Dynamics of the bacterial flagellar motor with multiple stators

Structure and Dynamics of the Bacterial Flagellar Motor Complex

Many bacteria swim in liquids and move over solid surfaces by rotating flagella. The bacterial flagellum is a supramolecular protein complex that is composed of about 30 different flagellar proteins ranging from a few to tens of thousands. Despite structural and functional diversities of the flagella among motile bacteria, the flagellum commonly consists of a membrane-embedded rotary motor fueled by an ion motive force across the cytoplasmic membrane, a universal joint, and a helical propeller that extends several micrometers beyond the cell surface. The flagellar motor consists of a rotor and several stator units, each of which acts as a transmembrane ion channel complex that converts the ion flux through the channel into the mechanical work required for force generation. The rotor ring complex is equipped with a reversible gear that is regulated by chemotactic signal transduction pathways. As a result, bacteria can move to more desirable locations in response to environmental changes. Recent high-resolution structural analyses of flagella using cryo-electron microscopy have provided deep insights into the assembly, rotation, and directional switching mechanisms of the flagellar motor complex. In this review article, we describe the current understanding of the structure and dynamics of the bacterial flagellum.

Questioning rotary functionality in the bacterial flagellar system and proposing a murburn model for motility

Bacterial flagellar system (BFS) was the primary example of a purported 'rotary-motor' functionality in a natural assembly. This mandates the translation of a circular motion of components inside into a linear displacement of the cell body outside, which is supposedly orchestrated with the following features of the BFS: (i) A chemical/electrical differential generates proton motive force (pmf, including a trans-membrane potential, TMP), which is electro-mechanically transduced by inward movement of protons via BFS. (ii) Membrane-bound proteins of BFS serve as stators and the slender filament acts as an external propeller, culminating into a hook-rod that pierces the membrane to connect to a 'broader assembly of deterministically movable rotor'. We had disclaimed the purported pmf/TMP-based respiratory/photosynthetic physiology involving Complex V, which was also perceived as a 'rotary machine' earlier. We pointed out that the murburn redox logic was operative therein. We pursue the following similar perspectives in BFS-context: (i) Low probability for the evolutionary attainment of an ordered/synchronized teaming of about two dozen types of proteins (assembled across five-seven distinct phases) towards the singular agendum of rotary motility. (ii) Vital redox activity (not the gambit of pmf/TMP!) powers the molecular and macroscopic activities of cells, including flagella. (iii) Flagellar movement is noted even in ambiances lacking/countering the directionality mandates sought by pmf/TMP. (iv) Structural features of BFS lack component(s) capable of harnessing/achieving pmf/TMP and functional rotation. A viable murburn model for conversion of molecular/biochemical activity into macroscopic/mechanical outcomes is proposed herein for understanding BFS-assisted motility. HIGHLIGHTSThe motor-like functionalism of bacterial flagellar system (BFS) is analyzedProton/Ion-differential based powering of BFS is unviable in bacteriaUncouplers-sponsored effects were misinterpreted, resulting in a detour in BFS researchThese findings mandate new explanation for nano-bio-mechanical movements in BFSA minimalist murburn model for the bacterial flagella-aided movement is proposedCommunicated by Ramaswamy H. Sarma.

Modeling Bacterial Flagellar Motor With New Structure Information: Rotational Dynamics of Two Interacting Protein Nano-Rings

In this article, we develop a mathematical model for the rotary bacterial flagellar motor (BFM) based on the recently discovered structure of the stator complex (MotA₅MotB₂). The structure suggested that the stator also rotates. The BFM is modeled as two rotating nano-rings that interact with each other. Specifically, translocation of protons through the stator complex drives rotation of the MotA pentamer ring, which in turn drives rotation of the FliG ring in the rotor via interactions between the MotA ring of the stator and the FliG ring of the rotor. Preliminary results from the structure-informed model are consistent with the observed torque-speed relation. More importantly, the model predicts distinctive rotor and stator dynamics and their load dependence, which may be tested by future experiments. Possible approaches to verify and improve the model to further understand the molecular mechanism for torque generation in BFM are also discussed.

A physical mechanism underlying the torque generation of the bacterial flagellar motor

This study proposes a physical mechanism underlying the torque generation of a bacterial flagellar motor (BFM), in which the torque for the rotation of the rotor can be generated from impulsive forces resulting from collisions between the randomly moving stator and rotor. The torque required for the rotation of the rotor may be generated through two coexisting mechanisms: mechanism (A), in which the stator collides with the rotor, whose rotation axis fluctuates asymmetrically, generating a torque in the direction of the rod, and mechanism (B), in which physical collisions between the stator and the asymmetric [Formula: see text]and [Formula: see text] generate the torque in the direction of the rod. Mechanism (A) might be related the bidirectional rotation and the tumbling of the motion of the cell. Mechanism (B) might be related to occurrence of the steps in the time traces of the rotational angle, backward stepping or switching of the rotational direction, and the knee-shaped [Formula: see text]-[Formula: see text] relation. The above-mentioned characteristics of the rotation of BFM are reproduced in a model device designed to confirm the applicability of the proposed concept to real BFM. Moreover, a prediction of the disappearance of the knee-shaped [Formula: see text]-[Formula: see text] relation of the actual BFM at a high temperature is proposed.

Statistics of pathogenic bacteria in the search of host cells

A crucial phase in the infection process, which remains poorly understood, is the localization of suitable host cells by bacteria. It is often assumed that chemotaxis plays a key role during this phase. Here, we report a quantitative study on how Salmonella Typhimurium search for T84 human colonic epithelial cells. Combining time-lapse microscopy and mathematical modeling, we show that bacteria can be described as chiral active particles with strong active speed fluctuations, which are of biological, as opposed to thermal, origin. We observe that there exists a giant range of inter-individual variability of the bacterial exploring capacity. Furthermore, we find Salmonella Typhimurium does not exhibit biased motion towards the cells and show that the search time statistics is consistent with a random search strategy. Our results indicate that in vitro localization of host cells, and also cell infection, are random processes, not involving chemotaxis, that strongly depend on bacterial motility parameters.

Motile ghosts of the halophilic archaeon, Haloferax volcanii

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

Measurement of the Internal Frictional Drag of the Bacterial Flagellar Motor by Fluctuation Analysis

The bacterial flagellar motor generates the torque that drives the rotation of bacterial flagellar filaments. The torque it generates depends sensitively on the frictional viscous drag on the motor, which includes the frictional viscous drag on the filaments (external load) and the internal frictional viscous drag on the rotor (internal load). The internal load was roughly estimated previously by modeling it as a sphere of a radius of 20 nm rotating in a lipid of viscosity of 100 cp but was never measured experimentally. Here, we measured the internal load by fluctuation analysis of the motor velocity traces. A similar approach should be applicable to other molecular motors.

Flagella-Driven Motility of Bacteria

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

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.

The Second Messenger c-di-GMP Adjusts Motility and Promotes Surface Aggregation of Bacteria

Bacteria can use the second messenger c-di-GMP to adjust their motility in response to environmental cues. The protein YcgR, upon binding of c-di-GMP, interacts with the flagellar motor to affect the motor behavior. However, the full feature of the effects of c-di-GMP::YcgR on the flagellar motor remains unclear, and its interacting partners on the motor is still controversial. Here, we characterized the effects of c-di-GMP::YcgR on the torque-speed curve of the flagellar motor, one of the most important properties of the motor, finding that it affects the motor behavior throughout the full range of load conditions from zero to high loads by shifting the motor torque-speed curve downward. We also investigated the interacting partner on the motor through dynamical fluorescent studies, finding that c-di-GMP::YcgR mainly interacts with the motor-switch complex instead of the torque-generating units (stators). To directly test the behavioral consequence of elevated c-di-GMP levels, we measured the distribution of bacteria swimming near a surface, finding that elevated c-di-GMP levels promote bacterial aggregation on surfaces. The effects of c-di-GMP on bacterial motile behavior that we characterized here are consistent with the key role that c-di-GMP plays in the transition between motile and sedentary forms of bacterial life.

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.

Limiting (zero-load) speed of the rotary motor of Escherichia coli is independent of the number of torque-generating units

Rotation of the bacterial flagellar motor is driven by multiple torque-generating units (stator elements). The torque-generating dynamics can be understood in terms of the "duty ratio" of the stator elements, that is, the fraction of time a stator element engages with the rotor during its mechanochemical cycle. The dependence of the limiting speed (zero-load speed) of the motor on the number of stator elements is the determining test of the duty ratio, which has been controversial experimentally and theoretically over the past decade. Here, we developed a method combining laser dark-field microscopy and optical trapping to resolve this controversy. We found that the zero-load speed is independent of the number of stator elements for the bacterial flagellar motor in Escherichia coli, demonstrating that these elements have a duty ratio close to 1.

Torque, but not FliL, regulates mechanosensitive flagellar motor-function

The stator-complex in the bacterial flagellar motor is responsible for surface-sensing. It remodels in response to perturbations in viscous loads, recruiting additional stator-units as the load increases. Here, we tested a hypothesis that the amount of torque generated by each stator-unit modulates its association with the rotor. To do this, we measured stator-binding to the rotor in mutants in which motors reportedly develop lower torque compared to wildtype motors. First, we employed a strain lacking fliL. Contrary to earlier reports, measurements indicated that the torque generated by motors in the fliL strain was similar to that in the wildtype, at high loads. In these motors, stator-binding was unchanged. Next, experiments with a paralyzed strain indicated that the stator-binding was measurably weaker when motors were unable to generate torque. An analytical model was developed that incorporated an exponential dependence of the unit’s dissociation rate on the force delivered to the rotor. The model provided accurate fits to measurements of stator-rotor binding over a wide range of loads. Based on these results, we propose that the binding of each stator-unit is enhanced by the force it develops. Furthermore, FliL does not play a significant role in motor function in E. coli.

The Limiting Speed of the Bacterial Flagellar Motor

Recent experiments on the bacterial flagellar motor have shown that the structure of this nanomachine, which drives locomotion in a wide range of bacterial species, is more dynamic than previously believed. Specifically, the number of active torque-generating complexes (stators) was shown to vary across applied loads. This finding brings under scrutiny the experimental evidence reporting that limiting (zero-torque) speed is independent of the number of active stators. In this study, we propose that, contrary to previous assumptions, the maximum speed of the motor increases as additional stators are recruited. This result arises from our assumption that stators disengage from the motor for a significant portion of their mechanochemical cycles at low loads. We show that this assumption is consistent with current experimental evidence in chimeric motors, as well as with the requirement that a processive motor driving a large load via an elastic linkage must have a high duty ratio.

Resonance in the response of the bacterial flagellar motor to thermal oscillations

We have studied the dynamics of the Escherichia coli flagellar motor's angular velocity in response to thermal oscillations. We find that the oscillations' amplitude of the motor's angular velocity exhibits resonance when the temperature is oscillated at frequencies around 4 Hz. This resonance appears to be due to the existence of a natural mode of oscillation in the state of the motor, specifically in the torque generated by the motor. Natural modes of oscillation in torque generation cannot result from random fluctuations in the state of the motor. Their presence points to the existence of a coupling mechanism between the magnitude of the torque generated by the motor and the rates of transition between the different states of the motor components responsible for torque generation. The results presented here show resonance response in torque generation to external perturbations. They are explained with a simple phenomenological model, which can help future studies identify the source of the feedback mechanism between the torque and the interactions responsible for its generation. It can also help us to quantitatively estimate the strength of these interactions and how they are affected by the magnitude of the torque they generate.

Biophysical Characterization of Flagellar Motor Functions

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

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.

Mechanism and kinetics of a sodium-driven bacterial flagellar motor

The bacterial flagellar motor is a large rotary molecular machine that propels swimming bacteria, powered by a transmembrane electrochemical potential difference. It consists of an ∼50-nm rotor and up to ∼10 independent stators anchored to the cell wall. We measured torque-speed relationships of single-stator motors under 25 different combinations of electrical and chemical potential. All 25 torque-speed curves had the same concave-down shape as fully energized wild-type motors, and each stator passes at least 37 ± 2 ions per revolution. We used the results to explore the 25-dimensional parameter space of generalized kinetic models for the motor mechanism, finding 830 parameter sets consistent with the data. Analysis of these sets showed that the motor mechanism has a "powerstroke" in either ion binding or transit; ion transit is channel-like rather than carrier-like; and the rate-limiting step in the motor cycle is ion binding at low concentration, ion transit, or release at high concentration.

Coupling between switching regulation and torque generation in bacterial flagellar motor

The bacterial flagellar motor plays a crucial role in both bacterial locomotion and chemotaxis. Recent experiments reveal that the switching dynamics of the motor depend on the rotation speed of the motor, and thus the motor torque, nonmonotonically. Here we present a unified mathematical model which treats motor torque generation based on experimental torque-speed curves and the torque-dependent switching based on the conformational spread model. The model successfully reproduces the observed switching rate as a function of the rotation speed, and provides a generic physical explanation independent of most details. A stator affects the switching dynamics through two mechanisms: accelerating the conformational flipping rate of individual rotor-switching units, which contributes most when the stator works at a high torque and thus a low speed; and influencing a larger number of rotor-switching units within unit time, whose contribution is the greatest when the motor rotates at a high speed. Consequently, the switching rate shows a maximum at intermediate speed, where the above two mechanisms find an optimal output. The load-switching relation may serve as a mechanism for sensing the physical environment, similar to the chemotaxis mechanism for sensing the chemical environment. It may also coordinate the switch dynamics of motors within the same cell.

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.

Molecular motors in conservative and dissipative regimes

We present a theoretical study of a rotatory molecular motor under a conservative torque regime. We show that conservative and dissipative regimes present a different observable phenomenology. Our approach starts with a preliminary deterministic calculation of the motor cycle, which is complemented with stochastic simulations of a Langevin equation under a flashing ratchet potential. Finally, by using parameter values obtained from independent experimental information, our theoretical predictions are compared with experimental data of the F(1)-ATPase motor of the Bacillus PS3.

Steps and bumps: precision extraction of discrete states of molecular machines

We report statistical time-series analysis tools providing improvements in the rapid, precision extraction of discrete state dynamics from time traces of experimental observations of molecular machines. By building physical knowledge and statistical innovations into analysis tools, we provide techniques for estimating discrete state transitions buried in highly correlated molecular noise. We demonstrate the effectiveness of our approach on simulated and real examples of steplike rotation of the bacterial flagellar motor and the F1-ATPase enzyme. We show that our method can clearly identify molecular steps, periodicities and cascaded processes that are too weak for existing algorithms to detect, and can do so much faster than existing algorithms. Our techniques represent a step in the direction toward automated analysis of high-sample-rate, molecular-machine dynamics. Modular, open-source software that implements these techniques is provided.

Noise characteristics of the Escherichia coli rotary motor

Background

The chemotaxis pathway in the bacterium Escherichia coli allows cells to detect changes in external ligand concentration (e.g. nutrients). The pathway regulates the flagellated rotary motors and hence the cells' swimming behaviour, steering them towards more favourable environments. While the molecular components are well characterised, the motor behaviour measured by tethered cell experiments has been difficult to interpret.

Results

We study the effects of sensing and signalling noise on the motor behaviour. Specifically, we consider fluctuations stemming from ligand concentration, receptor switching between their signalling states, adaptation, modification of proteins by phosphorylation, and motor switching between its two rotational states. We develop a model which includes all signalling steps in the pathway, and discuss a simplified version, which captures the essential features of the full model. We find that the noise characteristics of the motor contain signatures from all these processes, albeit with varying magnitudes.

Conclusions

Our analysis allows us to address how cell-to-cell variation affects motor behaviour and the question of optimal pathway design. A similar comprehensive analysis can be applied to other two-component signalling pathways.

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.

Asymmetry in the clockwise and counterclockwise rotation of the bacterial flagellar motor

Cells of 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). Rotation in either direction has been thought to be symmetric and exhibit the same torques and speeds. The relationship between torque and speed is one of the most important measurable characteristics of the motor, used to distinguish specific mechanisms of motor rotation. Previous measurements of the torque-speed relationship have been made with cells lacking the response regulator CheY that spin their motors exclusively CCW. In this case, the torque declines slightly up to an intermediate speed called the "knee speed" after which it falls rapidly to zero. This result is consistent with a "power-stroke" mechanism for torque generation. Here, we measure the torque-speed relationship for cells that express large amounts of CheY and only spin their motors CW. We find that the torque decreases linearly with speed, a result remarkably different from that for CCW rotation. We obtain similar results for wild-type cells by reexamining data collected in previous work. We speculate that CCW rotation might be optimized for runs, with higher speeds increasing the ability of cells to sense spatial gradients, whereas CW rotation might be optimized for tumbles, where the object is to change cell trajectories. But why a linear torque-speed relationship might be optimum for the latter purpose we do not know.

Modeling torque versus speed, shot noise, and rotational diffusion of the bacterial flagellar motor

We present a minimal physical model for the flagellar motor that enables bacteria to swim. Our model explains the experimentally measured torque-speed relationship of the proton-driven E. coli motor at various pH and temperature conditions. In particular, the dramatic drop of torque at high rotation speeds (the "knee") is shown to arise from saturation of the proton flux. Moreover, we show that shot noise in the proton current dominates the diffusion of motor rotation at low loads. This suggests a new way to probe the discreteness of the energy source, analogous to measurements of charge quantization in superconducting tunnel junctions.

The switching dynamics of the bacterial flagellar motor

Many bacteria are propelled by flagellar motors that stochastically switch between the clockwise and counterclockwise rotation direction. Although the switching dynamics is one of their most important characteristics, the mechanisms that control it are poorly understood. We present a statistical–mechanical model of the bacterial flagellar motor. At its heart is the assumption that the rotor protein complex, which is connected to the flagellum, can exist in two conformational states and that switching between these states depends on the interactions with the stator proteins, which drive the rotor. This couples switching to rotation, making the switch sensitive to torque and speed. Another key element is that after a switch, it takes time for the load to build up, due to conformational transitions of the flagellum. This slow relaxation dynamics of the filament leads, in combination with the load dependence of the switching frequency, to a characteristic switching time, as recently observed. Hence, our model predicts that the switching dynamics is not only controlled by the chemotaxis-signaling network, but also by mechanical feedback of the flagellum.

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.