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

Revisiting the protomotive vectorial motion of F0-ATPase

The elucidation of the detailed mechanism used by F₀ to convert proton gradient to torque and rotational motion presents a major puzzle despite significant biophysical and structural progress. Although the conceptual model has advanced our understanding of the working principles of such systems, it is crucial to explore the actual mechanism using structure-based models that actually reproduce a unidirectional proton-driven rotation. Our previous work used a coarse-grained (CG) model to simulate the action of F₀ However, the simulations were based on a very tentative structural model of the interaction between subunit a and subunit c. Here, we again use a CG model but with a recent cryo-EM structure of cF₁F₀ and also explore the proton path using our water flooding and protein dipole Langevin dipole semimacroscopic formalism with its linear response approximation version (PDLD/S-LRA) approaches. The simulations are done in the combined space defined by the rotational coordinate and the proton transport coordinate. The study reproduced the effect of the protomotive force on the rotation of the F₀ while establishing the electrostatic origin of this effect. Our landscape reproduces the correct unidirectionality of the synthetic direction of the F₀ rotation and shows that it reflects the combined electrostatic coupling between the proton transport path and the c-ring conformational change. This work provides guidance for further studies in other proton-driven mechanochemical systems and should lead (when combined with studies of F₁) to a complete energy transduction picture of the F₀F₁-ATPase system.

Molecular dynamics simulation of bacterial flagella

The bacterial flagellum is a biological nanomachine for the locomotion of bacteria, and is seen in organisms like Salmonella and Escherichia coli. The flagellum consists of tens of thousands of protein molecules and more than 30 different kinds of proteins. The basal body of the flagellum contains a protein export apparatus and a rotary motor that is powered by ion motive force across the cytoplasmic membrane. The filament functions as a propeller whose helicity is controlled by the direction of the torque. The hook that connects the motor and filament acts as a universal joint, transmitting torque generated by the motor to different directions. This report describes the use of molecular dynamics to study the bacterial flagellum. Molecular dynamics simulation is a powerful method that permits the investigation, at atomic resolution, of the molecular mechanisms of biomolecular systems containing many proteins and solvent. When applied to the flagellum, these studies successfully unveiled the polymorphic supercoiling and transportation mechanism of the filament, the universal joint mechanism of the hook, the ion transfer mechanism of the motor stator, the flexible nature of the transport apparatus proteins, and activation of proteins involved in chemotaxis.

Structure of the MotA/B Proton Channel

Flagellar motors utilize the motive force of protons and other ions as an energy source. To elucidate the mechanisms of ion permeation and torque generation, it is essential to investigate the structure of the motor stator complex; however, the atomic structure of the transmembrane region of the stator has not been determined experimentally. We recently constructed an atomic model structure of the transmembrane region of the Escherichia coli MotA/B stator complex based on previously published disulfide cross-linking and tryptophan scanning mutations. Dynamic permeation by hydronium ions, sodium ions, and water molecules was then observed using steered molecular dynamics simulations, and free energy profiles for ion/water permeation were calculated using umbrella sampling. We also examined the possible ratchet motion of the cytoplasmic domain induced by the protonation/deprotonation cycle of the MotB proton binding site, Asp32. In this chapter, we describe the methods used to conduct these analyses, including atomic structure modeling of the transmembrane region of the MotA/B complex; molecular dynamics simulations in equilibrium and in ion permeation processes; and ion permeation-free energy profile calculations.

Gate-controlled proton diffusion and protonation-induced ratchet motion in the stator of the bacterial flagellar motor

The proton permeation process of the stator complex MotA/B in the flagellar motor of Escherichia coli was investigated. The atomic model structure of the transmembrane part of MotA/B was constructed based on the previously published disulfide cross-linking and tryptophan scanning mutations. The dynamic permeation of hydronium/sodium ions and water molecule through the channel formed in MotA/B was observed using a steered molecular dynamics simulation. During the simulation, Leu46 of MotB acts as the gate for hydronium ion permeation, which induced the formation of water wire that may mediate the proton transfer to Asp32 on MotB. Free energy profiles for permeation were calculated by umbrella sampling. The free energy barrier for H3O(+) permeation was consistent with the proton transfer rate deduced from the flagellar rotational speed and number of protons per rotation, which suggests that the gating is the rate-limiting step. Structure and dynamics of the MotA/B with nonprotonated and protonated Asp32, Val43Met, and Val43Leu mutants in MotB were investigated using molecular dynamics simulation. A narrowing of the channel was observed in the mutants, which is consistent with the size-dependent ion selectivity. In MotA/B with the nonprotonated Asp32, the A3 segment in MotA maintained a kink whereas the protonation induced a straighter shape. Assuming that the cytoplasmic domain not included in the atomic model moves as a rigid body, the protonation/deprotonation of Asp32 is inferred to induce a ratchet motion of the cytoplasmic domain, which may be correlated to the motion of the flagellar rotor.

Realistic simulations of the coupling between the protomotive force and the mechanical rotation of the F0-ATPase

The molecular origin of the action of the F(0) proton gradient-driven rotor presents a major puzzle despite significant structural advances. Although important conceptual models have provided guidelines of how such systems should work, it has been challenging to generate a structure-based molecular model using physical principles that will consistently lead to the unidirectional proton-driven rotational motion during ATP synthesis. This work uses a coarse-grained (CG) model to simulate the energetics of the F(0)-ATPase system in the combined space defined by the rotational coordinate and the proton transport (PTR) from the periplasmic side (P) to the cytoplasmic side (N). The model establishes the molecular origin of the rotation, showing that this effect is due to asymmetry in the energetics of the proton path rather than only the asymmetry of the interaction of the Asp on the c-ring helices and Arg on the subunit-a. The simulation provides a clear conceptual background for further exploration of the electrostatic basis of proton-driven mechanochemical systems.

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.

Dynamics of the bacterial flagellar motor with multiple stators

The bacterial flagellar motor drives the rotation of flagellar filaments and enables many species of bacteria to swim. Torque is generated by interaction of stator units, anchored to the peptidoglycan cell wall, with the rotor. Recent experiments [Yuan J, Berg HC (2008) Proc Natl Acad Sci USA 105:1182-1185] show that at near-zero load the speed of the motor is independent of the number of stators. Here, we introduce a mathematical model of the motor dynamics that explains this behavior based on a general assumption that the stepping rate of a stator depends on the torque exerted by the stator on the rotor. We find that the motor dynamics can be characterized by two timescales: the moving-time interval for the mechanical rotation of the rotor and the waiting-time interval determined by the chemical transitions of the stators. We show that these two timescales depend differently on the load, and that their cross-over provides the microscopic explanation for the existence of two regimes in the torque-speed curves observed experimentally. We also analyze the speed fluctuation for a single motor by using our model. We show that the motion is smoothed by having more stator units. However, the mechanism for such fluctuation reduction is different depending on the load. We predict that the speed fluctuation is determined by the number of steps per revolution only at low load and is controlled by external noise for high load. Our model can be generalized to study other molecular motor systems with multiple power-generating units.

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.

Proposed model for the flagellar rotary motor

Flagellated bacteria swim by rotating helical filaments driven by motors embedded in the cell wall and cytoplasmic membrane. A model is proposed to explain the mechanism of the motor. The protons passing through the channels induce a strong electric field in Mot molecules. This field originates an impulse force to cause the flagellar rotation if the following conditions are fulfilled: (a) Mot molecules have a spontaneous electric polarization. (b) The lipid bilayers are viscoelastic. (c) There is a delay of deformation in response to stress in Mot molecules. The conclusions driven from the model are in agreement with the following experimental observations, denoting the flagellar rotation velocity as omega. (1) The torque is practically constant independent of omega from 0 to a critical value omega(cr) and then decreases sharply. (2) When omega is smaller than omega(cr), the torque varies little with temperature. (3) The critical velocity omega(cr) shifts to lower speed at lower temperatures. (4) Where omega is larger than omega(cr), declining of the torque steepens at lower temperatures. (5) When omega is smaller than omega(cr), one revolution of the flagellar rotation consists of a constant number of steps. (6) When omega is smaller than omega(cr), omega is proportional to the transmembrane potential difference. (7) The stator produces constant torque even when the stator is rotated relative to the rotor by external forces. (8) How the flagellar rotation velocity changes when the direction of the proton passage is reversed. (9) The motor has a switch that reverses the sense of the flagelllar rotation with the same absolute value of torque.

A kinetic and stochastic analysis of crossbridge-type stepping mechanisms in rotary molecular motors

The bacterial flagellar motor is generally supposed to be a stepping mechanism. The main evidence for this is based on a fluctuation analysis of experiments with tethered bacteria in which rotation frequency was varied by applying an external torque: the variance in time taken for a fixed number of revolutions was found to be essentially proportional to the inverse square of the frequency. This behavior was shown to characterize a Poissonian stepper. Here we present a rigorous kinetic and stochastic analysis of elastic crossbridge stepping in tethered bacteria. We demonstrate that Poissonian stepping is a virtually unachievable limit. To the extent that a system may approach Poissonian stepping it cannot be influenced by an externally applied torque; stepping mechanisms capable of being so influenced are necessarily non-Poissonian and exhibit an approximately inverse cubic dependence. This conclusion applies whatever the torsional characteristics of the tether may be, and contrary to claims, no perceptible relaxation of the tether following each step is found. Furthermore, the inverse square dependence is a necessary but not sufficient condition for Poissonian stepping, since a nonstepping mechanism, which closely reproduces most experimental data, also fulfills this condition. Hence the inference that crossbridge-type stepping occurs is not justified.

Molecular machines

Molecular machines are tiny energy conversion devices on the molecular-size scale. Whether naturally occurring or synthetic, these machines are generally more efficient than their macroscale counterparts. They have their own mechanochemistry, dynamics, workspace, and usability and are composed of nature's building blocks: namely proteins, DNA, and other compounds, built atom by atom. With modern scientific capabilities it has become possible to create synthetic molecular devices and interface them with each other. Countless such machines exist in nature, and it is possible to build artificial ones by mimicking nature. Here we review some of the known molecular machines, their structures, features, and characteristics. We also look at certain devices in their early development stages, as well as their future applications and challenges.

Forced rotation of Na+-driven flagellar motor in a coupling ion-free environment

Rotational characteristics of Na+-driven flagellar motor in the presence and absence of coupling ion were analyzed by electrorotation method. The motor rotated spontaneously in the presence of Na+, and the rotation accelerated or decelerated following the direction of the applied external torque. The spontaneous motor rotation was inhibited by removal of external Na+, however, the motor could be forcibly rotated by relatively small external torque applied by the electrorotation apparatus. The observed characteristic of the motor was completely different from that of ATP-driven motor systems, which form rigor bond when their energy source, ATP, is absent. The internal resistance of the flagellar motor increased significantly when the coupling ion could not access the inside of the motor, suggesting that the interaction between the rotor and the stator is changed by the binding of the coupling ion to the internal sites of the motor.

The bacterial flagellar motor: structure and function of a complex molecular machine

The bacterial flagellar motor harnesses ion flow to drive rotary motion, at speeds reaching 100000 rpm and with apparently tight coupling. The functional properties of the motor are quite well understood, but its molecular mechanism remains unknown. Studies of motor physiology, together with mutational and biochemical studies of the components, place significant constraints on the mechanism. Rotation is probably driven by conformational changes in membrane-protein complexes that form the stator. These conformational changes occur as protons move on and off a critical aspartate residue in the stator protein MotB, and the resulting forces are applied to the rotor protein FliG. The bacterial flagellum is a complex structure built from about two dozen proteins. Its construction requires an apparatus at the base that exports many flagellar components to their sites of installation by way of an axial channel through the structure. The sequence of events in assembly is understood in general terms, but not yet at the molecular level. A fuller understanding of motor rotation and flagellar assembly will require more data on the structures and organization of the constituent proteins.

Helix rotation model of the flagellar rotary motor

A new model of the flagellar motor is proposed that is based on established dynamics of the KcsA potassium ion channel and on known genetic, biochemical, and biophysical facts, which accounts for the mechanics of torque generation, force transmission, and reversals of motor rotation. It predicts that proton (or in some species sodium ion) flow generates short, reversible helix rotations of the MotA-MotB channel complex (the stator) that are transmitted by Coulomb forces to the FliG segments at the rotor surface. Channels are arranged as symmetric pairs, S and T, that swing back and forth in synchrony. S and T alternate in attaching to the rotor, so that force transmission proceeds in steps. The sense of motor rotation can be readily reversed by conformationally switching the position of charged groups on the rotor so that they interact with the stator during the reverse rather than forward strokes. An elastic device accounts for the observed smoothness of rotation and a prolonged attachment of the torque generators to the rotor, i.e., a high duty ratio of each torque-generating unit.

Flagellar movement driven by proton translocation

The bacterial flagellar motor couples ion flow to rotary motion at high speed and with apparently fixed stoichiometry. The functional properties of the motor are quite well understood, but its molecular mechanism remains unknown. Recent studies of motor physiology, coupled with mutational and biochemical studies of the components, put significant constraints on the mechanism. Rotation is probably driven by conformational changes in membrane-protein complexes that form the stator. These conformational changes occur as protons move on and off a critical Asp residue in the stator protein MotB, and the resulting forces are applied to the rotor protein FliG.

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.

Bacterial flagellar motor and H(+)/ATP synthase: two proton-driven rotary molecular devices with different functions

Both the bacterial flagellar motor and the H(+)/ATP synthase are membrane-bound macromolecular complexes in which the movement of protons through channels across the membrane is coupled to the rotation of a part of the complex around an axis perpendicular to the membrane. Despite this similarity, the two devices are designed for quite different functions. The flagellar motor is responsible for a practically smooth rotation of the flagellar filament in order to propel the cell. Smooth rotation is not essential for the H(+)/ATP synthase, which accumulates torque by twisting a rod-shaped structure. Possible mechanisms for generating torque in the two devices are presented, based on the models which have been proposed. The performances of the various mechanisms are discussed.

Changing the direction of flagellar rotation in bacteria by modulating the ratio between the rotational states of the switch protein FliM

One of the major questions in bacterial chemotaxis is how the switch, which controls the direction of flagellar rotation, functions. It is well established that binding of the signaling molecule CheY to the switch protein FliM shifts the rotation from the default direction, counterclockwise, to clockwise. How this shift is done is still a mystery. Our aim in this study was to determine the correlation between the fraction of FliM molecules in the clockwise state (i.e. occupied by CheY) and the probability of clockwise rotation. For this purpose we gradually expressed, from a plasmid, a clockwise FliM mutant protein in cells that express, from the chromosome, wild-type FliM but no chemotaxis proteins. We verified that plasmid-borne FliM exchanges chromosomal FliM in the switch. Surprisingly, a substantial clockwise probability was not obtained before the large majority of the FliM molecules in the switch were clockwise molecules. Thereafter, the rise in clockwise probability was very steep. These results suggest that an increase in the clockwise probability requires a high level of FliM occupancy by CheY approximately P. They further suggest that the steep increase in clockwise rotation upon increasing CheY levels, reported in several studies, is due, at least in part, to cooperativity of post-binding interactions within the switch. We also carried out the inverse experiment, in which wild-type FliM was gradually expressed in a background of a clockwise fliM mutant. In this case, the level of the clockwise mutant protein, required for establishing a certain clockwise probability, was lower than in the original experiment. If our system (in which the ratio between the rotational states of FliM in the switch is established by slow exchange) and the native system (in which the ratio is established by fast changes in FliM occupancy) are comparable, the results suggest that hysteresis is involved in the switch function. Such a situation might reflect a damping mechanism, which prevents a situation in which fluctuations in the phosphorylation level of CheY throw the switch from one direction of rotation to the other.

What determines the initiation of the heartbeat?

The origin of the heartbeat in the sino-atrial (SA) node is usually thought to arise from the sequential activation of a variety of ionic currents in pacemaker cells (Irisawa et al. 1993). Recently, the possibility has been considered that heart rate might be influenced by transient changes in cytosolic Ca2+. Rubenstein & Lipsius (1989) demonstrated that in cat subsidiary pacemaker cells the late phase of diastolic depolarization was slowed in the presence of ryanodine to selectively inhibit Ca2+ release from the sarcoplasmic reticulum (SR). Primary pacemaker cells also have a SR-dependence of cardiac pacemaking since the rate of beating of guinea-pig SA node/atrial preparations was slowed in the presence of either ryanodine or cyclopiazonic acid (an inhibitor of the SR Ca2+-ATPase). The reduction in rate was associated with changes in action potential characteristics recorded intracellularly (Rigg & Terrar, 1996). The role of Ca2+ release from the SR in influencing pacemaker rate appears to be a common mechanism in many types of pacemaking tissue since the rate reducing effects of ryanodine have been observed in other mammalian cells (rabbit SA, e.g. Hata et al. 1996; and atrioventricular node, Hancox et al. 1994) and in amphibian pacemaker cells (Ju & Allen, 1998).