Adaptation Dynamics in Densely Clustered Chemoreceptors

In many sensory systems, transmembrane receptors are spatially organized in large clusters. Such arrangement may facilitate signal amplification and the integration of multiple stimuli. However, this organization likely also affects the kinetics of signaling since the cytoplasmic enzymes that modulate the activity of the receptors must localize to the cluster prior to receptor modification. Here we examine how these spatial considerations shape signaling dynamics at rest and in response to stimuli. As a model system, we use the chemotaxis pathway of Escherichia coli, a canonical system for the study of how organisms sense, respond, and adapt to environmental stimuli. In bacterial chemotaxis, adaptation is mediated by two enzymes that localize to the clustered receptors and modulate their activity through methylation-demethylation. Using a novel stochastic simulation, we show that distributive receptor methylation is necessary for successful adaptation to stimulus and also leads to large fluctuations in receptor activity in the steady state. These fluctuations arise from noise in the number of localized enzymes combined with saturated modification kinetics between the localized enzymes and the receptor substrate. An analytical model explains how saturated enzyme kinetics and large fluctuations can coexist with an adapted state robust to variation in the expression levels of the pathway constituents, a key requirement to ensure the functionality of individual cells within a population. This contrasts with the well-mixed covalent modification system studied by Goldbeter and Koshland in which mean activity becomes ultrasensitive to protein abundances when the enzymes operate at saturation. Large fluctuations in receptor activity have been quantified experimentally and may benefit the cell by enhancing its ability to explore empty environments and track shallow nutrient gradients. Here we clarify the mechanistic relationship of these large fluctuations to well-studied aspects of the chemotaxis system, precise adaptation and functional robustness.     

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.     

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.     

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.     

The three adaptation systems of Bacillus subtilis chemotaxis

Adaptation has a crucial role in the gradient-sensing mechanism that underlies bacterial chemotaxis. The Escherichia coli chemotaxis pathway uses a single adaptation system involving reversible receptor methylation. In Bacillus subtilis, the chemotaxis pathway seems to use three adaptation systems. One involves reversible receptor methylation, although quite differently than in E. coli. The other two involve CheC, CheD and CheV, which are chemotaxis proteins not found in E. coli. Remarkably, no one system is absolutely required for adaptation or is independently capable of generating adaptation. In this review, we discuss these three novel adaptation systems in B. subtilis and propose a model for their integration.     

Chemotaxis in Escherichia coli: a molecular model for robust precise adaptation

The chemotaxis system in the bacterium Escherichia coli is remarkably sensitive to small relative changes in the concentrations of multiple chemical signals over a broad range of ambient concentrations. Interactions among receptors are crucial to this sensitivity as is precise adaptation, the return of chemoreceptor activity to prestimulus levels in a constant chemoeffector environment. Precise adaptation relies on methylation and demethylation of chemoreceptors by the enzymes CheR and CheB, respectively. Experiments indicate that when transiently bound to one receptor, these enzymes act on small assistance neighborhoods (AN) of five to seven receptor homodimers. In this paper, we model a strongly coupled complex of receptors including dynamic CheR and CheB acting on ANs. The model yields sensitive response and precise adaptation over several orders of magnitude of attractant concentrations and accounts for different responses to aspartate and serine. Within the model, we explore how the precision of adaptation is limited by small AN size as well as by CheR and CheB kinetics (including dwell times, saturation, and kinetic differences among modification sites) and how these kinetics contribute to noise in complex activity. The robustness of our dynamic model for precise adaptation is demonstrated by randomly varying biochemical parameters.     

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.     

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.     

Multiple methylation of methyl-accepting chemotaxis proteins during adaptation of E. coli to chemical stimuli

In bacterial chemotaxis, adaptation is correlated with methylation or demethylation of methyl-accepting chemotaxis proteins (MCPs). Each protein migrates as a characteristic set of multiple bands in sodium dodecylsulfate polyacrylamide gel electrophoresis. The changes in MCP methylation that accompany adaptation are not the same for all bands of a set. Adaptation to a type II repellent stimulus results in an overall decrease in MCP II methylation, but also in an increase in the amount of radioactive methyl groups in the upper band of the set. We demonstrate that this increase is not due to new methylation, but rather to reduced electrophoretic mobility of previously methylated molecules that have lost some but not all of their methyl groups. We suggest that the pattern of multiple bands is a direct reflection of multiple sites for methylation on MCP molecules, and that the distribution of radiolabel among the bands is determined by the total extent of methylation. The patterns of methylated peptides produced by limited proteolysis of different MCP bands imply that methylation of the multiple sites on a molecule may occur in a specific order.     

Adapt locally and act globally: strategy to maintain high chemoreceptor sensitivity in complex environments

In bacterial chemotaxis, several types of ligand‐specific receptors form mixed clusters, wherein receptor–receptor interactions lead to signal amplification and integration. However, it remains unclear how a mixed receptor cluster adapts to individual stimuli and whether it can differentiate between different types of ligands. Here, we combine theoretical modeling with experiments to reveal the adaptation dynamics of the mixed chemoreceptor cluster in Escherichia coli. We show that adaptation occurs locally and is ligand‐specific: only the receptor that binds the external ligand changes its methylation level when the system adapts, whereas other types of receptors change methylation levels transiently. Permanent methylation crosstalk occurs when the system fails to adapt accurately. This local adaptation mechanism enables cells to differentiate individual stimuli by encoding them into the methylation levels of corresponding types of chemoreceptors. It tunes each receptor to its most responsive state to maintain high sensitivity in complex environments and prevents saturation of the cluster by one signal.     

A Mechanism for Precision-Sensing via a Gradient-Sensing Pathway: A Model of Escherichia coli Thermotaxis

Thermotaxis is the phenomenon where an organism directs its movement toward its preferred temperature. So far, the molecular origin for this precision-sensing behavior remains a puzzle. We propose a model of Escherichia coli thermotaxis and show that the precision-sensing behavior in E. coli thermotaxis can be carried out by the gradient-sensing chemotaxis pathway under two general conditions. First, the thermosensor response to temperature is inverted by its internal adaptation state. For E. coli, chemoreceptor Tar changes from a warm sensor to a cold sensor on increase of its methylation level. Second, temperature directly affects the adaptation kinetics. The adapted activity in E. coli increases with temperature in contrast to the perfect adaptation to chemical stimuli. Given these two conditions, E. coli thermotaxis is achieved by the cryophilic and thermophilic responses for temperature above and below a critical temperature T_c, which is encoded by internal pathway parameters. Our model results are supported by both experiments with adaptation-disabled mutants and the recent temperature impulse response measurements for wild-type cells. T_c is predicted to decrease with the background attractant concentration. This mechanism for precision sensing in an adaptive gradient-sensing system may apply to other organisms, such as Dictyostelium discoideum and Caenorhabditis elegans.     

Receptor methylation controls the magnitude of stimulus-response coupling in bacterial chemotaxis

Motile prokaryotes employ a chemoreceptor-kinase array to sense changes in the media and properly adjust their swimming behavior. This array is composed of a family of Type I membrane receptors, a histidine protein kinase (CheA), and an Src homology 3-like protein (CheW). Binding of an attractant to the chemoreceptors inhibits CheA, which results in decreased phosphorylation of the chemotaxis response regulator (CheY). Sensitivity of the system to stimuli is modulated by a protein methyltransferase (CheR) and a protein methylesterase (CheB) that catalyze the methylation and demethylation of specific glutamyl residues in the cytoplasmic domain of the receptors. One of the most fundamental unanswered questions concerning the bacterial chemotaxis mechanism is the quantitative relationship between ligand binding to receptors and CheA inhibition. We show that the receptor glutamyl modifications cause adaptation by changing the gain (magnitude amplification) between attractant binding and kinase inhibition without substantially affecting ligand binding affinity. The mechanism adjusts receptor sensitivity to background stimulus intensity over several orders of magnitude of attractant concentrations. The cooperative effects of ligand binding appear to be minimal with Hill coefficients for kinase inhibition less than 2, independent of the state of glutamyl modification.     

Stochastic adaptation and fold-change detection: from single-cell to population behavior

Background  

In cell signaling terminology, adaptation refers to a system's capability of returning to its equilibrium upon a transient response. To achieve this, a network has to be both sensitive and precise. Namely, the system must display a significant output response upon stimulation, and later on return to pre-stimulation levels. If the system settles at the exact same equilibrium, adaptation is said to be 'perfect'. Examples of adaptation mechanisms include temperature regulation, calcium regulation and bacterial chemotaxis.     

The methyl-accepting chemotaxis proteins of Escherichia coli. Identification of the multiple methylation sites on methyl-accepting chemotaxis protein I

The methyl-accepting chemotaxis proteins (MCPs) are integral membrane proteins that undergo reversible methylation during adaptation of bacterial cells to environmental attractants and repellents. The numerous methylated forms of each MCP are seen as a pattern of multiple bands on polyacrylamide gels. We have characterized the methylation sites in MCPI by analyzing methyl-accepting tryptic peptides. At least two different tryptic peptides accept methyl esters; one methyl-accepting peptide contains methionine and lysine and may be methylated a maximum of four times. The second methyl-accepting tryptic peptide contains arginine and may be methylated twice. Base-catalyzed demethylations of tryptic peptides and analysis of the charge differences between the different methylated forms of MCPI show that MCPI molecules may be methylated a total of six times. The two methyl esters on the methyl-accepting arginine peptide appear to be preferentially methylated in most of the forms of MCPI in attractant-stimulated cells. The ability to acquire six methylations on MCPI allows the bacterial cells to adapt to a broad range of attractant and repellent concentrations.     

Control of transducer methylation levels in Escherichia coli: investigation of components essential for modulation of methylation and demethylation reactions.

During bacterial chemotaxis in Escherichia coli, adaptation is accomplished by reversible methylation of the transmembrane signal transducers. Methyl groups are added by the CheR protein in a slow response to attractants and removed by the CheB protein in response to repellents. The methylesterase activity of the CheB protein is modulated by a factor that is controlled in a global fashion throughout the cell. By controlling the level of expression of the cheR, cheB, and transducer genes with exogenous promoters on multicopy plasmids, we demonstrate that the modulating factor exists in stoichiometric concentrations relative to CheB protein and that the generation or efficacy of this factor requires the cheA and/or cheW gene products, suggesting that phosphorylation of the methylesterase by CheA may be involved in its global activation. We show that in the absence of any modulation of the CheB activity, the CheR methyltransferase activity is modulated in a local fashion at the transducers, most likely as a result of a conformational change in the transducer protein brought about by the binding of ligand, and does not require CheA or CheW.     

Evolution of taxis responses in virtual bacteria: non-adaptive dynamics

Bacteria are able to sense and respond to a variety of external stimuli, with responses that vary from stimuli to stimuli and from species to species. The best-understood is chemotaxis in the model organism Escherichia coli, where the dynamics and the structure of the underlying pathway are well characterised. It is not clear, however, how well this detailed knowledge applies to mechanisms mediating responses to other stimuli or to pathways in other species. Furthermore, there is increasing experimental evidence that bacteria integrate responses from different stimuli to generate a coherent taxis response. We currently lack a full understanding of the different pathway structures and dynamics and how this integration is achieved. In order to explore different pathway structures and dynamics that can underlie taxis responses in bacteria, we perform a computational simulation of the evolution of taxis. This approach starts with a population of virtual bacteria that move in a virtual environment based on the dynamics of the simple biochemical pathways they harbour. As mutations lead to changes in pathway structure and dynamics, bacteria better able to localise with favourable conditions gain a selective advantage. We find that a certain dynamics evolves consistently under different model assumptions and environments. These dynamics, which we call non-adaptive dynamics, directly couple tumbling probability of the cell to increasing stimuli. Dynamics that are adaptive under a wide range of conditions, as seen in the chemotaxis pathway of E. coli, do not evolve in these evolutionary simulations. However, we find that stimulus scarcity and fluctuations during evolution results in complex pathway dynamics that result both in adaptive and non-adaptive dynamics depending on basal stimuli levels. Further analyses of evolved pathway structures show that effective taxis dynamics can be mediated with as few as two components. The non-adaptive dynamics mediating taxis responses provide an explanation for experimental observations made in mutant strains of E. coli and in wild-type Rhodobacter sphaeroides that could not be explained with standard models. We speculate that such dynamics exist in other bacteria as well and play a role linking the metabolic state of the cell and the taxis response. The simplicity of mechanisms mediating such dynamics makes them a candidate precursor of more complex taxis responses involving adaptation. This study suggests a strong link between stimulus conditions during evolution and evolved pathway dynamics. When evolution was simulated under conditions of scarce and fluctuating stimulus conditions, the evolved pathway contained features of both adaptive and non-adaptive dynamics, suggesting that these two types of dynamics can have different advantages under distinct environmental circumstances.     

An Unorthodox Sensory Adaptation Site in the Escherichia coli Serine Chemoreceptor

The serine chemoreceptor of Escherichia coli contains four canonical methylation sites for sensory adaptation that lie near intersubunit helix interfaces of the Tsr homodimer. An unexplored fifth methylation site, E502, lies at an intrasubunit helix interface closest to the HAMP domain that controls input-output signaling in methyl-accepting chemotaxis proteins. We analyzed, with in vivo Förster resonance energy transfer (FRET) kinase assays, the serine thresholds and response cooperativities of Tsr receptors with different mutationally imposed modifications at sites 1 to 4 and/or at site 5. Tsr variants carrying E or Q at residue 502, in combination with unmodifiable D and N replacements at adaptation sites 1 to 4, underwent both methylation and demethylation/deamidation, although detection of the latter modifications required elevated intracellular levels of CheB. These Tsr variants could not mediate a chemotactic response to serine spatial gradients, demonstrating that adaptational modifications at E502 alone are not sufficient for Tsr function. Moreover, E502 is not critical for Tsr function, because only two amino acid replacements at this residue abrogated serine chemotaxis: Tsr-E502P had extreme kinase-off output and Tsr-E502I had extreme kinase-on output. These large threshold shifts are probably due to the unique HAMP-proximal location of methylation site 5. However, a methylation-mimicking glutamine at any Tsr modification site raised the serine response threshold, suggesting that all sites influence signaling by the same general mechanism, presumably through changes in packing stability of the methylation helix bundle. These findings are consistent with control of input-output signaling in Tsr through dynamic interplay of the structural stabilities of the HAMP and methylation bundles.     

A methyl-accepting protein is involved in benzoate taxis in Pseudomonas putida.

Pseudomonas putida is attracted to at least two groups of aromatic acids: a benzoate group and a benzoylformate group. Members of the benzoate group of chemoattractants stimulated the methylation of a P. putida polypeptide with an apparent molecular weight of 60,000 in sodium dodecyl sulfate-polyacrylamide gels. This polypeptide is presumed to be a methyl-accepting chemotaxis protein for several reasons: its molecular weight is similar to the molecular weights of Escherichia coli methyl-accepting chemotaxis proteins, the amount of time required to attain maximal methylation correlated with the time needed for behavioral adaptation of P. putida cells to benzoate, and methylation was stimulated by benzoate only in cells induced for chemotaxis to benzoate. Also, a mutant specifically defective in benzoate taxis failed to show any stimulation of methylation upon addition of benzoate. Benzoylformate did not stimulate protein methylation in cells induced for benzoylformate chemotaxis, suggesting that sensory input from this second group of aromatic-acid attractants is processed through a different kind of chemosensory pathway. The chemotactic responses of P. putida cells to benzoate and benzoylformate were not sensitive to external pH over a range (6.2 to 7.7) which would vary the protonated forms of these weak acids by a factor of about 30. This indicates that detection of cytoplasmic pH is not the basis for aromatic-acid taxis in P. putida.     

Phosphorylation of an N-terminal regulatory domain activates the CheB methylesterase in bacterial chemotaxis

Two types of reversible protein modification reactions have been identified in bacterial chemotaxis, methylation of membrane receptor-transducer proteins at glutamate side chains and phosphorylation of cytoplasmic signal transduction proteins at histidine and aspartate side chains. CheB is a bifunctional enzyme that is involved in both these modification processes. Its C-terminal domain is a methylesterase that catalyzes the hydrolysis of gamma-carboxyl glutamyl methyl esters in the cytoplasmic domain of chemoreceptor proteins. Its N-terminal domain is a phosphatase that catalyzes the hydrolysis of phospho-CheA, the central response regulator of bacterial chemotaxis. Phospho-CheB, produced as an intermediate in the phosphatase reaction, has dramatically increased methylesterase activity. The interplay between the methylesterase and phosphatase activities of CheB may provide a crucial link between adaptation and excitation in stimulus-response coupling.