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

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).

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.

Energy consumption and cooperation for optimal sensing

The reliable detection of environmental molecules in the presence of noise is an important cellular function, yet the underlying computational mechanisms are not well understood. We introduce a model of two interacting sensors which allows for the principled exploration of signal statistics, cooperation strategies and the role of energy consumption in optimal sensing, quantified through the mutual information between the signal and the sensors. Here we report that in general the optimal sensing strategy depends both on the noise level and the statistics of the signals. For joint, correlated signals, energy consuming (nonequilibrium), asymmetric couplings result in maximum information gain in the low-noise, high-signal-correlation limit. Surprisingly we also find that energy consumption is not always required for optimal sensing. We generalise our model to incorporate time integration of the sensor state by a population of readout molecules, and demonstrate that sensor interaction and energy consumption remain important for optimal sensing.

Cells exhibit exceptional chemical sensitivity, yet we haven’t fully understood how they achieve it. Here the authors consider the mutual information between signals and two coupled sensors as a proxy for sensing performance and show its optimisation depending on noise level and signal statistics.

Regulation of the chemotaxis histidine kinase CheA: A structural perspective

Bacteria sense and respond to their environment through a highly conserved assembly of transmembrane chemoreceptors (MCPs), the histidine kinase CheA, and the coupling protein CheW, hereafter termed "the chemosensory array". In recent years, great strides have been made in understanding the architecture of the chemosensory array and how this assembly engenders sensitive and cooperative responses. Nonetheless, a central outstanding question surrounds how receptors modulate the activity of the CheA kinase, the enzymatic output of the sensory system. With a focus on recent advances, we summarize the current understanding of array structure and function to comment on the molecular mechanism by which CheA, receptors and CheW generate the high sensitivity, gain and dynamic range emblematic of bacterial chemotaxis. The complexity of the chemosensory arrays has motivated investigation with many different approaches. In particular, structural methods, genetics, cellular activity assays, nanodisc technology and cryo-electron tomography have provided advances that bridge length scales and connect molecular mechanism to cellular function. Given the high degree of component integration in the chemosensory arrays, we ultimately aim to understand how such networked molecular interactions generate a whole that is truly greater than the sum of its parts. This article is part of a Special Issue entitled: Molecular biophysics of membranes and membrane proteins.

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.

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.

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.

Emergent properties of bacterial chemotaxis pathway

The chemotaxis pathway of Escherichia coli is the most studied sensory system in prokaryotes. The highly conserved general architecture of this pathway consists of two modules which mediate signal transduction and adaptation. The signal transduction module detects and amplifies changes in environmental conditions and rapidly transmits these signals to control bacterial swimming behavior. The adaptation module gradually resets the activity and sensitivity of the first module after initial stimulation and thereby enables the temporal comparisons necessary for bacterial chemotaxis. Recent experimental and theoretical work has unraveled multiple quantitative features emerging from the interplay between these two modules. This has laid the groundwork for rationalization of these emerging properties in the context of the evolutionary optimization of the chemotactic behavior.

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.

Networked Chemoreceptors Benefit Bacterial Chemotaxis Performance

Motile bacteria use large receptor arrays to detect and follow chemical gradients in their environment. Extended receptor arrays, composed of networked signaling complexes, promote cooperative stimulus control of their associated signaling kinases. Here, we used structural lesions at the communication interface between core complexes to create an Escherichia coli strain with functional but dispersed signaling complexes. This strain allowed us to directly study how networking of signaling complexes affects chemotactic signaling and gradient-tracking performance. We demonstrate that networking of receptor complexes provides bacterial cells with about 10-fold-heightened detection sensitivity to attractants while maintaining a wide dynamic range over which receptor adaptational modifications can tune response sensitivity. These advantages proved especially critical for chemotaxis toward an attractant source under conditions in which bacteria are unable to alter the attractant gradient.

Chemoreceptor arrays are found in many motile bacteria. However, although our understanding of bacterial chemotaxis is quite detailed, the signaling and behavioral advantages of networked receptor arrays had not been directly studied in cells. We have recently shown that lesions in a key interface of the E. coli receptor array diminish physical connections and functional coupling between core signaling complexes while maintaining their basic signaling capacity. In this study, we exploited an interface 2 mutant to show, for the first time, that coupling between core complexes substantially enhances stimulus detection and chemotaxis performance.

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.

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.

Non-monotonic dynamics and crosstalk in signaling pathways and their implications for pharmacology

Currently, drug discovery approaches commonly assume a monotonic dose-response relationship. However, the assumption of monotonicity is increasingly being challenged. Here we show that for two simple interacting linear signaling pathways that carry two different signals with different physiological responses, a non-monotonic input-output relation can arise with simple network topologies including coherent and incoherent feed-forward loops. We show that non-monotonicity of the response functions has severe implications for pharmacological treatment. Fundamental constraints are imposed on the effectiveness and toxicity of any drug independent of its chemical nature and selectivity due to the specific network structure.

Preformed Soluble Chemoreceptor Trimers That Mimic Cellular Assembly States and Activate CheA Autophosphorylation

Bacterial chemoreceptors associate with the histidine kinase CheA and coupling protein CheW to form extended membrane arrays that receive and transduce environmental signals. A receptor trimers-of-dimers resides at each vertex of the hexagonal protein lattice. CheA is fully activated and regulated when it is integrated into the receptor assembly. To mimic these states in solution, we have engineered chemoreceptor cytoplasmic kinase-control modules (KCMs) based on the Escherichia coli aspartate receptor Tar that are covalently fused and trimerized by a foldon domain (Tar(FO)). Small-angle X-ray scattering, multi-angle light scattering, and pulsed-dipolar electron spin resonance spectroscopy of spin-labeled proteins indicate that the Tar(FO) modules assemble into homogeneous trimers wherein the protein interaction regions closely associate at the end opposite to the foldon domains. The Tar(FO) variants greatly increase the saturation levels of phosphorylated CheA (CheA-P), indicating that the association with a trimer of receptor dimers changes the fraction of active kinase. However, the rate constants for CheA-P formation with the Tar variants are low compared to those for autophosphorylation by free CheA, and net phosphotransfer from CheA to CheY does not increase commensurately with CheA autophosphorylation. Thus, the Tar variants facilitate slow conversion to an active form of CheA that then undergoes stable autophosphorylation and is capable of subsequent phosphotransfer to CheY. Free CheA is largely incapable of phosphorylation but contains a small active fraction. Addition of Tar(FO) to CheA promotes a planar conformation of the regulatory domains consistent with array models for the assembly state of the ternary complex and different from that observed with a single inhibitory receptor. Introduction of Tar(FO) into E. coli cells activates endogenous CheA to produce increased clockwise flagellar rotation, with the effects increasing in the presence of the chemotaxis methylation system (CheB/CheR). Overall, the Tar(FO) modules demonstrate that trimerized signaling tips self-associate, bind CheA and CheW, and facilitate conversion of CheA to an active conformation.

The role of membrane-mediated interactions in the assembly and architecture of chemoreceptor lattices

In vivo fluorescence microscopy and electron cryo-tomography have revealed that chemoreceptors self-assemble into extended honeycomb lattices of chemoreceptor trimers with a well-defined relative orientation of trimers. The signaling response of the observed chemoreceptor lattices is remarkable for its extreme sensitivity, which relies crucially on cooperative interactions among chemoreceptor trimers. In common with other membrane proteins, chemoreceptor trimers are expected to deform the surrounding lipid bilayer, inducing membrane-mediated anisotropic interactions between neighboring trimers. Here we introduce a biophysical model of bilayer-chemoreceptor interactions, which allows us to quantify the role of membrane-mediated interactions in the assembly and architecture of chemoreceptor lattices. We find that, even in the absence of direct protein-protein interactions, membrane-mediated interactions can yield assembly of chemoreceptor lattices at very dilute trimer concentrations. The model correctly predicts the observed honeycomb architecture of chemoreceptor lattices as well as the observed relative orientation of chemoreceptor trimers, suggests a series of “gateway” states for chemoreceptor lattice assembly, and provides a simple mechanism for the localization of large chemoreceptor lattices to the cell poles. Our model of bilayer-chemoreceptor interactions also helps to explain the observed dependence of chemotactic signaling on lipid bilayer properties. Finally, we consider the possibility that membrane-mediated interactions might contribute to cooperativity among neighboring chemoreceptor trimers.

The chemotaxis system allows bacteria to respond to minute changes in chemical concentration, and serves as a paradigm for biological signal processing and the self-assembly of large protein lattices in living cells. The sensitivity of the chemotaxis system relies crucially on cooperative interactions among chemoreceptor trimers, which are organized into intricate honeycomb lattices. Chemoreceptors are membrane proteins and, hence, are expected to deform the surrounding lipid bilayer, leading to membrane-mediated interactions between chemoreceptor trimers. Using a biophysical model of bilayer-chemoreceptor interactions we show that the membrane-mediated interactions induced by chemoreceptor trimers provide a mechanism for the observed self-assembly of chemoreceptor lattices. We find that the directionality of membrane-mediated interactions between trimers complements protein-protein interactions in the stabilization of the observed honeycomb architecture of chemoreceptor lattices. Our results suggest that the symmetry of membrane protein complexes such as chemoreceptor trimers is reflected in the anisotropy of membrane-mediated interactions, yielding a general mechanism for the self-assembly of ordered protein lattices in cell membranes.

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.

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.

Ultrasensitivity in independent multisite systems

Multisite modifications are widely recognized as an essential feature of many switch-like responses in signal transduction. It is usually assumed that the modification of one site directly or indirectly increases the rate of modification of neighboring sites. In this paper we provide a new set of assumptions for a multisite system to become highly ultrasensitive even in the absence of cooperativity or allostery. We assume that the individual sites are modified independently of each other, and that protein activity is an ultrasensitive function of the fraction of modified sites. These assumptions are particularly useful in the context of multisite systems with a large (8+) number of sites. We estimate the apparent Hill coefficient of the dose responses in the sequential and nonsequential cases, highlight their different qualitative properties, and discuss a formula to approximate dose responses in the nonsequential case. As an example we describe a model of bacterial chemotaxis that features robust ultrasensitivity and perfect adaptation over a wide range of ligand concentrations, based on non-allosteric multisite behavior at the level of receptors and flagella. We also include a model of the inactivation of the yeast pheromone protein Ste5 by cell cycle proteins.

Positioning of chemosensory proteins and FtsZ through the Rhodobacter sphaeroides cell cycle

Bacterial chemotaxis depends on signalling through large protein complexes. Each cell must inherit a complex on division, suggesting some co-ordination with cell division. In Escherichia coli the membrane-spanning chemosensory complexes are polar and new static complexes form at pre-cytokinetic sites, ensuring positioning at the new pole after division and suggesting a role for the bacterial cytoskeleton. Rhodobacter sphaeroides has both membrane-associated and cytoplasmic, chromosome-associated chemosensory complexes. We followed the relative positions of the two chemosensory complexes, FtsZ and MreB in aerobic and in photoheterotrophic R. sphaeroides cells using fluorescence microscopy. FtsZ forms polar spots after cytokinesis, which redistribute to the midcell forming nodes from which FtsZ extends circumferentially to form the Z-ring. Membrane-associated chemosensory proteins form a number of dynamic unit-clusters with mature clusters containing about 1000 CheW(3) proteins. Individual clusters diffuse randomly within the membrane, accumulating at new poles after division but not colocalizing with either FtsZ or MreB. The cytoplasmic complex colocalizes with FtsZ at midcells in new-born cells. Before cytokinesis one complex moves to a daughter cell, followed by the second moving to the other cell. These data indicate that two homologous complexes use different mechanisms to ensure partitioning, and neither complex utilizes FtsZ or MreB for positioning.

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.

Prolonged stimuli alter the bacterial chemosensory clusters

The clustering of membrane-bound receptors plays an essential role in various biological systems. A notable model system for studying this phenomenon is the bacterial chemosensory cluster that allows motile bacteria to navigate along chemical gradients in their environment. While the basic structure of these chemosensory clusters is becoming clear, their dynamic nature and operation are not yet understood. By measuring the fluorescence polarization of tagged receptor clusters in live Escherichia coli cells, we provide evidence for stimulus-induced dynamics in these sensory clusters. We find that when a stimulus is applied, the packing of the receptors slowly decreases and that the process reverses when the stimulus is removed. Consistent with these physical changes we find that the effective cooperativity of the kinase response slowly evolves in the presence of a stimulus. Time-lapse fluorescence imaging indicates that, despite these changes, the receptor clusters do not generally dissociate upon ligand binding. These data reveal stimulus-dependent plasticity in chemoreceptor clusters.

Protein logic: a statistical mechanical study of signal integration at the single-molecule level

Information processing and decision-making is based upon logic operations, which in cellular networks has been well characterized at the level of transcription. In recent years, however, both experimentalists and theorists have begun to appreciate that cellular decision-making can also be performed at the level of a single protein, giving rise to the notion of protein logic. Here we systematically explore protein logic using a well-known statistical mechanical model. As an example system, we focus on receptors that bind either one or two ligands, and their associated dimers. Notably, we find that a single heterodimer can realize any of the 16 possible logic gates, including the XOR gate, by variation of biochemical parameters. We then introduce what to our knowledge is a novel idea: that a set of receptors with fixed parameters can encode functionally unique logic gates simply by forming different dimeric combinations. An exhaustive search reveals that the simplest set of receptors (two single-ligand receptors and one double-ligand receptor) can realize several different groups of three unique gates, a result for which the parametric analysis of single receptors and dimers provides a clear interpretation. Both results underscore the surprising functional freedom readily available to cells at the single-protein level.

Isolated bacterial chemosensory array possesses quasi- and ultrastable components: functional links between array stability, cooperativity, and order

Bacteria utilize a large multiprotein chemosensory array to sense attractants and repellents in their environment. The array is a hexagonal lattice formed from three core proteins: a transmembrane receptor, the His kinase CheA, and the adaptor protein CheW. The resulting, highly networked array architecture yields several advantages including strong positive cooperativity in the attractant response and rapid signal transduction through the preformed, integrated signaling circuit. Moreover, when isolated from cells or reconstituted in isolated bacterial membranes, the array possesses extreme kinetic stability termed ultrastability (Erbse and Falke (2009) Biochemistry 48:6975-87) and is the most long-lived multiprotein enzyme complex described to date. The isolated array retains kinase activity, attractant regulation, and its bound core proteins for days or more at 22 °C. The present work quantitates this ultrastability and investigates its origin. The results demonstrate that arrays consist of two major components: (i) a quasi-stable component with a lifetime of 1-2 days that decays due to slow proteolysis of CheA kinase in the lattice and (ii) a truly ultrastable component with a lifetime of ~20 days that is substantially more protected from proteolysis. Following proteolysis of the quasi-stable component the apparent positive cooperativity of the array increases, arguing the quasi-stable component is not as cooperative as the ultrastable component. Introduction of structural defects into the array by coupling a bulky probe to a subset of receptors reveals that modification of only 2% of the receptor population is sufficient to abolish ultrastability, supporting the hypothesis that the ultrastable component requires a high level of array spatial order. Overall, the findings are consistent with a model in which the quasi- and ultrastable components arise from distinct regions of the array, such that the ultrastable regions possess more extensive, better-ordered, multivalent interconnectivities between core components, thereby yielding extraordinary stability and cooperativity. Furthermore, the findings indicate that the chemosensory array is a promising platform for the development of ultrastable biosensors.

Chemotactic adaptation kinetics of individual Escherichia coli cells

Escherichia coli chemotaxis serves as a paradigm for the way living cells respond and adapt to changes in their environment. The chemotactic response has been characterized at the level of individual flagellar motors and in populations of swimming cells. However, it has not been previously possible to quantify accurately the adaptive response of a single, multiflagellated cell. Here, we use our recently developed optical trapping technique to characterize the swimming behavior of individual bacteria as they respond to sudden changes in the chemical environment. We follow the adaptation kinetics of E. coli to varying magnitudes of step-up and step-down changes in concentration of chemoattractant. We quantify two features of adaptation and how they vary with stimulus strength: abruptness (the degree to which return to prestimulus behavior occurs within a small number of run/tumble events) and overshoot (the degree of excessive response before the return to prestimulus behavior). We also characterize the asymmetry between step-up and step-down responses, observed at the single-cell level. Our findings provide clues to an improved understanding of chemotactic adaptation.

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.

Responding to chemical gradients: bacterial chemotaxis

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

A dynamic complex of signaling proteins uses polar localization to regulate cell-fate asymmetry in Caulobacter crescentus

Cellular asymmetry is critical to metazoan development and the life cycle of many microbes. In Caulobacter, cell cycle progression and the formation of asymmetric daughter cells depend on the polarly-localized histidine kinase CckA. How CckA is regulated and why activity depends on localization are unknown. Here, we demonstrate that the unorthodox kinase DivL promotes CckA activity and that the phosphorylated regulator DivK inhibits CckA by binding to DivL. Early in the cell cycle, CckA is activated by the dephosphorylation of DivK throughout the cell. However, in later stages, when phosphorylated DivK levels are high, CckA activation relies on polar localization with a DivK phosphatase. Localization thus creates a protected zone for CckA within the cell, without the use of membrane-enclosed compartments. Our results reveal the mechanisms by which CckA is regulated in a cell-type-dependent manner. More generally, our findings reveal how cells exploit subcellular localization to orchestrate sophisticated regulatory processes.

Lateral density of receptor arrays in the membrane plane influences sensitivity of the E. coli chemotaxis response

In chemotactic bacteria, transmembrane chemoreceptors, CheA and CheW form the core signalling complex of the chemotaxis sensory apparatus. These complexes are organized in extended arrays in the cytoplasmic membrane that allow bacteria to respond to changes in concentration of extracellular ligands via a cooperative, allosteric response that leads to substantial amplification of the signal induced by ligand binding. Here, we have combined cryo-electron tomographic studies of the 3D spatial architecture of chemoreceptor arrays in intact E. coli cells with computational modelling to develop a predictive model for the cooperativity and sensitivity of the chemotaxis response. The predictions were tested experimentally using fluorescence resonance energy transfer (FRET) microscopy. Our results demonstrate that changes in lateral packing densities of the partially ordered, spatially extended chemoreceptor arrays can modulate the bacterial chemotaxis response, and that information about the molecular organization of the arrays derived by cryo-electron tomography of intact cells can be translated into testable, predictive computational models of the chemotaxis response.