Cell orientation of swimming bacteria: From theoretical simulation to experimental evaluation

The motion of small bacteria consists of two phases: relatively long runs alternate with intermittent stops, back-ups, or tumbles, depending on the species. In polar monotrichous bacteria, the flagellum is anchored at the cell pole inherited from the parent generation (old pole) and is surrounded by a chemoreceptor cluster. During forward swimming, the leading pole is always the pole recently formed in cell division (new pole). The flagella of the peritrichous bacterium Escherichia coli often form a bundle behind the old pole. Its cell orientation and receptor positioning during runs generally mimic that of monotrichous bacteria. When encountering a solid surface, peritrichous bacteria exhibit a circular motion with the leading pole dipping downward. Some polar monotrichous bacteria also perform circular motion near solid boundaries, but during back-ups. In this case, the leading pole points upward. Very little is known about behavior near milieu-air interfaces. Biophysical simulations have revealed some of the mechanisms underlying these phenomena, but leave many questions unanswered. Combining biophysics with molecular techniques will certainly advance our understanding of bacterial locomotion.     

Direct Mapping from Intracellular Chemotaxis Signaling to Single-Cell Swimming Behavior

Bacterial chemotaxis allows bacteria to sense the chemical environment and modulate their swimming behavior accordingly. Although the intracellular chemotaxis signaling pathway has been studied extensively, experimental studies are still lacking that could provide direct link from the pathway output (the intracellular concentration of the phosphorylated form of the response regulator phosphorylated CheY (CheY-P)) to single-cell swimming behavior. Here, we measured the swimming behavior of individual Escherichia coli cells while simultaneously detecting the intracellular CheY-P concentration, thereby providing a direct relationship between the intracellular CheY-P concentration and the single-cell run-and-tumble behavior. The measured relationship is consistent with the ultrasensitivity of the motor switch and a “veto model” that describes the interaction among individual flagella, although contribution from the voting mechanism could not be ruled out.     

Three Mutations in Escherichia coli That Generate Transformable Functional Flagella

Hydrodynamics predicts that swimming bacteria generate a propulsion force when a helical flagellum rotates because rotating helices necessarily translate at a low Reynolds number. It is generally believed that the flagella of motile bacteria are semirigid helices with a fixed pitch determined by hydrodynamic principles. Here, we report the characterization of three mutations in laboratory strains of Escherichia coli that produce different steady-state flagella without losing cell motility. E. coli flagella rotate counterclockwise during forward swimming, and the normal form of the flagella is a left-handed helix. A single amino acid exchange A45G and a double mutation of A48S and S110A change the resting flagella to right-handed helices. The stationary flagella of the triple mutant were often straight or slightly curved at neutral pH. Deprotonation facilitates the helix formation of it. The helical and curved flagella can be transformed to the normal form by torsion upon rotation and thus propel the cell. These mutations arose in the long-term laboratory cultivation. However, flagella are under strong selection pressure as extracellular appendages, and similar transformable flagella would be common in natural environments.     

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.

Electronic supplementary material

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

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.     

The Flat-Ribbon Configuration of the Periplasmic Flagella of Borrelia burgdorferi and Its Relationship to Motility and Morphology

Electron cryotomography was used to analyze the structure of the Lyme disease spirochete, Borrelia burgdorferi. This methodology offers a new means for studying the native architecture of bacteria by eliminating the chemical fixing, dehydration, and staining steps of conventional electron microscopy. Using electron cryotomography, we noted that membrane blebs formed at the ends of the cells. These blebs may be precursors to vesicles that are released from cells grown in vivo and in vitro. We found that the periplasmic space of B. burgdorferi was quite narrow (16.0 nm) compared to those of Escherichia coli and Pseudomonas aeruginosa. However, in the vicinity of the periplasmic flagella, this space was considerably wider (42.3 nm). In contrast to previous results, the periplasmic flagella did not form a bundle but rather formed a tight-fitting ribbon that wraps around the protoplasmic cell cylinder in a right-handed sense. We show how the ribbon configuration of the assembled periplasmic flagella is more advantageous than a bundle for both swimming and forming the flat-wave morphology. Previous results indicate that B. burgdorferi motility is dependent on the rotation of the periplasmic flagella in generating backward-moving waves along the length of the cell. This swimming requires that the rotation of the flagella exerts force on the cell cylinder. Accordingly, a ribbon is more beneficial than a bundle, as this configuration allows each periplasmic flagellum to have direct contact with the cell cylinder in order to exert that force, and it minimizes interference between the rotating filaments.     

Dynamics of Bacterial Swarming

When vegetative bacteria that can swim are grown in a rich medium on an agar surface, they become multinucleate, elongate, synthesize large numbers of flagella, produce wetting agents, and move across the surface in coordinated packs: they swarm. We examined the motion of swarming Escherichia coli, comparing the motion of individual cells to their motion during swimming. Swarming cells' speeds are comparable to bulk swimming speeds, but very broadly distributed. Their speeds and orientations are correlated over a short distance (several cell lengths), but this correlation is not isotropic. We observe the swirling that is conspicuous in many swarming systems, probably due to increasingly long-lived correlations among cells that associate into groups. The normal run-tumble behavior seen in swimming chemotaxis is largely suppressed, instead, cells are continually reoriented by random jostling by their neighbors, randomizing their directions in a few tenths of a second. At the edge of the swarm, cells often pause, then swim back toward the center of the swarm or along its edge. Local alignment among cells, a necessary condition of many flocking theories, is accomplished by cell body collisions and/or short-range hydrodynamic interactions.     

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.     

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.     

Motility and chemotaxis in Agrobacterium tumefaciens surface attachment and biofilm formation

Bacterial motility mechanisms, including swimming, swarming, and twitching, are known to have important roles in biofilm formation, including colonization and the subsequent expansion into mature structured surface communities. Directed motility requires chemotaxis functions that are conserved among many bacterial species. The biofilm-forming plant pathogen Agrobacterium tumefaciens drives swimming motility by utilizing a small group of flagella localized to a single pole or the subpolar region of the cell. There is no evidence for twitching or swarming motility in A. tumefaciens. Site-specific deletion mutations that resulted in either aflagellate, flagellated but nonmotile, or flagellated but nonchemotactic A. tumefaciens derivatives were examined for biofilm formation under static and flowing conditions. Nonmotile mutants were significantly deficient in biofilm formation under static conditions. Under flowing conditions, however, the aflagellate mutant rapidly formed aberrantly dense, tall biofilms. In contrast, a nonmotile mutant with unpowered flagella was clearly debilitated for biofilm formation relative to the wild type. A nontumbling chemotaxis mutant was only weakly affected with regard to biofilm formation under nonflowing conditions but was notably compromised in flow, generating less adherent biomass than the wild type, with a more dispersed cellular arrangement. Extragenic suppressor mutants of the chemotaxis-impaired, straight-swimming phenotype were readily isolated from motility agar plates. These mutants regained tumbling at a frequency similar to that of the wild type. Despite this phenotype, biofilm formation by the suppressor mutants in static cultures was significantly deficient. Under flowing conditions, a representative suppressor mutant manifested a phenotype similar to yet distinct from that of its nonchemotactic parent.     

An MCP-Like Protein Interacts with the MamK Cytoskeleton and Is Involved in Magnetotaxis in Magnetospirillum magneticum AMB-1

Magnetotactic bacteria have the unique capacity of aligning and swimming along geomagnetic field lines, a behavior called magnetotaxis. Although this behavior has been observed for 40 years, little is known about its mechanism. Magnetotactic bacteria synthesize unique organelles, magnetosomes, which are magnetic crystals enveloped by membrane. They form chains with the help of the filamentous cytoskeletal protein MamK and impart a net magnetic-dipole moment to the bacterium. The current model proposes that magnetotaxis comprises passive magnetic orientation and active swimming due to flagellar rotation. We thought that magnetic sensing, via the widely used chemotaxis mechanism, might be actively involved in magnetotaxis. We found that the methyl-accepting chemotaxis protein Amb0994 of Magnetospirillum magneticum AMB-1 was capable of carrying out such a function. Amb0994 is encoded by a gene in the magnetosome island, in which genes essential for magnetosome biosynthesis and magnetotaxis are concentrated. Amb0994 lacks periplasmic sensing domain, which is generally involved in sensing stimuli from outside of cells. By constructing fusions with a derivative of yellow-fluorescent-protein, we showed that Amb0994 localizes to the cell poles, where methyl-accepting chemotaxis proteins are usually clustered. We then showed that Amb0994 specifically interacts, via its C-terminal domain, with MamK, using a bimolecular fluorescence complementation assay. Moreover, overproduction of Amb0994 slowed down the response of the bacterium to changes in the direction of the magnetic field. Most importantly, the C-terminal domain of Amb0994, which interacts with MamK, is responsible for this phenotype, suggesting that the interaction between Amb0994 and MamK plays a key role in magnetotaxis. These results lead to a novel explanation for magnetotaxis at the molecular level.     

Flagella proteins contribute to the production of outer membrane vesicles from Escherichia coli W3110

Gram-negative bacteria, including Escherichia coli, release outer membrane vesicles (OMVs) that are derived from the bacterial outer membrane. OMVs contribute to bacterial cell–cell communications and host–microbe interactions by delivering components to locations outside the bacterial cell. In order to explore the molecular machinery involved in OMV biogenesis, the role of a major OMV protein was examined in the production of OMVs from E. coli W3110, which is a widely used standard E. coli K-12 strain. In addition to OmpC and OmpA, which are used as marker proteins for OMVs, an analysis of E. coli W3110 OMVs revealed that they also contain abundant levels of FliC, which is also known as flagellin. A membrane-impermeable biotin-labeling reagent did not label FliC in intact OMVs, but labeled FliC in sonically disrupted OMVs, suggesting that FliC is localized in the lumen of OMV. Compared to the parental strain expressing wild-type fliC, an E. coli strain with a fliC-null mutation produced reduced amounts of OMVs based on both protein and phosphate levels. In addition, an E. coli W3110-derived strain with a null-mutation in flgK, which encodes flagellar hook-associated protein that is essential along with FliC for flagella synthesis, also produced fewer OMVs than the parental strain. Taken together, these results indicate that the ability to form flagella, including the synthesis of flagella proteins, affects the production of E. coli W3110 OMVs.     

Synchronization,Slippage, and Unbundling of Driven Helical Flagella

Peritrichous bacteria exploit bundles of helical flagella for propulsion and chemotaxis. Here, changes in the swimming direction (tumbling) are induced by a change of the rotational frequency of some flagella. Employing coarse-grained modeling and simulations, we investigate the dynamical properties of helical flagella bundles driven by mismatched motor torques. Over a broad range of distances between the flagella anchors and applied torque differences, we find a stable bundled state, which is important for a robust directional motion of a bacterium. With increasing torque difference, a phase lag in the flagellar rotations develops, followed by slippage and ultimately unbundling, which sensitively depends on the anchoring distance of neighboring flagella. In the slippage and drift states, the different rotation frequencies of the flagella generate a tilting torque on the bacterial body, which implies a change of the swimming direction as observed experimentally.     

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.     

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.     

Genetic Manipulation of Glycogen Allocation Affects Replicative Lifespan in E. coli

In bacteria, replicative aging manifests as a difference in growth or survival between the two cells emerging from division. One cell can be regarded as an aging mother with a decreased potential for future survival and division, the other as a rejuvenated daughter. Here, we aimed at investigating some of the processes involved in aging in the bacterium Escherichia coli, where the two types of cells can be distinguished by the age of their cell poles. We found that certain changes in the regulation of the carbohydrate metabolism can affect aging. A mutation in the carbon storage regulator gene, csrA, leads to a dramatically shorter replicative lifespan; csrA mutants stop dividing once their pole exceeds an age of about five divisions. These old-pole cells accumulate glycogen at their old cell poles; after their last division, they do not contain a chromosome, presumably because of spatial exclusion by the glycogen aggregates. The new-pole daughters produced by these aging mothers are born young; they only express the deleterious phenotype once their pole is old. These results demonstrate how manipulations of nutrient allocation can lead to the exclusion of the chromosome and limit replicative lifespan in E. coli, and illustrate how mutations can have phenotypic effects that are specific for cells with old poles. This raises the question how bacteria can avoid the accumulation of such mutations in their genomes over evolutionary times, and how they can achieve the long replicative lifespans that have recently been reported.     

Collective Bacterial Dynamics Revealed Using a Three-Dimensional Population-Scale Defocused Particle Tracking Technique

An ability to monitor bacterial locomotion and collective dynamics is crucial to our understanding of a number of well-characterized phenotypes including biofilm formation, chemotaxis, and virulence. Here, we report the tracking of multiple swimming Escherichia coli cells in three spatial dimensions and at single-cell resolution using a novel three-dimensional (3D) defocused particle tracking (DPT) method. The 3D trajectories were generated for wild-type Escherichia coli strain RP437 as well as for isogenic derivatives that display smooth swimming due to a cheA deletion (strain RP9535) or incessant tumbling behavior due to a cheZ deletion (strain RP1616). The 3D DPT method successfully differentiated these three modes of locomotion and allowed direct calculation of the diffusion coefficient for each strain. As expected, we found that the smooth swimmer diffused more readily than the wild type, and both the smooth swimmer and the wild-type cells exhibited diffusion coefficients that were at least two orders of magnitude larger than that of the tumbler. Finally, we found that the diffusion coefficient increased with increasing cell density, a phenomenon that can be attributed to the hydrodynamic disturbances caused by neighboring bacteria.     

A novel gene inactivation system reveals altered periplasmic flagellar orientation in a Borrelia burgdorferi fliL mutant

Motility and chemotaxis are essential components of pathogenesis for many infectious bacteria, including Borrelia burgdorferi, the causative agent of Lyme disease. Motility and chemotaxis genes comprise 5 to 6% of the genome of B. burgdorferi, yet the functions of most of those genes remain uncharacterized, mainly due to the paucity of a nonpolar gene inactivation system. In this communication, we describe the development of a novel gene inactivation methodology to target B. burgdorferi fliL, a putative periplasmic flagellar gene located in a large motility operon and transcribed by RNA polymerase containing σ(70). Although the morphology of nonpolar fliL mutant cells was indistinguishable from that of wild-type cells, the mutant exhibited a defective-motility phenotype. Cryo-electron tomography (cryo-ET) of intact organisms revealed that the periplasmic flagella in the fliL mutant were frequently tilted toward the cell pole instead of their normal orientation toward the cell body. These defects were corrected when the mutant was complemented in cis. Moreover, a comparative analysis of flagellar motors from the wild type and the mutant provides the first structural evidence that FliL is localized between the stator and rotor. Our results suggest that FliL is likely involved in coordinating or regulating the orientation of periplasmic flagella in B. burgdorferi.     

Methyl-accepting chemotaxis proteins are distributed in the membrane independently from basal ends of bacterial flagella

Chemotactic behavior of Escherichia coli involves communication between methyl-accepting chemotaxis proteins and basal ends, the rotary motors of bacterial flagella. Both the proteins and the basal ends are embedded in the cytoplasmic membrane, but the spatial relationship between the two has not been determined. This communication describes a procedure for obtaining a preparation of membrane vesicles enriched in basal ends and thus in the regions of membrane immediately surrounding them. Methyl-accepting chemotaxis proteins were neither enriched nor depleted in this membrane fraction but instead were distributed throughout the membrane. Thus functional linkages between these proteins and flagellar motors must be mediated by processes other than direct physical interaction.     

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.