Temperature Dependences of Torque Generation and Membrane Voltage in the Bacterial Flagellar Motor

In their natural habitats bacteria are frequently exposed to sudden changes in temperature that have been shown to affect their swimming. With our believed to be new methods of rapid temperature control for single-molecule microscopy, we measured here the thermal response of the Na⁺-driven chimeric motor expressed in Escherichia coli cells. Motor torque at low load (0.35 μm bead) increased linearly with temperature, twofold between 15°C and 40°C, and torque at high load (1.0 μm bead) was independent of temperature, as reported for the H⁺-driven motor. Single cell membrane voltages were measured by fluorescence imaging and these were almost constant (∼120 mV) over the same temperature range. When the motor was heated above 40°C for 1–2 min the torque at high load dropped reversibly, recovering upon cooling below 40°C. This response was repeatable over as many as 10 heating cycles. Both increases and decreases in torque showed stepwise torque changes with unitary size ∼150 pN nm, close to the torque of a single stator at room temperature (∼180 pN nm), indicating that dynamic stator dissociation occurs at high temperature, with rebinding upon cooling. Our results suggest that the temperature-dependent assembly of stators is a general feature of flagellar motors.     

Temperature Dependences of Torque Generation and Membrane Voltage in the Bacterial Flagellar Motor

In their natural habitats bacteria are frequently exposed to sudden changes in temperature that have been shown to affect their swimming. With our believed to be new methods of rapid temperature control for single-molecule microscopy, we measured here the thermal response of the Na⁺-driven chimeric motor expressed in Escherichia coli cells. Motor torque at low load (0.35 μm bead) increased linearly with temperature, twofold between 15°C and 40°C, and torque at high load (1.0 μm bead) was independent of temperature, as reported for the H⁺-driven motor. Single cell membrane voltages were measured by fluorescence imaging and these were almost constant (∼120 mV) over the same temperature range. When the motor was heated above 40°C for 1–2 min the torque at high load dropped reversibly, recovering upon cooling below 40°C. This response was repeatable over as many as 10 heating cycles. Both increases and decreases in torque showed stepwise torque changes with unitary size ∼150 pN nm, close to the torque of a single stator at room temperature (∼180 pN nm), indicating that dynamic stator dissociation occurs at high temperature, with rebinding upon cooling. Our results suggest that the temperature-dependent assembly of stators is a general feature of flagellar motors.     

Quantification of flagellar motor stator dynamics through in vivo proton‐motive force control

The bacterial flagellar motor, one of the few rotary motors in nature, produces torque to drive the flagellar filament by ion translocation through membrane‐bound stator complexes. We used the light‐driven proton pump proteorhodopsin (pR) to control the proton‐motive force (PMF) in vivo by illumination. pR excitation was shown to be sufficient to replace native PMF generation, and when excited in cells with intact native PMF generation systems increased motor speed beyond the physiological norm. We characterized the effects of rapid in vivo PMF changes on the flagellar motor. Transient PMF disruption events from loss of illumination caused motors to stop, with rapid recovery of their previous rotation rate after return of illumination. However, extended periods of PMF loss led to stepwise increases in rotation rate upon PMF return as stators returned to the motor. The rate constant for stator binding to a putative single binding site on the motor was calculated to be 0.06 s^?1. Using GFP‐tagged MotB stator proteins, we found that transient PMF disruption leads to reversible stator diffusion away from the flagellar motor, showing that PMF presence is necessary for continued motor integrity, and calculated a stator dissociation rate of 0.038 s^?1.     

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.     

Direct observation of speed fluctuations of flagellar motor rotation at extremely low load close to zero

The bacterial flagellar motor accommodates ten stator units around the rotor to produce large torque at high load. But when external load is low, some previous studies showed that a single stator unit can spin the rotor at the maximum speed, suggesting that the maximum speed does not depend on the number of active stator units, whereas others reported that the speed is also dependent on the stator number. To clarify these two controversial observations, much more precise measurements of motor rotation would be required at external load as close to zero as possible. Here, we constructed a Salmonella filament-less mutant that produces a rigid, straight, twice longer hook to efficiently label a 60 nm gold particle and analyzed flagellar motor dynamics at low load close to zero. The maximum motor speed was about 400 Hz. Large speed fluctuations and long pausing events were frequently observed, and they were suppressed by either over-expression of the MotAB stator complex or increase in the external load, suggesting that the number of active stator units in the motor largely fluctuates near zero load. We conclude that the lifetime of the active stator unit becomes much shorter when the motor operates near zero load.     

Model Studies of the Dynamics of Bacterial Flagellar Motors

The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel swimming bacteria. Extensive experimental and theoretical studies exist on the structure, assembly, energy input, power generation, and switching mechanism of the motor. In a previous article, we explained the general physics underneath the observed torque-speed curves with a simple two-state Fokker-Planck model. Here, we further analyze that model, showing that 1), the model predicts that the two components of the ion motive force can affect the motor dynamics differently, in agreement with latest experiments; 2), with explicit consideration of the stator spring, the model also explains the lack of dependence of the zero-load speed on stator number in the proton motor, as recently observed; and 3), the model reproduces the stepping behavior of the motor even with the existence of the stator springs and predicts the dwell-time distribution. The predicted stepping behavior of motors with two stators is discussed, and we suggest future experimental procedures for verification.     

Dual stator dynamics in the Shewanella oneidensis MR‐1 flagellar motor

The bacterial flagellar motor is an intricate nanomachine which converts ion gradients into rotational movement. Torque is created by ion‐dependent stator complexes which surround the rotor in a ring. Shewanella oneidensis MR‐1 expresses two distinct types of stator units: the Na⁺‐dependent PomA₄B₂ and the H⁺‐dependent MotA₄B₂. Here, we have explored the stator unit dynamics in the MR‐1 flagellar system by using mCherry‐labeled PomAB and MotAB units. We observed a total of between 7 and 11 stator units in each flagellar motor. Both types of stator units exchanged between motors and a pool of stator complexes in the membrane, and the exchange rate of MotAB, but not of PomAB, units was dependent on the environmental Na⁺‐levels. In 200 mM Na⁺, the numbers of PomAB and MotAB units in wild‐type motors was determined to be about 7:2 (PomAB:MotAB), shifting to about 6:5 without Na⁺. Significantly, the average swimming speed of MR‐1 cells at low Na⁺ conditions was increased in the presence of MotAB. These data strongly indicate that the S. oneidensis flagellar motors simultaneously use H⁺ and Na⁺ driven stators in a configuration governed by MotAB incorporation efficiency in response to environmental Na⁺ levels.     

Sodium‐powered stators of the bacterial flagellar motor can generate torque in the presence of phenamil with mutations near the peptidoglycan‐binding region

The bacterial flagellar motor powers the rotation that propels the swimming bacteria. Rotational torque is generated by harnessing the flow of ions through ion channels known as stators which couple the energy from the ion gradient across the inner membrane to rotation of the rotor. Here, we used error‐prone PCR to introduce single point mutations into the sodium‐powered Vibrio alginolyticus/Escherichia coli chimeric stator PotB and selected for motors that exhibited motility in the presence of the sodium‐channel inhibitor phenamil. We found single mutations that enable motility under phenamil occurred at two sites: (i) the transmembrane domain of PotB, corresponding to the TM region of the PomB stator from V. alginolyticus and (ii) near the peptidoglycan binding region that corresponds to the C‐terminal region of the MotB stator from E. coli. Single cell rotation assays confirmed that individual flagellar motors could rotate in up to 100 µM phenamil. Using phylogenetic logistic regression, we found correlation between natural residue variation and ion source at positions corresponding to PotB F22Y, but not at other sites. Our results demonstrate that it is not only the pore region of the stator that moderates motility in the presence of ion‐channel blockers.     

Exchange of rotor components in functioning bacterial flagellar motor

The bacterial flagellar motor is a rotary motor driven by the electrochemical potential of a coupling ion. The interaction between a rotor and stator units is thought to generate torque. The overall structure of flagellar motor has been thought to be static, however, it was recently proved that stators are exchanged in a rotating motor. Understanding the dynamics of rotor components in functioning motor is important for the clarifying of working mechanism of bacterial flagellar motor. In this study, we focused on the dynamics and the turnover of rotor components in a functioning flagellar motor. Expression systems for GFP-FliN, FliM-GFP, and GFP-FliG were constructed, and each GFP-fusion was functionally incorporated into the flagellar motor. To investigate whether the rotor components are exchanged in a rotating motor, we performed fluorescence recovery after photobleaching experiments using total internal reflection fluorescence microscopy. After photobleaching, in a tethered cell producing GFP-FliN or FliM-GFP, the recovery of fluorescence at the rotational center was observed. However, in a cell producing GFP-FliG, no recovery of fluorescence was observed. The transition phase of fluorescence intensity after full or partially photobleaching allowed the turnover of FliN subunits to be calculated as 0.0007 s⁻¹, meaning that FliN would be exchanged in tens of minutes. These novel findings indicate that a bacterial flagellar motor is not a static structure even in functioning state. This is the first report for the exchange of rotor components in a functioning bacterial flagellar motor.     

Mechanical limits of bacterial flagellar motors probed by electrorotation.

We used the technique of electrorotation to apply steadily increasing external torque to tethered cells of the bacterium Escherichia coli while continuously recording the speed of cell rotation. We found that the bacterial flagellar motor generates constant torque when rotating forward at low speeds and constant but considerably higher torque when rotating backward. At intermediate torques, the motor stalls. The torque-speed relationship is the same in both directional modes of switching motors. Motors forced backward usually break, either suddenly and irreversibly or progressively. Motors broken progressively rotate predominantly at integral multiples of a unitary speed during the course of both breaking and subsequent recovery, as expected if progressive breaking affects individual torque-generating units. Torque is reduced by the same factor at all speeds in partially broken motors, implying that the torque-speed relationship is a property of the individual torque-generating units.     

Switching of the Bacterial Flagellar Motor Near Zero Load

Flagellated bacteria, such as Escherichia coli, are able to swim up gradients of chemical attractants by modulating the direction of rotation of their flagellar motors, which spin alternately clockwise (CW) and counterclockwise (CCW). Chemotactic behavior has been studied under a variety of conditions, mostly at high loads (at large motor torques). Here, we examine motor switching at low loads. Nano-gold spheres of various sizes were attached to hooks (the flexible coupling at the base of the flagellar filament) of cells lacking flagellar filaments in media containing different concentrations of the viscous agent Ficoll. The speeds and directions of rotation of the spheres were measured. Contrary to the case at high loads, motor switching rates increased appreciably with load. Both the CW → CCW and CCW → CW switching rates increased linearly with motor torque. Evidently, the switch senses stator-rotor interactions as well as the CheY-P concentration.     

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.     

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.     

Torque-speed relationship of the flagellar rotary motor of Escherichia coli

The output of a rotary motor is characterized by its torque and speed. We measured the torque-speed relationship of the flagellar rotary motor of Escherichia coli by a new method. Small latex spheres were attached to flagellar stubs on cells fixed to the surface of a glass slide. The angular speeds of the spheres were monitored in a weak optical trap by back-focal-plane interferometry in solutions containing different concentrations of the viscous agent Ficoll. Plots of relative torque (viscosity x speed) versus speed were obtained over a wide dynamic range (up to speeds of approximately 300 Hz) at three different temperatures, 22.7, 17.7, and 15.8 degrees C. Results obtained earlier by electrorotation (, Biophys. J. 65:2201-2216) were confirmed. The motor operates in two dynamic regimes. At 23 degrees C, the torque is approximately constant up to a knee speed of nearly 200 Hz, and then it falls rapidly with speed to a zero-torque speed of approximately 350 Hz. In the low-speed regime, torque is insensitive to changes in temperature. In the high-speed regime, it decreases markedly at lower temperature. These results are consistent with models in which torque is generated by a powerstroke mechanism (, Biophys. J. 76:580-587).     

Mutations targeting the C-terminal domain of FliG can disrupt motor assembly in the Na(+)-driven flagella of Vibrio alginolyticus

The torque of the bacterial flagellar motor is generated by the rotor-stator interaction coupled with specific ion translocation through the stator channel. To produce a fully functional motor, multiple stator units must be properly incorporated around the rotor by an as yet unknown mechanism to engage the rotor-stator interactions. Here, we investigated stator assembly using a mutational approach of the Na⁺-driven polar flagellar motor of Vibrio alginolyticus, whose stator is localized at the flagellated cell pole. We mutated a rotor protein, FliG, which is located at the C ring of the basal body and closely participates in torque generation, and found that point mutation L259Q, L270R or L271P completely abolishes both motility and polar localization of the stator without affecting flagellation. Likewise, mutations V274E and L279P severely affected motility and stator assembly. Those residues are localized at the core of the globular C-terminal domain of FliG when mapped onto the crystal structure of FliG from Thermotoga maritima, which suggests that those mutations induce quite large structural alterations at the interface responsible for the rotor-stator interaction. These results show that the C-terminal domain of FliG is critical for the proper assembly of PomA/PomB stator complexes around the rotor and probably functions as the target of the stator at the rotor side.     

Low spring constant regulates P-selectin-PSGL-1 bond rupture

Forced dissociation of selectin-ligand bonds is crucial to such biological processes as leukocyte recruitment, thrombosis formation, and tumor metastasis. Although the bond rupture has been well known at high loading rate r_f (≥10² pN/s), defined as the product of spring constant k and retract velocity v, how the low r_f (<10² pN/s) or the low k regulates the bond dissociation remains unclear. Here an optical trap assay was used to quantify the bond rupture at r_f ≤ 20 pN/s with low k (∼10⁻³-10⁻² pN/nm) when P-selectin and P-selectin glycoprotein ligand 1 (PSGL-1) were respectively coupled onto two glass microbeads. Our data indicated that the bond rupture force f retained the similar values when r_f increased up to 20 pN/s. It was also found that f varied with different combinations of k and v even at the same r_f. The most probable force, f*, was enhanced with the spring constant when k < 47.0 × 10⁻³ pN/nm, indicating that the bond dissociation at low r_f was spring constant dependent and that bond rupture force depended on both the loading rate and the mechanical compliance of force transducer. These results provide new insights into understanding the P-selectin glycoprotein ligand 1 bond dissociation at low r_f or k.     

The Effect of Myofilament Compliance on Kinetics of Force Generation by Myosin Motors in Muscle

We use the inhibitor of isometric force of skeletal muscle N-benzyl-p-toluene sulfonamide (BTS) to decrease, in a dose dependent way, the number of myosin motors attached to actin during the steady isometric contraction of single fibers from frog skeletal muscle (4°C, 2.1 μm sarcomere length). In this way we can reduce the strain in the myofilament compliance during the isometric tetanus (T₀) from 3.54 nm in the control solution (T_0,NR) to ∼0.5 nm in 1 μM BTS, where T₀ is reduced to ∼0.15 T_0,NR. The quick force recovery after a step release (1-3 nm per half-sarcomere) becomes faster with the increase of BTS concentration and the decrease of T₀. The simulation of quick force recovery with a multistate model of force generation, that adapts Huxley and Simmons model to account for both the high stiffness of the myosin motor (∼3 pN/nm) and the myofilament compliance, shows that the increase in the rate of quick force recovery by BTS is explained by the reduced strain in the myofilaments, consequent to the decrease in half-sarcomere force. The model estimates that i), for the same half-sarcomere release the state transition kinetics in the myosin motor are five times faster in the absence of filament compliance than in the control; and ii), the rate of force recovery from zero to T₀ is ∼6000/s in the absence of filament compliance.     

BB0326 is responsible for the formation of periplasmic flagellar collar and assembly of the stator complex in Borrelia burgdorferi

Borrelia burgdorferi is a highly motile spirochete due to its periplasmic flagella. Unlike flagella of other bacteria, spirochetes' periplasmic flagella possess a complex structure called the collar, about which little is known in terms of function and composition. Using various approaches, we have identified a novel protein, BB0326, as a key component of the collar. We show that a peripheral portion of the collar is diminished in the Δbb0326 mutant and restored in the complemented bb0326+ cells, leading us to rename BB0326 as periplasmic flagellar collar protein A or FlcA. The ΔflcA mutant cells produced fewer, abnormally tilted and shorter flagella, as well as diminished stators, suggesting that FlcA is crucial for flagellar and stator assemblies. We provide further evidence that FlcA interacts with the stator and that this collar–stator interaction is essential for the high torque needed to power the spirochete's periplasmic flagellar motors. These observations suggest that the collar provides various important functions to the spirochete's periplasmic flagellar assembly and rotation.     

Molecular mechanism regulating myosin and cardiac functions by ELC

The essential myosin light chain (ELC) is involved in modulation of force generation of myosin motors and cardiac contraction, while its mechanism of action remains elusive. We hypothesized that ELC could modulate myosin stiffness which subsequently determines its force production and cardiac contraction. Therefore, we generated heterologous transgenic mouse (TgM) strains with cardiomyocyte-specific expression of ELC with human ventricular ELC (hVLC-1; TgM^hVLC-1) or E56G-mutated hVLC-1 (hVLC-1^E56G; TgM^E56G). hVLC-1 or hVLC-1^E56G expression in TgM was around 39% and 41%, respectively of total VLC-1. Laser trap and in vitro motility assays showed that stiffness and actin sliding velocity of myosin with hVLC-1 prepared from TgM^hVLC-1 (1.67 pN/nm and 2.3 μm/s, respectively) were significantly higher than myosin with hVLC-1^E56G prepared from TgM^E56G (1.25 pN/nm and 1.7 μm/s, respectively) or myosin with mouse VLC-1 (mVLC-1) prepared from C57/BL6 (1.41 pN/nm and 1.5 μm/s, respectively). Maximal left ventricular pressure development of isolated perfused hearts in vitro prepared from TgM^hVLC-1 (80.0 mmHg) were significantly higher than hearts from TgM^E56G (66.2 mmHg) or C57/BL6 (59.3 ± 3.9 mmHg). These findings show that ELCs decreased myosin stiffness, in vitro motility, and thereby cardiac functions in the order hVLC-1 > hVLC-1^E56G ≈ mVLC-1. They also suggest a molecular pathomechanism of hypertrophic cardiomyopathy caused by hVLC-1 mutations.     

Atomic force microscopy and force spectroscopy study of Langmuir-Blodgett films formed by heteroacid phospholipids of biological interest

Langmuir-Blodgett (LB) films of two heteroacid phospholipids of biological interest 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), as well as a mixed monolayer with χ_POPC = 0.4, were transferred onto mica in order to investigate by a combination of atomic force microscopy (AFM) and force spectroscopy (FS) their height, and particularly, their nanomechanical properties. AFM images of such monolayers extracted at 30 mN m^− 1 revealed a smooth and defect-free topography except for the POPE monolayer. Since scratching such soft monolayers in contact mode was proved unsuccessful, their molecular height was measured by means of the width of the jump present in the respective force-extension curves. While for pure POPC a small jump occurs near zero force, for the mixed monolayer with χ_POPC = 0.4 the jump occurs at ∼ 800 pN. Widths of ∼ 2 nm could be established for POPC and χ_POPC = 0.4, but not for POPE monolayer at this extracting pressure. Such different mechanical stability allowed us to directly measure the threshold area/lipid range value needed to induce mechanical stability to the monolayers. AFM imaging and FS were next applied to get further structural and mechanical insight into the POPE phase transition (LC-LC′) occurring at pressures > 36.5 mN m^− 1. This phase transition was intimately related to a sudden decrease in the area/molecule value, resulting in a jump in the force curve occurring at high force (∼ 1.72 nN). FS reveals to be the unique experimental technique able to unveil structural and nanomechanical properties for such soft phospholipid monolayers. The biological implications of the nanomechanical properties of the systems under investigation are discussed considering that the annular phospholipids region of some transmembrane proteins is enriched in POPE.