Helix rotation model of the flagellar rotary motor

Theoretical study of a molecular turbine

We present an analytic and stochastic simulation study of a molecular engine working with a flux of particles as a turbine. We focus on the physical observables of velocity, flux, power, and efficiency. The control parameters are the external conservative force and the particle densities. We revise a simpler previous study by using a more realistic model containing multiple equidistant vanes complemented by stochastic simulations of the particles and the turbine. Here we show that the effect of the thermal fluctuations into the flux and the efficiency of these nanometric devices are relevant to the working scale of the system. The stochastic simulations of the Brownian motion of the particles and turbine support the simplified analytical calculations performed.

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.

Flagellar motility in bacteria structure and function of flagellar motor

Bacterial flagella are filamentous organelles that drive cell locomotion. They thrust cells in liquids (swimming) or on surfaces (swarming) so that cells can move toward favorable environments. At the base of each flagellum, a reversible rotary motor, which is powered by the proton- or the sodium-motive force, is embedded in the cell envelope. The motor consists of two parts: the rotating part, or rotor, that is connected to the hook and the filament, and the nonrotating part, or stator, that conducts coupling ion and is responsible for energy conversion. Intensive genetic and biochemical studies of the flagellum have been conducted in Salmonella typhimurium and Escherichia coli, and more than 50 gene products are known to be involved in flagellar assembly and function. The energy-coupling mechanism, however, is still not known. In this chapter, we survey our current knowledge of the flagellar system, based mostly on studies from Salmonella, E. coli, and marine species Vibrio alginolyticus, supplemented with distinct aspects of other bacterial species revealed by recent studies.

Flagella of Pyrococcus furiosus: multifunctional organelles, made for swimming, adhesion to various surfaces, and cell-cell contacts

Pyrococcus furiosus ("rushing fireball") was named for the ability of this archaeal coccus to rapidly swim at its optimal growth temperature, around 100 degrees C. Early electron microscopic studies identified up to 50 cell surface appendages originating from one pole of the coccus, which have been called flagella. We have analyzed these putative motility organelles and found them to be composed primarily (>95%) of a glycoprotein that is homologous to flagellins from other archaea. Using various electron microscopic techniques, we found that these flagella can aggregate into cable-like structures, forming cell-cell connections between ca. 5% of all cells during stationary growth phase. P. furiosus cells could adhere via their flagella to carbon-coated gold grids used for electron microscopic analyses, to sand grains collected from the original habitat (Porto di Levante, Vulcano, Italy), and to various other surfaces. P. furiosus grew on surfaces in biofilm-like structures, forming microcolonies with cells interconnected by flagella and adhering to the solid supports. Therefore, we concluded that P. furiosus probably uses flagella for swimming but that the cell surface appendages also enable this archaeon to form cable-like cell-cell connections and to adhere to solid surfaces.

Torque-speed relationship of the bacterial flagellar motor

Many swimming bacteria are propelled by flagellar filaments driven by a rotary motor. Each of these tiny motors can generate an impressive torque. The motor torque vs. speed relationship is considered one of the most important measurable characteristics of the motor and therefore is a major criterion for judging models proposed for the working mechanism. Here we give an explicit explanation for this torque-speed curve. The same physics also can explain certain puzzling properties of other motors.

A chimeric N-terminal Escherichia coli--C-terminal Rhodobacter sphaeroides FliG rotor protein supports bidirectional E. coli flagellar rotation and chemotaxis

Flagellate bacteria such as Escherichia coli and Salmonella enterica serovar Typhimurium typically express 5 to 12 flagellar filaments over their cell surface that rotate in clockwise (CW) and counterclockwise directions. These bacteria modulate their swimming direction towards favorable environments by biasing the direction of flagellar rotation in response to various stimuli. In contrast, Rhodobacter sphaeroides expresses a single subpolar flagellum that rotates only CW and responds tactically by a series of biased stops and starts. Rotor protein FliG transiently links the MotAB stators to the rotor, to power rotation and also has an essential function in flagellar export. In this study, we sought to determine whether the FliG protein confers directionality on flagellar motors by testing the functional properties of R. sphaeroides FliG and a chimeric FliG protein, EcRsFliG (N-terminal and central domains of E. coli FliG fused to an R. sphaeroides FliG C terminus), in an E. coli FliG null background. The EcRsFliG chimera supported flagellar synthesis and bidirectional rotation; bacteria swam and tumbled in a manner qualitatively similar to that of the wild type and showed chemotaxis to amino acids. Thus, the FliG C terminus alone does not confer the unidirectional stop-start character of the R. sphaeroides flagellar motor, and its conformation continues to support tactic, switch-protein interactions in a bidirectional motor, despite its evolutionary history in a bacterium with a unidirectional motor.

Control of speed modulation (chemokinesis) in the unidirectional rotary motor ofSinorhizobium meliloti

Swimming cells of Sinorhizobium meliloti are driven by flagella that rotate only clockwise. They can modulate rotary speed (achieve chemokinesis) and reorient the swimming path by slowing flagellar rotation. The flagellar motor is energized by proton motive force, and torque is generated by electrostatic interactions at the rotor/stator (FliG/MotA-MotB) interface. Like the Escherichia coli flagellar motor that switches between counterclockwise and clockwise rotation, the S. meliloti rotary motor depends on electrostatic interactions between conserved charged residues, namely, Arg294 and Glu302 (FliG) and Arg90, Glu98 and Glu150 (MotA). Unlike in E. coli, however, Glu150 is essential for torque generation, whereas residues Arg90 and Glu98 are crucial for the chemotaxis-controlled variation of rotary speed. Substitutions of either Arg90 or Glu98 by charge-neutralizing residues or even by their smaller, charge-maintaining isologues, lysine and aspartate, resulted in top-speed flagellar rotation and decreased potential to slow down in response to tactic signalling (chemokinesis-defective mutants). The data infer a novel mechanism of flagellar speed control by electrostatic forces acting at the rotor/stator interface. These features have been integrated into a working model of the speed-modulating rotary motor.

Concerted effects of amino acid substitutions in conserved charged residues and other residues in the cytoplasmic domain of PomA, a stator component of Na+-driven flagella

PomA is a membrane protein that is one of the essential components of the sodium-driven flagellar motor in Vibrio species. The cytoplasmic charged residues of Escherichia coli MotA, which is a PomA homolog, are believed to be required for the interaction of MotA with the C-terminal region of FliG. It was previously shown that a PomA variant with neutral substitutions in the conserved charged residues (R88A, K89A, E96Q, E97Q, and E99Q; AAQQQ) was functional. In the present study, five other conserved charged residues were replaced with neutral amino acids in the AAQQQ PomA protein. These additional substitutions did not affect the function of PomA. However, strains expressing the AAQQQ PomA variant with either an L131F or a T132M substitution, neither of which affected motor function alone, exhibited a temperature-sensitive (TS) motility phenotype. The double substitutions R88A or E96Q together with L131F were sufficient for the TS phenotype. The motility of the PomA TS mutants immediately ceased upon a temperature shift from 20 to 42 degrees C and was restored to the original level approximately 10 min after the temperature was returned to 20 degrees C. It is believed that PomA forms a channel complex with PomB. The complex formation of TS PomA and PomB did not seem to be affected by temperature. Suppressor mutations of the TS phenotype were mapped in the cytoplasmic boundaries of the transmembrane segments of PomA. We suggest that the cytoplasmic surface of PomA is changed by the amino acid substitutions and that the interaction of this surface with the FliG C-terminal region is temperature sensitive.

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.

Point mutations in transmembrane helices 2 and 3 of ExbB and TolQ affect their activities in Escherichia coli K-12

Replacement of glutamate 176, the only charged amino acid in the third transmembrane helix of ExbB, with alanine (E176A) abolished ExbB activity in all determined ExbB-dependent functions of Escherichia coli. Combination of the mutations T148A in the second transmembrane helix and T181A in the third transmembrane helix, proposed to form part of a proton pathway through ExbB, also resulted in inactive ExbB. E176 and T148 are strictly conserved in ExbB and TolQ proteins, and T181 is almost strictly conserved in ExbB, TolQ, and MotA.