The stall torque of the bacterial flagellar motor.

The bacterial flagellar motor couples the flow of protons across the cytoplasmic membrane to the rotation of a helical flagellar filament. Using tethered cells, we have measured the stall torque required to block this rotation and compared it with the torque of the running motor over a wide range of values of proton-motive force and pH. The stall torque and the running torque vary identically: both appear to saturate at large values of the proton-motive force and both decrease at low or high pH. This suggests that up to speeds of approximately 5 Hz the operation of the motor is not limited by the mobility of its internal components or the rates of proton transfer reactions coupled to flagellar rotation.     

A model for bacterial flagellar motor: free energy transduction and self-organization of rotational motion

A bacterial flagellar motor is an energy transducing molecular machine which shows some attractive characteristics. First, this motor is driven by a protonmotive force (PMF) across the membrane, two components of which, electric potential delta psi and chemical potential -(2.3RT/F)delta pH, are equivalently transduced to the mechanical work of the motor rotation. Second, a PMF threshold for rotation is observed. Third, this motor can rotate reversibly either counterclockwise (CCW) or clockwise (CW) at almost the same speed. To clarify the osmomechanical coupling of this motor, these characteristics must be explained consistently at the molecular level. In this paper, in order to allow quantitative analyses of the above characteristics, a theoretical model of a bacterial flagellar motor is constructed assuming that the torque generating sites are electrodes which can be charged by protons and that the electrostatic interaction between the electrodes generates the rotation torque. Electrode reaction reasonably derives the equivalence of delta psi and -(2.3RT/F)delta pH. In this model, rates of charging and discharging of protons are influenced by the motor rotation rate, so that the torque generating sites co-operatively work through the motor rotation. We named this kind of co-operativity among them "dynamic co-operativity" in torque generation. This co-operativity causes autocatalytic generation of motor torque and the existence of the rotation threshold. In this model, the appearance of the stable rotational states can be described by phase transition caused by the dynamic co-operativity among torque generating sites. According to this model, the flagellar motor has two stable rotational states corresponding to CCW and CW, which show the same torques. The motor selects one direction from them to rotate, and that is self-organization of rotational motion. Interpretation of the transition between the two stable rotational states as the chemotactic reversals of the flagellar motor is also discussed.     

Single-Cell Bacterial Electrophysiology Reveals Mechanisms of Stress-Induced Damage

An electrochemical gradient of protons, or proton motive force (PMF), is at the basis of bacterial energetics. It powers vital cellular processes and defines the physiological state of the cell. Here, we use an electric circuit analogy of an Escherichia coli cell to mathematically describe the relationship between bacterial PMF, electric properties of the cell membrane, and catabolism. We combine the analogy with the use of bacterial flagellar motor as a single-cell “voltmeter” to measure cellular PMF in varied and dynamic external environments (for example, under different stresses). We find that butanol acts as an ionophore and functionally characterize membrane damage caused by the light of shorter wavelengths. Our approach coalesces noninvasive and fast single-cell voltmeter with a well-defined mathematical framework to enable quantitative bacterial electrophysiology.     

Study of the torque of the bacterial flagellar motor using a rotating electric field.

Bacterial flagella are driven by a rotary motor that is energized by an electrochemical ion gradient across the cell membrane. In this study the torque generated by the flagellar motor was measured in tethered cells of a smooth-swimming Escherichia coli strain by using rotating electric fields to determine the relationship between the torque and speed over a wide range. By measuring the electric current applied to the sample cell and combining the data obtained at different viscosities, the torque of the flagellar motor was estimated up to 55 Hz, and also at negative rotation rates. By this method we have found that the torque of the flagellar motor linearly decreases with rotation rate from negative through positive rate of rotation. In addition, the dependence of torque upon temperature was also investigated. We showed that torque at the high speeds encountered in swimming cells had a much steeper dependence on temperature that at the low speeds encountered in tethered cells. From these results, the activation energy of the proton transfer reaction in the torque-generating unit was calculated to be about 7.0 x 10(-20) J.     

Functional reconstitution of the Na(+)-driven polar flagellar motor component of Vibrio alginolyticus

The bacterial flagellar motor is a molecular machine that couples the influx of specific ions to the generation of the force necessary to drive rotation of the flagellar filament. Four integral membrane proteins, PomA, PomB, MotX, and MotY, have been suggested to be directly involved in torque generation of the Na(+)-driven polar flagellar motor of Vibrio alginolyticus. In the present study, we report the isolation of the functional component of the torque-generating unit. The purified protein complex appears to consist of PomA and PomB and contains neither MotX nor MotY. The PomA/B protein, reconstituted into proteoliposomes, catalyzed (22)Na(+) influx in response to a potassium diffusion potential. Sodium uptake was abolished by the presence of Li(+) ions and phenamil, a sodium channel blocker. This is the first demonstration of a purification and functional reconstitution of the bacterial flagellar motor component involved in torque generation. In addition, this study demonstrates that the Na(+)-driven motor component, PomA and PomB, forms the Na(+)-conducting channel.     

Simultaneous measurement of bacterial flagellar rotation rate and swimming speed.

Swimming speeds and flagellar rotation rates of individual free-swimming Vibrio alginolyticus cells were measured simultaneously by laser dark-field microscopy at 25, 30, and 35 degrees C. A roughly linear relation between swimming speed and flagellar rotation rate was observed. The ratio of swimming speed to flagellar rotation rate was 0.113 microns, which indicated that a cell progressed by 7% of pitch of flagellar helix during one flagellar rotation. At each temperature, however, swimming speed had a tendency to saturate at high flagellar rotation rate. That is, the cell with a faster-rotating flagellum did not always swim faster. To analyze the bacterial motion, we proposed a model in which the torque characteristics of the flagellar motor were considered. The model could be analytically solved, and it qualitatively explained the experimental results. The discrepancy between the experimental and the calculated ratios of swimming speed to flagellar rotation rate was about 20%. The apparent saturation in swimming speed was considered to be caused by shorter flagella that rotated faster but produced less propelling force.     

Protein dynamics and mechanisms controlling the rotational behaviour of the bacterial flagellar motor

The proteins that make up the bacterial flagellar rotary motor have recently been shown to be more dynamic than previously thought, with some key proteins exchanging with pools of proteins in the membrane/cytoplasm. It has also become clear that in addition to simply switching in response to chemosensory signals, the rotation of the bacterial flagellar motor can be slowed or stopped, using a clutch or a brake, by signals from metabolism and growth state.     

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.     

Dynamics of a tightly coupled mechanism for flagellar rotation. Bacterial motility, chemiosmotic coupling, protonmotive force.

The bacterial flagellar motor is a molecular engine that couples the flow of protons across the cytoplasmic membrane to rotation of the flagellar filament. We analyze the steady-state behavior of an explicit mechanical model in which a fixed number of protons carries the filament through one revolution. Predictions of this model are compared with experimentally determined relationships between protonmotive force, proton flux, torque, and speed. All such tightly coupled mechanisms produce the same torque when the motor is stalled but vary greatly in their behavior at high speed. The speed at zero load predicted by our model is limited by the rates of association and dissociation of protons at binding sites on the rotor and by the mobility of force generators containing transmembrane channels that interact with these sites. Our analysis suggests that more could be learned about the motor if it were driven by an externally applied torque backwards (at negative speed) or forwards at speeds greater than the zero-load speed.     

Molecular modeling of the bacterial outer membrane receptor energizer, ExbBD/TonB, based on homology with the flagellar motor, MotAB

The MotA/MotB proteins serve as the motor that drives bacterial flagellar rotation in response to the proton motive force (pmf). They have been shown to comprise a transmembrane proton pathway. The ExbB/ExbD/TonB protein complex serves to energize transport of iron siderophores and vitamin B₁₂ across the outer membrane of the Gram-negative bacterial cell using the pmf. These two protein complexes have the same topology and are homologous. Based on molecular data for the MotA/MotB proteins, we propose simple three-dimensional channel structures for both MotA/MotB and ExbB/ExbD/TonB using modeling methods. Features of the derived channels are discussed, and two possible proton transfer pathways for the ExbBD/TonB system are proposed. These analyses provide a guide for molecular studies aimed at elucidating the mechanism by which chemiosmotic energy can be transferred either between two adjacent membranes to energize outer membrane transport or to the bacterial flagellum to generate torque.     

Molecular modeling of the bacterial outer membrane receptor energizer,ExbBD/TonB,based on homology with the flagellar motor,MotAB

The MotA/MotB proteins serve as the motor that drives bacterial flagellar rotation in response to the proton motive force (pmf). They have been shown to comprise a transmembrane proton pathway. The ExbB/ExbD/TonB protein complex serves to energize transport of iron siderophores and vitamin B12 across the outer membrane of the Gram-negative bacterial cell using the pmf. These two protein complexes have the same topology and are homologous. Based on molecular data for the MotA/MotB proteins, we propose simple three-dimensional channel structures for both MotA/MotB and ExbB/ExbD/TonB using modeling methods. Features of the derived channels are discussed, and two possible proton transfer pathways for the ExbBD/TonB system are proposed. These analyses provide a guide for molecular studies aimed at elucidating the mechanism by which chemiosmotic energy can be transferred either between two adjacent membranes to energize outer membrane transport or to the bacterial flagellum to generate torque.     

Molecular Dynamics Simulations of Lipid Membrane Electroporation

The permeability of cell membranes can be transiently increased following the application of external electric fields. Theoretical approaches such as molecular modeling provide a significant insight into the processes affecting, at the molecular level, the integrity of lipid cell membranes when these are subject to voltage gradients under similar conditions as those used in experiments. This article reports on the progress made so far using such simulations to model membrane—lipid bilayer—electroporation. We first describe the methods devised to perform in silico experiments of membranes subject to nanosecond, megavolt-per-meter pulsed electric fields and of membranes subject to charge imbalance, mimicking therefore the application of low-voltage, long-duration pulses. We show then that, at the molecular level, the two types of pulses produce similar effects: provided the TM voltage these pulses create are higher than a certain threshold, hydrophilic pores stabilized by the membrane lipid headgroups form within the nanosecond time scale across the lipid core. Similarly, when the pulses are switched off, the pores collapse (close) within similar time scales. It is shown that for similar TM voltages applied, both methods induce similar electric field distributions within the membrane core. The cascade of events following the application of the pulses, and taking place at the membrane, is a direct consequence of such an electric field distribution.     

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.     

Genetic analysis of Vibrio cholerae monolayer formation reveals a key role for DeltaPsi in the transition to permanent attachment

A bacterial monolayer biofilm is a collection of cells attached to a surface but not to each other. Monolayer formation is initiated when a bacterial cell forms a transient attachment to a surface. While some transient attachments are broken, others transition into the permanent attachments that define a monolayer biofilm. In this work, we describe the results of a large-scale, microscopy-based genetic screen for Vibrio cholerae mutants that are defective in formation of a monolayer biofilm. This screen identified mutations that alter both transient and permanent attachment. Transient attachment was somewhat slower in the absence of flagellar motility. However, flagellar mutants eventually formed a robust monolayer. In contrast, in the absence of the flagellar motor, monolayer formation was severely impaired. A number of proteins that modulate the V. cholerae ion motive force were also found to affect the transition from transient to permanent attachment. Using chemicals that dissipate various components of the ion motive force, we discovered that dissipation of the membrane potential (DeltaPsi) completely blocks the transition from transient to permanent attachment. We propose that as a bacterium approaches a surface, the interaction of the flagellum with the surface leads to transient hyperpolarization of the bacterial cell membrane. This, in turn, initiates the transition to permanent attachment.     

Bacterial cell-body rotation driven by a single flagellar motor and by a bundle

Using self-trapped Escherichia coli bacteria that have intact flagellar bundles on glass surfaces, we study statistical fluctuations of cell-body rotation in a steady (unstimulated) state. These fluctuations underline direction randomization of bacterial swimming trajectories and plays a fundamental role in bacterial chemotaxis. A parallel study is also conducted using a classical rotation assay in which cell-body rotation is driven by a single flagellar motor. These investigations allow us to draw the important conclusion that during periods of counterclockwise motor rotation, which contributes to a run, all flagellar motors are strongly correlated, but during the clockwise period, which contributes to a tumble, individual motors are uncorrelated in long times. Our observation is consistent with the physical picture that formation and maintenance of a coherent flagellar bundle is provided by a single dominant flagellum in the bundle.     

Nonequivalence of membrane voltage and ion-gradient as driving forces for the bacterial flagellar motor at low load

Many bacterial species swim using flagella. The flagellar motor couples ion flow across the cytoplasmic membrane to rotation. Ion flow is driven by both a membrane potential (V(m)) and a transmembrane concentration gradient. To investigate their relation to bacterial flagellar motor function we developed a fluorescence technique to measure V(m) in single cells, using the dye tetramethyl rhodamine methyl ester. We used a convolution model to determine the relationship between fluorescence intensity in images of cells and intracellular dye concentration, and calculated V(m) using the ratio of intracellular/extracellular dye concentration. We found V(m) = -140 +/- 14 mV in Escherichia coli at external pH 7.0 (pH(ex)), decreasing to -85 +/- 10 mV at pH(ex) 5.0. We also estimated the sodium-motive force (SMF) by combining single-cell measurements of V(m) and intracellular sodium concentration. We were able to vary the SMF between -187 +/- 15 mV and -53 +/- 15 mV by varying pH(ex) in the range 7.0-5.0 and extracellular sodium concentration in the range 1-85 mM. Rotation rates for 0.35-microm- and 1-microm-diameter beads attached to Na(+)-driven chimeric flagellar motors varied linearly with V(m). For the larger beads, the two components of the SMF were equivalent, whereas for smaller beads at a given SMF, the speed increased with sodium gradient and external sodium concentration.     

Force generation in the outer hair cell of the cochlea.

The outer hair cell of the mammalian cochlea has a unique motility directly dependent on the membrane potential. Examination of the force generated by the cell is an important step in clarifying the detailed mechanism as well as the biological importance of this motility. We performed a series of experiments to measure force in which an elastic probe was attached to the cell near the cuticular plate and the cell was driven with voltage pulses delivered from a patch pipette under whole-cell voltage clamp. The axial stiffness was also determined with the same cell by stretching it with the patch pipette. The isometric force generated by the cell is around 0.1 nN/mV, somewhat smaller than 0.15 nN/mV, predicted by an area motor model based on mechanical isotropy, but larger than in earlier reports in which the membrane potential was not controlled. The axial stiffness obtained, however, was, on average, 510 nN per unit strain, about half of the value expected from the mechanical isotropy of the membrane. We extended the area motor theory incorporating mechanical orthotropy to accommodate the axial stiffness determined. The force expected from the orthotropic model was within experimental uncertainties.     

Theoretical evaluation of voltage inducement on internal membranes of biological cells exposed to electric fields

Several reports have recently been published on effects of very short and intense electric pulses on cellular organelles; in a number of cases, the cell plasma membrane appeared to be affected less than certain organelle membranes, whereas with longer and less intense pulses the opposite is the case. The effects are the consequence of the voltages induced on the membranes, and in this article we investigate the conditions under which the induced voltage on an organelle membrane could exceed its counterpart on the cell membrane. This would provide a possible explanation of the observed effects of very short pulses. Frequency-domain analysis yields an insight into the dependence of the voltage inducement on the electric and geometric parameters characterizing the cell and its vicinity. We show that at sufficiently high field frequencies, for a range of parameter values the voltage induced on the organelle membrane can indeed exceed the voltage induced on the cell membrane. Particularly, this can occur if the organelle interior is electrically more conductive than the cytosol, or if the organelle membrane has a lower dielectric permittivity than the cell membrane, and we discuss the plausibility of these conditions. Time-domain analysis is then used to determine the courses of the voltage induced on the membranes by pulses with risetimes and durations in the nanosecond range. The particularly high resting voltage in mitochondria, to which the induced voltage superimposes, could contribute to the explanation why these organelles are the primary target of many observed effects.     

Function of Protonatable Residues in the Flagellar Motor of Escherichia coli: a Critical Role for Asp 32 of MotB

Rotation of the bacterial flagellar motor is powered by a transmembrane gradient of protons or, in some species, sodium ions. The molecular mechanism of coupling between ion flow and motor rotation is not understood. The proteins most closely involved in motor rotation are MotA, MotB, and FliG. MotA and MotB are transmembrane proteins that function in transmembrane proton conduction and that are believed to form the stator. FliG is a soluble protein located on the cytoplasmic face of the rotor. Two other proteins, FliM and FliN, are known to bind to FliG and have also been suggested to be involved to some extent in torque generation. Proton (or sodium)-binding sites in the motor are likely to be important to its function and might be formed from the side chains of acidic residues. To investigate the role of acidic residues in the function of the flagellar motor, we mutated each of the conserved acidic residues in the five proteins that have been suggested to be involved in torque generation and measured the effects on motility. None of the conserved acidic residues of MotA, FliG, FliM, or FliN proved essential for torque generation. An acidic residue at position 32 of MotB did prove essential. Of 15 different substitutions studied at this position, only the conservative-replacement D32E mutant retained any function. Previous studies, together with additional data presented here, indicate that the proteins involved in motor rotation do not contain any conserved basic residues that are critical for motor rotation per se. We propose that Asp 32 of MotB functions as a proton-binding site in the bacterial flagellar motor and that no other conserved, protonatable residues function in this capacity.     

Solution structure analysis of the periplasmic region of bacterial flagellar motor stators by small angle X-ray scattering

The bacterial flagellar motor drives the rotation of helical flagellar filaments to propel bacteria through viscous media. It consists of a dynamic population of mechanosensitive stators that are embedded in the inner membrane and activate in response to external load. This entails assembly around the rotor, anchoring to the peptidoglycan layer to counteract torque from the rotor and opening of a cation channel to facilitate an influx of cations, which is converted into mechanical rotation. Stator complexes are comprised of four copies of an integral membrane A subunit and two copies of a B subunit. Each B subunit includes a C-terminal OmpA-like peptidoglycan-binding (PGB) domain. This is thought to be linked to a single N-terminal transmembrane helix by a long unstructured peptide, which allows the PGB domain to bind to the peptidoglycan layer during stator anchoring. The high-resolution crystal structures of flagellar motor PGB domains from Salmonella enterica (MotB_C2) and Vibrio alginolyticus (PomB_C5) have previously been elucidated. Here, we use small-angle X-ray scattering (SAXS). We show that unlike MotB_C2, the dimeric conformation of the PomB_C5 in solution differs to its crystal structure, and explore the functional relevance by characterising gain-of-function mutants as well as wild-type constructs of various lengths. These provide new insight into the conformational diversity of flagellar motor PGB domains and experimental verification of their overall topology.