Model studies of the dynamics of bacterial flagellar motors

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.

Bacterial Vivisection: How Fluorescence-Based Imaging Techniques Shed a Light on the Inner Workings of Bacteria

The rise in fluorescence-based imaging techniques over the past 3 decades has improved the ability of researchers to scrutinize live cell biology at increased spatial and temporal resolution. In microbiology, these real-time vivisections structurally changed the view on the bacterial cell away from the "watery bag of enzymes" paradigm toward the perspective that these organisms are as complex as their eukaryotic counterparts. Capitalizing on the enormous potential of (time-lapse) fluorescence microscopy and the ever-extending pallet of corresponding probes, initial breakthroughs were made in unraveling the localization of proteins and monitoring real-time gene expression. However, later it became clear that the potential of this technique extends much further, paving the way for a focus-shift from observing single events within bacterial cells or populations to obtaining a more global picture at the intra- and intercellular level. In this review, we outline the current state of the art in fluorescence-based vivisection of bacteria and provide an overview of important case studies to exemplify how to use or combine different strategies to gain detailed information on the cell's physiology. The manuscript therefore consists of two separate (but interconnected) parts that can be read and consulted individually. The first part focuses on the fluorescent probe pallet and provides a perspective on modern methodologies for microscopy using these tools. The second section of the review takes the reader on a tour through the bacterial cell from cytoplasm to outer shell, describing strategies and methods to highlight architectural features and overall dynamics within cells.

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.

Frequent pauses in Escherichia coli flagella elongation revealed by single cell real-time fluorescence imaging

The bacterial flagellum is a large extracellular protein organelle that extrudes from the cell surface. The flagellar filament is assembled from tens of thousands of flagellin subunits that are exported through the flagellar type III secretion system. Here, we measure the growth of Escherichia coli flagella in real time and find that, although the growth rate displays large variations at similar lengths, it decays on average as flagella lengthen. By tracking single flagella, we show that the large variations in growth rate occur as a result of frequent pauses. Furthermore, different flagella on the same cell show variable growth rates with correlation. Our observations are consistent with an injection-diffusion model, and we propose that an insufficient cytoplasmic flagellin supply is responsible for the pauses in flagellar growth in E. coli.

The bacterial flagellar filament is assembled from tens of thousands of flagellin subunits that are exported by a dedicated secretion system. Here, the authors show that, on average, the growth rate of flagella in E. coli decays as flagella lengthen, with large variations due to frequent pauses.

Measurements of the Rotation of the Flagellar Motor by Bead Assay

The bacterial flagellar motor is a reversible rotary nano-machine powered by the ion flux across the cytoplasmic membrane. Each motor rotates a long helical filament that extends from the cell body at several hundreds revolutions per second. The output of the motor is characterized by its generated torque and rotational speed. The torque can be calculated as the rotational frictional drag coefficient multiplied by the angular velocity. Varieties of methods, including a bead assay, have been developed to measure the flagellar rotation rate under various load conditions on the motor. In this chapter, we describe a method to monitor the motor rotation through a position of a 1 μm bead attached to a truncated flagellar filament.

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.

Speed of the bacterial flagellar motor near zero load depends on the number of stator units

The bacterial flagellar motor (BFM) rotates hundreds of times per second to propel bacteria driven by an electrochemical ion gradient. The motor consists of a rotor 50 nm in diameter surrounded by up to 11 ion-conducting stator units, which exchange between motors and a membrane-bound pool. Measurements of the torque-speed relationship guide the development of models of the motor mechanism. In contrast to previous reports that speed near zero torque is independent of the number of stator units, we observe multiple speeds that we attribute to different numbers of units near zero torque in both Na⁺- and H⁺-driven motors. We measure the full torque-speed relationship of one and two H⁺ units in Escherichia coli by selecting the number of H⁺ units and controlling the number of Na⁺ units in hybrid motors. These experiments confirm that speed near zero torque in H⁺-driven motors increases with the stator number. We also measured 75 torque-speed curves for Na⁺-driven chimeric motors at different ion-motive force and stator number. Torque and speed were proportional to ion-motive force and number of stator units at all loads, allowing all 77 measured torque-speed curves to be collapsed onto a single curve by simple rescaling.

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.

Mannose-Binding Lectin Inhibits the Motility of Pathogenic Salmonella by Affecting the Driving Forces of Motility and the Chemotactic Response

Mannose-binding lectin (MBL) is a key pattern recognition molecule in the lectin pathway of the complement system, an important component of innate immunity. MBL functions as an opsonin which enhances the sequential immune process such as phagocytosis. We here report an inhibitory effect of MBL on the motility of pathogenic bacteria, which occurs by affecting the energy source required for motility and the signaling pathway of chemotaxis. When Salmonella cells were treated with a physiological concentration of MBL, their motile fraction and free-swimming speed decreased. Rotation assays of a single flagellum showed that the flagellar rotation rate was significantly reduced by the addition of MBL. Measurements of the intracellular pH and membrane potential revealed that MBL affected a driving force for the Salmonella flagellum, the electrochemical potential difference of protons. We also found that MBL treatment increased the reversal frequency of Salmonella flagellar rotation, which interfered with the relative positive chemotaxis toward an attractive substrate. We thus propose that the motility inhibition effect of MBL may be secondarily involved in the attack against pathogens, potentially facilitating the primary role of MBL in the complement system.

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.

Propulsion of liposomes using bacterial motors

Here we describe the utilization of flagellated bacteria as actuators to propel spherical liposomes by attaching bacteria to the liposome surface. Bacteria were stably attached to liposomes using a cross-linking antibody. The effect of the number of attached bacteria on propulsion speed was experimentally determined. The effects of bacterial propulsion on the bacteria-antibody-liposome complex were stochastic. We demonstrated that liposomal mobility increased when bacteria were attached, and the propulsion speed correlated with the number of bacteria.

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.

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.

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.

A molecular brake, not a clutch, stops the Rhodobacter sphaeroides flagellar motor

Many bacterial species swim by employing ion-driven molecular motors that power the rotation of helical filaments. Signals are transmitted to the motor from the external environment via the chemotaxis pathway. In bidirectional motors, the binding of phosphorylated CheY (CheY-P) to the motor is presumed to instigate conformational changes that result in a different rotor-stator interface, resulting in rotation in the alternative direction. Controlling when this switch occurs enables bacteria to accumulate in areas favorable for their survival. Unlike most species that swim with bidirectional motors, Rhodobacter sphaeroides employs a single stop-start flagellar motor. Here, we asked, how does the binding of CheY-P stop the motor in R. sphaeroides--using a clutch or a brake? By applying external force with viscous flow or optical tweezers, we show that the R. sphaeroides motor is stopped using a brake. The motor stops at 27-28 discrete angles, locked in place by a relatively high torque, approximately 2-3 times its stall torque.