A model for bacterial flagellar motor: free energy transduction and self-organization of rotational motion

A bacterial flagellar motor is an energy transducing molecular machine which shows some attractive characteristics. First, this motor is driven by a protonmotive force (PMF) across the membrane, two components of which, electric potential delta psi and chemical potential -(2.3RT/F)delta pH, are equivalently transduced to the mechanical work of the motor rotation. Second, a PMF threshold for rotation is observed. Third, this motor can rotate reversibly either counterclockwise (CCW) or clockwise (CW) at almost the same speed. To clarify the osmomechanical coupling of this motor, these characteristics must be explained consistently at the molecular level. In this paper, in order to allow quantitative analyses of the above characteristics, a theoretical model of a bacterial flagellar motor is constructed assuming that the torque generating sites are electrodes which can be charged by protons and that the electrostatic interaction between the electrodes generates the rotation torque. Electrode reaction reasonably derives the equivalence of delta psi and -(2.3RT/F)delta pH. In this model, rates of charging and discharging of protons are influenced by the motor rotation rate, so that the torque generating sites co-operatively work through the motor rotation. We named this kind of co-operativity among them "dynamic co-operativity" in torque generation. This co-operativity causes autocatalytic generation of motor torque and the existence of the rotation threshold. In this model, the appearance of the stable rotational states can be described by phase transition caused by the dynamic co-operativity among torque generating sites. According to this model, the flagellar motor has two stable rotational states corresponding to CCW and CW, which show the same torques. The motor selects one direction from them to rotate, and that is self-organization of rotational motion. Interpretation of the transition between the two stable rotational states as the chemotactic reversals of the flagellar motor is also discussed.     

Resolving cargo-motor-track interactions with bifocal parallax single-particle tracking

Resolving coordinated biomolecular interactions in living cellular environments is vital for understanding the mechanisms of molecular nanomachines. The conventional approach relies on localizing and tracking target biomolecules and/or subcellular organelles labeled with imaging probes. However, it is challenging to gain information on rotational dynamics, which can be more indicative of the work done by molecular motors and their dynamic binding status. Herein, a bifocal parallax single-particle tracking method using half-plane point spread functions has been developed to resolve the full-range azimuth angle (0–360°), polar angle, and three-dimensional (3D) displacement in real time under complex living cell conditions. Using this method, quantitative rotational and translational motion of the cargo in a 3D cell cytoskeleton was obtained. Not only were well-known active intracellular transport and free diffusion observed, but new interactions (tight attachment and tethered rotation) were also discovered for better interpretation of the dynamics of cargo-motor-track interactions at various types of microtubule intersections.     

Orientation and location of the finite helical axis of the equine forelimb joints

To reduce anatomically unrealistic limb postures in a virtual musculoskeletal model of a horse's forelimb, accurate knowledge on forelimb joint constraints is essential. The aim of this cadaver study is to report all orientation and position changes of the finite helical axes (FHA) as a function of joint angle for different equine forelimb joints. Five horse cadaver forelimbs with standardized cuts at the midlevel of each segment were used. Bone pins with reflective marker triads were drilled into the forelimb bones. Unless joint angles were anatomically coupled, each joint was manually moved independently in all three rotational degrees of freedom (flexion–extension, abduction–adduction, internal–external rotation). The 3D coordinates of the marker triads were recorded using a six infra-red camera system. The FHA and its orientational and positional properties were calculated and expressed against joint angle over the entire range of motion using a finite helical axis method. When coupled, joint angles and FHA were expressed in function of flexion–extension angle. Flexion–extension movement was substantial in all forelimb joints, the shoulder allowed additional considerable motion in all three rotational degrees of freedoms. The position of the FHA was constant in the fetlock and elbow and a constant orientation of the FHA was found in the shoulder. Orientation and position changes of the FHA over the entire range of motion were observed in the carpus and the interphalangeal joints. We report FHA position and orientation changes as a function of flexion–extension angle to allow for inclusion in a musculoskeletal model of a horse to minimize calculation errors caused by incorrect location of the FHA.     

Environmental modulation of M13 coat protein tryptophan fluorescence dynamics

The effects of detergent [deoxycholate (DOC) and phospholipid [dimyristoylphosphatidylcholine (DMPC)] environments on the rotational dynamics of the single tryptophan residue 26 of bacteriophage M13 coat protein have been investigated by using time-resolved single photon counting measurements of the fluorescence intensity and anisotropy decay. The total fluorescence decay of tryptophan-26 is complex but rather similar in DOC as compared to DMPC when analyzed in terms of a lifetime distribution (exponential series method). This similarity, in conjunction with the almost identical steady-state fluorescence spectra, indicates only minor differences between the tryptophan environments in DOC and DMPC. The reorientational dynamics of tryptophan-26 are dominated by slow rotation of the entire protein in both detergent and phospholipid environments. The resolved anisotropy decay in DOC can be approximated by a simple hydrodynamic model of protein/detergent micelle rotational diffusion, although the data indicative slightly greater complexity in the rotational motion. The tryptophan fluorescence anisotropy is not sensitive to protein conformational changes in DOC detected by nuclear magnetic resonance on the basis of pH independence in the range 7.5-9.1. In DMPC bilayers, restricted tryptophan motion with a correlation time of approximately 2 ns is observed together with a second very slow reorientational component. Resolution of the time constant for this slow rotation is obscured by the tryptophan fluorescence time window being too short to clearly locate its anisotropic limit. The possible contribution made by axial rotational diffusion of the protein to this slow rotational process is discussed.(ABSTRACT TRUNCATED AT 250 WORDS)     

Bacterial Tethering Analysis Reveals a “Run-Reverse-Turn” Mechanism for Pseudomonas Species Motility

We have developed a program that can accurately analyze the dynamic properties of tethered bacterial cells. The program works especially well with cells that tend to give rise to unstable rotations, such as polar-flagellated bacteria. The program has two novel components. The first dynamically adjusts the center of the cell''s rotational trajectories. The second applies piecewise linear approximation to the accumulated rotation curve to reduce noise and separate the motion of bacteria into phases. Thus, it can separate counterclockwise (CCW) and clockwise (CW) rotations distinctly and measure rotational speed accurately. Using this program, we analyzed the properties of tethered Pseudomonas aeruginosa and Pseudomonas putida cells for the first time. We found that the Pseudomonas flagellar motor spends equal time in both CCW and CW phases and that it rotates with the same speed in both phases. In addition, we discovered that the cell body can remain stationary for short periods of time, leading to the existence of a third phase of the flagellar motor which we call “pause.” In addition, P. aeruginosa cells adopt longer run lengths, fewer pause frequencies, and shorter pause durations as part of their chemotactic response. We propose that one purpose of the pause phase is to allow the cells to turn at a large angle, where we show that pause durations in free-swimming cells positively correlate with turn angle sizes. Taken together, our results suggest a new “run-reverse-turn” paradigm for polar-flagellated Pseudomonas motility that is different from the “run-and-tumble” paradigm established for peritrichous Escherichia coli.     

Rotational diffusion of cytochrome P-450 in the microsomal membrane—Evidence for a clusterlike organization from saturation transfer electron paramagnetic resonance spectroscopy

Rotational diffusion of cytochrome P-450 in rabbit liver microsomes has been studied by saturation transfer EPR spectroscopy. Sulfhydryl groups of cytochrome P-450 were selectively modified using a maleimide spin label. The effective rotational correlation time for the rotation of cytochrome P-450 was calculated to be about 480 μs which corresponds to a very strong immobilization thus evidencing protein aggregation within the membrane. The anisotropic character of the spectra indicates a nonspherical shape and/or anisotropic rotational motion of the cluster. The temperature dependence of the rotational correlation time shows a relatively sharp break at about 4 °C but only small changes above this temperature. The break at about 4 °C is probably caused by the onset of the cluster rotation. Below 4 °C the enzyme is almost immobilized. A similar complete immobilization can be achieved by treating the microsomes with glutaraldehyde.     

Anisotropic motion of cholesterol in oriented DPPC bilayers studied by quasielastic neutron scattering: the liquid-ordered phase.

Quasielastic neutron scattering (QENS) at two energy resolutions (1 and 14 microeV) was employed to study high-frequency cholesterol motion in the liquid ordered phase (lo-phase) of oriented multilayers of dipalmitoylphosphatidylcholine at three temperatures: T = 20 degrees C, T = 36 degrees C, and T = 50 degrees C. We studied two orientations of the bilayer stack with respect to the incident neutron beam. This and the two energy resolutions for each orientation allowed us to determine the cholesterol dynamics parallel to the normal of the membrane stack and in the plane of the membrane separately at two different time scales in the GHz range. We find a surprisingly high, model-independent motional anisotropy of cholesterol within the bilayer. The data analysis using explicit models of molecular motion suggests a superposition of two motions of cholesterol: an out-of-plane diffusion of the molecule parallel to the bilayer normal combined with a locally confined motion within the bilayer plane. The rather high amplitude of the out-of-plane diffusion observed at higher temperatures (T >/= 36 degrees C) strongly suggests that cholesterol can move between the opposite leaflets of the bilayer while it remains predominantly confined within its host monolayer at lower temperatures (T = 20 degrees C). The locally confined in-plane cholesterol motion is dominated by discrete, large-angle rotational jumps of the steroid body rather than a quasicontinous rotational diffusion by small angle jumps. We observe a significant increase of the rotational jump rate between T = 20 degrees C and T = 36 degrees C, whereas a further temperature increase to T = 50 degrees C leaves this rate essentially unchanged.     

Direct Measurement of Helical Cell Motion of the Spirochete Leptospira

Leptospira are spirochete bacteria distinguished by a short-pitch coiled body and intracellular flagella. Leptospira cells swim in liquid with an asymmetric morphology of the cell body; the anterior end has a long-pitch spiral shape (S-end) and the posterior end is hook-shaped (H-end). Although the S-end and the coiled cell body called the protoplasmic cylinder are thought to be responsible for propulsion together, most observations on the motion mechanism have remained qualitative. In this study, we analyzed the swimming speed and rotation rate of the S-end, protoplasmic cylinder, and H-end of individual Leptospira cells by one-sided dark-field microscopy. At various viscosities of media containing different concentrations of Ficoll, the rotation rate of the S-end and protoplasmic cylinder showed a clear correlation with the swimming speed, suggesting that these two helical parts play a central role in the motion of Leptospira. In contrast, the H-end rotation rate was unstable and showed much less correlation with the swimming speed. Forces produced by the rotation of the S-end and protoplasmic cylinder showed that these two helical parts contribute to propulsion at nearly equal magnitude. Torque generated by each part, also obtained from experimental motion parameters, indicated that the flagellar motor can generate torque >4000 pN nm, twice as large as that of Escherichia coli. Furthermore, the S-end torque was found to show a markedly larger fluctuation than the protoplasmic cylinder torque, suggesting that the unstable H-end rotation might be mechanically related to changes in the S-end rotation rate for torque balance of the entire cell. Variations in torque at the anterior and posterior ends of the Leptospira cell body could be transmitted from one end to the other through the cell body to coordinate the morphological transformations of the two ends for a rapid change in the swimming direction.     

Direct Measurement of Helical Cell Motion of the Spirochete Leptospira

Leptospira are spirochete bacteria distinguished by a short-pitch coiled body and intracellular flagella. Leptospira cells swim in liquid with an asymmetric morphology of the cell body; the anterior end has a long-pitch spiral shape (S-end) and the posterior end is hook-shaped (H-end). Although the S-end and the coiled cell body called the protoplasmic cylinder are thought to be responsible for propulsion together, most observations on the motion mechanism have remained qualitative. In this study, we analyzed the swimming speed and rotation rate of the S-end, protoplasmic cylinder, and H-end of individual Leptospira cells by one-sided dark-field microscopy. At various viscosities of media containing different concentrations of Ficoll, the rotation rate of the S-end and protoplasmic cylinder showed a clear correlation with the swimming speed, suggesting that these two helical parts play a central role in the motion of Leptospira. In contrast, the H-end rotation rate was unstable and showed much less correlation with the swimming speed. Forces produced by the rotation of the S-end and protoplasmic cylinder showed that these two helical parts contribute to propulsion at nearly equal magnitude. Torque generated by each part, also obtained from experimental motion parameters, indicated that the flagellar motor can generate torque >4000 pN nm, twice as large as that of Escherichia coli. Furthermore, the S-end torque was found to show a markedly larger fluctuation than the protoplasmic cylinder torque, suggesting that the unstable H-end rotation might be mechanically related to changes in the S-end rotation rate for torque balance of the entire cell. Variations in torque at the anterior and posterior ends of the Leptospira cell body could be transmitted from one end to the other through the cell body to coordinate the morphological transformations of the two ends for a rapid change in the swimming direction.     

Saturation transfer electron spin resonance study on the rotational diffusion of calcium- and magnesium-dependent adenosine triphosphatase in sarcoplasmic reticulum membranes.

The technique of saturation transfer electron spin resonance has been applied to study the rotational diffusion of spin-labeled Ca2+, Mg2+-dependent ATPase molecules in the membranes of sarcoplasmic reticulum vesicles. Comparison of the present data with those for spin-labeled hemoglobin undergoing isotropic rotation leads to a value of 2 X 10(-4) s for the apparent rotational correlation time at 20 degrees C for the membrane-bound protein. Consideration of the anisotropy of the Brownian rotation of the membrane-bound ATPase suggests that the true correlation time for the expected axial rotation may be somewhat smaller than the apparent value. An Arrhenius plot of the rotational motion shows a break, which is interpreted as indicating the occurrence of a conformational change of the ATPase molecule at about 15 degrees C.     

Bending and flexibility of kinetoplast DNA

We have evaluated the extent of bending at an anomalous locus in DNA restriction fragments from the kinetoplast body of Leishmania tarentolae using transient electric dichroism to measure the rate of rotational diffusion of DNA fragments in solution. We compare the rate of rotational diffusion of two fragments identical in sequence except for circular permutation, which places the bend near the center in one case and near one end of the molecule in the other. Hydrodynamic theory was used to conclude that the observed 20% difference in rotational relaxation times is a consequence of an overall average bending angle of 84 +/- 6 degrees between the end segments of the fragment that contains the bending locus near its center. If it is assumed that bending results from structural dislocations at the junctions between oligo(dA).oligo(dT) tracts and adjacent segments of B DNA, a bend angle of 9 +/- 0.5 degrees at each junction is required to explain the observations. The extent of bending is little affected by ionic conditions and is weakly dependent on temperature. Comparison of one of the anomalous fragments with an electrophoretically normal control fragment leads to the conclusion that they differ measurably in apparent stiffness, consistent with a significantly increased persistence length or contour length in the kinetoplast fragments.     

Time-dependent absorption anisotropy and rotational diffusion of proteins in membranes.

The decay of flash-induced absorption anisotropy, r(t), of a chromophore in a membrane protein is closely correlated with rotational diffusion of the protein in the membrane. We develop a theory of time-dependent absorption anisotropy which is applicable to both linear chromophores and planar chromophores which have two different absorption moments at right angles to one another. The theory treats two types of rotational diffusion of membrane proteins: one is rotation of the whole protein about the normal to the plane of the membrane, and the other is restricted wobbling of the whole or part of the protein molecule. In the former case, r(t) is determined by a rotational diffusion coefficient and an angle between the absorption moment(s) and the normal to the plane of the membrane. Rotation of rigid transmembrane proteins can be described by this treatment. In the latter case, r(t) is characterized by a wobbling diffusion coefficient and the degree of orientational constraint. This treatment may be applicable to independent wobbling of the hydrophilic part of membrane proteins. We further show that, for linear and circularly degenerate chromophores, the effect of the excitation flash intensity on r(t) can be accounted for by a constant scaling factor.     

Diffusion coefficients of segmentally flexible macromolecules with two subunits: a study of broken rods

A general treatment for the solution dynamics of segmentally flexible macromolecules having two subunits is presented. Bead modeling allows for a complete inclusion of hydrodynamic interactions in this treatment. The finite size of the beads is also considered, so that it is therefore possible to account properly for torsional motions of the subunits. Expressions for the components of the resistance matrix are derived. From them, the translational and rotational diffusion coefficients can be calculated. Distinction is made between hinged macromolecules, whose only internal motion is bending, and swivel-jointed macromolecules, for which torsions of the subunits are also allowed. Numerical results are presented for broken rods with the two types of flexibility. The effects of hydrodynamic interaction between arms of broken rods are about 25% for translation and under 10% for rotation. These findings give support to the treatments of Harvey, Wegener, and co-workers in which interactions were neglected. The rotational dynamics of hinged and swivel-jointed rods are compared. Although there are differences in the short-time behavior, the longest relaxation time is the same for the two cases. Finally, the validity of Wegener's rotational diffusion constants is discussed.     

Characterization and development of rotational behavior in Helisoma embryos: role of endogenous serotonin.

Cilia-driven rotational behavior displayed by embryos of the pond snail Helisoma trivolvis was characterized in terms of its behavioral subcomponents, developmental changes, and response to exogenous serotonin. Rotation was found to be a complex behavior characterized by four parameters; rotational direction, rotation rate, rotational surges, and periods of inactivity. These parameters all exhibited characteristic developmental changes from embryonic stage E15 through stage E30. Notably, both rotation rate and frequency of rotational surges increased from stage E15 to E25 and declined to an intermediate level by stage E30. It appeared that the developmental increase in overall rotation rate was caused primarily by an increase in surge frequency, rather than an increase in the rate of nonsurge rotation. Immersion of embryos inserotonin-containing pond water resulted in a dose-dependent, reversible increase in rotation rate as well as a dose-dependent, reversible decrease in surge frequency. The serotonin antagonist, mianserin, abolished the excitatory effect of exogenous serotonin. Furthermore, application of mianserin alone reduced rotation rate and virtually abolished rotational surges. Taken together, these pharmacological results suggest that endogenous serotonin is responsible for generating rotational surges. Given that early embryos contain only a single pair of serotonergic neurons (Goldberg and Kater, 1989) during the stages when rotational surges are expressed, these results also prompt the hypothesis that these neurons, embryonic neurons C1, act as cilioexcitatory motor neurons during embryonic development.     

Measurement of rotational motion in membranes using fluorescence recovery after photobleaching.

A method has been developed for the measurement of the rotational motion of membrane components. In this method fluorescent molecules whose transition dipole moments lie in a given direction are preferentially destroyed with a short intense burst of polarized laser radiation. The fluorescence intensity, excited with a low intensity observation beam of polarized laser radiation, changes with time as the remaining fluorescent molecules rotate. The feasibility of the method has been demonstrated in a study of the rotation of the fluorescent lipid probe, dil ([bis,-2-(N-octadecyl-3,3-dimethyl-1-benzo[b]pyrrole]-trimethincyanine iodide) incorporated into membranes composed of distearoylphosphatidylcholine (DSPC) or dipalmitoylphosphatidylcholine (DPPC) and 0.20 mol% cholesterol, below the main chain-melting transition temperatures of the phosphatidylcholines. Rotation times in the 0.6-800 s range were observed. The fluorescence recovery (or decay) curves are in satisfactory agreement with theoretical calculations.     

Characterization and development of rotational behavior in Helisoma embryos: Role of endogenous serotonin

Cilia-driven rotational behavior displayed by embryos of the pond snail Helisoma trivolvis was characterized in terms of its behavioral subcomponents, developmental changes, and response to exogenous serotonin. Rotation was found to be a complex behavior characterized by four parameters; rotational direction, rotation rate, rotational surges, and periods of inactivity. These parameters all exhibited characteristic developmental changes from embryonic stage E15 through stage E30. Notably, both rotation rate and frequency of rotational surges increased from stage E15 to E25 and declined to an intermediate level by stage E30. It appeared that the developmental increase in overall rotation rate was caused primarily by an increase in surge frequency, rather than an increase in the rate of nonsurge rotation. Immersion of embryos inserotonin-containing pond water resulted in a dose-dependent, reversible increase in rotation rate as well as a dose-dependent, reversible decrease in surge frequency. The serotonin antagonist, mianserin, abolished the excitatory effect of exogenous serotonin. Furthermore, application of mianserin alone reduced rotation rate and virtually abolished rotational surges. Taken together, these pharmacological results suggest that endogenous serotonin is responsible for generating rotational surges. Given that early embryos contain only a single pair of serotonergic neurons (Goldberg and Kater, 1989) during the stages when rotational surges are expressed, these results also prompt the hypothesis that these neurons, embryonic neurons C1, act as cilioexcitatory motor neurons during embryonic development.     

Mound-cell movement and morphogenesis in Dictyostelium

To examine the mechanisms of cell locomotion within a three-dimensional (3-D) cell mass, we have undertaken a systematic 3-D analysis of individual cell movements in the Dictyostelium mound, the first 3-D structure to form during development of the fruiting body. We used time-lapse deconvolution microscopy to examine two strains whose motion represents endpoints on the spectrum of motile behaviors that we have observed in mounds. In AX-2 mounds, cell motion is slow and trajectories are a combination of random and radial, compared to KAX-3, in which motion is fivefold faster and most trajectories are rotational. Although radial or rotational motion was correlated with the optical-density wave patterns present in each strain, we also found small but significant subpopulations of cells that moved differently from the majority, demonstrating that optical-density waves are at best insufficient to explain all motile behavior in mounds. In examining morphogenesis in these strains, we noted that AX-2 mounds tended to culminate directly to a fruiting body, whereas KAX-3 mounds first formed a migratory slug. By altering buffering conditions we could interchange these behaviors and then found that mound-cell motions also changed accordingly. This demonstrates a correlation between mound-cell motion and subsequent development, but it is not obligatory. Chimeric mounds composed of only 10% KAX-3 cells and 90% AX-2 cells exhibited rotational motion, suggesting that a diffusible molecule induces rotation, but many of these mounds still culminated directly, demonstrating that rotational motion does not always lead to slug migration. Our observations provide a detailed analysis of cell motion for two distinct modes of mound and slug formation in Dictyostelium.     

Transport properties and hydrodynamic centers of rigid macromolecules with arbitrary shapes

A general formalism, which includes translation–rotation coupling, is proposed for calculating translational and rotational transport properties, as well as intrinsic viscosities, of rigid macromolecules with an arbitrary shape. This formalism is based on Brenner's theory of translational–rotational dynamics and on methods for the calculation of hydrodynamic properties that have been already presented, and can be regarded as a generalization of the one proposed by Nakajima and Wada. The calculated transport properties depend on the origin as predicted by Brenner's theory, but in a disagreement with him, the center of resistance and the center of diffusion do not coincide. As one can define several hydrodynamic centers, which in practice turn out to be located at different points, the influence of the choice of the center on the calculated transport properties is discussed. An analysis of the translation–rotation coupling effects in translational diffusion reveals that they arise exclusively from hydrodynamic interactions and are rather small in some cases of interest. Finally, we present a study of the rotational diffusion of rigid bent rods with a fixed length-to-diameter ratio. The diffusion coefficients obtained can be useful to estimate changes with respect to a straight rod.     

Simultaneous measurement of bacterial flagellar rotation rate and swimming speed.

Swimming speeds and flagellar rotation rates of individual free-swimming Vibrio alginolyticus cells were measured simultaneously by laser dark-field microscopy at 25, 30, and 35 degrees C. A roughly linear relation between swimming speed and flagellar rotation rate was observed. The ratio of swimming speed to flagellar rotation rate was 0.113 microns, which indicated that a cell progressed by 7% of pitch of flagellar helix during one flagellar rotation. At each temperature, however, swimming speed had a tendency to saturate at high flagellar rotation rate. That is, the cell with a faster-rotating flagellum did not always swim faster. To analyze the bacterial motion, we proposed a model in which the torque characteristics of the flagellar motor were considered. The model could be analytically solved, and it qualitatively explained the experimental results. The discrepancy between the experimental and the calculated ratios of swimming speed to flagellar rotation rate was about 20%. The apparent saturation in swimming speed was considered to be caused by shorter flagella that rotated faster but produced less propelling force.     

Microsecond time scale rotation measurements of single F1-ATPase molecules

A novel method for detecting F(1)-ATPase rotation in a manner sufficiently sensitive to achieve acquisition rates with a time resolution of 2.5 micros (equivalent to 400,000 fps) is reported. This is sufficient for resolving the rate at which the gamma-subunit travels from one dwell state to another (transition time). Rotation is detected via a gold nanorod attached to the rotating gamma-subunit of an immobilized F(1)-ATPase. Variations in scattered light intensity allow precise measurement of changes in the angular position of the rod below the diffraction limit of light. Using this approach, the transition time of Escherichia coli F(1)-ATPase gamma-subunit rotation was determined to be 7.62 +/- 0.15 (standard deviation) rad/ms. The average rate-limiting dwell time between rotation events observed at the saturating substrate concentration was 8.03 ms, comparable to the observed Mg(2+)-ATPase k(cat) of 130 s(-)(1) (7.7 ms). Histograms of scattered light intensity from ATP-dependent nanorod rotation as a function of polarization angle allowed the determination of the nanorod orientation with respect to the axis of rotation and plane of polarization. This information allowed the drag coefficient to be determined, which implied that the instantaneous torque generated by F(1) was 63.3 +/- 2.9 pN nm. The high temporal resolution of rotation allowed the measurement of the instantaneous torque of F(1), resulting in direct implications for its rotational mechanism.