Fine-Tuning of Chemotactic Response in E. coli Determined by High-Throughput Capillary Assay

In E. coli, chemotactic behavior exhibits perfect adaptation that is robust to changes in the intracellular concentration of the chemotactic proteins, such as CheR and CheB. However, the robustness of the perfect adaptation does not explicitly imply a robust chemotactic response. Previous studies on the robustness of the chemotactic response relied on swarming assays, which can be confounded by processes besides chemotaxis, such as cellular growth and depletion of nutrients. Here, using a high-throughput capillary assay that eliminates the effects of growth, we experimentally studied how the chemotactic response depends on the relative concentration of the chemotactic proteins. We simultaneously measured both the chemotactic response of E. coli cells to L: -aspartate and the concentrations of YFP-CheR and CheB-CFP fusion proteins. We found that the chemotactic response is fine-tuned to a specific ratio of [CheR]/[CheB] with a maximum response comparable to the chemotactic response of wild-type behavior. In contrast to adaptation in chemotaxis, that is robust and exact, capillary assays revealed that the chemotactic response in swimming bacteria is fined-tuned to wild-type level of the [CheR]/[CheB] ratio.     

Imprecision of Adaptation in Escherichia coli Chemotaxis

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

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.     

Perfect and near-perfect adaptation in a model of bacterial chemotaxis

The signaling apparatus mediating bacterial chemotaxis can adapt to a wide range of persistent external stimuli. In many cases, the bacterial activity returns to its prestimulus level exactly, and this perfect adaptability is robust against variations in various chemotaxis protein concentrations. We model the bacterial chemotaxis signaling pathway, from ligand binding to CheY phosphorylation. By solving the steady-state equations of the model analytically, we derive a full set of conditions for the system to achieve perfect adaptation. The conditions related to the phosphorylation part of the pathway are discovered for the first time, while other conditions are generalizations of the ones found in previous works. Sensitivity of the perfect adaptation is evaluated by perturbing these conditions. We find that, even in the absence of some of the perfect adaptation conditions, adaptation can be achieved with near-perfect precision as a result of the separation of scales in both chemotaxis protein concentrations and reaction rates, or specific properties of the receptor distribution in different methylation states. Since near-perfect adaptation can be found in much larger regions of the parameter space than that defined by the perfect adaptation conditions, their existence is essential to understand robustness in bacterial chemotaxis.     

Nonadaptive Fluctuation in an Adaptive Sensory System: Bacterial Chemoreceptor

Background

Sensory systems often exhibit an adaptation or desensitization after a transient response, making the system ready to receive a new signal over a wide range of backgrounds. Because of the strong influence of thermal stochastic fluctuations on the biomolecules responsible for the adaptation, such as many membrane receptors and channels, their response is inherently noisy, and the adaptive property is achieved as a statistical average.

Methodology/Principal Findings

Here, we study a simple kinetic model characterizing the essential aspects of these adaptive molecular systems and show theoretically that, while such an adaptive sensory system exhibits a perfect adaptation property on average, its temporal stochastic fluctuations are able to be sensitive to the environmental conditions. Among the adaptive sensory systems, an extensively studied model system is the bacterial receptor responsible for chemotaxis. The model exhibits a nonadaptive fluctuation sensitive to the environmental ligand concentration, while perfect adaptation is achieved on average. Furthermore, we found that such nonadaptive fluctuation makes the bacterial behavior dependent on the environmental chemoattractant concentrations, which enhances the chemotactic performance.

Conclusions/Significance

This result indicates that adaptive sensory systems can make use of such stochastic fluctuation to carry environmental information, which is not possible by means of the average, while keeping responsive to the changing stimulus.     

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.     

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.     

Reverse Engineering of Bacterial Chemotaxis Pathway via Frequency Domain Analysis

Chemotaxis is defined as a behavior involving organisms sensing attractants or repellents and leading towards or away from them. Therefore, it is possible to reengineer chemotaxis network to control the movement of bacteria to our advantage. Understanding the design principles of chemotaxis pathway is a prerequisite and an important topic in synthetic biology. Here, we provide guidelines for chemotaxis pathway design by employing control theory and reverse engineering concept on pathway dynamic design. We first analyzed the mathematical models for two most important kinds of E. coli chemotaxis pathway—adaptive and non-adaptive pathways, and concluded that the control units of the pathway de facto function as a band-pass filter and a low-pass filter, respectively, by abstracting the frequency response properties of the pathways. The advantage of the band-pass filter is established, and we demonstrate how to tune the three key parameters of it—A (max amplification), ω₁ (down cut-off frequency) and ω₂ (up cut-off frequency) to optimize the chemotactic effect. Finally, we hypothesized a similar but simpler version of the dynamic pathway model based on the principles discovered and show that it leads to similar properties with native E. coli chemotactic behaviors. Our study provides an example of simulating and designing biological dynamics in silico and indicates how to make use of the native pathway''s features in this process. Furthermore, the characteristics we discovered and tested through reverse engineering may help to understand the design principles of the pathway and promote the design of artificial chemotaxis pathways.     

Models of Eukaryotic Gradient Sensing: Application to Chemotaxis of Amoebae and Neutrophils

Eukaryotic cells can detect shallow gradients of chemoattractants with exquisite precision and respond quickly to changes in the gradient steepness and direction. Here, we describe a set of models explaining both adaptation to uniform increases in chemoattractant and persistent signaling in response to gradients. We demonstrate that one of these models can be mapped directly onto the biochemical signal-transduction pathways underlying gradient sensing in amoebae and neutrophils. According to this scheme, a locally acting activator (PI3-kinase) and a globally acting inactivator (PTEN or a similar phosphatase) are coordinately controlled by the G-protein activation. This signaling system adapts perfectly to spatially homogeneous changes in the chemoattractant. In chemoattractant gradients, an imbalance between the action of the activator and the inactivator results in a spatially oriented persistent signaling, amplified by a substrate supply-based positive feedback acting through small G-proteins. The amplification is activated only in a continuous presence of the external signal gradient, thus providing the mechanism for sensitivity to gradient alterations. Finally, based on this mapping, we make predictions concerning the dynamics of signaling. We propose that the underlying principles of perfect adaptation and substrate supply-based positive feedback will be found in the sensory systems of other chemotactic cell types.     

Stochastic signal inputs for chemotactic response in Dictyostelium cells revealed by single molecule imaging techniques

Chemotactic cells can exhibit extreme sensitivity to chemical gradients. Theoretical estimations of the signal inputs required for chemotaxis suggest that the response can be achieved under the strong influence of stochastic input noise generated by the receptors during the transmembrane signaling. This arises a fundamental question regarding the mechanisms for directional sensing: how do cells obtain reliable information regarding gradient direction by using stochastically operating receptors and the downstream molecules? To address this question, we have developed single molecule imaging techniques to visualize signaling molecules responsible for chemotaxis in living Dictyostelium cells, allowing us to monitor the stochastic signaling processes directly. Single molecule imaging of a chemoattractant bound to a receptor demonstrates that signal inputs fluctuate with time and space. Downstream signaling molecules, such as PTEN and a PH domain-containing protein that are constituent parts of chemotactic signaling system, can also be followed at single molecule level in living cells, illuminating the stochastic nature of chemotactic signaling processes. In this report, we start with a brief introduction of chemotactic response of the eukaryotic cells, followed by an explanation for single molecule imaging techniques, and finally discuss these applications to chemotactic signaling system of Dictyostelium cells.     

Collective Signal Processing in Cluster Chemotaxis: Roles of Adaptation,Amplification, and Co-attraction in Collective Guidance

Single eukaryotic cells commonly sense and follow chemical gradients, performing chemotaxis. Recent experiments and theories, however, show that even when single cells do not chemotax, clusters of cells may, if their interactions are regulated by the chemoattractant. We study this general mechanism of “collective guidance” computationally with models that integrate stochastic dynamics for individual cells with biochemical reactions within the cells, and diffusion of chemical signals between the cells. We show that if clusters of cells use the well-known local excitation, global inhibition (LEGI) mechanism to sense chemoattractant gradients, the speed of the cell cluster becomes non-monotonic in the cluster’s size—clusters either larger or smaller than an optimal size will have lower speed. We argue that the cell cluster speed is a crucial readout of how the cluster processes chemotactic signals; both amplification and adaptation will alter the behavior of cluster speed as a function of size. We also show that, contrary to the assumptions of earlier theories, collective guidance does not require persistent cell-cell contacts and strong short range adhesion. If cell-cell adhesion is absent, and the cluster cohesion is instead provided by a co-attraction mechanism, e.g. chemotaxis toward a secreted molecule, collective guidance may still function. However, new behaviors, such as cluster rotation, may also appear in this case. Co-attraction and adaptation allow for collective guidance that is robust to varying chemoattractant concentrations while not requiring strong cell-cell adhesion.     

Polymorphonuclear Leucocyte Chemotaxis in Patients with Bacterial Infections

A new in vitro method of measuring the chemotaxis of polymorphonuclear leucocytes from peripheral blood has been used to calculate a chemotactic index. The mean chemotactic index in 15 patients with bacterial infection (434) was significantly less (P <0·0005) than in 15 normal controls (553) matched for age and sex. The reduction in chemotaxis could be correlated with the duration of the infection, with the greatest impairment being found in those patients with the shortest duration of infection. In five patients studied before and after appropriate therapy the chemotactic index returned to normal values with clearing of the infection. It is suggested that the impairment in chemotaxis may be due to prior phagocytosis of antibody-antigen complexes by the polymorphonuclear leucocytes.     

Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis I: The Single Cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area.     

Signal transduction in chemotaxis mediated by the bacterial phosphotransferase system

Gram-negative bacteria are able to respond chemotactically to carbohydrates which are substrates of the bacterial phosphoenolpyruvate:sugar phosphotransferase system (PTS). The mechanism of signal transduction in PTS-mediated chemotaxis is different from the well-studied mechanism involving methyl-accepting chemotaxis proteins (MCPs). In PTS-mediated chemotaxis, carbohydrate transport is required, and phosphorylation seems to be involved in both excitation and adaptation. In this review the roles of the components of the PTS in chemotactic signal transduction are discussed. © 1993 Wiley-Liss, Inc.     

The Role of Adaptation in Bacterial Speed Races

Evolution of biological sensory systems is driven by the need for efficient responses to environmental stimuli. A paradigm among prokaryotes is the chemotaxis system, which allows bacteria to navigate gradients of chemoattractants by biasing their run-and-tumble motion. A notable feature of chemotaxis is adaptation: after the application of a step stimulus, the bacterial running time relaxes to its pre-stimulus level. The response to the amino acid aspartate is precisely adapted whilst the response to serine is not, in spite of the same pathway processing the signals preferentially sensed by the two receptors Tar and Tsr, respectively. While the chemotaxis pathway in E. coli is well characterized, the role of adaptation, its functional significance and the ecological conditions where chemotaxis is selected, are largely unknown. Here, we investigate the role of adaptation in the climbing of gradients by E. coli. We first present theoretical arguments that highlight the mechanisms that control the efficiency of the chemotactic up-gradient motion. We discuss then the limitations of linear response theory, which motivate our subsequent experimental investigation of E. coli speed races in gradients of aspartate, serine and combinations thereof. By using microfluidic techniques, we engineer controlled gradients and demonstrate that bacterial fronts progress faster in equal-magnitude gradients of serine than aspartate. The effect is observed over an extended range of concentrations and is not due to differences in swimming velocities. We then show that adding a constant background of serine to gradients of aspartate breaks the adaptation to aspartate, which results in a sped-up progression of the fronts and directly illustrate the role of adaptation in chemotactic gradient-climbing.     

Continuous-Flow Capillary Assay for Measuring Bacterial Chemotaxis

Bacterial chemotaxis may have a significant impact on the structure and function of bacterial communities. Quantification of chemotactic motion is necessary to identify chemoeffectors and to determine the bacterial transport parameters used in predictive models of chemotaxis. When the chemotactic bacteria consume the chemoeffector, the chemoeffector gradient to which the bacteria respond may be significantly perturbed by the consumption. Therefore, consumption of the chemoeffector can confound chemotaxis measurements if it is not accounted for. Current methods of quantifying chemotaxis use bacterial concentrations that are too high to preclude chemoeffector consumption or involve ill-defined conditions that make quantifying chemotaxis difficult. We developed a method of quantifying bacterial chemotaxis at low cell concentrations (~10⁵ CFU/ml), so metabolism of the chemoeffector is minimized. The method facilitates quantification of bacterial-transport parameters by providing well-defined boundary conditions and can be used with volatile and semivolatile chemoeffectors.     

Actin dynamics rapidly reset chemoattractant receptor sensitivity following adaptation in neutrophils

Neutrophils are cells of the innate immune system that hunt and kill pathogens using directed migration. This process, known as chemotaxis, requires the regulation of actin polymerization downstream of chemoattractant receptors. Reciprocal interactions between actin and intracellular signals are thought to underlie many of the sophisticated signal processing capabilities of the chemotactic cascade including adaptation, amplification and long-range inhibition. However, with existing tools, it has been difficult to discern actin''s role in these processes. Most studies investigating the role of the actin cytoskeleton have primarily relied on actin-depolymerizing agents, which not only block new actin polymerization but also destroy the existing cytoskeleton. We recently developed a combination of pharmacological inhibitors that stabilizes the existing actin cytoskeleton by inhibiting actin polymerization, depolymerization and myosin-based rearrangements; we refer to these processes collectively as actin dynamics. Here, we investigated how actin dynamics influence multiple signalling responses (PI3K lipid products, calcium and Pak phosphorylation) following acute agonist addition or during desensitization. We find that stabilized actin polymer extends the period of receptor desensitization following agonist binding and that actin dynamics rapidly reset receptors from this desensitized state. Spatial differences in actin dynamics may underlie front/back differences in agonist sensitivity in neutrophils.     

Monocyte Chemoattractant Activity of Ser → Ala Active Site Mutant Recombinant α-Thrombin

α-Thrombin is chemotactic for human monocytes with optimal activity between 10-100 nM. The mechanism by which this response is mediated remains a point of controversy. The purpose of this study was to compare the chemotactic activity of proteolytically inactive thrombin (active site Ser¹⁹⁵ → Ala mutant or Phe-Pro-Arg-chloromethyl ketone-inactivated thrombin) to thrombin and the "tethered ligand" thrombin receptor agonist peptide SFLLRN (single-letter amino acid code). Monocyte chemotaxis was compared to an optimal concentration (10 nM, considered to be 100%) of formyl-Met-Leu-Phe (fMLP). Proteolytically inactive thrombin (38% of fMLP) had similar chemotactic activity to active thrombin (46% of fMLP) at a concentration of 100 nM. Chemotaxis to SFLLRN was comparable to that of a control hexapeptide (FSLNLR) which is not an agonist for the tethered ligand thrombin receptor. Cross-desensitization experiments showed that pretreatment of monocytes with either mutant or active thrombin reduced subsequent chemotaxis to both thrombin chemotaxins. Pretreatment with SFLLRN did not decrease subsequent chemotaxis to either form of thrombin. Calcium flux measurements showed that both active thrombin and SFLLRN induced a rapid increase in monocyte and platelet intracellular calcium concentration. However, there was no intracellular calcium change in response to mutant thrombin or FSLNLR. Likewise, active thrombin and SFLLRN induced a rapid net increase in polymerized actin, but mutant thrombin and FSLNLR did not. By contrast, both active and mutant thrombin induced a polarization of monotocyte morphology and actin distribution. This polarization has been associated with directed migration in many cell types. SFLLRN, however, induced a symmetrical increase in polymerized actin. These results suggest that measurements of intracellular calcium and polymerized actin are not perfect surrogate tests for true chemotactic activity. These results show that thrombin proteolysis is not required for monocyte chemotaxis and may be mediated by interaction with a binding site other than the tethered ligand thrombin receptor.