligand-receptor interactions based on recent experimental data possesses the capacity for bistability. Consequently, the model supports threshold-like switching between unambiguous life and death states; intuitively, the defining characteristic of an effective cell death mechanism. We thus highlight the role of death receptors, the first component along the apoptotic pathway, in deciding cell fate. Furthermore, the model suggests an explanation for various biologically observed phenomena, including the trimeric character of the death ligand and the tendency for death receptors to colocalize, in terms of bistability. Our work hence informs the molecular basis of the apoptotic point-of-no-return, and may influence future drug therapies against cancer and other diseases.

Disruption of chemoreceptor signalling arrays by high levels of CheW, the receptor-kinase coupling protein

During chemotactic signalling by Escherichia coli, the small cytoplasmic CheW protein couples the histidine kinase CheA to chemoreceptor control. Although essential for assembly and operation of receptor signalling complexes, CheW in stoichiometric excess disrupts chemotactic behaviour. To explore the mechanism of the CheW excess effect, we measured the physiological consequences of high cellular levels of wild-type CheW and of several CheW variants with reduced or enhanced binding affinities for receptor molecules. We found that high levels of CheW interfered with trimer assembly, prevented CheA activation, blocked cluster formation, disrupted chemotactic ability and elevated receptor methylation levels. The severity of these effects paralleled the receptor-binding affinities of the CheW variants. Because trimer formation may be an obligate step in the assembly of ternary signalling complexes and higher-order receptor arrays, we suggest that all CheW excess effects stem from disruption of trimer assembly. We propose that the CheW-binding sites in receptor dimers overlap their trimer contact sites and that high levels of CheW saturate the receptor-binding sites, preventing trimer assembly. The CheW-trapped receptor dimers seem to be improved substrates for methyltransferase reactions, but cannot activate CheA or assemble into clusters, processes that are essential for chemotactic signalling.

Spatial organization in bacterial chemotaxis

Spatial organization of signalling is not an exclusive property of eukaryotic cells. Despite the fact that bacterial signalling pathways are generally simpler than those in eukaryotes, there are several well-documented examples of higher-order intracellular signalling structures in bacteria. One of the most prominent and best-characterized structures is formed by proteins that control bacterial chemotaxis. Signals in chemotaxis are processed by ordered arrays, or clusters, of receptors and associated proteins, which amplify and integrate chemotactic stimuli in a highly cooperative manner. Receptor clusters further serve to scaffold protein interactions, enhancing the efficiency and specificity of the pathway reactions and preventing the formation of signalling gradients through the cell body. Moreover, clustering can also ensure spatial separation of multiple chemotaxis systems in one bacterium. Assembly of receptor clusters appears to be a stochastic process, but bacteria evolved mechanisms to ensure optimal cluster distribution along the cell body for partitioning to daughter cells at division.

A dynamic-signaling-team model for chemotaxis receptors in Escherichia coli

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.

Differences in signalling by directly and indirectly binding ligands in bacterial chemotaxis

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.

Modeling chemotaxis reveals the role of reversed phosphotransfer and a bi-functional kinase-phosphatase

Understanding how multiple signals are integrated in living cells to produce a balanced response is a major challenge in biology. Two-component signal transduction pathways, such as bacterial chemotaxis, comprise histidine protein kinases (HPKs) and response regulators (RRs). These are used to sense and respond to changes in the environment. Rhodobacter sphaeroides has a complex chemosensory network with two signaling clusters, each containing a HPK, CheA. Here we demonstrate, using a mathematical model, how the outputs of the two signaling clusters may be integrated. We use our mathematical model supported by experimental data to predict that: (1) the main RR controlling flagellar rotation, CheY₆, aided by its specific phosphatase, the bifunctional kinase CheA₃, acts as a phosphate sink for the other RRs; and (2) a phosphorelay pathway involving CheB₂ connects the cytoplasmic cluster kinase CheA₃ with the polar localised kinase CheA₂, and allows CheA₃-P to phosphorylate non-cognate chemotaxis RRs. These two mechanisms enable the bifunctional kinase/phosphatase activity of CheA₃ to integrate and tune the sensory output of each signaling cluster to produce a balanced response. The signal integration mechanisms identified here may be widely used by other bacteria, since like R. sphaeroides, over 50% of chemotactic bacteria have multiple cheA homologues and need to integrate signals from different sources.

Chemotactic bacteria sense nutrient gradients and swim towards better environments for growth. A cluster of receptors in the cell membrane detects nutrient levels and signals via a cytoplasmic signaling pathway to the flagellum. The complexity of this signaling pathway varies across different bacterial species. The relatively simple pathway used by Escherichia coli is well understood; however, many bacteria, for example Rhodobacter sphaeroides, have more sophisticated pathways that, as well as being able to detect nutrients, are also able to assess the metabolic state of the cell. The receptors that detect metabolic state are located within an additional cluster that is physically distinct from the one that senses nutrients. In this work, we use a combination of experimentation and mathematical modeling to gain insight into the complex decision-making mechanisms that enable bacteria to weigh-up different stimuli and decide upon an appropriate response. We find novel communication mechanisms between the two signaling clusters that allow the outputs of the signaling pathways to be balanced and tuned according to the prevailing environmental conditions. The signaling principles identified here are likely to be used in other complex sensory networks.

Chemotactic response and adaptation dynamics in Escherichia coli

Adaptation of the chemotaxis sensory pathway of the bacterium Escherichia coli is integral for detecting chemicals over a wide range of background concentrations, ultimately allowing cells to swim towards sources of attractant and away from repellents. Its biochemical mechanism based on methylation and demethylation of chemoreceptors has long been known. Despite the importance of adaptation for cell memory and behavior, the dynamics of adaptation are difficult to reconcile with current models of precise adaptation. Here, we follow time courses of signaling in response to concentration step changes of attractant using in vivo fluorescence resonance energy transfer measurements. Specifically, we use a condensed representation of adaptation time courses for efficient evaluation of different adaptation models. To quantitatively explain the data, we finally develop a dynamic model for signaling and adaptation based on the attractant flow in the experiment, signaling by cooperative receptor complexes, and multiple layers of feedback regulation for adaptation. We experimentally confirm the predicted effects of changing the enzyme-expression level and bypassing the negative feedback for demethylation. Our data analysis suggests significant imprecision in adaptation for large additions. Furthermore, our model predicts highly regulated, ultrafast adaptation in response to removal of attractant, which may be useful for fast reorientation of the cell and noise reduction in adaptation.

Bacterial chemotaxis is a paradigm for sensory systems, and thus has attracted immense interest from biologists and modelers alike. Using this pathway, cells can sense chemical molecules in their environment, and bias their movement towards nutrients and away from toxins. To avoid over- or understimulation of the signaling pathway, receptors adapt to current external conditions by covalent receptor modification, ultimately allowing cells to chemotax over a wide range of background concentrations. While the robustness and precision in adaptation was previously explained, we quantify the dynamics of adaptation, important for cell memory and behavior, as well as noise filtering in the pathway. Specifically, we study the intracellular signaling response and subsequent adaptation to concentration step changes in attractant chemicals. We combine measurements of signaling in living cells with a dynamic model for strongly coupled receptors, even including the effects of concentration flow in the experiment. Using a novel way of summarizing time-dependent data, we derive a new adaptation model, predicting additional layers of feedback regulation. As a consequence, adaptation to sudden exposure of unfavorable conditions is very fast, which may be useful for a quick reorientation and escape of the cell.