Torque-speed relationship of the Na+-driven flagellar motor of Vibrio alginolyticus

Physical mechanism reveals bacterial slowdown above a critical number of flagella

Numerous studies have explored the link between bacterial swimming and the number of flagella, a distinguishing feature of motile multi-flagellated bacteria. We revisit this open question using augmented slender-body theory simulations, in which we resolve the full hydrodynamic interactions within a bundle of helical filaments rotating and translating in synchrony. Unlike previous studies, our model considers the full torque-speed relationship of the bacterial flagellar motor, revealing its significant impact on multi-flagellated swimming. Because the viscous load per motor decreases with the flagellar number, the bacterial flagellar motor transitions from the high-load to the low-load regime at a critical number of filaments, leading to bacterial slowdown as further flagella are added to the bundle. We explain the physical mechanism behind the observed slowdown as an interplay between the load-dependent generation of torque by the motor, and the load-reducing cooperativity between flagella, which consists of both hydrodynamic and non-hydrodynamic components. The theoretically predicted critical number of flagella is remarkably close to the values reported for the model organism Escherichia coli. Our model further predicts that the critical number of flagella increases with viscosity, suggesting that bacteria can enhance their swimming capacity by growing more flagella in more viscous environments, consistent with empirical observations.

Bacterial Electrophysiology

Bacterial ion fluxes are involved in the generation of energy, transport, and motility. As such, bacterial electrophysiology is fundamentally important for the bacterial life cycle, but it is often neglected and consequently, by and large, not understood. Arguably, the two main reasons for this are the complexity of measuring relevant variables in small cells with a cell envelope that contains the cell wall and the fact that, in a unicellular organism, relevant variables become intertwined in a nontrivial manner. To help give bacterial electrophysiology studies a firm footing, in this review, we go back to basics. We look first at the biophysics of bacterial membrane potential, and then at the approaches and models developed mostly for the study of neurons and eukaryotic mitochondria. We discuss their applicability to bacterial cells. Finally, we connect bacterial membrane potential with other relevant (electro)physiological variables and summarize methods that can be used to both measure and influence bacterial electrophysiology.

Lighting the way: how the Vibrio fischeri model microbe reveals the complexity of Earth's "simplest" life forms

Vibrio (Aliivibrio) fischeri's initial rise to fame derived from its alluring production of blue-green light. Subsequent studies to probe the mechanisms underlying this bioluminescence helped the field discover the phenomenon now known as quorum sensing. Orthologs of quorum-sensing regulators (i.e., LuxR and LuxI) originally identified in V. fischeri were subsequently uncovered in a plethora of bacterial species, and analogous pathways were found in yet others. Over the past three decades, the study of this microbe has greatly expanded to probe the unique role of V. fischeri as the exclusive symbiont of the light organ of the Hawaiian bobtail squid, Euprymna scolopes. Buoyed by this optically amenable host and by persistent and insightful researchers who have applied novel and cross-disciplinary approaches, V. fischeri has developed into a robust model for microbe-host associations. It has contributed to our understanding of how bacteria experience and respond to specific, often fluxing environmental conditions and the mechanisms by which bacteria impact the development of their host. It has also deepened our understanding of numerous microbial processes such as motility and chemotaxis, biofilm formation and dispersal, and bacterial competition, and of the relevance of specific bacterial genes in the context of colonizing an animal host. Parallels in these processes between this symbiont and bacteria studied as pathogens are readily apparent, demonstrating functional conservation across diverse associations and permitting a reinterpretation of "pathogenesis." Collectively, these advances built a foundation for microbiome studies and have positioned V. fischeri to continue to expand the frontiers of our understanding of the microbial world inside animals.

Direct Measurement of the Stall Torque of the Flagellar Motor in Escherichia coli with Magnetic Tweezers

The flagellar motor drives the rotation of flagellar filaments, propelling the swimming of flagellated bacteria. The maximum torque the motor generates, the stall torque, is a key characteristic of the motor function. Direct measurements of the stall torque carried out 3 decades ago suffered from large experimental uncertainties, and subsequently there were only indirect measurements. Here, we applied magnetic tweezers to directly measure the stall torque in E. coli. We precisely calibrated the torsional stiffness of the magnetic tweezers and performed motor resurrection experiments at stall, accomplishing a precise determination of the stall torque per torque-generating unit (stator unit). From our measurements, each stator passes 2 protons per step, indicating a tight coupling between motor rotation and proton flux. IMPORTANCE The maximum torque the bacterial flagellar motor generates, the stall torque, is a critical parameter that describes the motor energetics. As the motor operates in equilibrium near stall, from the stall torque one can determine how many protons each torque-generating unit (stator) of the motor passes per revolution and then test whether motor rotation and proton flux are tightly or loosely coupled, which has been controversial in recent years. Direct measurements performed 3 decades ago suffered from large uncertainties, and subsequently, only indirect measurements were attempted, obtaining a range of values inconsistent with the previous direct measurements. Here, we developed a method that used magnetic tweezers to perform motor resurrection experiments at stall, resulting in a direct precise measurement of the stall torque per stator. Our study resolved the previous inconsistencies and provided direct experimental support for the tight coupling mechanism between motor rotation and proton flux.

The ecological roles of bacterial chemotaxis

How bacterial chemotaxis is performed is much better understood than why. Traditionally, chemotaxis has been understood as a foraging strategy by which bacteria enhance their uptake of nutrients and energy, yet it has remained puzzling why certain less nutritious compounds are strong chemoattractants and vice versa. Recently, we have gained increased understanding of alternative ecological roles of chemotaxis, such as navigational guidance in colony expansion, localization of hosts or symbiotic partners and contribution to microbial diversity by the generation of spatial segregation in bacterial communities. Although bacterial chemotaxis has been observed in a wide range of environmental settings, insights into the phenomenon are mostly based on laboratory studies of model organisms. In this Review, we highlight how observing individual and collective migratory behaviour of bacteria in different settings informs the quantification of trade-offs, including between chemotaxis and growth. We argue that systematically mapping when and where bacteria are motile, in particular by transgenerational bacterial tracking in dynamic environments and in situ approaches from guts to oceans, will open the door to understanding the rich interplay between metabolism and growth and the contribution of chemotaxis to microbial life.

Dynamics of Switching at Stall Reveals Nonequilibrium Mechanism in the Allosteric Regulation of the Bacterial Flagellar Switch

Behavior of the bacterial flagellar motor depends sensitively on the external loads it drives. Motor switching, which provides the basis for the run-and-tumble behavior of flagellated bacteria, has been studied for motors under zero to high loads, revealing a nonequilibrium effect that is proportional to the motor torque. However, behavior of the motor switching at stall (with maximum torque) remains unclear. An extrapolation from previous studies would suggest the maximum nonequilibrium effect for motor switching at stall. Here, we stalled the motor using optical tweezers and studied the motor switching with a high time resolution of about 2 ms. Surprisingly, our results showed exponentially distributed counterclockwise (CCW) and clockwise (CW) intervals, indicating that motor switching at stall is probably an equilibrium process. Combined with previous experiments at other loads, our result suggested that the nonequilibrium effect in motor switching arises from the asymmetry of the torque generation in the CCW and CW directions. By including this nonequilibrium effect in the general Ising-type conformation spread model of the flagellar switch, we consistently explained the motor switching over the whole range of load conditions. We expect to see a similar mechanism of nonequilibrium regulation in other molecular machines.

Stator Dynamics Depending on Sodium Concentration in Sodium-Driven Bacterial Flagellar Motors

Bacterial flagellar motor (BFM) is a large membrane-spanning molecular rotary machine for swimming motility. Torque is generated by the interaction between the rotor and multiple stator units powered by ion-motive force (IMF). The number of bound stator units is dynamically changed in response to the external load and the IMF. However, the detailed dynamics of stator unit exchange process remains unclear. Here, we directly measured the speed changes of sodium-driven chimeric BFMs under fast perfusion of different sodium concentration conditions using computer-controlled, high-throughput microfluidic devices. We found the sodium-driven chimeric BFMs maintained constant speed over a wide range of sodium concentrations by adjusting stator units in compensation to the sodium-motive force (SMF) changes. The BFM has the maximum number of stator units and is most stable at 5 mM sodium concentration rather than higher sodium concentration. Upon rapid exchange from high to low sodium concentration, the number of functional stator units shows a rapidly excessive reduction and then resurrection that is different from predictions of simple absorption model. This may imply the existence of a metastable hidden state of the stator unit during the sudden loss of sodium ions.

Coral mucus rapidly induces chemokinesis and genome-wide transcriptional shifts toward early pathogenesis in a bacterial coral pathogen

Elevated seawater temperatures have contributed to the rise of coral disease mediated by bacterial pathogens, such as the globally distributed Vibrio coralliilyticus, which utilizes coral mucus as a chemical cue to locate stressed corals. However, the physiological events in the pathogens that follow their entry into the coral host environment remain unknown. Here, we present simultaneous measurements of the behavioral and transcriptional responses of V. coralliilyticus BAA-450 incubated in coral mucus. Video microscopy revealed a strong and rapid chemokinetic behavioral response by the pathogen, characterized by a two-fold increase in average swimming speed within 6 min of coral mucus exposure. RNA sequencing showed that this bacterial behavior was accompanied by an equally rapid differential expression of 53% of the genes in the V. coralliilyticus genome. Specifically, transcript abundance 10 min after mucus exposure showed upregulation of genes involved in quorum sensing, biofilm formation, and nutrient metabolism, and downregulation of flagella synthesis and chemotaxis genes. After 60 min, we observed upregulation of genes associated with virulence, including zinc metalloproteases responsible for causing coral tissue damage and algal symbiont photoinactivation, and secretion systems that may export toxins. Together, our results suggest that V. coralliilyticus employs a suite of behavioral and transcriptional responses to rapidly shift into a distinct infection mode within minutes of exposure to the coral microenvironment.

Using Experimentally Calibrated Regularized Stokeslets to Assess Bacterial Flagellar Motility Near a Surface

The presence of a nearby boundary is likely to be important in the life cycle and evolution of motile flagellate bacteria. This has led many authors to employ numerical simulations to model near-surface bacterial motion and compute hydrodynamic boundary effects. A common choice has been the method of images for regularized Stokeslets (MIRS); however, the method requires discretization sizes and regularization parameters that are not specified by any theory. To determine appropriate regularization parameters for given discretization choices in MIRS, we conducted dynamically similar macroscopic experiments and fit the simulations to the data. In the experiments, we measured the torque on cylinders and helices of different wavelengths as they rotated in a viscous fluid at various distances to a boundary. We found that differences between experiments and optimized simulations were less than 5% when using surface discretizations for cylinders and centerline discretizations for helices. Having determined optimal regularization parameters, we used MIRS to simulate an idealized free-swimming bacterium constructed of a cylindrical cell body and a helical flagellum moving near a boundary. We assessed the swimming performance of many bacterial morphologies by computing swimming speed, motor rotation rate, Purcell’s propulsive efficiency, energy cost per swimming distance, and a new metabolic energy cost defined to be the energy cost per body mass per swimming distance. All five measures predicted that the optimal flagellar wavelength is eight times the helical radius independently of body size and surface proximity. Although the measures disagreed on the optimal body size, they all predicted that body size is an important factor in the energy cost of bacterial motility near and far from a surface.

Vibrio cholerae motility in aquatic and mucus-mimicking environments

Cholera disease is caused by Vibrio cholerae infecting the lining of the small intestine and results in severe diarrhea. V. cholerae’s swimming motility is known to play a crucial role in pathogenicity and may aid the bacteria in crossing the intestinal mucus barrier to reach sites of infection, but the exact mechanisms are unknown. The cell can be either pushed or pulled by its single polar flagellum, but there is no consensus on the resulting repertoire of motility behaviors. We use high-throughput three-dimensional (3D) bacterial tracking to observe V. cholerae swimming in buffer, in viscous solutions of the synthetic polymer PVP, and in mucin solutions that may mimic the host environment. We perform a statistical characterization of its motility behavior on the basis of large 3D trajectory data sets. We find that V. cholerae performs asymmetric run-reverse-flick motility, consisting of a sequence of a forward run, reversal, and a shorter backward run, followed by a turn by approximately 90°, called a flick, preceding the next forward run. Unlike many run-reverse-flick swimmers, V. cholerae’s backward runs are much shorter than its forward runs, resulting in an increased effective diffusivity. We also find that the swimming speed is not constant but subject to frequent decreases. The turning frequency in mucin matches that observed in buffer. Run-reverse-flick motility and speed fluctuations are present in all environments studied, suggesting that these behaviors also occur in natural aquatic habitats as well as the host environment.

IMPORTANCE Cholera disease produces vomiting and severe diarrhea and causes approximately 100,000 deaths per year worldwide. The disease is caused by the bacterium Vibrio cholerae colonizing the lining of the small intestine. V. cholerae’s ability to swim is known to increase its infectivity, but the underlying mechanisms are not known. One possibility is that swimming aids in crossing the protective mucus barrier that covers the lining of the small intestine. Our work characterizing how V. cholerae swims in environments that mimic properties of the host environment may advance the understanding of how motility contributes to infection.

The Dynamic Ion Motive Force Powering the Bacterial Flagellar Motor

The bacterial flagellar motor (BFM) is a rotary molecular motor embedded in the cell membrane of numerous bacteria. It turns a flagellum which acts as a propeller, enabling bacterial motility and chemotaxis. The BFM is rotated by stator units, inner membrane protein complexes that stochastically associate to and dissociate from individual motors at a rate which depends on the mechanical and electrochemical environment. Stator units consume the ion motive force (IMF), the electrochemical gradient across the inner membrane that results from cellular respiration, converting the electrochemical energy of translocated ions into mechanical energy, imparted to the rotor. Here, we review some of the main results that form the base of our current understanding of the relationship between the IMF and the functioning of the flagellar motor. We examine a series of studies that establish a linear proportionality between IMF and motor speed, and we discuss more recent evidence that the stator units sense the IMF, altering their rates of dynamic assembly. This, in turn, raises the question of to what degree the classical dependence of motor speed on IMF is due to stator dynamics vs. the rate of ion flow through the stators. Finally, while long assumed to be static and homogeneous, there is mounting evidence that the IMF is dynamic, and that its fluctuations control important phenomena such as cell-to-cell signaling and mechanotransduction. Within the growing toolbox of single cell bacterial electrophysiology, one of the best tools to probe IMF fluctuations may, ironically, be the motor that consumes it. Perfecting our incomplete understanding of how the BFM employs the energy of ion flow will help decipher the dynamical behavior of the bacterial IMF.

Ligand sensing enhances bacterial flagellar motor output via stator recruitment

It is well known that flagellated bacteria, such as Escherichia coli, sense chemicals in their environment by a chemoreceptor and relay the signals via a well-characterized signaling pathway to the flagellar motor. It is widely accepted that the signals change the rotation bias of the motor without influencing the motor speed. Here, we present results to the contrary and show that the bacteria is also capable of modulating motor speed on merely sensing a ligand. Step changes in concentration of non-metabolizable ligand cause temporary recruitment of stator units leading to a momentary increase in motor speeds. For metabolizable ligand, the combined effect of sensing and metabolism leads to higher motor speeds for longer durations. Experiments performed with mutant strains delineate the role of metabolism and sensing in the modulation of motor speed and show how speed changes along with changes in bias can significantly enhance response to changes in its environment.

Alkaline pH Increases Swimming Speed and Facilitates Mucus Penetration for Vibrio cholerae

The diarrheal disease cholera is still a burden for populations in developing countries with poor sanitation. To develop effective vaccines and prevention strategies against Vibrio cholerae, we must understand the initial steps of infection leading to the colonization of the small intestine.

Intestinal mucus is the first line of defense against intestinal pathogens. It acts as a physical barrier between epithelial tissues and the lumen that enteropathogens must overcome to establish a successful infection. We investigated the motile behavior of two Vibrio cholerae strains (El Tor C6706 and Classical O395) in mucus using single-cell tracking in unprocessed porcine intestinal mucus. We determined that V. cholerae can penetrate mucus using flagellar motility and that alkaline pH increases swimming speed and, consequently, improves mucus penetration. Microrheological measurements indicate that changes in pH between 6 and 8 (the physiological range for the human small intestine) had little effect on the viscoelastic properties of mucus. Finally, we determined that acidic pH promotes surface attachment by activating the mannose-sensitive hemagglutinin (MshA) pilus in V. cholerae El Tor C6706 without a measurable change in the total cellular concentration of the secondary messenger cyclic dimeric GMP (c-di-GMP). Overall, our results support the hypothesis that pH is an important factor affecting the motile behavior of V. cholerae and its ability to penetrate mucus. Therefore, changes in pH along the human small intestine may play a role in determining the preferred site for V. cholerae during infection.

IMPORTANCE The diarrheal disease cholera is still a burden for populations in developing countries with poor sanitation. To develop effective vaccines and prevention strategies against Vibrio cholerae, we must understand the initial steps of infection leading to the colonization of the small intestine. To infect the host and deliver the cholera toxin, V. cholerae has to penetrate the mucus layer protecting the intestinal tissues. However, the interaction of V. cholerae with intestinal mucus has not been extensively investigated. In this report, we demonstrated using single-cell tracking that V. cholerae can penetrate intestinal mucus using flagellar motility. In addition, we observed that alkaline pH improves the ability of V. cholerae to penetrate mucus. This finding has important implications for understanding the dynamics of infection, because pH varies significantly along the small intestine, between individuals, and between species. Blocking mucus penetration by interfering with flagellar motility in V. cholerae, reinforcing the mucosa, controlling intestinal pH, or manipulating the intestinal microbiome will offer new strategies to fight cholera.

Bacterial biomechanics-From individual behaviors to biofilm and the gut flora

Bacteria inhabit a variety of locations and play important roles in the environment and health. Our understanding of bacterial biomechanics has improved markedly in the last decade and has revealed that biomechanics play a significant role in microbial biology. The obtained knowledge has enabled investigation of complex phenomena, such as biofilm formation and the dynamics of the gut flora. A bottom-up strategy, i.e., from the cellular to the macroscale, facilitates understanding of macroscopic bacterial phenomena. In this Review, we first cover the biomechanics of individual bacteria in the bulk liquid and on surfaces as the base of complex phenomena. The collective behaviors of bacteria in simple environments are next introduced. We then introduce recent advances in biofilm biomechanics, in which adhesion force and the flow environment play crucial roles. We also review transport phenomena in the intestine and the dynamics of the gut flora, focusing on that in zebrafish. Finally, we provide an overview of the future prospects for the field.

Large deformations of the hook affect free-swimming singly flagellated bacteria during flick motility

Hook dynamics are important in the motility of singly flagellated bacteria during flick motility. Although the hook is relatively short, during reorientation events it may undergo large deformations, leading to nonlinear behavior. Here, we explore when these nonlinear and large deformations are important for the swimming dynamics in different ranges of hook flexibilities and flagellar motor torques. For this purpose, we investigate progressively more faithful models for the hook, starting with linear springs, then models that incorporate nonlinearities due to larger hook deformations. We also employ these models both with and without hydrodynamic interactions between the flagellum and cell body to test the importance of those hydrodynamic interactions. We show that for stiff hooks, bacteria swim with a flagellum rotating on-axis in orbits and hydrodynamic interactions between the cell body and flagellum change swimming speeds by about 40%. As the hook stiffness decreases, there is a critical hook stiffness that predicts the initiation of the dynamic instability causing flicks. We compare the transition value of stiffnesses predicted by our models to experiments and show that nonlinearity and large deflections do not significantly affect critical transition values, while hydrodynamic interactions can change transition values by up to 13%. Below the transition value, we observe precession of the flagellum, in which it deflects off-axis to undergo nearly circular stable trajectories. However, only slightly below the transition stiffness, nonlinearity in hook response destabilizes precession, leading to unstable deflections of the flagellum. We conclude that while the linear hook response can qualitatively predict transition stiffnesses, nonlinear models are necessary to capture the behavior of hooks for stiffnesses below transition. Furthermore, we show that for the lower range of hook stiffnesses observed in actual bacteria, models which capture the full deformations of hooks are necessary. Inclusion of the hydrodynamic interactions of the cell body, hook, and flagellum is required to quantitatively simulate nonlinear dynamics of soft hooks during flick motility.

Motile ghosts of the halophilic archaeon, Haloferax volcanii

Archaea swim using the archaellum (archaeal flagellum), a reversible rotary motor consisting of a torque-generating motor and a helical filament, which acts as a propeller. Unlike the bacterial flagellar motor (BFM), ATP (adenosine-5'-triphosphate) hydrolysis probably drives both motor rotation and filamentous assembly in the archaellum. However, direct evidence is still lacking due to the lack of a versatile model system. Here, we present a membrane-permeabilized ghost system that enables the manipulation of intracellular contents, analogous to the triton model in eukaryotic flagella and gliding Mycoplasma We observed high nucleotide selectivity for ATP driving motor rotation, negative cooperativity in ATP hydrolysis, and the energetic requirement for at least 12 ATP molecules to be hydrolyzed per revolution of the motor. The response regulator CheY increased motor switching from counterclockwise (CCW) to clockwise (CW) rotation. Finally, we constructed the torque-speed curve at various [ATP]s and discuss rotary models in which the archaellum has characteristics of both the BFM and F₁-ATPase. Because archaea share similar cell division and chemotaxis machinery with other domains of life, our ghost model will be an important tool for the exploration of the universality, diversity, and evolution of biomolecular machinery.

Bacterial flagellar motor as a multimodal biosensor

Bacterial Flagellar Motor is one of nature's rare rotary molecular machines. It enables bacterial swimming and it is the key part of the bacterial chemotactic network, one of the best studied chemical signalling networks in biology, which enables bacteria to direct its movement in accordance with the chemical environment. The network can sense down to nanomolar concentrations of specific chemicals on the time scale of seconds. Motor's rotational speed is linearly proportional to the electrochemical gradients of either proton or sodium driving ions, while its direction is regulated by the chemotactic network. Recently, it has been discovered that motor is also a mechanosensor. Given these properties, we discuss the motor's potential to serve as a multifunctional biosensor and a tool for characterising and studying the external environment, the bacterial physiology itself and single molecular motor biophysics.

The Architectural Dynamics of the Bacterial Flagellar Motor Switch

The rotary bacterial flagellar motor is remarkable in biochemistry for its highly synchronized operation and amplification during switching of rotation sense. The motor is part of the flagellar basal body, a complex multi-protein assembly. Sensory and energy transduction depends on a core of six proteins that are adapted in different species to adjust torque and produce diverse switches. Motor response to chemotactic and environmental stimuli is driven by interactions of the core with small signal proteins. The initial protein interactions are propagated across a multi-subunit cytoplasmic ring to switch torque. Torque reversal triggers structural transitions in the flagellar filament to change motile behavior. Subtle variations in the core components invert or block switch operation. The mechanics of the flagellar switch have been studied with multiple approaches, from protein dynamics to single molecule and cell biophysics. The architecture, driven by recent advances in electron cryo-microscopy, is available for several species. Computational methods have correlated structure with genetic and biochemical databases. The design principles underlying the basis of switch ultra-sensitivity and its dependence on motor torque remain elusive, but tantalizing clues have emerged. This review aims to consolidate recent knowledge into a unified platform that can inspire new research strategies.

Mechanisms and Dynamics of the Bacterial Flagellar Motor

Many bacteria are able to actively propel themselves through their complex environment, in search of resources and suitable niches. The source of this propulsion is the Bacterial Flagellar Motor (BFM), a molecular complex embedded in the bacterial membrane which rotates a flagellum. In this chapter we review the known physical mechanisms at work in the motor. The BFM shows a highly dynamic behavior in its power output, its structure, and in the stoichiometry of its components. Changes in speed, rotation direction, constituent protein conformations, and the number of constituent subunits are dynamically controlled in accordance to external chemical and mechanical cues. The mechano-sensitivity of the motor is likely related to the surface-sensing ability of bacteria, relevant in the initial stage of biofilm formation.

Insights into flagellar function and mechanism from the squid-vibrio symbiosis

Flagella are essential and multifunctional nanomachines that not only move symbionts towards their tissue colonization site, but also play multiple roles in communicating with the host. Thus, untangling the activities of flagella in reaching, interacting, and signaling the host, as well as in biofilm formation and the establishment of a persistent colonization, is a complex problem. The squid-vibrio system offers a unique model to study the many ways that bacterial flagella can influence a beneficial association and, generally, other bacteria-host interactions. Vibrio fischeri is a bioluminescent bacterium that colonizes the Hawaiian bobtail squid, Euprymna scolopes. Over the last 15 years, the structure, assembly, and functions of V. fischeri flagella, including not only motility and chemotaxis, but also biofilm formation and symbiotic signaling, have been revealed. Here we discuss these discoveries in the perspective of other host-bacteria interactions.

Flagella-Driven Motility of Bacteria

The bacterial flagellum is a helical filamentous organelle responsible for motility. In bacterial species possessing flagella at the cell exterior, the long helical flagellar filament acts as a molecular screw to generate thrust. Meanwhile, the flagella of spirochetes reside within the periplasmic space and not only act as a cytoskeleton to determine the helicity of the cell body, but also rotate or undulate the helical cell body for propulsion. Despite structural diversity of the flagella among bacterial species, flagellated bacteria share a common rotary nanomachine, namely the flagellar motor, which is located at the base of the filament. The flagellar motor is composed of a rotor ring complex and multiple transmembrane stator units and converts the ion flux through an ion channel of each stator unit into the mechanical work required for motor rotation. Intracellular chemotactic signaling pathways regulate the direction of flagella-driven motility in response to changes in the environments, allowing bacteria to migrate towards more desirable environments for their survival. Recent experimental and theoretical studies have been deepening our understanding of the molecular mechanisms of the flagellar motor. In this review article, we describe the current understanding of the structure and dynamics of the bacterial flagellum.

Motor torque measurement of Halobacterium salinarum archaellar suggests a general model for ATP-driven rotary motors

It is unknown how the archaellum-the rotary propeller used by Archaea for motility-works. To further understand the molecular mechanism by which the hexameric ATPase motor protein FlaI drives rotation of the membrane-embedded archaellar motor, we determined motor torque by imposition of various loads on Halobacterium salinarum archaella. Markers of different sizes were attached to single archaella, and their trajectories were quantified using three-dimensional tracking and high-speed recording. We show that rotation slows as the viscous drag of markers increases, but torque remains constant at 160 pN·nm independent of rotation speed. Notably, the estimated work done in a single rotation is twice the expected energy that would come from hydrolysis of six ATP molecules in the hexamer, indicating that more ATP molecules are required for one rotation of archaellum. To reconcile the apparent contradiction, we suggest a new and general model for the mechanism of ATP-driven rotary motors.

Evaluation of the Duty Ratio of the Bacterial Flagellar Motor by Dynamic Load Control

The bacterial flagellar motor is one of the most complex and sophisticated nanomachineries in nature. A duty ratio D is a fraction of time that the stator and the rotor interact and is a fundamental property to characterize the motor but remains to be determined. It is known that the stator units of the motor bind to and dissociate from the motor dynamically to control the motor torque depending on the load on the motor. At low load, at which the kinetics such as proton translocation speed limits the rotation rate, the dependency of the rotation rate on the number of stator units N implies D: the dependency becomes larger for smaller D. Contradicting observations supporting both the small and large D have been reported. A dilemma is that it is difficult to explore a broad range of N at low load because the stator units easily dissociate, and N is limited to one or two at vanishing load. Here, we develop an electrorotation method to dynamically control the load on the flagellar motor of Salmonella with a calibrated magnitude of the torque. By instantly reducing the load for keeping N high, we observed that the speed at low load depends on N, implying a small duty ratio. We recovered the torque-speed curves of individual motors and evaluated the duty ratio to be 0.14 ± 0.04 from the correlation between the torque at high load and the rotation rate at low load.

Dynamic instability in the hook-flagellum system that triggers bacterial flicks

Dynamical bending, buckling, and polymorphic transformations of the flagellum are known to affect bacterial motility, but run-reverse-flick motility of monotrichous bacteria also involves the even more flexible hook connecting the flagellum to its rotary motor. Although flick initiation has been hypothesized to involve either static Euler buckling or dynamic bending of the hook, the precise mechanism of flick initiation remains unknown. Here, we find that flicks initiate via a dynamic instability requiring flexibility in both the hook and flagellum. We obtain accurate estimates of forces and torques on the hook that suggest that flicks occur for stresses below the (static) Euler buckling criterion, then provide a mechanistic model for flick initiation that requires combined bending of the hook and flagellum. We calculate the triggering torque-stiffness ratio and find that our predicted onset of dynamic instability corresponds well with experimental observations.

Bacterial Biohybrid Microswimmers

Over millions of years, Nature has optimized the motion of biological systems at the micro and nanoscales. Motor proteins to motile single cells have managed to overcome Brownian motion and solve several challenges that arise at low Reynolds numbers. In this review, we will briefly describe naturally motile systems and their strategies to move, starting with a general introduction that surveys a broad range of developments, followed by an overview about the physical laws and parameters that govern and limit motion at the microscale. We characterize some of the classes of biological microswimmers that have arisen in the course of evolution, as well as the hybrid structures that have been constructed based on these, ranging from Montemagno's ATPase motor to the SpermBot. Thereafter, we maintain our focus on bacteria and their biohybrids. We introduce the inherent properties of bacteria as a natural microswimmer and explain the different principles bacteria use for their motion. We then elucidate different strategies that have been employed for the coupling of a variety of artificial microobjects to the bacterial surface, and evaluate the different effects the coupled objects have on the motion of the "biohybrid." Concluding, we give a short overview and a realistic evaluation of proposed applications in the field.

The role of conserved charged residues in the bidirectional rotation of the bacterial flagellar motor

Many bacteria rotate their flagella both counterclockwise (CCW) and clockwise (CW) to achieve swimming toward attractants or away from repellents. Highly conserved charged residues are important for that motility, which suggests that electrostatic interactions are crucial for the rotor-stator function. It remains unclear if those residues contribute equally to rotation in the CCW and CW directions. To address this uncertainty, in this study, we expressed chimeric rotors and stators from Vibrio alginolyticus and Escherichia coli in E. coli, and measured the rotational speed of each motor in both directions using a tethered-cell assay. In wild-type cells, the rotational speeds in both directions were equal, as demonstrated previously. Some charge-neutralizing residue replacements in the stator decreased the rotational speed in both directions to the same extent. However, mutations in two charged residues in the rotor decreased the rotational speed only in the CCW direction. Subsequent analysis and previous results suggest that these amino acid residues are involved in supporting the conformation of the rotor, which is important for proper torque generation in the CCW direction.

Measurements of the Rotation of the Flagellar Motor by Bead Assay

The bacterial flagellar motor is a reversible rotary nano-machine powered by the ion flux across the cytoplasmic membrane. Each motor rotates a long helical filament that extends from the cell body at several hundreds revolutions per second. The output of the motor is characterized by its generated torque and rotational speed. The torque can be calculated as the rotational frictional drag coefficient multiplied by the angular velocity. Varieties of methods, including a bead assay, have been developed to measure the flagellar rotation rate under various load conditions on the motor. In this chapter, we describe a method to monitor the motor rotation through a position of a 1 μm bead attached to a truncated flagellar filament.

Speed of the bacterial flagellar motor near zero load depends on the number of stator units

The bacterial flagellar motor (BFM) rotates hundreds of times per second to propel bacteria driven by an electrochemical ion gradient. The motor consists of a rotor 50 nm in diameter surrounded by up to 11 ion-conducting stator units, which exchange between motors and a membrane-bound pool. Measurements of the torque-speed relationship guide the development of models of the motor mechanism. In contrast to previous reports that speed near zero torque is independent of the number of stator units, we observe multiple speeds that we attribute to different numbers of units near zero torque in both Na⁺- and H⁺-driven motors. We measure the full torque-speed relationship of one and two H⁺ units in Escherichia coli by selecting the number of H⁺ units and controlling the number of Na⁺ units in hybrid motors. These experiments confirm that speed near zero torque in H⁺-driven motors increases with the stator number. We also measured 75 torque-speed curves for Na⁺-driven chimeric motors at different ion-motive force and stator number. Torque and speed were proportional to ion-motive force and number of stator units at all loads, allowing all 77 measured torque-speed curves to be collapsed onto a single curve by simple rescaling.

Load- and polysaccharide-dependent activation of the Na+-type MotPS stator in the Bacillus subtilis flagellar motor

The flagellar motor of Bacillus subtilis possesses two distinct H⁺-type MotAB and Na⁺-type MotPS stators. In contrast to the MotAB motor, the MotPS motor functions efficiently at elevated viscosity in the presence of 200 mM NaCl. Here, we analyzed the torque-speed relationship of the Bacillus MotAB and MotPS motors over a wide range of external loads. The stall torque of the MotAB and MotPS motors at high load was about 2,200 pN nm and 220 pN nm, respectively. The number of active stators in the MotAB and MotPS motors was estimated to be about ten and one, respectively. However, the number of functional stators in the MotPS motor was increased up to ten with an increase in the concentration of a polysaccharide, Ficoll 400, as well as in the load. The maximum speeds of the MotAB and MotPS motors at low load were about 200 Hz and 50 Hz, respectively, indicating that the rate of the torque-generation cycle of the MotPS motor is 4-fold slower than that of the MotAB motor. Domain exchange experiments showed that the C-terminal periplasmic domain of MotS directly controls the assembly and disassembly dynamics of the MotPS stator in a load- and polysaccharide-dependent manner.

Biophysical Characterization of Flagellar Motor Functions

The role of flagellar motors in bacterial motility and chemotaxis is well-understood. Recent discoveries suggest that flagellar motors are able to remodel in response to a variety of environmental stimuli and are among the triggers for surface colonization and infections. The precise mechanisms by which motors remodel and promote cellular adaptation likely depend on key motor attributes. The photomultiplier-based bead-tracking technique presented here enables accurate biophysical characterization of motor functions, including adaptations in motor speeds and switch-dynamics. This approach offers the advantage of real-time tracking and the ability to probe motor behavior over extended durations. The protocols discussed can be readily extended to study flagellar motors in a variety of bacterial species.

Chemotactic Behaviors of Vibrio cholerae Cells

Vibrio cholerae, the causative agent of cholera, swims in aqueous environments with a single polar flagellum. In a spatial gradient of a chemical, the bacterium can migrate in "favorable" directions, a property that is termed chemotaxis. The chemotaxis of V. cholerae is not only critical for survival in various environments and but also is implicated in pathogenicity. In this chapter, we describe how to characterize the chemotactic behaviors of V. cholerae: these methods include swarm assay, temporal stimulation assay, capillary assay, and receptor methylation assay.

Bacterial Flagellar Motor Switch in Response to CheY-P Regulation and Motor Structural Alterations

The bacterial flagellar motor (BFM) is a molecular machine that rotates the helical filaments and propels the bacteria swimming toward favorable conditions. In our previous works, we built a stochastic conformational spread model to explain the dynamic and cooperative behavior of BFM switching. Here, we extended this model to test whether it can explain the latest experimental observations regarding CheY-P regulation and motor structural adaptivity. We show that our model predicts a strong correlation between rotational direction and the number of CheY-Ps bound to the switch complex, in agreement with the latest finding from Fukuoka et al. It also predicts that the switching sensitivity of the BFM can be fine-tuned by incorporating additional units into the switch complex, as recently demonstrated by Yuan et al., who showed that stoichiometry of FliM undergoes dynamic change to maintain ultrasensitivity in the motor switching response. In addition, by locking some rotor switching units on the switch complex into the stable clockwise-only conformation, our model has accurately simulated recent experiments expressing clockwise-locked FliG(ΔPAA) into the switch complex and reproduced the increased switching rate of the motor.

Evolution of Cell Size Homeostasis and Growth Rate Diversity during Initial Surface Colonization of Shewanella oneidensis

Cell size control and homeostasis are fundamental features of bacterial metabolism. Recent work suggests that cells add a constant size between birth and division ("adder" model). However, it is not known how cell size homeostasis is influenced by the existence of heterogeneous microenvironments, such as those during biofilm formation. Shewanella oneidensis MR-1 can use diverse energy sources on a range of surfaces via extracellular electron transport (EET), which can impact growth, metabolism, and size diversity. Here, we track bacterial surface communities at single-cell resolution to show that not only do bacterial motility appendages influence the transition from two- to three-dimensional biofilm growth and control postdivisional cell fates, they strongly impact cell size homeostasis. For every generation, we find that the average growth rate for cells that stay on the surface and continue to divide (nondetaching population) and that for cells that detach before their next division (detaching population) are roughly constant. However, the growth rate distribution is narrow for the nondetaching population, but broad for the detaching population in each generation. Interestingly, the appendage deletion mutants (ΔpilA, ΔmshA-D, Δflg) have significantly broader growth rate distributions than that of the wild type for both detaching and nondetaching populations, which suggests that Shewanella appendages are important for sensing and integrating environmental inputs that contribute to size homeostasis. Moreover, our results suggest multiplexing of appendages for sensing and motility functions contributes to cell size dysregulation. These results can potentially provide a framework for generating metabolic diversity in S. oneidensis populations to optimize EET in heterogeneous environments.

Using Biophysics to Monitor the Essential Protonmotive Force in Bacteria

Protonmotive force is an essential biological energy format in all levels of cells. Protonmotive force comprises electrical and chemical potential difference across biological membrane. In bacteria, protonmotive force couples to metabolism and ATP production. Moreover, protonmotive force directly provides driving energy of bacterial flagellar motor that is critical for bacterial motility and infection. Due to the small size of bacterial cells, there were limited experimental tools to measure protonmotive force in bacteria. Recent developments of optical membrane potential and intracellular pH indicators provide valuable information on bacterial studies. These new biophysical techniques allow us to monitor the protonmotive force even in single bacterial cell level that shed the light of next generation single-cell physiological experiments towards the understanding of bacterial infection process.

Force per cross-sectional area from molecules to muscles: a general property of biological motors

We propose to formally extend the notion of specific tension, i.e. force per cross-sectional area-classically used for muscles, to quantify forces in molecular motors exerting various biological functions. In doing so, we review and compare the maximum tensions exerted by about 265 biological motors operated by about 150 species of different taxonomic groups. The motors considered range from single molecules and motile appendages of microorganisms to whole muscles of large animals. We show that specific tensions exerted by molecular and non-molecular motors follow similar statistical distributions, with in particular, similar medians and (logarithmic) means. Over the 10(19) mass (M) range of the cell or body from which the motors are extracted, their specific tensions vary as M(α) with α not significantly different from zero. The typical specific tension found in most motors is about 200 kPa, which generalizes to individual molecular motors and microorganisms a classical property of macroscopic muscles. We propose a basic order-of-magnitude interpretation of this result.

Diverse high-torque bacterial flagellar motors assemble wider stator rings using a conserved protein scaffold

Although it is known that diverse bacterial flagellar motors produce different torques, the mechanism underlying torque variation is unknown. To understand this difference better, we combined genetic analyses with electron cryo-tomography subtomogram averaging to determine in situ structures of flagellar motors that produce different torques, from Campylobacter and Vibrio species. For the first time, to our knowledge, our results unambiguously locate the torque-generating stator complexes and show that diverse high-torque motors use variants of an ancestrally related family of structures to scaffold incorporation of additional stator complexes at wider radii from the axial driveshaft than in the model enteric motor. We identify the protein components of these additional scaffold structures and elucidate their sequential assembly, demonstrating that they are required for stator-complex incorporation. These proteins are widespread, suggesting that different bacteria have tailored torques to specific environments by scaffolding alternative stator placement and number. Our results quantitatively account for different motor torques, complete the assignment of the locations of the major flagellar components, and provide crucial constraints for understanding mechanisms of torque generation and the evolution of multiprotein complexes.

Torque-induced precession of bacterial flagella

The bacterial flagellar motor is an ion-driven rotary machine in the cell envelope of bacteria. Using a gold nanoparticle as a probe, we observed the precession of flagella during rotation. Since the mechanism of flagella precession was unknown, we investigated it using a combination of full simulations, theory, and experiments. The results show that the mechanism can be well explained by fluid mechanics. The validity of our theory was confirmed by our full simulation, which was utilized to predict both the filament tilt angle and motor torque from experimental flagellar precession data. The knowledge obtained is important in understanding mechanical properties of the bacterial motor and hook.

A Delicate Nanoscale Motor Made by Nature-The Bacterial Flagellar Motor

The bacterial flagellar motor (BFM) is a molecular complex ca. 45 nm in diameter that rotates the propeller that makes nearly all bacteria swim. The motor self-assembles out of ca. 20 different proteins and can not only rotate at up to 50 000 rpm, but can also switch rotational direction in milliseconds and navigate its environment to maneuver, on average, towards regions of greater benefit. The BFM is a pinnacle of evolution that informs and inspires the design of novel nanotechnology in the new era of synthetic biology.

Evidence for two extremes of ciliary motor response in a single swimming microorganism

Because arrays of motile cilia drive fluids for a range of processes, the versatile mechano-chemical mechanism coordinating them has been under scrutiny. The protist Paramecium presents opportunities to compare how groups of cilia perform two distinct functions, swimming propulsion and nutrient uptake. We present how the body cilia responsible for propulsion and the oral-groove cilia responsible for nutrient uptake respond to changes in their mechanical environment accomplished by varying the fluid viscosity over a factor of 7. Analysis with a phenomenological model of trajectories of swimmers made neutrally buoyant with magnetic forces combined with high-speed imaging of ciliary beating reveal that the body cilia exert a nearly constant propulsive force primarily by reducing their beat frequency as viscosity increases. By contrast, the oral-groove cilia beat at a nearly constant frequency. The existence of two extremes of motor response in a unicellular organism prompts unique investigations of factors controlling ciliary beating.