Variation of swimming speed enhances the chemotactic migration of Escherichia coli

Studies on chemotaxis of Escherichia coli have shown that modulation of tumble frequency causes a net drift up the gradient of attractants. Recently, it has been demonstrated that the bacteria is also capable of varying its runs speed in uniform concentration of attractant. In this study, we investigate the role of swimming speed on the chemotactic migration of bacteria. To this end, cells are exposed to gradients of a non-metabolizable analogue of glucose which are sensed via the Trg sensor. When exposed to a gradient, the cells modulate their tumble duration, which is accompanied with variation in swimming speed leading to drift velocities that are much higher than those achieved through the modulation of the tumble duration alone. We use an existing intra-cellular model developed for the Tar receptor and incorporate the variation of the swimming speed along with modulation of tumble frequency to predict drift velocities close to the measured values. The main implication of our study is that E. coli not only modulates the tumble frequency, but may also vary the swimming speed to affect chemotaxis and thereby efficiently sample its nutritionally rich environment.

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The online version of this article (doi:10.1007/s11693-015-9174-x) contains supplementary material, which is available to authorized users.     

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.     

Dependence of Bacterial Chemotaxis on Gradient Shape and Adaptation Rate

Simulation of cellular behavior on multiple scales requires models that are sufficiently detailed to capture central intracellular processes but at the same time enable the simulation of entire cell populations in a computationally cheap way. In this paper we present RapidCell, a hybrid model of chemotactic Escherichia coli that combines the Monod-Wyman-Changeux signal processing by mixed chemoreceptor clusters, the adaptation dynamics described by ordinary differential equations, and a detailed model of cell tumbling. Our model dramatically reduces computational costs and allows the highly efficient simulation of E. coli chemotaxis. We use the model to investigate chemotaxis in different gradients, and suggest a new, constant-activity type of gradient to systematically study chemotactic behavior of virtual bacteria. Using the unique properties of this gradient, we show that optimal chemotaxis is observed in a narrow range of CheA kinase activity, where concentration of the response regulator CheY-P falls into the operating range of flagellar motors. Our simulations also confirm that the CheB phosphorylation feedback improves chemotactic efficiency by shifting the average CheY-P concentration to fit the motor operating range. Our results suggest that in liquid media the variability in adaptation times among cells may be evolutionary favorable to ensure coexistence of subpopulations that will be optimally tactic in different gradients. However, in a porous medium (agar) such variability appears to be less important, because agar structure poses mainly negative selection against subpopulations with low levels of adaptation enzymes. RapidCell is available from the authors upon request.     

Chemosensory and thermosensory excitation in adaptation-deficient mutants of Escherichia coli

Methyl-accepting chemotaxis protein-methyltransferase-deficient mutants, cheR mutants, of Escherichia coli showed a tumble response to repellents only at low temperatures, and the resultant tumbling lasted unless the condition was changed. The swimming pattern of the repellent-treated cells was different at different temperatures, indicating that the absolute temperature is a determinant of the tumbling frequency of those cells. The tumbling of those cells was also suppressed by the addition of attractants. Under a suitable repellent concentration, the tumbling frequency of the cells was found to be simply determined by the ligand occupancy of chemoreceptors for many attractants. In a methyl-accepting chemotaxis protein-methylesterase-deficient mutant, a cheB deletion mutant, the tumbling frequency was also determined by receptor occupancy of some attractants. These results indicate that in the adaptation-deficient mutants, sensory signals are produced in proportion to the amount of ligand-bound or of thermally altered receptors and transmitted to the flagellar motors without any modification. Thus, it is concluded that the adaptation system, namely, the methylation-demethylation system of methyl-accepting chemotaxis proteins, is not concerned with the step of chemosensory or thermosensory excitation. A simple model is proposed to explain how the swimming pattern of the adaptation-deficient mutants is determined.     

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.     

The physics of flagellar motion of E. coli during chemotaxis

Flagellar motion has been an active area of study right from the discovery of bacterial chemotaxis in 1882. During chemotaxis, E. coli moves with the help of helical flagella in an aquatic environment. Helical flagella are rotated in clockwise or counterclockwise direction using reversible flagellar motors situated at the base of each flagellum. The swimming of E. coli is characterized by a low Reynolds number that is unique and time reversible. The random motion of E. coli is influenced by the viscosity of the fluid and the Brownian motion of molecules of fluid, chemoattractants, and chemorepellants. This paper reviews the literature about the physics involved in the propulsion mechanism of E. coli. Starting from the resistive-force theory, various theories on flagellar hydrodynamics are critically reviewed. Expressions for drag force, elastic force and velocity of flagellar elements are derived. By taking the elastic nature of flagella into account, linear and nonlinear equations of motions are derived and their solutions are presented.     

Populational Heterogeneity vs. Temporal Fluctuation in Escherichia coli Flagellar Motor Switching

The dynamic switching of the bacterial flagellar motor regulates cell motility in bacterial chemotaxis. It has been reported under physiological conditions that the switching bias of the flagellar motor undergoes large temporal fluctuations, which reflects noise propagating in the chemotactic signaling network. On the other hand, nongenetic heterogeneity is also observed in flagellar motor switching, as a large group of switching motors show different switching bias and frequency under the same physiological condition. In this work, we present simultaneous measurement of groups of Escherichia coli flagellar motor switching and compare them to long time recording of single switching motors. Consistent with previous studies, we observed temporal fluctuations in switching bias in long time recording experiments. However, the variability in switching bias at the populational level showed much higher volatility than its temporal fluctuation. These results suggested stable individuality in E. coli motor switching. We speculate that uneven expression of key regulatory proteins with amplification by the ultrasensitive response of the motor can account for the observed populational heterogeneity and temporal fluctuations.     

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.     

Populational Heterogeneity vs. Temporal Fluctuation in Escherichia coli Flagellar Motor Switching

The dynamic switching of the bacterial flagellar motor regulates cell motility in bacterial chemotaxis. It has been reported under physiological conditions that the switching bias of the flagellar motor undergoes large temporal fluctuations, which reflects noise propagating in the chemotactic signaling network. On the other hand, nongenetic heterogeneity is also observed in flagellar motor switching, as a large group of switching motors show different switching bias and frequency under the same physiological condition. In this work, we present simultaneous measurement of groups of Escherichia coli flagellar motor switching and compare them to long time recording of single switching motors. Consistent with previous studies, we observed temporal fluctuations in switching bias in long time recording experiments. However, the variability in switching bias at the populational level showed much higher volatility than its temporal fluctuation. These results suggested stable individuality in E. coli motor switching. We speculate that uneven expression of key regulatory proteins with amplification by the ultrasensitive response of the motor can account for the observed populational heterogeneity and temporal fluctuations.     

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.     

Bacterial motility and chemotaxis: Light-induced tumbling response and visualization of individual flagella

High intensity visible light induces tumbling in Salmonella typhimurium, the effect being reversible provided short pulses are used. Fully aerated cultures are more sensitive to light than cultures with a lower oxygen tension. Bacteria which have been subjected to a sufficient positive chemotactic stimulus (concentration increase of attractant) are immune to the light stimulus. Light with a wavelength of 510 nm or shorter is effective, suggesting that absorption by a flavin may be involved. The light source used, with a yellow filter inserted to prevent light-induced tumbling, is bright enough to allow visualization of individual flagella as well as flagellar bundles. This has provided information on flagellar aggregation, rigidity, and behavior during tumbling. Since the occurrence of tumbles is modified as a result of chemical gradient sensing, these techniques are valuable in the study of bacterial chemotaxis.     

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.     

Chemotaxis in Escherichia coli proceeds efficiently from different initial tumble frequencies.

The relationships between the level of tumbling, tumble frequency, and chemotactic ability were tested by constructing two Escherichia coli strains with the same signaling apparatus but with different adapted levels of tumbling, above and below the level of wild-type E. coli. This was achieved by introducing two different aspartate receptor genes into E. coli: a wild-type (wt-tars) and a mutant (m-tars) Salmonella typhimurium receptor gene. These cells were compared with each other and with wild-type E. coli (containing the wild-type E. coli aspartate receptor gene, wt-tare). It was found that in spite of the differences in the adapted levels of tumbling, the three strains had essentially equal response times and chemotactic ability toward aspartate. This shows that the absolute level of the tumbling can be varied without impairing chemotaxis if the signal processing system is normal. It also appears that a largely smooth-swimming mutant may undergo chemotaxis by increasing tumbling frequency in negative gradients.     

Roles of cheY and cheZ gene products in controlling flagellar rotation in bacterial chemotaxis of Escherichia coli.

To understand output control in bacterial chemotaxis, we varied the levels of expression of cellular cheY and cheZ genes and found that the overproduction of the corresponding proteins affected Escherichia coli swimming behavior. In the absence of other signal-transducing gene products, CheY overproduction made free-swimming cells tumble more frequently. A plot of the fraction of the population that are tumbling versus the CheY concentration was hyperbolic, with half of the population tumbling at 30 microM (25,000 copies per cell) CheY monomers in the cytosol. Overproduction of aspartate receptor (Tar) by 30-fold had a negligible effect on CheY-induced tumbling, so Tar does not sequester CheY. CheZ overproduction decreased tumbling in all tumbling mutants except certain flaAII(cheC) mutants. In the absence of other chemotaxis gene products, CheZ overproduction inhibited CheY-induced tumbling. Models for CheY as a tumbling signal and CheZ as a smooth-swimming signal to control flagellar rotation are discussed.     

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.     

Limits of Feedback Control in Bacterial Chemotaxis

Inputs to signaling pathways can have complex statistics that depend on the environment and on the behavioral response to previous stimuli. Such behavioral feedback is particularly important in navigation. Successful navigation relies on proper coupling between sensors, which gather information during motion, and actuators, which control behavior. Because reorientation conditions future inputs, behavioral feedback can place sensors and actuators in an operational regime different from the resting state. How then can organisms maintain proper information transfer through the pathway while navigating diverse environments? In bacterial chemotaxis, robust performance is often attributed to the zero integral feedback control of the sensor, which guarantees that activity returns to resting state when the input remains constant. While this property provides sensitivity over a wide range of signal intensities, it remains unclear how other parameters such as adaptation rate and adapted activity affect chemotactic performance, especially when considering that the swimming behavior of the cell determines the input signal. We examine this issue using analytical models and simulations that incorporate recent experimental evidences about behavioral feedback and flagellar motor adaptation. By focusing on how sensory information carried by the response regulator is best utilized by the motor, we identify an operational regime that maximizes drift velocity along chemical concentration gradients for a wide range of environments and sensor adaptation rates. This optimal regime is outside the dynamic range of the motor response, but maximizes the contrast between run duration up and down gradients. In steep gradients, the feedback from chemotactic drift can push the system through a bifurcation. This creates a non-chemotactic state that traps cells unless the motor is allowed to adapt. Although motor adaptation helps, we find that as the strength of the feedback increases individual phenotypes cannot maintain the optimal operational regime in all environments, suggesting that diversity could be beneficial.     

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.     

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.     

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.     

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.