Mechanical limits of bacterial flagellar motors probed by electrorotation

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.

Torque-dependent remodeling of the bacterial flagellar motor

Multisubunit protein complexes are ubiquitous in biology and perform a plethora of essential functions. Most of the scientific literature treats such assemblies as static: their function is assumed to be independent of their manner of assembly, and their structure is assumed to remain intact until they are degraded. Recent observations of the bacterial flagellar motor, among others, bring these notions into question. The torque-generating stator units of the motor assemble and disassemble in response to changes in load. Here, we used electrorotation to drive tethered cells forward, which decreases motor load, and measured the resulting stator dynamics. No disassembly occurred while the torque remained high, but all of the stator units were released when the motor was spun near the zero-torque speed. When the electrorotation was turned off, so that the load was again high, stator units were recruited, increasing motor speed in a stepwise fashion. A model in which speed affects the binding rate and torque affects the free energy of bound stator units captures the observed torque-dependent stator assembly dynamics, providing a quantitative framework for the environmentally regulated self-assembly of a major macromolecular machine.

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.

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.

Experimental thermodynamics of single molecular motor

Molecular motor is a nano-sized chemical engine that converts chemical free energy to mechanical motions. Hence, the energetics is as important as kinetics in order to understand its operation principle. We review experiments to evaluate the thermodynamic properties of a rotational F1-ATPase motor (F1-motor) at a single-molecule level. We show that the F1-motor achieves 100% thermo dynamic efficiency at the stalled state. Furthermore, the motor reduces the internal irreversible heat inside the motor to almost zero and achieves a highly-efficient free energy transduction close to 100% during rotations far from quasistatic process. We discuss the mechanism of how the F1-motor achieves such a high efficiency, which highlights the remarkable property of the nano-sized engine F1-motor.

Construction and operation of a microrobot based on magnetotactic bacteria in a microfluidic chip

Magnetotactic bacteria (MTB) are capable of swimming along magnetic field lines. This unique feature renders them suitable in the development of magnetic-guided, auto-propelled microrobots to serve in target molecule separation and detection, drug delivery, or target cell screening in a microfluidic chip. The biotechnology to couple these bacteria with functional loads to form microrobots is the critical point in its application. Although an immunoreaction approach to attach functional loads to intact MTB was suggested, details on its realization were hardly mentioned. In the current paper, MTB-microrobots were constructed by attaching 2 μm diameter microbeads to marine magnetotactic ovoid MO-1 cells through immunoreactions. These microrobots were controlled using a special control and tracking system. Experimental results prove that the attachment efficiency can be improved to ∼30% via an immunoreaction. The motility of the bacteria attached with different number of loads was also assessed. The results show that MTB can transport one load at a velocity of ∼21 μm/s and still move and survive for over 30 min. The control and tracking system is fully capable of directing and monitoring the movement of the MTB-microrobots. The rotating magnetic fields can stop the microrobots by trapping them as they swim within a circular field with a controllable size. The system has potential use in chemical analyses and medical diagnoses using biochips as well as in nano/microscale transport.

Thermodynamic efficiency and mechanochemical coupling of F1-ATPase

F(1)-ATPase is a nanosized biological energy transducer working as part of F(o)F(1)-ATP synthase. Its rotary machinery transduces energy between chemical free energy and mechanical work and plays a central role in the cellular energy transduction by synthesizing most ATP in virtually all organisms. However, information about its energetics is limited compared to that of the reaction scheme. Actually, fundamental questions such as how efficiently F(1)-ATPase transduces free energy remain unanswered. Here, we demonstrated reversible rotations of isolated F(1)-ATPase in discrete 120° steps by precisely controlling both the external torque and the chemical potential of ATP hydrolysis as a model system of F(o)F(1)-ATP synthase. We found that the maximum work performed by F(1)-ATPase per 120° step is nearly equal to the thermodynamical maximum work that can be extracted from a single ATP hydrolysis under a broad range of conditions. Our results suggested a 100% free-energy transduction efficiency and a tight mechanochemical coupling of F(1)-ATPase.

Evidence for symmetry in the elementary process of bidirectional torque generation by the bacterial flagellar motor

The bacterial flagellar motor can rotate in both counterclockwise (CCW) and clockwise (CW) directions. It has been shown that the sodium ion-driven chimeric flagellar motor rotates with 26 steps per revolution, which corresponds to the number of FliG subunits that form part of the rotor ring, but the size of the backward step is smaller than the forward one. Here we report that the proton-driven flagellar motor of Salmonella also rotates with 26 steps per revolution but symmetrical in both CCW and CW directions with occasional smaller backward steps in both directions. Occasional shift in the stepping positions is also observed, suggesting the frequent exchange of stators in one of the 11-12 possible anchoring positions around the rotor. These observations indicate that the elementary process of torque generation by the cyclic association/dissociation of the stator with every FliG subunit along the circumference of the rotor is symmetric in CCW and CW rotation even though the structure of FliG is highly asymmetric and suggests a 180° rotation of a FliG domain for the rotor-stator interaction to reverse the direction of rotation.

Nonequilibrium energetics of a single F1-ATPase molecule

Molecular motors drive mechanical motions utilizing the free energy liberated from chemical reactions such as ATP hydrolysis. Although it is essential to know the efficiency of this free energy transduction, it has been a challenge due to the system's microscopic scale. Here, we evaluate the single-molecule energetics of a rotary molecular motor, F1-ATPase, by applying a recently derived nonequilibrium equality together with an electrorotation method. We show that the sum of the heat flow through the probe's rotational degree of freedom and the work against an external load is almost equal to the free energy change per a single ATP hydrolysis under various conditions. This implies that F1-ATPase works at an efficiency of nearly 100% in a thermally fluctuating environment.

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.

A programmable optical angle clamp for rotary molecular motors

Optical tweezers are widely used for experimental investigation of linear molecular motors. The rates and force dependence of steps in the mechanochemical cycle of linear motors have been probed giving detailed insight into motor mechanisms. With similar goals in mind for rotary molecular motors we present here an optical trapping system designed as an angle clamp to study the bacterial flagellar motor and F(1)-ATPase. The trap position was controlled by a digital signal processing board and a host computer via acousto-optic deflectors, the motor position via a three-dimensional piezoelectric stage and the motor angle using a pair of polystyrene beads as a handle for the optical trap. Bead-pair angles were detected using back focal plane interferometry with a resolution of up to 1 degrees , and controlled using a feedback algorithm with a precision of up to 2 degrees and a bandwidth of up to 1.6 kHz. Details of the optical trap, algorithm, and alignment procedures are given. Preliminary data showing angular control of F(1)-ATPase and angular and speed control of the bacterial flagellar motor are presented.

Stoichiometry and turnover in single, functioning membrane protein complexes

Many essential cellular processes are carried out by complex biological machines located in the cell membrane. The bacterial flagellar motor is a large membrane-spanning protein complex that functions as an ion-driven rotary motor to propel cells through liquid media. Within the motor, MotB is a component of the stator that couples ion flow to torque generation and anchors the stator to the cell wall. Here we have investigated the protein stoichiometry, dynamics and turnover of MotB with single-molecule precision in functioning bacterial flagellar motors in Escherichia coli. We monitored motor function by rotation of a tethered cell body, and simultaneously measured the number and dynamics of MotB molecules labelled with green fluorescent protein (GFP-MotB) in the motor by total internal reflection fluorescence microscopy. Counting fluorophores by the stepwise photobleaching of single GFP molecules showed that each motor contains approximately 22 copies of GFP-MotB, consistent with approximately 11 stators each containing two MotB molecules. We also observed a membrane pool of approximately 200 GFP-MotB molecules diffusing at approximately 0.008 microm2 s(-1). Fluorescence recovery after photobleaching and fluorescence loss in photobleaching showed turnover of GFP-MotB between the membrane pool and motor with a rate constant of the order of 0.04 s(-1): the dwell time of a given stator in the motor is only approximately 0.5 min. This is the first direct measurement of the number and rapid turnover of protein subunits within a functioning molecular machine.

The maximum number of torque-generating units in the flagellar motor of Escherichia coli is at least 11

Torque is generated in the rotary motor at the base of the bacterial flagellum by ion translocating stator units anchored to the peptidoglycan cell wall. Stator units are composed of the proteins MotA and MotB in proton-driven motors, and they are composed of PomA and PomB in sodium-driven motors. Strains of Escherichia coli lacking functional stator proteins produce flagella that do not rotate, and induced expression of the missing proteins leads to restoration of motor rotation in discrete speed increments, a process known as "resurrection." Early work suggested a maximum of eight units. More recent indications that WT motors may contain more than eight units, based on recovery of disrupted motors, are inconclusive. Here we demonstrate conclusively that the maximum number of units in a motor is at least 11. Using back-focal-plane interferometry of 1-mum polystyrene beads attached to flagella, we observed at least 11 distinct speed increments during resurrection with three different combinations of stator proteins in E. coli. The average torques generated by a single unit and a fully induced motor were lower than previous estimates. Speed increments at high numbers of units are smaller than those at low numbers, indicating that not all units in a fully induced motor are equivalent.

Direct observation of steps in rotation of the bacterial flagellar motor

The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel many species of swimming bacteria. The rotor is a set of rings up to 45 nm in diameter in the cytoplasmic membrane; the stator contains about ten torque-generating units anchored to the cell wall at the perimeter of the rotor. The free-energy source for the motor is an inward-directed electrochemical gradient of ions across the cytoplasmic membrane, the protonmotive force or sodium-motive force for H+-driven and Na+-driven motors, respectively. Here we demonstrate a stepping motion of a Na+-driven chimaeric flagellar motor in Escherichia coli at low sodium-motive force and with controlled expression of a small number of torque-generating units. We observe 26 steps per revolution, which is consistent with the periodicity of the ring of FliG protein, the proposed site of torque generation on the rotor. Backwards steps despite the absence of the flagellar switching protein CheY indicate a small change in free energy per step, similar to that of a single ion transit.

Rotary protein motors

Three protein motors have been unambiguously identified as rotary engines: the bacterial flagellar motor and the two motors that constitute ATP synthase (F(0)F(1) ATPase). Of these, the bacterial flagellar motor and F(0) motors derive their energy from a transmembrane ion-motive force, whereas the F(1) motor is driven by ATP hydrolysis. Here, we review the current understanding of how these protein motors convert their energy supply into a rotary torque.

Difference between forward and backward swimming speeds of the single polar-flagellated bacterium, Vibrio alginolyticus

The forward and backward swimming speeds and periods of a Vibrio alginolyticus strain that has a single polar flagellum were measured. The backward swimming speeds were 1.5 times greater than the forward ones on average and the average period of backward swimming was shorter than forward swimming. However, the swimming speed and period were not correlated. Similar results were obtained for a mutant that has a 1.6 times longer flagellum on average.

An electrostatic mechanism closely reproducing observed behavior in the bacterial flagellar motor

A mechanism coupling the transmembrane flow of protons to the rotation of the bacterial flagellum is studied. The coupling is accomplished by means of an array of tilted rows of positive and negative charges around the circumference of the rotor, which interacts with a linear array of proton binding sites in channels. We present a rigorous treatment of the electrostatic interactions using minimal assumptions. Interactions with the transition states are included, as well as proton-proton interactions in and between channels. In assigning values to the parameters of the model, experimentally determined structural characteristics of the motor have been used. According to the model, switching and pausing occur as a consequence of modest conformational changes in the rotor. In contrast to similar approaches developed earlier, this model closely reproduces a large number of experimental findings from different laboratories, including the nonlinear behavior of the torque-frequency relation in Escherichia coli, the stoichiometry of the system in Streptococcus, and the pH-dependence of swimming speed in Bacillus subtilis.

The bacterial flagella motor

The bacterial flagellum is probably the most complex organelle found in bacteria. Although the ribosome may be made of slightly more subunits, the bacterial flagellum is a more organized and complex structure. The limited number of flagella must be targeted to the correct place on the cell membrane and a structure with cytoplasmic, cytoplasmic membrane, outer membrane and extracellular components must be assembled. The process of controlled transcription and assembly is still not fully understood. Once assembled, the motor complex in the cytoplasmic membrane rotates, driven by the transmembrane ion gradient, at speeds that can reach many 100 Hz, driving the bacterial cell at several body lengths a second. This coupling of an electrochemical gradient to mechanical rotational work is another fascinating feature of the bacterial motor. A significant percentage of a bacterium's energy may be used in synthesizing the complex structure of the flagellum and driving its rotation. Although patterns of swimming may be random in uniform environments, in the natural environment, where cells are confronted with gradients of metabolites and toxins, motility is used to move bacteria towards their optimum environment for growth and survival. A sensory system therefore controls the switching frequency of the rotating flagellum. This review deals primarily with the structure and operation of the bacterial flagellum. There has been a great deal of research in this area over the past 20 years and only some of this has been included. We apologize in advance if certain areas are covered rather thinly, but hope that interested readers will look at the excellent detailed reviews on those areas cited at those points.

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

A cell of the bacterium Escherichia coli was tethered covalently to a glass coverslip by a single flagellum, and its rotation was stopped by using optical tweezers. The tweezers acted directly on the cell body or indirectly, via a trapped polystyrene bead. The torque generated by the flagellar motor was determined by measuring the displacement of the laser beam on a quadrant photodiode. The coverslip was mounted on a computer-controlled piezo-electric stage that moved the tether point in a circle around the center of the trap so that the speed of rotation of the motor could be varied. The motor generated approximately 4500 pN nm of torque at all angles, regardless of whether it was stalled, allowed to rotate very slowly forwards, or driven very slowly backwards. This argues against models of motor function in which rotation is tightly coupled to proton transit and back-transport of protons is severely limited.

Symmetries in bacterial motility

Descriptions are given of three kinds of symmetries encountered in studies of bacterial locomotion, and of the ways in which they are circumvented or broken. A bacterium swims at very low Reynolds number: it cannot propel itself using reciprocal motion (by moving through a sequence of shapes, first forward and then in reverse); cyclic motion is required. A common solution is rotation of a helical filament, either right- or left-handed. The flagellar rotary motor that drives each filament generates the same torque whether spinning clockwise or counterclockwise. This symmetry is broken by coupling to the filament. Finally, bacterial populations, grown in a nutrient medium from an inoculum placed at a single point, usually move outward in symmetric circular rings. Under certain conditions, the cells excrete a chemoattractant, and the rings break up into discrete aggregates that can display remarkable geometric order.

Torque generated by the bacterial flagellar motor close to stall

In earlier work in which electrorotation was used to apply external torque to tethered cells of the bacterium Escherichia coli, it was found that the torque required to force flagellar motors backward was considerably larger than the torque required to stop them. That is, there appeared to be substantial barrier to backward rotation. Here, we show that in most, possibly all, cases this barrier is an artifact due to angular variation of the torque applied by electrorotation, of the motor torque, or both; the motor torque appears to be independent to speed or to vary linearly with speed up to speeds of tens of Hertz, in either direction. However, motors often break catastrophically when driven backward, so backward rotation is not equivalent to forward rotation. Also, cells can rotate backward while stalled, either in randomly timed jumps of 180 degrees or very slowly and smoothly. When cells rotate slowly and smoothly backward, the motor takes several seconds to recover after electrorotation is stopped, suggesting that some form of reversible damage has occurred. These findings do not affect the interpretation of electrorotation experiments in which motors are driven rapidly forward.

Torque-generating units of the bacterial flagellar motor step independently

Measurements of the variance in rotation period of tethered cells as a function of mean rotation rate have shown that the flagellar motor of Escherichia coli is a stepping motor. Here, by measurement of the variance in rotation period as a function of the number of active torque-generating units, it is shown that each unit steps independently.