Single Molecule

Development of a Single Molecule Assay to Measure F₁-g Subunit Rotation.

We have also successfully completed the aim to improve the single molecule γ subunit rotation assay to enable an investigation of the mechanism of ATPase-dependent rotation. When this aim was proposed, single molecule g subunit rotation was measured via a 3000 nm fluorescent actin filament [1]. An accurate measurement of rotation rate was impossible because viscous drag on the actin was rate limiting, it was difficult to control the length of the actin filament that attached to the g subunit, and photobleaching of the fluorophores made it difficult to observe the rotation for more than short time periods. Rotation was observed in only 1% of the F₁ molecules examined.

Weeks after our project was funded, a significant improvement in the assay was reported that substituted the actin filament with a 40 nm diameter gold sphere [2]. Viscous drag no longer limited rotation rate when spheres (or sphere dimers) smaller than 105 nm were used such that the observed rotation rate was due to the rate limiting step of F₁. Since 40 nm gold spheres efficiently scatter green light, observation of rotation could be made without the need of fluorophores that photobleach. Measurements made with this assay revealed that the TF₁g subunit rotates about 90º upon Mg²⁺ATP binding, followed by a 2 ms pause that corresponds to the rate-limiting step in the reaction, and a 30º rotation step to complete a catalytic event. These measurements make a major contribution to the understanding of the mechanism of the F₁-ATPase. However, this assay is still inadequate to determine the stepwise mechanism in which ATP binding, hydrolysis, and product release contribute to the generation of rotational motion of the g subunit. Rotation data collected as fast as 8000 frames per second (fastest on record) were still too slow to resolve the g subunit rotation rate (sweep time). Consequently, this assay was only able to measure the dwell times (pauses) that occur between rotation events. The rotational substeps were revised from 90º and 30º to 80º and 40º, respectively, upon reevaluation using 1000 nm polystyrene spheres [3].

To measure the rotational position of the g subunit as a function of time, the centroid of the visible light scattered by the 40nm or 1000nm spheres was determined in each frame of the movie which was displaced from the axis of rotation because the rotation of the g subunit is eccentric (44). The eccentricity of the g subunit rotation is no more than 5 nm such that the rotation of many F₁ molecules may not be visible by this method. Using this method, typically 1% of F₁ molecules are observed to rotate such that it is difficult to know if the molecules observed are representative of the population of F₁ as a whole.

In summary, the challenges in developing a suitable single molecule rotation assay were to find: (i) a probe small enough such that the observed rate of rotation represents the rate limitations of the enzyme and not the viscous drag of the probe; (ii) a probe bright enough to be observable when data are collected at very high frame rates, and that does not depend on fluorophores that could photobleach; (iii) a probe that provides a sensitive measure of the rotational position of the g subunit that does not depend on the physical displacement of the probe; (iv) a detection system capable of recording the rotation at speeds of 100,000 frames per second, thereby providing time resolution of rotational events on the order of microseconds; and (v) a detection system that can accumulate rotation data over a span of minutes. An additional goal was to improve the assay so that a larger fraction of the F₁ molecules are observed to rotate, to be certain that the observed rotation was characteristic of the enzyme rather than an anomaly.

We have developed four technologies to achieve these goals that include: (i) making gold nanorods and developing the conditions for their use as a probe of rotation; (ii) flattening and coating cover slip surfaces to improve consistency of the rotation assay; (iii) devising and building a detector that can measure rotation of the gold nanorod with a time resolution sufficient for the rotation of the F₁ g subunit with high signal to noise; and (iv) software development to extract the time constants of the dwells and the sweep time of rotation.

Use of Gold Nanorods to Probe g Subunit Rotation. Due to the difficulty determining rotational position of a nanosphere as described above, we substituted gold spheres for gold nanorods with approximate dimensions of 40 nm x 80 nm. The size of the rods is still below the threshold where viscous drag limits rotation rate such that measured rates are due to F₁. Due to surface plasmon resonance, the long and short axes of the nanorods scatter red and green light, respectively. This efficient light scattering property allows them to be easily observed with dark field microscopy in which the incident light passes through the sample at an oblique angle and is stopped by an iris if it does not interact with the nanorod. Only the light scattered by the gold nanorod is observed, thereby eliminating the need for fluorophores that can photobleach.

The color that the gold nanorod appears changes as a function of the angle of the rod to the plane of polarization .

Click Here to see a movie of a field of view of rods.

Click Here to see a movie of a single rod.

Nanorods also have ideal optical properties for use in determining the rotational position of the g subunit. We found that the scattered light intensity from a nanorod observed through a polarizing filter depends on the angle between the nanorod axis and the filter because light is scattered most efficiently along each axis of the rod. Thus, when the long axis of the rod is parallel to the plane of polarization, the intensity of the scattered red light is maximal while that of the green light is minimal. Similarly, the intensities of the scattered red and green light are reversed when the long axis of the nanorod is perpendicular to the plane of polarization. We determined the intensities of red and green light scattered from individual immobilized gold nanorods as a function of the polarization angle under the same conditions used to record ATP-dependent rotation of a nanorod attached to the F₁-g subunit. Under these conditions the intensity profiles of the red and green light follow out of phase sine curves.

Electron micrograph of a preparation of gold nanorods used in rotation assays.

Consequently, the relative intensity of the red or green light scattered from the nanorod probe serves as a sensitive measure of the rotational position of the g subunit. ATP-driven g subunit rotation using a gold nanorod as a probe is then observed as an oscillation in the intensities of red and green light when viewed through a polarizing filter. Simply stated, the nanorod appears to blink red and green when rotating. This method allows measurements below the resolution of the wavelength of light because it does not depend upon physical displacement of the probe due to the eccentricity of rotation. The fraction of ATPase-dependent rotating rods varies among experiments, but has been observed as high as 35%. This increase in the fraction of F₁ observed to rotate was made with the additional improvements described below.

Gold nanorods are not commercially available, and procedures to make them are still being developed to manipulate them [4]. To prepare nanorods, 30 nm spheres are first “grown” from HAuCl₄ under reducing conditions that form elemental gold. The elemental gold is treated with a detergent, CTAB, that elongates the spheres into rods. The yield of the first published procedures was about 30% rods with significant variability in the rod length [5]. The low yield of rods reduced the number of F₁ molecules that could be examined for rotation to 30%. The wavelength of light scattered by the nanorod is a function of rod length as described by Mie theory [6]. Thus, longer rods scattered light at wavelengths in the infrared, too long to be detected, further limiting the number of F₁ molecules that could be examined.

We can now prepare gold nanorods with 100% yield and a narrow length distribution (Figure 8). We can control the length of the nanorods so that the wavelength of light scattered by the rod is optimized to the microscope light source and the detector used to record rotation. These procedures significantly increase the fraction of F₁ molecules that can be observed to rotate. In addition, the signal to noise of the measurement is increased since the intensity of light scattered from each nanorod and detected has been increased substantially allowing rotation data to be collected with higher time resolution.

(A) Nonspecific binding of freshly made avidinated gold after 5 minute incubation. (B) Clumping of 1 week old avidinated gold. (C) Nonspecific binding of BSA treated avidinated gold. (D) Specifically bound BSA treated gold to F1.

The CTAB used to promote elongation of nanospheres into rods is also required as a coating to prevent the gold in the nanorods from dispersing. This detergent is also a potent inhibitor of F₁-ATPase activity at concentrations needed to stabilize the nanorods. We developed procedures to replace the CTAB coating on the nanorods with avidin so that the CTAB can be removed before the nanorods come in contact with F₁. The avidin coating is also capable of binding with very high affinity to the g subunit of F₁ that has been biotinylated in a location optimal for nanorod attachment.

Although nanorods prepared in this manner can be used for rotation assays, within hours of their preparation they become extremely sticky (Figure 9A) resulting in the irreversible nonspecific binding of nanorods in large numbers directly to the coverslip and causing the nanorods to clump together (Figure 9B). Thus it was difficult to locate nanorods attached to F₁ that were separated far enough from other rods to prevent

Atomic Force Microscopy of (A) untreated cover slips, left, and treated, right. (B) F1 on the surface shown on the mm scale.

clumping and allow rotation. We developed a procedure in which the avidin-coated nanorods were given a second protein coat that virtually eliminated both the clumping and nonspecific binding of the rods to the coverslip (Figure 9C). This increased the fraction of F₁ molecules observed to rotate during an assay dramatically (Figure 1D).

b. Development of Ni-coated Coverslips for Use in Rotation Assays. To attach Histidine-tagged F₁ to the coverslip, the coverslip must be silanated with a derivative of NTA that coordinates nickel. Although commercially available, the number of F₁ molecules that rotate is low with these coverslips is low. Using atomic force microscopy to examine the surface of these coverslips we found crevices large enough to engulf an F₁ molecule such that the nanorod is unable either to attach or rotate (Figure 10A). We have now developed a procedure to flatten glass coverslips (Figure 10A), and then coat them with Ni-NTA. As a result,F1 moleculres can be clearly resolved on the cover slip by AFM (Figure 10B). This contributes significantly to the fraction of F₁ molecules observed to rotate upon addition of Mg²⁺ATP.

c. Detection System Development and Data Analysis.

Microsecond Time Scale Rotation Measurements of Single F₁-ATPase Molecules

David Spetzler, Justin York, Douglas Daniel, Raimund Fromme, David Lowry, and Wayne Frasch*

Biochemistry, ASAP Article 10.1021/bi052363n S0006-2960(05)02363-9
Web Release Date: February 17, 2006

The F₁F_o-ATP synthase couples the energy provided by a transmembrane proton gradient to the production of ATP from ADP and phosphate. The intrinsic membrane complex of ab₂c_10-14 subunits known as F_o¹ functions as a proton channel, and the F₁ peripheral membrane complex of ₃₃ subunits contains one site for ATP synthesis and/or hydrolysis per heterodimer. When F₁ is purified from F_o and the membrane, it retains the ability to hydrolyze ATP (1-3). There are three catalytic sites which are coupled such that the binding of the substrate to one site induces conformational changes that result in product release at an adjacent site. The three heterodimers form a ring around the -subunit that rotates in response to ATP hydrolysis activity (4, 5).

Visualization of -subunit rotation of single F₁ molecules fixed to a coverslip can be observed by microscopy (6, 7). Rotation appears as discrete 120 steps for each Mg²⁺-ATP consumed at saturating Mg²⁺-ATP concentrations. When the substrate is limiting, each 120 step is resolved into 80 and 40 substeps that correspond to ATP binding and the rate-limiting step, respectively (6, 8). Binding of Mg²⁺-ATP to the empty catalytic site was found to initiate a 80 rotation of the -subunit in F₁ from the thermophilic bacteria PS3 (9). After a 2 ms pause thought to involve product release, a 40 rotation of the -subunit completes the cycle for a total of 120. The kinetics of the 2 ms pause are consistent with the presence of sequential 1 ms steps which suggest the existence of a rate-limiting intermediate state that follows the transition state (10, 11). Recent experiments may indicate that the completion of a catalytic cycle at any one site involves the rotation of the -subunit by 240 (6, 12-15).

The rotation of F₁-ATPase has been observed using large actin filaments, where the rate is dependent upon the viscous drag of the reporter group, not the intrinsic mechanism of the enzyme (16, 17). It has been reported that the viscous drag of 40 nm diameter gold nanospheres does not limit the rate of rotation (6). These probes have been used to measure the pause or dwell time between rotation events via determination of the centroid of light scattered from the probe. However, under these conditions, attempts to measure the rate of rotation between dwells with recording speeds as high as 8000 fps were insufficient for measuring the velocity of the -subunit as it rotates from one dwell to the next. We now report a method for recording F₁-ATPase -subunit rotation with a time resolution of 2.5 s (equivalent to 400 000 fps), which resolves the velocity of the -subunit as it rotates between dwells.

Experimental Procedures

Escherichia coli F₁-ATPase was purified from strain XL10 (18). This strain was mutated to contain a His₆ on the N-terminus of the -subunit and S193C for biotinylation. Biotinylation was performed by adding an equimolar amount of biotin-maleimide (Pierce) to F₁, followed by shaking at room temperature for 1 h. Unreacted biotin-maleimide was removed after the solution was run through a protein desalting column (Pierce). Reaction specificity to the -subunit was verified by SDS-PAGE with a fluorescent maleimide. The activity of the enzyme was confirmed using the pyruvate kinase coupled assay (18-20).

Gold nanorods were prepared by the reduction of HAuCl₄ to form 4 nm seeds (21). The seeds were grown into gold nanorods in the presence of the surfactant CTAB and additional HAuCl₄. The length and width of the gold rods were determined to be 75.08 ± 4.1 and 34.7 ± 2.2 nm, respectively (N = 30), using transmission electron microscopy. Avidination of gold rods began with an exchange of the gold rod buffer (100 mM CTAB) with 1 mM CTAB. Neutravidin was added directly to the nanorod/CTAB solution to a final concentration of 40 g/mL. The mixture was shaken at room temperature for 1 h and could be stored at room temperature for up to 1 week. Successful avidination was verified by observing a 4-10 nm red shift in the absorbance spectrum of the gold nanorods (Figure 1). This red shift was attributed to a change in the dielectric environment of the gold nanorod surface (22). For use in the rotation assay, avidinated gold nanorods were further diluted 1:10 in F₁ buffer [50 mM Tris-HCl and 10 mM KCl (pH 8.0)] containing 0.1% modified BSA.

Figure 1 Absorption spectra of gold nanorods before and after coating with avidin. Prior to avidination (bottom trace), gold spheres and nanorods absorb 529 and 639 nm light, respectively. Incubation of the gold rods with avidin (top trace) results in a red shift of the nanorod absorption to 642 nm.

In a typical experiment, a Ni-NTA resin-coated glass slide was spotted with 5 L of 85 g/mL F₁ such that the F₁ molecules became immobilized to the Ni-NTA resin via the three His₆ tags. After a 5 min incubation, the slide was washed for 30 s with F₁ buffer. After excess liquid was wicked from the surface, the spot containing immobilized F₁ was exposed to 5 L of avidinated gold nanorods for 5 min. A final 30 s wash with F₁ buffer removed unbound and nonspecifically bound gold nanorods. Excess liquid was wicked away, and 5 L of 2 mM MgCl₂ and 1 mM ATP in F₁ buffer was added.

A Leica DMIRE II inverted dark-field microscope was used to obtain quantitative data for gold nanorod rotation driven by F₁. A Sutter LB-17 xenon light with a custom Chroma cold mirror was coupled with a Series 2000 Lumatec light guide to deliver 400-925 nm collimated light to the dark-field condenser. The light not scattered by a gold nanorod was stopped by an iris in the 63× variable-aperture objective. Scattered light from single molecules was focused onto a 100 m pinhole mounted on an xyz translation stage (Thorlabs) in the image plane at the microscope side port. The pinhole acted as a spatial filter, blocking all light except that originating from the molecule under study. The scattered light then passed through a polarization filter mounted in a rotational stage (Standa, 8SMC1-USB) and was refocused onto a single photon counting avalanche photodiode (PerkinElmer SPCM-AQR-15). The detector has a dark count of ~50 photons/s with a temporal resolution of 50 ns, equivalent to 20 million fps. Single rotating rods were positioned confocal to the pinhole using a motorized stage from Prior Scientific (0.002 m/micro-step resolution) and a digital camera (Optronics, MagnaFire SP). The refresh rate of the camera was sufficiently fast to detect the strobe effect due to rotation, which allowed identification of the rotating gold nanorods and their corresponding alignment to the photon counter. Output from the detector was fed directly into a National Instruments DAQ PCI-6602 counter/timer board. Custom software was written in LabView 7.1 to control data acquisition, storage, and analysis of dwell times. Additional custom software was written in Matlab 6.5 to compute the rate of rotation (transition time).

Results

The optical properties of gold nanorods were exploited in taking sensitive measurements of rotational position. When viewed using dark-field microscopy, an 75 nm × 35 nm nanorod resonantly scatters red and green light from the long and short axis of the rod, respectively (23). Incident light illuminated the sample at an oblique angle so that only light scattered from the nanorods entered the objective. When scattered light from a nanorod was viewed through a polarizing filter, its intensity changed as a function of the relative angle between its longitudinal and translational axes and the polarizing filter (Figure 2A). Light is scattered most efficiently along the rod axes such that the intensity of scattered red light is maximal and minimal when the long and short axes of the rod are parallel and orthogonal to the plane of polarization, respectively. The converse is true for the intensity of scattered green light. Therefore, the intensities of light scattered from a gold nanorod immobilized to a single F₁ -subunit change as a function of the polarization angle (Figure 2B). The resulting intensity profiles of red and green light follow out-of-phase sine curves.

Figure 2 Light scattering properties of gold nanorods viewed through a polarizing filter. (A) Consecutive dark-field micrographs of a stationary rod observed when (1) the plane of polarization is parallel to the long axis of the rod and (2-5) the filter was rotated in 45

increments. (B) Schematic of a gold nanorod attached to the F₁

-subunit as it would rotate vs A.

To measure Mg²⁺-ATP-dependent -subunit rotation, the intensity of red light scattered from single nanorods was acquired as a function of time. As a control, the scattered light intensity at a given rate of data acquisition was established when the rod was not rotating (Figure 3A). The signal generated by the nanorod in the presence of 1 mM MgCl₂ and 2 mM ATP, acquired at the same collection rate and scale, is shown in Figure 3B. To establish the maximum and minimum intensities of scattered light at that data acquisition rate, the polarizing filter was rotated when the nanorod was not rotating (Figure 3C). The observed depth of oscillation in the presence of substrate was consistent with the intensity range predicted by Figure 3C, indicating that the variation in signal was due to Mg²⁺-ATP-dependent -subunit rotation. The average rate-limiting dwell time from 22 molecules was determined to be 8.3 ms. The k_cat of Mg²⁺-ATP hydrolysis for these F₁ preparations was 130 s^-1 (7.7 ms) at 1 mM Mg²⁺-ATP, which is consistent with the 8.3 ms rate-limiting dwell observed between rotational events.

Figure 3 Confirmation of F₁-dependent rotation of a gold nanorod using a single photon counter. Data sets of the same gold rod were collected after assembly with F₁ at an acquisition rate of 1 kHz. Scattered red light intensity profiles of the gold nanorod were measured (A) while it was not rotating, (B) during ATP-dependent F₁ rotation, and (C) while the rod was stationary but the polarizer was rotated 360

to establish maximum and minimum intensity values of scattered red light.

The minimum and maximum intensity values occur when the rod is perpendicular and parallel to the plane of polarization, respectively. Therefore, transitions between these extremes correspond to rotation of the gold nanorod by 90. Figure 4A shows -subunit rotation data collected at 400 kHz when the polarizing lens was aligned with one of the dwell states parallel to the plane of polarization (Figure 4B). Consequently, when aligned as in Figure 4C, a 120 rotational event from dwell position I to II would cause the rod to begin at an intermediate intensity value, pass through a minimum, and end near a maximum. The converse is true for rotation events from dwell position II to III. Rotation data from dwell position III to I do not span the entire range of light intensity and thus did not meet the selection criteria for further analysis.

Figure 4 Measurements of F₁-ATPase

-subunit rotation. (A) F₁-ATPase rotation-dependent changes in scattered red light intensity collected at 400 kHz. (B) Schematic of the rod orientation between F₁ and the plane of polarization. Approximate position of dwell states I-III relative to the maximum and minimum intensity values of scattered red light.

The stochastic nature of each rotational event makes it difficult to determine the rod position at the start and end of any single rotation event. Since the most sensitive measure of the 120 rotation is the 90 subset that caused a change between minimum and maximum intensity values, these changes were used to measure rotation rate. The effects of intensity range and linearity on the calculation of transition time were determined. Figure 5 shows the average calculated transition time as a function of R² values which span five different intensity ranges. When transitions that spanned 90% of the total possible range were considered, there was substantial variation for R² values of <0.95. As larger intensity ranges were considered, the calculated transition time was more consistent as the R² value decreased. Calculated transition times converged to similar values for data that spanned at least 90% of the total intensity range and had R² values greater than 0.95.

Figure 5 Effects of data selection criteria on the calculated transition time. Transition times were calculated as a function of R² values from light intensity changes between percentile ranges from 99th to 1st (98%), 98th to 2nd (96%), 97th to 3rd (94%), 96th to 4th (92%), and 95th to 5th (90%). The difference in the calculated transition time is not sensitive to the R² values greater than 0.95 for each percentile range as shown in the boxed region.

An example transition from a data set collected at 400 kHz is shown in Figure 6A. This transition, which had an R² value of 0.987 from a linear least-squares regression, did not contain any apparent variation in rate over the 90 of rotation that was assessed. The variation of transitions that satisfy the selection criteria is shown in Figure 6B. Most events show a constant slope during rotation. However, there is evidence of a short pause in some of the transitions. Although each 120 step is composed of 80 and 40 substeps, the stochastic nature of a single rotational event causes variability in the proportion of 80 and 40 substeps that are included in any 90 data acquisition. Therefore, attempts to distinguish differences in the transition time of these substeps were not made.

Figure 7 depicts the average time required for the -subunit to rotate 90 as a function of the data acquisition rate to show the minimum acquisition rate required to resolve the sweep time. These measurements were obtained at resolutions between 100 and 2.5 s (equivalent to acquisition rates of 10000-400000 fps). The transition time calculated from data acquired at rates faster than 50 kHz showed no significant deviation. The average transition time from these data for 22 F₁ molecules containing more than 72 000 rotational events was determined to be 7.62 ± 0.15 (standard deviation) rad/ms.

Each catalytic event can be examined as both a dwell associated with the rate-limiting step and a rotational transition related to the power stroke of an engine. Torque generated by F₁ is calculated using the laminar flow Stokes equation

where

is the angular velocity and

is the drag coefficient. However, torque changes with the drag coefficient depending upon how the rod binds to the

-subunit according to the following equation:

where

is the nanorod radius, x₁ and x₂ correspond to the length of the nanorod in terms of the attachment point, and

is the viscosity of the medium (1 × 10^-3 N s m^-2 at 25

C). However, to use this equation, knowledge of the nanorod orientation relative to the axis of rotation is required. Since this information is not generally available, it has been assumed that, on average, attachment of the

-subunit to the nanoparticle occurs near the middle of its longitudinal axis so that

can be modeled by

On the basis of eq 3, a constant velocity of 7.62 rad/ms implies that the average torque generated by the

-subunit is ~47.4 ± 4.2 pN nm, similar to values reported elsewhere (1, 24).

Figure 6 Subset of rotational events. (A) A single transition from the data set in Figure 4A showing data points and the associated trend line (R² = 0.987). (B) Superposition of transitions acquired at 100 kHz. The transition depicted in red is representative of the fastest and most common type of transition observed. The transition depicted in yellow represents a subpopulation of events that contain an intermediate pause.

Figure 7 Average transition time calculated from data collected from five F₁ molecules at acquisition rates between 10 and 400 kHz.

Information concerning the orientation of a gold nanorod relative to the axis of rotation and the plane of polarization was obtained by examining the relationship between time-averaged locations of the three dwells and the angle of the polarizing filter. When the axis of rotation is orthonormal to the plane of polarization, three peaks in the histograms of the intensity values should be observed that correspond to each dwell. As the polarizer is rotated, the contribution of each dwell state should follow three sine curves offset by 60 (Figure 8A). The following equation models the behavior of the F₁ molecule when it is aligned as in Figure 8A

where

is a scaling term dependent upon the data acquisition rate and each X represents a normally distributed population of values for relative positions of the dwell states to the polarization filter.

Figure 8 Contributions of dwell states to the intensity profile as a function of polarizing filter alignment acquired at 1 kHz. (A) Simulation of relative contributions from each dwell when the axis of rotation is orthonormal to the plane of polarization. As the polarizer is rotated, the contribution of each dwell state is modeled by three sine curves offset by 60

. Vertical lines B-D correspond to relative dwell locations depicted in the insets of panels B-D. Intersections between the sine curves and the vertical lines correspond to peaks in the intensity profiles. (B-D) Histograms of intensity values from rotation data acquired at 1 kHz when the orientations between the plane of polarization and dwell states occur as depicted in the respective insets. Positions I-III represent consecutive dwell states which contribute to intensity peaks as labeled.

Panels B and D of Figure 8 show histograms of dwell states during ATP-dependent rotation when the polarized lens was oriented such that a dwell was aligned with maximum and minimum intensity values, respectively. In these cases, two peaks overlap and were maximally spaced from the other as predicted by alignment of states B and D in Figure 8A. When the polarized lens was moved out of alignment with a dwell state, light intensity values of the three dwell states diverged (Figure 8C), as predicted by alignment state C in Figure 8A. Therefore, the orientation of the gold rod to the axis of rotation and the plane of polarization can be determined by observing the changes in the relationship between intensity peaks as a function of the polarization angle. Of the 22 molecules examined, 19 exhibited this behavior.

The three remaining molecules did not follow the pattern predicted by the model described by eq 4. Figure 9A shows consecutive histograms of intensity values as a function of the polarization angle during ATP-dependent rotation of one such molecule. When viewed collectively, only two dwell states offset by 90 were observed. This observation strongly suggests a molecule orientation where the axis of rotation of the -subunit was at a 45 angle with respect to the plane of polarization, and the end of the longitudinal axis of the gold nanorod was bound at a 45 angle with respect to the -subunit (Figure 9C). This configuration likely resulted from variation in the glass surface and the location of attachment of avidin to the gold nanorod. The motion of the gold rod was limited to a cone oriented such that the tip of the cone was at the axis of rotation and the body was contained within a single octant. In this case, the projection of the rod onto the plane of polarization would result in one state contributing a constant minimum intensity value while the other two states appear to be 90 from one another. Consequently, an intensity change from the minimum to the maximum values should correspond to rotation of the -subunit by 120 rather than 90.

Figure 9 Consecutive histograms of intensity values as a function of the polarization angle during ATP-dependent rotation. Histogram series of experimental results from a single molecule (A) and simulated results (B) of intensity values as a function of the relative angle between the plane of polarization and the dwell states. (C) Three-dimensional model of rod orientation, where the projection of the dwell states into the two-dimensional viewing plane results in two distinguishable states that appear 90

apart.

A simulation of the changes in the histograms as a function of the angle of polarization (Figure 9B) was generated using the following function:

This equation models the behavior of the F₁ molecule when it is aligned as in Figure 9C, where

is a scaling term dependent upon the data acquisition rate. Each X_n represents a normally distributed population of values for relative positions of the polarization filter. The function

(X₃) is a term for the contribution of the dwell state that is aligned with the observation perspective. The observed behavior of the molecules was consistent with the trends predicted by the model. In addition, the instantaneous velocity of these three molecules was consistent with values determined for the other molecules traveling 90

when these molecules were assumed to rotate 120

. Both results support the proposed orientation of the axis of rotation and nanorod attachment. On the basis of this orientation of the gold nanorod, eq 2 was used to calculate the instantaneous torque of 63.3 ± 2.9 pN nm for these F₁ molecules.

Discussion

Rotation of the F₁ -subunit was first measured using an actin filament probe where the rate of rotation was limited by the viscous drag of the filament (16, 17). Minimal differences observed between rotation rates using gold beads 40 and 60 nm in diameter suggest that the viscous drag does not limit the rate of rotation (25, 26). Since the 75 nm × 35 nm rods have an effective drag between that observed for the 40 and 60 nm beads, it is likely that the intrinsic mechanism of the enzyme limits the rate of rotation.

The results presented here show that the instantaneous velocity of -subunit rotation occurs at a constant rate of 7.62 ± 0.15 (standard deviation) rad/ms. This measurement was made using a novel technology capable of achieving a temporal resolution of 2.5 s (400 kHz). The measurement was confirmed by comparing transition times observed at increasing acquisition rates, until the transition time was independent of the temporal resolution. This occurred at an acquisition rate of at least 50 kHz, corresponding to a resolution of 20 s.

Observed dwell times at saturating substrate concentrations were consistent with bulk measurements of E. coli F₁ Mg²⁺-ATPase activity. The average dwell time was 8.3 ms, which was substantially longer than that measured in F₁ from the thermophilic bacterium PS3 (6). Dwells were best resolved at an acquisition rate of 1 kHz such that each dwell measurement was the sum of the time spent pausing and rotating. Consequently, the actual dwell time for E. coli F₁ is ~8.03 ms since it takes approximately 0.27 ms for the -subunit to rotate 120 during a single catalytic event.

On the basis of the results presented here, the average torque generated during rotation was ~47.4 ± 4.2 pN nm, comparable to that previously reported for F₁ from PS3 (1, 24, 27). The maximum observed torque was determined to be 63.3 ± 2.9 pN nm for those molecules oriented as in Figure 9. A factor that could affect the torque is increased viscous drag due to the interfacial properties of ordered water near the surface of the slide. However, these effects become minimal more than 2-3 nm from the surface (28, 29). The biotinylation site of the -subunit is ~12 nm from the surface, and therefore, these interfacial effects on the drag coefficient should be negligible. The calculated work done by F₁ during a single transition was, on average, 99.3 ± 8.8 pN nm. Since the gold rod is unlikely to limit the rate of rotation, the work done will be the minimum required to move it. The potential work that can be done during a single transition may be greater than the actual work needed to move the rod, implying that existing measurements are likely to underestimate the possible torque. Thus, any measurement that results in a larger torque value is likely to reflect the potential torque of the motor. The maximum amount of work observed during a 120 transition was 132.5 ± 6.0 pN nm. This is significantly larger than the free energy of ATP hydrolysis (90 pN nm) under physiological conditions (8). Therefore, the observed torque generated by the motor cannot be explained by the free energy of ATP hydrolysis alone. Another possible source of free energy might be derived from the differences in affinities for the substrate and product in the catalytic site under conditions of a favorable chemical gradient (30).

Acknowledgment

We thank Matthew Barber, Ana Bengston, Lars Chapsky, Matthew Green, and Liyan He for insightful conversations.

Supporting Information Available

Movie showing the strobe effect used to identify rotating gold nanorods. This material is available free of charge via the Internet at http://pubs.acs.org.

This work was supported by National Institutes of Health Grant GM50202 to W.D.F.

* To whom correspondence should be addressed. E-mail: frasch@ asu.edu. Telephone: (480) 965-8663. Fax: (480) 965-6899.

These authors contributed equally to this work.

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