Predicted Auxiliary Navigation Mechanism of Peritrichously Flagellated Chemotactic Bacteria

Chemotactic movement of Escherichia coli is one of the most thoroughly studied paradigms of simple behavior. Due to significant competitive advantage conferred by chemotaxis and to high evolution rates in bacteria, the chemotaxis system is expected to be strongly optimized. Bacteria follow gradients by performing temporal comparisons of chemoeffector concentrations along their runs, a strategy which is most efficient given their size and swimming speed. Concentration differences are detected by a sensory system and transmitted to modulate rotation of flagellar motors, decreasing the probability of a tumble and reorientation if the perceived concentration change during a run is positive. Such regulation of tumble probability is of itself sufficient to explain chemotactic drift of a population up the gradient, and is commonly assumed to be the only navigation mechanism of chemotactic E. coli. Here we use computer simulations to predict existence of an additional mechanism of gradient navigation in E. coli. Based on the experimentally observed dependence of cell tumbling angle on the number of switching motors, we suggest that not only the tumbling probability but also the degree of reorientation during a tumble depend on the swimming direction along the gradient. Although the difference in mean tumbling angles up and down the gradient predicted by our model is small, it results in a dramatic enhancement of the cellular drift velocity along the gradient. We thus demonstrate a new level of optimization in E. coli chemotaxis, which arises from the switching of several flagellar motors and a resulting fine tuning of tumbling angle. Similar strategy is likely to be used by other peritrichously flagellated bacteria, and indicates yet another level of evolutionary development of bacterial chemotaxis.     

Enhancement of Swimming Speed Leads to a More-Efficient Chemotactic Response to Repellent

Negative chemotaxis refers to the motion of microorganisms away from regions with high concentrations of chemorepellents. In this study, we set controlled gradients of NiCl₂, a chemorepellent, in microchannels to quantify the motion of Escherichia coli over a broad range of concentrations. The experimental technique measured the motion of the bacteria in space and time and further related the motion to the local concentration profile of the repellent. Results show that the swimming speed of bacteria increases with an increasing concentration of repellent, which in turn enhances the drift velocity. The contribution of the increased swimming speed to the total drift velocity was in the range of 20 to 40%, with the remaining contribution coming from the modulation of the tumble frequency. A simple model that incorporates receptor dynamics, including adaptation, intracellular signaling, and swimming speed variation, was able to qualitatively capture the observed trend in drift velocity.     

Biased reorientation in the chemotaxis of peritrichous bacteria Salmonella enterica serovar Typhimurium

Many kinds of peritrichous bacteria that repeat runs and tumbles by using multiple flagella exhibit chemotaxis by sensing a difference in the concentration of the attractant or repellent between two adjacent time points. If a cell senses that the concentration of an attractant has increased, their flagellar motors decrease the switching frequency from counterclockwise to clockwise direction of rotation, which causes a longer run in swimming up the concentration gradient than swimming down. We investigated the turn angle in tumbles of peritrichous bacteria swimming across the concentration gradient of a chemoattractant because the change in the switching frequency in the rotational direction may affect the way tumbles. We tracked several hundreds of runs and tumbles of single cells of Salmonella enterica serovar Typhimurium in the concentration gradient of L-serine and found that the turn angle depends on the concentration gradient that the cell senses just before the tumble. The turn angle is biased toward a smaller value when the cells swim up the concentration gradient, whereas the distribution of the angle is almost uniform (random direction) when the cells swim down the gradient. The effect of the observed bias in the turn angle on the degree of chemotaxis was investigated by random walk simulation. In the concentration field where attractants diffuse concentrically from the point source, we found that this angular distribution clearly affects the reduction of the mean-square displacement of the cell that has started at the attractant source, that is, the bias in the turn angle distribution contributes to chemotaxis in peritrichous bacteria.     

Persistence of direction increases the drift velocity of run and tumble chemotaxis

Escherichia coli is a motile bacterium that moves up a chemoattractant gradient by performing a biased random walk composed of alternating runs and tumbles. Previous models of run and tumble chemotaxis neglect one or more features of the motion, namely (a) a cell cannot directly detect a chemoattractant gradient but rather makes temporal comparisons of chemoattractant concentration, (b) rather than being entirely random, tumbles exhibit persistence of direction, meaning that the new direction after a tumble is more likely to be in the forward hemisphere, and (c) rotational Brownian motion makes it impossible for an E. coli cell to swim in a straight line during a run. This paper presents an analytic calculation of the chemotactic drift velocity taking account of (a), (b) and (c), for weak chemotaxis. The analytic results are verified by Monte Carlo simulation. The results reveal a synergy between temporal comparisons and persistence that enhances the drift velocity, while rotational Brownian motion reduces the drift velocity. This work was supported by an Oliver Gatty Studentship from the University of Cambridge.     

A biochemical mechanism for bacterial chemotaxis

Peritrichous bacteria alternately swim and tumble (thrash about with little forward progress). By selective modulation of tumbling frequency, these bacteria carry out chemotaxis, which is migration to higher concentrations of attractant or lower concentrations of repellent. A model for chemotaxis is presented in which tumbling frequency is regulated by concentration of Ca²⁺ ion at the switch that controls tumbling and swimming. Attractants cause decreased levels of free cytoplasmic Ca²⁺ ion due to binding of Ca²⁺ ion by specific proteins. This Ca²⁺ ion is released when these proteins become methylated. An alternative model. involving a cytoplasmic metabolite “compound X”, is discussed.     

Run and Tumble Chemotaxis in a Shear Flow: The Effect of Temporal Comparisons,Persistence, Rotational Diffusion,and Cell Shape

Escherichia coli is a motile bacterium that moves up a chemoattractant gradient by performing a biased random walk composed of alternating runs and tumbles. This paper presents calculations of the chemotactic drift velocity v _d (the mean velocity up the chemoattractant gradient) of an E. coli cell performing chemotaxis in a uniform, steady shear flow, with a weak chemoattractant gradient at right angles to the flow. Extending earlier models, a combined analytic and numerical approach is used to assess the effect of several complications, namely (i) a cell cannot detect a chemoattractant gradient directly but rather makes temporal comparisons of chemoattractant concentration, (ii) the tumbles exhibit persistence of direction, meaning that the swimming directions before and after a tumble are correlated, (iii) the cell suffers random re-orientations due to rotational Brownian motion, and (iv) the non-spherical shape of the cell affects the way that it is rotated by the shear flow. These complications influence the dependence of v _d on the shear rate γ. When they are all included, it is found that (a) shear disrupts chemotaxis and shear rates beyond γ≈2 s⁻¹ render chemotaxis ineffective, (b) in terms of maximizing drift velocity, persistence of direction is advantageous in a quiescent fluid but disadvantageous in a shear flow, and (c) a more elongated body shape is advantageous in performing chemotaxis in a shear flow. J.T. Locsei is supported by an Oliver Gatty Studentship from the University of Cambridge.     

The Asymmetric Flagellar Distribution and Motility of Escherichia coli

Rod-shaped bacteria such as Escherichia coli divide by binary fission. They inherit an old pole from the parent cell. The new pole is recently derived from the septum. Because the chemoreceptor accumulates linearly with time on the cell pole, the old pole carries more receptors than does the new pole. Here, further evidence is provided that the old pole appears more frequently at the rear when bacteria swim. This phenomenon had been observed, yet not extensively explored in the literature. The biased swimming orientation is the consequence of the asymmetric distribution of flagella over the cell surface. On about 75% of cells, there are more flagella on the old-pole half of the cell than on the new-pole half, regardless of growth conditions. Most flagella are lateral, and few were found on the cell pole per se. The asymmetric flagellar distribution makes cells more efficient in chemotaxis. Both swimming orientation and receptor localization are components of chemotaxis, by which bacteria follow environmental stimuli. If unipolarly flagellated cells, such as the swarmer cells of Caulobacter crescentus, are regarded as 100% polar with respect to chemotaxis, E. coli is about 75%. The difference is quantitative. The peritrichous flagellation might enhance the motility and chemotaxis in the viscous environment of enteric bacteria.     

Steady-state running rate sets the speed and accuracy of accumulation of swimming bacteria

We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system, where the steady-state rate of the switching changes in different environments. Understanding chemotaxis quantitatively requires that one links the measured steady-state switching rates of the rotary system, as well as the directional changes of individual swimming bacteria in a gradient of chemoattractant/repellant, to the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model, parametrized with our experimental data, and show that the response of a population to the gradient is complex. We find the changes to the steady-state switching rate in the absence of gradients affect the average speed of the swimming bacterial population response as well as the width of the distribution. Both must be taken into account when optimizing the overall response of the population in complex environments.     

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.     

Bacterial cell-body rotation driven by a single flagellar motor and by a bundle

Using self-trapped Escherichia coli bacteria that have intact flagellar bundles on glass surfaces, we study statistical fluctuations of cell-body rotation in a steady (unstimulated) state. These fluctuations underline direction randomization of bacterial swimming trajectories and plays a fundamental role in bacterial chemotaxis. A parallel study is also conducted using a classical rotation assay in which cell-body rotation is driven by a single flagellar motor. These investigations allow us to draw the important conclusion that during periods of counterclockwise motor rotation, which contributes to a run, all flagellar motors are strongly correlated, but during the clockwise period, which contributes to a tumble, individual motors are uncorrelated in long times. Our observation is consistent with the physical picture that formation and maintenance of a coherent flagellar bundle is provided by a single dominant flagellum in the bundle.     

Theoretical results for chemotactic response and drift of E. coli in a weak attractant gradient

The bacterium Escherichia coli (E. coli) moves in its natural environment in a series of straight runs, interrupted by tumbles which cause change of direction. It performs chemotaxis towards chemo-attractants by extending the duration of runs in the direction of the source. When there is a spatial gradient in the attractant concentration, this bias produces a drift velocity directed towards its source, whereas in a uniform concentration, E. coli adapts, almost perfectly in case of methyl aspartate. Recently, microfluidic experiments have measured the drift velocity of E. coli in precisely controlled attractant gradients, but no general theoretical expression for the same exists. With this motivation, we study an analytically soluble model here, based on the Barkai-Leibler model, originally introduced to explain the perfect adaptation. Rigorous mathematical expressions are obtained for the chemotactic response function and the drift velocity in the limit of weak gradients and under the assumption of completely random tumbles. The theoretical predictions compare favorably with experimental results, especially at high concentrations. We further show that the signal transduction network weakens the dependence of the drift on concentration, thus enhancing the range of sensitivity.     

Anomalies in the motion dynamics of long-flagella mutants of Chlamydomonas reinhardtii

Chlamydomonas reinhardtii has long been used as a model organism in studies of cell motility and flagellar dynamics. The motility of the well-conserved ‘9+2’ axoneme in its flagella remains a subject of immense curiosity. Using high-speed videography and morphological analyses, we have characterized long-flagella mutants (lf1, lf2-1, lf2-5, lf3-2, and lf4) of C. reinhardtii for biophysical parameters such as swimming velocities, waveforms, beat frequencies, and swimming trajectories. These mutants are aberrant in proteins involved in the regulation of flagellar length and bring about a phenotypic increase in this length. Our results reveal that the flagellar beat frequency and swimming velocity are negatively correlated with the length of the flagella. When compared to the wild-type, any increase in the flagellar length reduces both the swimming velocities (by 26–57%) and beat frequencies (by 8–16%). We demonstrate that with no apparent aberrations/ultrastructural deformities in the mutant axonemes, it is this increased length that has a critical role to play in the motion dynamics of C. reinhardtii cells, and, provided there are no significant changes in their flagellar proteome, any increase in this length compromises the swimming velocity either by reduction of the beat frequency or by an alteration in the waveform of the flagella.     

Bacterial Thermotaxis by Speed Modulation

Naturally occurring gradients often extend over relatively long distances such that their steepness is too small for bacteria to detect. We studied the bacterial behavior in such thermal gradients. We find that bacteria migrate along shallow thermal gradients due to a change in their swimming speed resulting from the effect of temperature on the intracellular pH, which also depends on the chemical environment. When nutrients are scarce in the environment the bacteria''s intracellular pH decreases with temperature. As a result, the swimming speed of the bacteria decreases with temperature, which causes them to slowly drift toward the warm end of the thermal gradient. However, when serine is added to the medium at concentrations >300 μM, the intracellular pH increases causing the swimming speed to increase continuously with temperature, and the bacteria to drift toward the cold end of the temperature gradient. This directional migration is not a result of bacterial thermotaxis in the classical sense, because the steepness of the gradients applied is below the sensing threshold of bacteria. Nevertheless, our results show that the directional switch requires the presence of the bacterial sensing receptors. This seems to be due to the involvement of the receptors in regulating the intracellular pH.     

Implications of three-step swimming patterns in bacterial chemotaxis

We recently found that marine bacteria Vibrio alginolyticus execute a cyclic three-step (run-reverse-flick) motility pattern that is distinctively different from the two-step (run-tumble) pattern of Escherichia coli. How this novel, to our knowledge, swimming pattern is regulated by cells of V. alginolyticus is not currently known, but its significance for bacterial chemotaxis is self-evident and will be delineated herein. Using a statistical approach, we calculated the migration speed of a cell executing the three-step pattern in a linear chemical gradient, and found that a biphasic chemotactic response arises naturally. The implication of such a response for the cells to adapt to ocean environments and its possible connection to E. coli's response are also discussed.     

Analysis of HubP-dependent cell pole protein targeting in Vibrio cholerae uncovers novel motility regulators

In rod-shaped bacteria, the emergence and maintenance of long-axis cell polarity is involved in key cellular processes such as cell cycle, division, environmental sensing and flagellar motility among others. Many bacteria achieve cell pole differentiation through the use of polar landmark proteins acting as scaffolds for the recruitment of functional macromolecular assemblies. In Vibrio cholerae a large membrane-tethered protein, HubP, specifically interacts with proteins involved in chromosome segregation, chemotaxis and flagellar biosynthesis. Here we used comparative proteomics, genetic and imaging approaches to identify additional HubP partners and demonstrate that at least six more proteins are subject to HubP-dependent polar localization. These include a cell-wall remodeling enzyme (DacB), a likely chemotaxis sensory protein (HlyB), two presumably cytosolic proteins of unknown function (VC1210 and VC1380) and two membrane-bound proteins, named here MotV and MotW, that exhibit distinct effects on chemotactic motility. We show that while both ΔmotW and ΔmotV mutants retain monotrichous flagellation, they present significant to severe motility defects when grown in soft agar. Video-tracking experiments further reveal that ΔmotV cells can swim in liquid environments but are unable to tumble or penetrate a semisolid matrix, whereas a motW deletion affects both tumbling frequency and swimming speed. Motility suppressors and gene co-occurrence analyses reveal co-evolutionary linkages between MotV, a subset of non-canonical CheV proteins and flagellar C-ring components FliG and FliM, whereas MotW regulatory inputs appear to intersect with specific c-di-GMP signaling pathways. Together, these results reveal an ever more versatile role for the landmark cell pole organizer HubP and identify novel mechanisms of motility regulation.     

Responses of Escherichia coli Bacteria to Two Opposing Chemoattractant Gradients Depend on the Chemoreceptor Ratio

Escherichia coli chemotaxis has long served as a simple model of environmental signal processing, and bacterial responses to single chemical gradients are relatively well understood. Less is known about the chemotactic behavior of E. coli in multiple chemical gradients. In their native environment, cells are often exposed to multiple chemical stimuli. Using a recently developed microfluidic chemotaxis device, we exposed E. coli cells to two opposing but equally potent gradients of major attractants, methyl-aspartate and serine. The responses of E. coli cells demonstrated that chemotactic decisions depended on the ratio of the respective receptor number of Tar/Tsr. In addition, the ratio of Tar to Tsr was found to vary with cells’ growth conditions, whereby it depended on the culture density but not on the growth duration. These results provide biological insights into the decision-making processes of chemotactic bacteria that are subjected to multiple chemical stimuli and demonstrate the importance of the cellular microenvironment in determining phenotypic behavior.In their natural environment, both prokaryotic and eukaryotic cells are exposed to multiple chemical stimuli. It is thus important to learn how cells make a decision when confronted with complex chemical stimuli. Escherichia coli bacteria have long served as a model system for chemotaxis studies due to their known and simple genetic makeup. Signaling in bacterial chemotaxis is comparatively well understood (3, 18, 19). To summarize it briefly, there are five types of chemoreceptors in E. coli, of which Tar and Tsr are the most abundant. The basic functional chemosensing unit is a ternary complex that consists of transmembrane chemoreceptors, a linker molecule, CheW, and a histidine kinase, CheA. Within each functional receptor complex, the receptors are known to function in a cooperative manner (9, 12, 16). Upon the binding of attractant molecules, this sensory complex undergoes a conformational change that suppresses the autophosphorylation activity of CheA. This response is then transmitted to the flagellar motor via a regulator protein, CheY. As a result, the run time of an E. coli bacterium is lengthened when swimming toward a high-chemoattractant-concentration region (4).While the molecular mechanisms governing bacterial chemotaxis in a single gradient have been investigated extensively both in experiments and in theory (see reference 8 and references therein), very little is known about how bacteria behave in the presence of dual chemical gradients (1, 17). Early work by Adler and Tso explored the chemotactic responses of E. coli cells in the presence of both attractant and repellent gradients by using a microcapillary chemotaxis assay (1). Twenty years later, Strauss et al. (17) revisited the problem by using a stop-flow chamber. Both investigations concluded that bacteria sum the chemical signals to provide a coordinated output to control flagellar rotation. However, the molecular mechanisms responsible for this calculation have not yet been explored.In this paper, we investigated the molecular mechanism that underlies the bacterial decision-making processes in two opposing attractant gradients that are sensed by the two most abundant E. coli receptors, Tar and Tsr, respectively. By varying the relative expression levels of Tar and Tsr, we demonstrated that the receptor ratio defines the attractant preference in dual gradients of their ligands. The Tar-to-Tsr ratio itself depends on the cell culture density but not on the duration of growth.     

Unique Regulation of Carbohydrate Chemotaxis in Bacillus subtilis by the Phosphoenolpyruvate-Dependent Phosphotransferase System and the Methyl-Accepting Chemotaxis Protein McpC

The phosphoenolpyruvate-dependent phosphotransferase system (PTS) plays a major role in the ability of Escherichia coli to migrate toward PTS carbohydrates. The present study establishes that chemotaxis toward PTS substrates in Bacillus subtilis is mediated by the PTS as well as by a methyl-accepting chemotaxis protein (MCP). As for E. coli, a B. subtilis ptsH null mutant is severely deficient in chemotaxis toward most PTS carbohydrates. Tethering analysis revealed that this mutant does respond normally to the stepwise addition of a PTS substrate (positive stimulus) but fails to respond normally to the stepwise removal of such a substrate (negative stimulus). An mcpC null mutant showed no response to the stepwise addition or removal of d-glucose or d-mannitol, both of which are PTS substrates. Therefore, in contrast to E. coli PTS carbohydrate chemotaxis, B. subtilis PTS carbohydrate chemotaxis is mediated by both MCPs and the PTS; the response to positive stimulus is primarily McpC mediated, while the duration or magnitude of the response to negative PTS carbohydrate stimulus is greatly influenced by components of the PTS and McpC. In the case of the PTS substrate d-glucose, the response to negative stimulus is also partially mediated by McpA. Finally, we show that B. subtilis EnzymeI-P has the ability to inhibit B. subtilis CheA autophosphorylation in vitro. We hypothesize that chemotaxis in the spatial gradient of the capillary assay may result from a combination of a transient increase in the intracellular concentration of EnzymeI-P and a decrease in the concentration of carbohydrate-associated McpC as the cell moves down the carbohydrate concentration gradient. Both events appear to contribute to inhibition of CheA activity that increases the tendency of the bacteria to tumble. In the case of d-glucose, a decrease in d-glucose-associated McpA may also contribute to the inhibition of CheA. This bias on the otherwise random walk allows net migration, or chemotaxis, to occur.  In enteric bacteria, chemotaxis toward many carbohydrate attractants is dependent upon components of the phosphoenolpyruvate (PEP)-dependent phosphotransferase system (PTS) (1, 9, 15). This carbohydrate transport system consists of an autophosphorylating histidine kinase, EnzymeI, a common phosphocarrier protein, HPr, and a number of substrate-specific transporters, the EnzymeII complexes. At the expense of PEP, EnzymeI autophosphorylates on a histidine residue and transfers this phosphoryl group to a histidine residue on HPr. HPr-P then donates this phosphoryl group to a carbohydrate-specific EnzymeII complex. The carbohydrate substrate is the final phosphoryl group acceptor, as it is transported into the cell and is concomitantly phosphorylated by EnzymeII (13).Chemotaxis is also controlled by a phosphoryl transfer cascade. CheA, in response to an attractant- or repellent-bound receptor (methyl-accepting chemotaxis protein [MCP]), alters its rate of autophosphorylation appropriately to transiently increase or decrease the intracellular CheY-P pool and thereby modulate swimming behavior (4, 16). In enteric bacteria, increased CheY-P leads to tumbling (19). In Bacillus subtilis, increased CheY-P leads to smooth swimming (3). In enteric bacteria, chemotaxis toward PTS substrates requires CheA, CheY, EnzymeI, and HPr but does not depend on the presence of an MCP (12, 18). These observations have led investigators to suggest that the changes in the phosphorylation state of PTS components that accompany carbohydrate transport regulate CheA activity (10).Recent work has provided the following model for the role of the PTS in chemotaxis toward its substrates in Escherichia coli. As the bacteria encounter a PTS carbohydrate, HPr dephosphorylates EnzymeI faster than the latter protein can be rephosphorylated. The resulting increase in unphosphorylated EnzymeI and the resulting decrease in PEP both function to decrease the rate of CheA autophosphorylation. This is believed to lead to a transient decrease in the CheY-P pool that suppresses tumbling, allowing the bacteria to move up the carbohydrate gradient (10).This article describes studies on the process of carbohydrate chemotaxis in B. subtilis. In particular, we provide evidence that McpC is absolutely required for any response to all of the PTS carbohydrates tested. This is surprising considering the fact that McpC has previously been shown to also mediate chemotaxis toward eight different amino acids (11). McpA has previously been shown to partially mediate chemotaxis toward glucose (7). This result is confirmed in the present study with the use of direct behavioral assays. Our results suggest the existence of a multidimensional signaling mechanism involving both the PTS and specific MCPs, an unprecedented finding in the study of the molecular control of bacterial carbohydrate chemotaxis.     

Logarithmic Sensing in Escherichia coli Bacterial Chemotaxis

We studied the response of swimming Escherichia coli (E. coli) bacteria in a comprehensive set of well-controlled chemical concentration gradients using a newly developed microfluidic device and cell tracking imaging technique. In parallel, we carried out a multi-scale theoretical modeling of bacterial chemotaxis taking into account the relevant internal signaling pathway dynamics, and predicted bacterial chemotactic responses at the cellular level. By measuring the E. coli cell density profiles across the microfluidic channel at various spatial gradients of ligand concentration grad[L] and the average ligand concentration near the peak chemotactic response region, we demonstrated unambiguously in both experiments and model simulation that the mean chemotactic drift velocity of E. coli cells increased monotonically with grad [L]/ or ∼grad(log[L])—that is E. coli cells sense the spatial gradient of the logarithmic ligand concentration. The exact range of the log-sensing regime was determined. The agreements between the experiments and the multi-scale model simulation verify the validity of the theoretical model, and revealed that the key microscopic mechanism for logarithmic sensing in bacterial chemotaxis is the adaptation kinetics, in contrast to explanations based directly on ligand occupancy.     

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.     

The Hydrodynamics of a Run-and-Tumble Bacterium Propelled by Polymorphic Helical Flagella

To study the swimming of a peritrichous bacterium such as Escherichia coli, which is able to change its swimming direction actively, we simulate the “run-and-tumble” motion by using a bead-spring model to account for: 1), the hydrodynamic and the mechanical interactions among the cell body and multiple flagella; 2), the reversal of the rotation of a flagellum in a tumble; and 3), the associated polymorphic transformations of the flagellum. Because a flexible hook connects the cell body and each flagellum, the flagella can take independent orientations with respect to the cell body. This simulation reproduces the experimentally observed behaviors of E. coli, namely, a three-dimensional random-walk trajectory in run-and-tumble motion and steady clockwise swimming near a wall. We show that the polymorphic transformation of a flagellum in a tumble facilitates the reorientation of the cell, and that the time-averaged flow-field near a cell in a run has double-layered helical streamlines, with a time-dependent flow magnitude large enough to affect the transport of surrounding chemoattractants.