Absence of a barrier to backwards rotation of the bacterial flagellar motor demonstrated with optical tweezers

Nanovibrational Stimulation of Escherichia coli Mitigates Surface Adhesion by Altering Cell Membrane Potential

Mechanical forces shape living matter from the macro- to the microscale as both eukaryotic and prokaryotic cells are force wielders and sensors. However, whereas such forces have been used to control mechanically dependent behaviors in mammalian cells, we lack the same level of understanding in bacteria. Surface adhesion, the initial stages of biofilm formation and surface biofouling, is a mechanically dependent process, which makes it an ideal target for mechano-control. In this study, we employed nanometer surface vibrations to mechanically stimulate bacteria and investigate their effect on adhesion. We discovered that vibrational stimulation at the nanoscale consistently reduces surface adhesion by altering cell membrane potential. Our findings identify a link between bacteria electrophysiology and surface adhesion and provide evidence that the nanometric mechanical "tickling" of bacteria can inhibit surface adhesion.

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.

Optical tweezers for probing the interactions of ZnO and Ag nanoparticles with E. coli

The antibacterial effect of nanoparticles is mainly studied on the ensembles of the bacteria. In contrast, the optical tweezer technique allows the investigation of similar effects on individual bacterium. E. coli is a self-propelled micro-swimmer and ATP-driven active microorganism. In this work, an optical tweezer is employed to examine the mechanical properties of E. coli incubated with ZnO and Ag nanoparticles (NP) in the growth medium. ZnO and Ag NP with a concentration of 10 µg/ml were dispersed in growth medium during active log-growth phase of E. coli. This E. coli-NP incubation is further continued for 12 h. The E. coli after incubation for 2 h, 6 h and 12 h were separately studied by the optical tweezer for their mechanical property. The IR laser (λ = 975 nm; power = 100 mW) was used for trapping the individual cells and estimated trapping force, trapping stiffness and corner frequency. The optical trapping force on E. coli incubated in nanoparticle suspension shows linear decreases with incubation time. This work brings the importance of optical trapping force measurement in probing the antibacterial stress due to nanoparticles on the individual bacterium.

Lysinoalanine cross-linking is a conserved post-translational modification in the spirochete flagellar hook

Spirochetes cause Lyme disease, leptospirosis, syphilis, and several other human illnesses. Unlike other bacteria, spirochete flagella are enclosed within the periplasmic space where the filaments distort and push the cell body by the action of the flagellar motors. We previously demonstrated that the oral pathogen Treponema denticola (Td) and Lyme disease pathogen Borreliella burgdorferi (Bb) form covalent lysinoalanine (Lal) cross-links between conserved cysteine and lysine residues of the FlgE protein that composes the flagellar hook. In Td, Lal is unnecessary for hook assembly but is required for motility, presumably due to the stabilizing effect of the cross-link. Herein, we extend these findings to other, representative spirochete species across the phylum. We confirm the presence of Lal cross-linked peptides in recombinant and in vivo-derived samples from Treponema spp., Borreliella spp., Brachyspira spp., and Leptospira spp. As was observed with Td, a mutant strain of Bb unable to form the cross-link has greatly impaired motility. FlgE from Leptospira spp. does not conserve the Lal-forming cysteine residue which is instead substituted by serine. Nevertheless, Leptospira interrogans FlgE also forms Lal, with several different Lal isoforms being detected between Ser-179 and Lys-145, Lys-148, and Lys-166, thereby highlighting species or order-specific differences within the phylum. Our data reveal that the Lal cross-link is a conserved and necessary posttranslational modification across the spirochete phylum and may thus represent an effective target for the development of spirochete-specific antimicrobials.

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.

Materials science and mechanosensitivity of living matter

Living systems are composed of molecules that are synthesized by cells that use energy sources within their surroundings to create fascinating materials that have mechanical properties optimized for their biological function. Their functionality is a ubiquitous aspect of our lives. We use wood to construct furniture, bacterial colonies to modify the texture of dairy products and other foods, intestines as violin strings, bladders in bagpipes, and so on. The mechanical properties of these biological materials differ from those of other simpler synthetic elastomers, glasses, and crystals. Reproducing their mechanical properties synthetically or from first principles is still often unattainable. The challenge is that biomaterials often exist far from equilibrium, either in a kinetically arrested state or in an energy consuming active state that is not yet possible to reproduce de novo. Also, the design principles that form biological materials often result in nonlinear responses of stress to strain, or force to displacement, and theoretical models to explain these nonlinear effects are in relatively early stages of development compared to the predictive models for rubberlike elastomers or metals. In this Review, we summarize some of the most common and striking mechanical features of biological materials and make comparisons among animal, plant, fungal, and bacterial systems. We also summarize some of the mechanisms by which living systems develop forces that shape biological matter and examine newly discovered mechanisms by which cells sense and respond to the forces they generate themselves, which are resisted by their environment, or that are exerted upon them by their environment. Within this framework, we discuss examples of how physical methods are being applied to cell biology and bioengineering.

Superhybrid Mode-Enhanced Optical Torques on Mie-Resonant Particles

Circularly polarized light carries spin angular momentum, so it can exert an optical torque on the polarization-anisotropic particle by the spin momentum transfer. Here, we show that giant positive and negative optical torques on Mie-resonant (gain) particles arise from the emergence of superhybrid modes with magnetic multipoles and electric toroidal moments, excited by linearly polarized beams. Anomalous positive and negative torques on particles (doped with judicious amount of dye molecules) are over 800 and 200 times larger than the ordinary lossy counterparts, respectively. Meanwhile, a rotational motor can be configured by switching the s- and p-polarized beams, exhibiting opposite optical torques. These giant and reversed optical torques are unveiled for the first time in the scattering spectrum, paving another avenue toward exploring unprecedented physics of hybrid and superhybrid multipoles in metaoptics and optical manipulations.

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.

The bank of swimming organisms at the micron scale (BOSO-Micro)

Unicellular microscopic organisms living in aqueous environments outnumber all other creatures on Earth. A large proportion of them are able to self-propel in fluids with a vast diversity of swimming gaits and motility patterns. In this paper we present a biophysical survey of the available experimental data produced to date on the characteristics of motile behaviour in unicellular microswimmers. We assemble from the available literature empirical data on the motility of four broad categories of organisms: bacteria (and archaea), flagellated eukaryotes, spermatozoa and ciliates. Whenever possible, we gather the following biological, morphological, kinematic and dynamical parameters: species, geometry and size of the organisms, swimming speeds, actuation frequencies, actuation amplitudes, number of flagella and properties of the surrounding fluid. We then organise the data using the established fluid mechanics principles for propulsion at low Reynolds number. Specifically, we use theoretical biophysical models for the locomotion of cells within the same taxonomic groups of organisms as a means of rationalising the raw material we have assembled, while demonstrating the variability for organisms of different species within the same group. The material gathered in our work is an attempt to summarise the available experimental data in the field, providing a convenient and practical reference point for future studies.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Flagellar arrangements in elongated peritrichous bacteria: bundle formation and swimming properties

The surface distribution of flagella in peritrichous bacterial cells has been traditionally assumed to be random. Recently, the presence of a regular grid-like pattern of basal bodies has been suggested. Experimentally, the manipulation of the anchoring points of flagella in the cell membrane is difficult, and thus, elucidation of the consequences of a particular pattern on bacterial locomotion is challenging. We analyze the bundle formation process and swimming properties of Bacillus subtilis-like cells considering random, helical, and ring-like arrangements of flagella by means of mesoscale hydrodynamics simulations. Helical and ring patterns preferentially yield configurations with a single bundle, whereas configurations with no clear bundles are most likely for random anchoring. For any type of pattern, there is an almost equally low probability to form V-shaped bundle configurations with at least two bundles. Variation of the flagellum length yields a clear preference for a single major bundle in helical and ring patterns as soon as the flagellum length exceeds the body length. The average swimming speed of cells with a single or two bundles is rather similar, and approximately [Formula: see text] larger than that of cells of other types of flagellar organization. Considering the various anchoring patterns, rings yield the smallest average swimming speed independent of the type of bundle, followed by helical arrangements, and largest speeds are observed for random anchoring. Hence, a regular pattern provides no advantage in terms of swimming speed compared to random anchoring of flagella, but yields more likely single-bundle configurations.

Optimal trapping stability of Escherichia coli in oscillating optical tweezers

Single-beam oscillating optical tweezers can be used to trap rod-shaped bacterial cells and align them with their long axis lying within the focal plane. While such configuration is useful for imaging applications, the corresponding imaging resolution is limited by the fluctuations of the trapped cell. We study the fluctuations of four of the coordinates of the trapped cell, two for its center of mass position and two for its angular orientation, showing the way they depend on the trap length and the trapping beam power. We find that optimal trapping stability is obtained when the trap length is about the same as the cell length and that cell fluctuations in the focal plane decrease like the inverse of the trapping power.

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.

Wall entrapment of peritrichous bacteria: a mesoscale hydrodynamics simulation study

Microswimmers such as E. coli bacteria accumulate and exhibit an intriguing dynamics near walls, governed by hydrodynamic and steric interactions. Insight into the underlying mechanisms and predominant interactions demand a detailed characterization of the entrapment process. We employ a mesoscale hydrodynamics simulation approach to study entrapment of an E. coli-type cell at a no-slip wall. The cell is modeled by a spherocylindrical body with several explicit helical flagella. Three stages of the entrapment process can be distinguished: the approaching regime, where a cell swims toward a wall on a nearly straight trajectory; a scattering regime, where the cell touches the wall and reorients; and a surface-swimming regime. Our simulations show that steric interactions may dominate the entrapment process, yet, hydrodynamic interactions slow down the adsorption dynamics close to the boundary and imply a circular motion on the wall. The locomotion of the cell is characterized by a strong wobbling dynamics, with cells preferentially pointing toward the wall during surface swimming.

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.

Load-dependent adaptation near zero load in the bacterial flagellar motor

The bacterial flagellar motor is an ion-powered transmembrane protein complex which drives swimming in many bacterial species. The motor consists of a cytoplasmic 'rotor' ring and a number of 'stator' units, which are bound to the cell wall of the bacterium. Recently, it has been shown that the number of functional torque-generating stator units in the motor depends on the external load, and suggested that mechanosensing in the flagellar motor is driven via a 'catch bond' mechanism in the motor's stator units. We present a method that allows us to measure-on a single motor-stator unit dynamics across a large range of external loads, including near the zero-torque limit. By attaching superparamagnetic beads to the flagellar hook, we can control the motor's speed via a rotating magnetic field. We manipulate the motor to four different speed levels in two different ion-motive force (IMF) conditions. This framework allows for a deeper exploration into the mechanism behind load-dependent remodelling by separating out motor properties, such as rotation speed and energy availability in the form of IMF, that affect the motor torque.

Functional Regulators of Bacterial Flagella

Bacteria move by a variety of mechanisms, but the best understood types of motility are powered by flagella (72). Flagella are complex machines embedded in the cell envelope that rotate a long extracellular helical filament like a propeller to push cells through the environment. The flagellum is one of relatively few biological machines that experience continuous 360° rotation, and it is driven by one of the most powerful motors, relative to its size, on earth. The rotational force (torque) generated at the base of the flagellum is essential for motility, niche colonization, and pathogenesis. This review describes regulatory proteins that control motility at the level of torque generation.

Nanoscale Lamb wave-driven motors in nonliquid environments

Achieving light-driven motions in nonliquid environments presents formidable challenges, because microsized objects experience strong dry adhesion and intend to be stuck to contact surfaces with great tenacity. Here, in air and vacuum, we show rotary locomotion of a micrometer-sized metal plate with ~30 nm thickness, revolving around a microfiber. This motor is powered by pulsed light guided into the fiber as a coordinated consequence of an optically excited Lamb wave on the plate and favorable configuration of plate-fiber geometry. The motor, actuated by designed light pulses, crawls stepwise with subnanometer locomotion resolution. Furthermore, we can control the rotation velocity and step resolution by varying the repetition rate and pulse power, respectively. A light-actuated micromirror scanning with 0.001° resolution is then demonstrated on the basis of this motor. It offers unprecedented application potential for integrated micro-opto-electromechanical systems, outer-space all-optical precision mechanics and controls, and laser scanning for miniature lidar systems.

Computing the motor torque of Escherichia coli

The rotary motor of bacteria is a natural nano-technological marvel that enables cell locomotion by powering the rotation of semi-rigid helical flagellar filaments in fluid environments. It is well known that the motor operates essentially at constant torque in counter-clockwise direction but past work have reported a large range of values of this torque. Focusing on Escherichia coli cells that are swimming and cells that are stuck on a glass surface for which all geometrical and environmental parameters are known (N. C. Darnton et al., J. Bacteriol., 2007, 189, 1756-1764), we use two validated numerical methods to compute the value of the motor torque consistent with experiments. Specifically, we use (and compare) a numerical method based on the boundary integral representation of Stokes flow and also develop a hybrid method combining boundary element and slender body theory to model the cell body and flagellar filament, respectively. Using measured rotation speed of the motor, our computations predict a value of the motor torque in the range 440 pN nm to 829 pN nm, depending critically on the distance between the flagellar filaments and the nearby surface.

Design principles and optimal performance for molecular motors under realistic constraints

The performance of a molecular motor, characterized by its power output and energy efficiency, is investigated in the motor design space spanned by the stepping rate function and the motor-track interaction potential. Analytic results and simulations show that a gating mechanism that restricts forward stepping in a narrow window in configuration space is needed for generating high power at physiologically relevant loads. By deriving general thermodynamics laws for nonequilibrium motors, we find that the maximum torque (force) at stall is less than its theoretical limit for any realistic motor-track interactions due to speed fluctuations. Our study reveals a tradeoff for the motor-track interaction: while a strong interaction generates a high power output for forward steps, it also leads to a higher probability of wasteful spontaneous back steps. Our analysis and simulations show that this tradeoff sets a fundamental limit to the maximum motor efficiency in the presence of spontaneous back steps, i.e., loose-coupling. Balancing this tradeoff leads to an optimal design of the motor-track interaction for achieving a maximum efficiency close to 1 for realistic motors that are not perfectly coupled with the energy source. Comparison with existing data and suggestions for future experiments are discussed.

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.

Viscous drag on the flagellum activates Bacillus subtilis entry into the K-state

Bacillus subtilis flagella are not only required for locomotion but also act as sensors that monitor environmental changes. Although how the signal transmission takes place is poorly understood, it has been shown that flagella play an important role in surface sensing by transmitting a mechanical signal to control the DegS-DegU two-component system. Here we report a role for flagella in the regulation of the K-state, which enables transformability and antibiotic tolerance (persistence). Mutations impairing flagellar synthesis are inferred to increase DegU-P, which inhibits the expression of ComK, the master regulator for the K-state, and reduces transformability. Tellingly, both deletion of the flagellin gene and straight filament (hag^A233V ) mutations increased DegU phosphorylation despite the fact that both mutants had wild type numbers of basal bodies and the flagellar motors were functional. We propose that higher viscous loads on flagellar motors result in lower DegU-P levels through an unknown signaling mechanism. This flagellar-load based mechanism ensures that cells in the motile subpopulation have a tenfold enhanced likelihood of entering the K-state and taking up DNA from the environment. Further, our results suggest that the developmental states of motility and competence are related and most commonly occur in the same epigenetic cell type.

Applying torque to the Escherichia coli flagellar motor using magnetic tweezers

The bacterial flagellar motor of Escherichia coli is a nanoscale rotary engine essential for bacterial propulsion. Studies on the power output of single motors rely on the measurement of motor torque and rotation under external load. Here, we investigate the use of magnetic tweezers, which in principle allow the application and active control of a calibrated load torque, to study single flagellar motors in Escherichia coli. We manipulate the external load on the motor by adjusting the magnetic field experienced by a magnetic bead linked to the motor, and we probe the motor’s response. A simple model describes the average motor speed over the entire range of applied fields. We extract the motor torque at stall and find it to be similar to the motor torque at drag-limited speed. In addition, use of the magnetic tweezers allows us to force motor rotation in both forward and backward directions. We monitor the motor’s performance before and after periods of forced rotation and observe no destructive effects on the motor. Our experiments show how magnetic tweezers can provide active and fast control of the external load while also exposing remaining challenges in calibration. Through their non-invasive character and straightforward parallelization, magnetic tweezers provide an attractive platform to study nanoscale rotary motors at the single-motor level.

Biophysical Tools to Study Cellular Mechanotransduction

The cell membrane is the interface that volumetrically isolates cellular components from the cell's environment. Proteins embedded within and on the membrane have varied biological functions: reception of external biochemical signals, as membrane channels, amplification and regulation of chemical signals through secondary messenger molecules, controlled exocytosis, endocytosis, phagocytosis, organized recruitment and sequestration of cytosolic complex proteins, cell division processes, organization of the cytoskeleton and more. The membrane's bioelectrical role is enabled by the physiologically controlled release and accumulation of electrochemical potential modulating molecules across the membrane through specialized ion channels (e.g., Na⁺, Ca2+, K⁺ channels). The membrane's biomechanical functions include sensing external forces and/or the rigidity of the external environment through force transmission, specific conformational changes and/or signaling through mechanoreceptors (e.g., platelet endothelial cell adhesion molecule (PECAM), vascular endothelial (VE)-cadherin, epithelial (E)-cadherin, integrin) embedded in the membrane. Certain mechanical stimulations through specific receptor complexes induce electrical and/or chemical impulses in cells and propagate across cells and tissues. These biomechanical sensory and biochemical responses have profound implications in normal physiology and disease. Here, we discuss the tools that facilitate the understanding of mechanosensitive adhesion receptors. This article is structured to provide a broad biochemical and mechanobiology background to introduce a freshman mechano-biologist to the field of mechanotransduction, with deeper study enabled by many of the references cited herein.

Bacterial swarmer cells in confinement: a mesoscale hydrodynamic simulation study

A wide spectrum of Peritrichous bacteria undergo considerable physiological changes when they are inoculated onto nutrition-rich surfaces and exhibit a rapid and collective migration denoted as swarming. Thereby, the length of such swarmer cells and their number of flagella increases substantially. In this article, we investigated the properties of individual E. coli-type swarmer cells confined between two parallel walls via mesoscale hydrodynamic simulations, combining molecular dynamics simulations of the swarmer cell with the multiparticle particle collision dynamics approach for the embedding fluid. E. coli-type swarmer cells are three-times longer than their planktonic counter parts, but their flagella density is comparable. By varying the wall separation, we analyze the confinement effect on the flagella arrangement, on the distribution of cells in the gap between the walls, and on the cell dynamics. We find only a weak dependence of confinement on the bundle structure and dynamics. The distribution of cells in the gap changes from a geometry-dominated behavior for very narrow to fluid-dominated behavior for wider gaps, where cells are preferentially located in the gap center for narrower gaps and stay preferentially next to one of the walls for wider gaps. Dynamically, the cells exhibit a wide spectrum of migration behaviors, depending on their flagella bundle arrangement, and ranges from straight swimming to wall rolling.

Photonic Torque Microscopy of the Nonconservative Force Field for Optically Trapped Silicon Nanowires

We measure, by photonic torque microscopy, the nonconservative rotational motion arising from the transverse components of the radiation pressure on optically trapped, ultrathin silicon nanowires. Unlike spherical particles, we find that nonconservative effects have a significant influence on the nanowire dynamics in the trap. We show that the extreme shape of the trapped nanowires yields a transverse component of the radiation pressure that results in an orbital rotation of the nanowire about the trap axis. We study the resulting motion as a function of optical power and nanowire length, discussing its size-scaling behavior. These shape-dependent nonconservative effects have implications for optical force calibration and optomechanics with levitated nonspherical particles.

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.

Modelling the mechanics and hydrodynamics of swimming E. coli

The swimming properties of an E. coli-type model bacterium are investigated by mesoscale hydrodynamic simulations, combining molecular dynamics simulations of the bacterium with the multiparticle particle collision dynamics method for the embedding fluid. The bacterium is composed of a spherocylindrical body with attached helical flagella, built up from discrete particles for an efficient coupling with the fluid. We measure the hydrodynamic friction coefficients of the bacterium and find quantitative agreement with experimental results of swimming E. coli. The flow field of the bacterium shows a force-dipole-like pattern in the swimming plane and two vortices perpendicular to its swimming direction arising from counterrotation of the cell body and the flagella. By comparison with the flow field of a force dipole and rotlet dipole, we extract the force-dipole and rotlet-dipole strengths for the bacterium and find that counterrotation of the cell body and the flagella is essential for describing the near-field hydrodynamics of the bacterium.

Flagellar motility of the pathogenic spirochetes

Bacterial pathogens are often classified by their toxicity and invasiveness. The invasiveness of a given bacterium is determined by how capable the bacterium is at invading a broad range of tissues in its host. Of mammalian pathogens, some of the most invasive come from a group of bacteria known as the spirochetes, which cause diseases, such as syphilis, Lyme disease, relapsing fever and leptospirosis. Most of the spirochetes are characterized by their distinct shapes and unique motility. They are long, thin bacteria that can be shaped like flat-waves, helices, or have more irregular morphologies. Like many other bacteria, the spirochetes use long, helical appendages known as flagella to move; however, the spirochetes enclose their flagella in the periplasm, the narrow space between the inner and outer membranes. Rotation of the flagella in the periplasm causes the entire cell body to rotate and/or undulate. These deformations of the bacterium produce the force that drives the motility of these organisms, and it is this unique motility that likely allows these bacteria to be highly invasive in mammals. This review will describe the current state of knowledge on the motility and biophysics of these organisms and provide evidence on how this knowledge can inform our understanding of spirochetal diseases.

Bio-Hybrid Micro/Nanodevices Powered by Flagellar Motor: Challenges and Strategies

Molecular motors, which are precision engineered by nature, offer exciting possibilities for bio-hybrid engineered systems. They could enable real applications ranging from micro/nano fluidics, to biosensing, to medical diagnoses. This review describes the fundamental biological insights and fascinating potentials of these remarkable sensing and actuation machines, in particular, bacterial flagellar motors, as well as their engineering perspectives with regard to applications in bio-engineered hybrid systems.

Mechanics of torque generation in the bacterial flagellar motor

The bacterial flagellar motor (BFM) is responsible for driving bacterial locomotion and chemotaxis, fundamental processes in pathogenesis and biofilm formation. In the BFM, torque is generated at the interface between transmembrane proteins (stators) and a rotor. It is well established that the passage of ions down a transmembrane gradient through the stator complex provides the energy for torque generation. However, the physics involved in this energy conversion remain poorly understood. Here we propose a mechanically specific model for torque generation in the BFM. In particular, we identify roles for two fundamental forces involved in torque generation: electrostatic and steric. We propose that electrostatic forces serve to position the stator, whereas steric forces comprise the actual "power stroke." Specifically, we propose that ion-induced conformational changes about a proline "hinge" residue in a stator α-helix are directly responsible for generating the power stroke. Our model predictions fit well with recent experiments on a single-stator motor. The proposed model provides a mechanical explanation for several fundamental properties of the flagellar motor, including torque-speed and speed-ion motive force relationships, backstepping, variation in step sizes, and the effects of key mutations in the stator.

Physical Sensing of Surface Properties by Microswimmers--Directing Bacterial Motion via Wall Slip

Bacteria such as Escherichia coli swim along circular trajectories adjacent to surfaces. Thereby, the orientation (clockwise, counterclockwise) and the curvature depend on the surface properties. We employ mesoscale hydrodynamic simulations of a mechano-elastic model of E. coli, with a spherocylindrical body propelled by a bundle of rotating helical flagella, to study quantitatively the curvature of the appearing circular trajectories. We demonstrate that the cell is sensitive to nanoscale changes in the surface slip length. The results are employed to propose a novel approach to directing bacterial motion on striped surfaces with different slip lengths, which implies a transformation of the circular motion into a snaking motion along the stripe boundaries. The feasibility of this approach is demonstrated by a simulation of active Brownian rods, which also reveals a dependence of directional motion on the stripe width.

Evaluating the toxic effect of an antimicrobial agent on single bacterial cells with optical tweezers

We implement an optical tweezers technique to assess the effects of chemical agents on single bacterial cells. As a proof of principle, the viability of a trapped Escherichia coli bacterium is determined by monitoring its flagellar motility in the presence of varying concentrations of ethyl alcohol. We show that the "killing time" of the bacterium can be effectively identified from the correlation statistics of the positional time series recorded from the trap, while direct quantification from the time series or associated power spectra is intractable. Our results, which minimize the lethal effects of bacterial photodamage, are consistent with previous reports of ethanol toxicity that used conventional culture-based methods. This approach can be adapted to study other pairwise combinations of drugs and motile bacteria, especially to measure the response times of single cells with better precision.

Viscous dynamics of Lyme disease and syphilis spirochetes reveal flagellar torque and drag

The spirochetes that cause Lyme disease (Borrelia burgdorferi) and syphilis (Treponema pallidum) swim through viscous fluids, such as blood and interstitial fluid, by undulating their bodies as traveling, planar waves. These undulations are driven by rotation of the flagella within the periplasmic space, the narrow (∼20-40 nm in width) compartment between the inner and outer membranes. We show here that the swimming speeds of B. burgdorferi and T. pallidum decrease with increases in viscosity of the external aqueous milieu, even though the flagella are entirely intracellular. We then use mathematical modeling to show that the measured changes in speed are consistent with the exertion of constant torque by the spirochetal flagellar motors. Comparison of simulations, experiments, and a simple model for power dissipation allows us to estimate the torque and resistive drag that act on the flagella of these major spirochetal pathogens.

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.

Dynamics of mechanosensing in the bacterial flagellar motor

Mechanosensing by flagella is thought to trigger bacterial swarmer-cell differentiation, an important step in pathogenesis. How flagellar motors sense mechanical stimuli is not known. To study this problem, we suddenly increased the viscous drag on motors by a large factor, from very low loads experienced by motors driving hooks or hooks with short filament stubs, to high loads, experienced by motors driving tethered cells or 1-μm latex beads. From the initial speed (after the load change), we inferred that motors running at very low loads are driven by one or at most two force-generating units. Following the load change, motors gradually adapted by increasing their speeds in a stepwise manner (over a period of a few minutes). Motors initially spun exclusively counterclockwise, but then increased the fraction of time that they spun clockwise over a time span similar to that observed for adaptation in speed. Single-motor total internal reflection fluorescence imaging of YFP-MotB (part of a stator force-generating unit) confirmed that the response to sudden increments in load occurred by the addition of new force-generating units. We estimate that 6-11 force-generating units drive motors at high loads. Wild-type motors and motors locked in the clockwise or counterclockwise state behaved in a similar manner, as did motors in cells deleted for the motor protein gene fliL or for genes in the chemotaxis signaling pathway. Thus, it appears that stators themselves act as dynamic mechanosensors. They change their structure in response to changes in external load. How such changes might impact cellular functions other than motility remains an interesting question.

Torque measurement at the single-molecule level

Methods for exerting and measuring forces on single molecules have revolutionized the study of the physics of biology. However, it is often the case that biological processes involve rotation or torque generation, and these parameters have been more difficult to access experimentally. Recent advances in the single-molecule field have led to the development of techniques that add the capability of torque measurement. By combining force, displacement, torque, and rotational data, a more comprehensive description of the mechanics of a biomolecule can be achieved. In this review, we highlight a number of biological processes for which torque plays a key mechanical role. We describe the various techniques that have been developed to directly probe the torque experienced by a single molecule, and detail a variety of measurements made to date using these new technologies. We conclude by discussing a number of open questions and propose systems of study that would be well suited for analysis with torsional measurement techniques.

A simple technique based on a single optical trap for the determination of bacterial swimming pattern

Bacterial motility is associated to a wide range of biological processes and it plays a key role in the virulence of many pathogens. Here we describe a method to distinguish the dynamic properties of bacteria by analyzing the statistical functions derived from the trajectories of a bacterium trapped by a single optical beam. The approach is based on the model of the rotation of a solid optically trapped sphere. The technique is easily implemented in a biological laboratory, since with only a small number of optical and electronic components a simple biological microscope can be converted into the required analyzer. To illustrate the functionality of this method, we probed several Salmonella enterica serovar Typhimurium mutants that differed from the wild-type with respect to their swimming patterns. In a further application, the motility dynamics of the S. Typhimurium cheV mutant were characterized.

High hydrostatic pressure induces counterclockwise to clockwise reversals of the Escherichia coli flagellar motor

The bacterial flagellar motor is a reversible rotary machine that rotates a left-handed helical filament, allowing bacteria to swim toward a more favorable environment. The direction of rotation reverses from counterclockwise (CCW) to clockwise (CW), and vice versa, in response to input from the chemotaxis signaling circuit. CW rotation is normally caused by binding of the phosphorylated response regulator CheY (CheY-P), and strains lacking CheY are typically locked in CCW rotation. The detailed mechanism of switching remains unresolved because it is technically difficult to regulate the level of CheY-P within the concentration range that produces flagellar reversals. Here, we demonstrate that high hydrostatic pressure can induce CW rotation even in the absence of CheY-P. The rotation of single flagellar motors in Escherichia coli cells with the cheY gene deleted was monitored at various pressures and temperatures. Application of >120 MPa pressure induced a reversal from CCW to CW at 20°C, although at that temperature, no motor rotated CW at ambient pressure (0.1 MPa). At lower temperatures, pressure-induced changes in direction were observed at pressures of <120 MPa. CW rotation increased with pressure in a sigmoidal fashion, as it does in response to increasing concentrations of CheY-P. Application of pressure generally promotes the formation of clusters of ordered water molecules on the surfaces of proteins. It is possible that hydration of the switch complex at high pressure induces structural changes similar to those caused by the binding of CheY-P.

Physics of bacterial morphogenesis

Bacterial cells utilize three-dimensional (3D) protein assemblies to perform important cellular functions such as growth, division, chemoreception, and motility. These assemblies are composed of mechanoproteins that can mechanically deform and exert force. Sometimes, small-nucleotide hydrolysis is coupled to mechanical deformations. In this review, we describe the general principle for an understanding of the coupling of mechanics with chemistry in mechanochemical systems. We apply this principle to understand bacterial cell shape and morphogenesis and how mechanical forces can influence peptidoglycan cell wall growth. We review a model that can potentially reconcile the growth dynamics of the cell wall with the role of cytoskeletal proteins such as MreB and crescentin. We also review the application of mechanochemical principles to understand the assembly and constriction of the FtsZ ring. A number of potential mechanisms are proposed, and important questions are discussed.

Proposed model for the flagellar rotary motor with shear stress transmission

Most bacteria that swim are propelled by flagellar filaments, which are driven by a rotary motor powered by proton flux. The motor consists of the rotor and the stator. The stator consists of about 8 MotA-Mot B complex. There seems to be no definite information about the structure between the rotor and the stator, and it is examined whether the experimental data can be explained based upon the following assumptions. (a) There is viscoelastic medium between the rotor and the stator. (b) MotA-MotB complex has an electric dipole moment and produces shear stress in the electric field by a proton in the channel. Calculation results based upon these assumptions are in good agreement with the following experimental observations. (1) One revolution of the flagellar rotation consists of a constant number of steps. (2) The rotation velocity of the rotor is proportional to the trans-membrane potential difference. (3) When the rotational velocity of a flagellum is changed by adjusting the viscosity of the outer fluid, the torque for the cell to rotate a flagellum is practically constant but sharply decreases when the rotational velocity increases over a critical value. (4) The rotation direction remains the same when the sign of the electrochemical potential gradient is reversed. (5) The cell produces constant torque to rotate the flagellum even when the cell is rotated by externally applied torque. (6) A simple switch mechanism is proposed for chemotaxis.

Dynamics of the bacterial flagellar motor: the effects of stator compliance, back steps, temperature, and rotational asymmetry

The rotation of a bacterial flagellar motor (BFM) is driven by multiple stators tethered to the cell wall. Here, we extend a recently proposed power-stroke model to study the BFM dynamics under different biophysical conditions. Our model explains several key experimental observations and reveals their underlying mechanisms. 1), The observed independence of the speed at low load on the number of stators is explained by a force-dependent stepping mechanism that is independent of the strength of the stator tethering spring. Conversely, without force-dependent stepping, an unrealistically weak stator spring is required. 2), Our model with back-stepping naturally explains the observed absence of a barrier to backward rotation. Using the same set of parameters, it also explains BFM behaviors in the high-speed negative-torque regime. 3), From the measured temperature dependence of the maximum speed, our model shows that stator-stepping is a thermally activated process with an energy barrier. 4), The recently observed asymmetry in the torque-speed curve between counterclockwise- and clockwise-rotating BFMs can be quantitatively explained by the asymmetry in the stator-rotor interaction potentials, i.e., a quasilinear form for the counterclockwise motor and a quadratic form for the clockwise motor.

Superresolution imaging in optical tweezers using high-speed cameras

High-speed cameras are reliable alternatives for the direct characterization of optical trap force and particle motion in optical tweezers setups, replacing indirect motion measurements often performed by quadrant detectors. In the present approach, subpixel motion data of the trapped particle is retrieved from a high-speed low-resolution video sequence. Due to the richness structure of motion diversity of microscopic trapped particles, which are subjected to a Brownian motion, we propose to also use the obtained motion information for tackling the inherent lack of resolution by applying superresolution algorithms on the low-resolution image sequence. The obtained results both for trapping calibration beads and for living bacteria show that the proposed approach allows the proper characterization of the optical tweezers by obtaining the real particle motion directly from the image domain, while still providing high resolution imaging.

Shear stress transmission model for the flagellar rotary motor

Most bacteria that swim are propelled by flagellar filaments, which are driven by a rotary motor powered by proton flux. The mechanism of the flagellar motor is discussed by reforming the model proposed by the present authors in 2005. It is shown that the mean strength of Coulomb field produced by a proton passing the channel is very strong in the Mot assembly so that the Mot assembly can be a shear force generator and induce the flagellar rotation. The model gives clear calculation results in agreement with experimental observations, e g., for the charasteristic torque-velocity relationship of the flagellar rotation.

Dynamics of the bacterial flagellar motor with multiple stators

The bacterial flagellar motor drives the rotation of flagellar filaments and enables many species of bacteria to swim. Torque is generated by interaction of stator units, anchored to the peptidoglycan cell wall, with the rotor. Recent experiments [Yuan J, Berg HC (2008) Proc Natl Acad Sci USA 105:1182-1185] show that at near-zero load the speed of the motor is independent of the number of stators. Here, we introduce a mathematical model of the motor dynamics that explains this behavior based on a general assumption that the stepping rate of a stator depends on the torque exerted by the stator on the rotor. We find that the motor dynamics can be characterized by two timescales: the moving-time interval for the mechanical rotation of the rotor and the waiting-time interval determined by the chemical transitions of the stators. We show that these two timescales depend differently on the load, and that their cross-over provides the microscopic explanation for the existence of two regimes in the torque-speed curves observed experimentally. We also analyze the speed fluctuation for a single motor by using our model. We show that the motion is smoothed by having more stator units. However, the mechanism for such fluctuation reduction is different depending on the load. We predict that the speed fluctuation is determined by the number of steps per revolution only at low load and is controlled by external noise for high load. Our model can be generalized to study other molecular motor systems with multiple power-generating units.

A giant liposome for single-molecule observation of conformational changes in membrane proteins

We present an experimental system that allows visualization of conformational changes in membrane proteins at the single-molecule level. The target membrane protein is reconstituted in a giant liposome for independent control of the aqueous environments on the two sides of the membrane. For direct observation of conformational changes, an extra-liposomal site(s) of the target protein is bound to a glass surface, and a probe that is easily visible under a microscope, such as a micron-sized plastic bead, is attached to another site on the intra-liposomal side. A conformational change, or an angular motion in the tiny protein molecule, would manifest as a visible motion of the probe. The attachment of the protein on the glass surface also immobilizes the liposome, greatly facilitating its manipulation such as the probe injection. As a model system, we reconstituted ATP synthase (F(O)F(1)) in liposomes tens of mum in size, attached the protein specifically to a glass surface, and demonstrated its ATP-driven rotation in the membrane through the motion of a submicron bead.

Bacterial flagellar motor

The bacterial flagellar motor is a reversible rotary nano-machine, about 45 nm in diameter, embedded in the bacterial cell envelope. It is powered by the flux of H+or Na+ions across the cytoplasmic membrane driven by an electrochemical gradient, the proton-motive force or the sodium-motive force. Each motor rotates a helical filament at several hundreds of revolutions per second (hertz). In many species, the motor switches direction stochastically, with the switching rates controlled by a network of sensory and signalling proteins. The bacterial flagellar motor was confirmed as a rotary motor in the early 1970s, the first direct observation of the function of a single molecular motor. However, because of the large size and complexity of the motor, much remains to be discovered, in particular, the structural details of the torque-generating mechanism. This review outlines what has been learned about the structure and function of the motor using a combination of genetics, single-molecule and biophysical techniques, with a focus on recent results and single-molecule techniques.

Optical tweezers for single cells

Optical tweezers (OT) have emerged as an essential tool for manipulating single biological cells and performing sophisticated biophysical/biomechanical characterizations. Distinct advantages of using tweezers for these characterizations include non-contact force for cell manipulation, force resolution as accurate as 100aN and amiability to liquid medium environments. Their wide range of applications, such as transporting foreign materials into single cells, delivering cells to specific locations and sorting cells in microfluidic systems, are reviewed in this article. Recent developments of OT for nanomechanical characterization of various biological cells are discussed in terms of both their theoretical and experimental advancements. The future trends of employing OT in single cells, especially in stem cell delivery, tissue engineering and regenerative medicine, are prospected. More importantly, current limitations and future challenges of OT for these new paradigms are also highlighted in this review.