Biophysical Characterization of a Thermoalkaliphilic Molecular Motor with a High Stepping Torque Gives Insight into Evolutionary ATP Synthase Adaptation

Abstract

F₁F₀ ATP synthases are bidirectional molecular motors that translocate protons across the cell membrane by either synthesizing or hydrolyzing ATP. Alkaliphile ATP synthases are highly adapted, performing oxidative phosphorylation at high pH against an inverted pH gradient (acid_in/alkaline_out). Unlike mesophilic ATP synthases, alkaliphilic enzymes have tightly regulated ATP hydrolysis activity, which can be relieved in the presence of lauryldimethylamine oxide. Here, we characterized the rotary dynamics of the Caldalkalibacillus thermarum TA2.A1 F₁ ATPase (TA2F₁) with two forms of single molecule analysis, a magnetic bead duplex and a gold nanoparticle. TA2F₁ rotated in a counterclockwise direction in both systems, adhering to Michaelis-Menten kinetics with a maximum rotation rate (V_max) of 112.4 revolutions/s. TA2F₁ displayed 120° unitary steps coupled with ATP hydrolysis. Torque measurements revealed the highest torque (52.4 piconewtons) derived from an F₁ molecule using fluctuation theorem. The implications of high torque in terms of extreme environment adaptation are discussed.

Introduction

ATP synthases are membrane-bound rotary molecular motors that are the major enzymes responsible for ATP synthesis in the majority of aerobic life (1, 2). A key feature of the enzyme is the mechanism by which the translocation of protons (or Na⁺ ions) across the membrane barrier is linked to either synthesizing or hydrolyzing ATP (1–3). Bacterial F₁F₀-type ATP synthases are two-domain enzymes and are typically composed of eight subunits, α₃β₃γδϵab₂c_10–15 (4, 5). The soluble F₁ domain is composed of the α₃β₃γδϵ subunits in which the α- and β-subunits are alternatively arranged in a hexameric ring-shaped catalytic core. ATP hydrolysis and synthesis occur in the catalytic sites that are formed by each of the β-subunits (4, 6). The core rotary shaft is composed of the γ- and ϵ-subunits. The γ-subunit penetrates the center of the α₃β₃ catalytic hexamer at one end and is associated with the a- and c-subunits of the F₀ domain at the other end (7). The F₀ domain is composed of ab₂c_9–15 subunits and is membrane-bound (8). The c-subunits form a ring parallel to the membrane (9); however, although stoichiometry is fixed within a species, it is variable between species (10–15). The a-subunit forms a collar around the c-ring and is thought to conduct ions both into and out of the c-ring in a two-channel model (16–19). The c-ring rotates and, together with a-subunit, conducts protons or Na⁺ ions across the cell membrane (9, 20). The tightly associated γ- and ϵ-subunits together with the c-ring functionally form the rotor portion of the enzyme, whereas the α₃β₃δab₂ subunits form the stator (4, 5). The coupling of ion translocation through the ac-ring complex to the clockwise rotation of the rotor forces conformational changes within the β-subunits in the α₃β₃ catalytic hexamer, catalyzing the synthesis of ATP from ADP and inorganic phosphate (21). Conversely, the α₃β₃ catalytic hexamer can hydrolyze ATP, causing anticlockwise rotation of the γϵc_10–15 rotor, resulting in the pumping of either protons or Na⁺ ions into the bulk phase (21–24). It is also noteworthy that ATP hydrolysis is suppressed in aerobic alkaliphilic organisms (25–27).

When the F₁ domain is separated from the F₀ domain it can be regarded as an ATPase and is useful for the study of the mechanical properties of ATP/ADP-P_i catalysis and enzyme function (28). Indeed, the rotation of F₁ ATPases has been visualized using optical microscopy by attaching a probe to the γ- or ϵ-subunit in the relative area of where the F₀ domain would be located had it been attached (23, 28, 29). As this method of study has developed, the type of probe utilized has diversified from actin filaments (23, 30) into gold nanoparticles/nanorods (31, 32), magnetic beads (33, 34), polystyrene beads (35, 36), and fluorescent molecules (37–39). The two most heavily studied bacterial F₁ ATPases come from the thermophile Bacillus PS3 (TF₁) and the mesophile Escherichia coli (EF₁). Both enzymes are capable of ATP hydrolysis activity, rotating stepwise at an ATP concentration-dependent rate in an anticlockwise direction (23, 40). Because the hexameric α₃β₃ structure harbors three catalytic sites, the basic step size is 120° coupled to either the consumption or production of one ATP molecule (41). For both TF₁ and EF₁, these 120° steps have been shown to consist of substeps of 80° and 40° and of 85° and 35° substeps, respectively (35, 40, 42). The 80°/85° substeps are proposed to be triggered by ATP binding and ADP release and are referred to as ATP-binding (ATP-waiting) dwells (37), whereas the 40°/35° substeps have been shown to occur after ATP cleavage and release of inorganic phosphate and are referred to as catalytic dwells (43).

Upon catalysis, the generation of torque at the interface between the rotor (γϵ subcomplex) and the stator (α₃β₃δ subcomplex) results in the rotation of the F₁ by using the chemical free energy from ATP hydrolysis. Due to the interconversion of chemical free energy and electrochemical potential via mechanical rotation, torque is an important factor affecting the energy conversion efficiency of a molecular rotor. Stepping torque has been estimated for TF₁ (41, 44), EF₁ (40), the thermophilic Thermus thermophilus V₁ ATPase (TtV₁) (44, 45), and the acidophilic Enterococcus hirae V₁ ATPase (EhV₁) (44), the last of which is proposed to act solely as a V₁V₀-type ATPase (24, 44, 46). Interestingly, of the F₁-type enzymes described here, the torque appears to be higher in the thermophilic TF₁ and, according to some reports, lower in EF₁. This implies that adaptation to temperature might result in an enzyme with higher torque. In agreement with this, of the V₁-type enzymes, the TtV₁ torque is greater than that of EhV₁; however, the torque difference between TtV₁ and EhV₁ is much greater than that between TF₁ and EF₁, suggesting that function may also have a role in defining torque, i.e. ATP synthesis versus hydrolysis (see Table 1).

TABLE 1.

Torque of TA2F₁ and other rotary ATPases

Protein	Torque	Known function	Organism growth conditions	Ref.
	pNnm
TA2F1	52 ± 4a,b	ATP synthase	pH 9.5/65 °C	This study
EhV1	20a,b	ATP hydrolase	pH 5.0/25 °C	41
TtV1	35a,b	ATP Synthase/hydrolase	pH 7.5/65 °C	45
	33 ± 2a,b			44
TF1	41 ± 2a,b	ATP Synthase/hydrolase	pH 7.5/65 °C	This study
	39 ± 4a,b			41
EF1	30c	ATP Synthase/hydrolase	pH 6.5/35 °C	40

^a The values were determined by fluctuation theorem.

^b The values are the means ± S.D.

^c The value was determined from the angular velocity and frictional drag coefficient of the probe.

In this study, we examine the F₁ ATPase from the thermoalkaliphilic Caldalkalibacillus thermarum TA2.A1. Alkaliphile ATP synthases are highly adapted, performing oxidative phosphorylation at high pH against an inverted pH gradient (acid_in/alkaline_out), thereby challenging Mitchell's chemiosmotic model (25, 27, 47–49). The environmental pressure of an alkaline environment, together with increased membrane permeability to ions at high temperature (50), results in a severe pressure to conserve energy. Unlike the ATP synthases/hydrolases described here, alkaliphilic enzymes have tightly regulated ATP hydrolysis activity (25–27), which can be relieved in the presence of LDAO³ (26, 51–53). In addition to this, both the γ- and ϵ-subunits of the C. thermarum TA2.A1 ATP synthase (TA2F₁F₀) are proposed to have regulatory roles in ATP hydrolysis (51, 53). Because this enzyme is the antithesis of the EhV₁V₀ (i.e. it only performs ATP synthesis (26)), it was of significant interest to examine both catalytic mechanism and torque. In addition, due to the thermophilic origin of TA2F₁F₀, we are also able to directly compare the effect of alkaliphily on torque. Here, we characterized the rotary dynamics of TA2F₁ with two forms of single molecule analysis, a magnetic bead and a gold nanoparticle.

Results

Expression of TA2F₁ and TA2F₁γ2c in E. coli

To examine rotary dynamics in F₁ ATPases, the enzyme must be capable of being labeled with a trackable probe such as a 200-nm magnetic bead duplex or a 40-nm gold nanoparticle. For other enzymes such as the TF₁ ATPase (23, 31, 34, 42, 54), this was achieved by the introduction of two cysteine residues in the γ-subunit. The F₁ portion of the atp operon from C. thermarum TA2.A1, coding for TA2F₁ α₃β₃γδϵ, with a hexahistidine tag at the N terminus of the β-subunit, and the same enzyme including two cysteines introduced at positions 107 and 210 in the γ-subunit (TA2F₁γ2c; Fig. 1A) were cloned into the expression plasmid pTrc99A and overexpressed in the unc deletion mutant E. coli DK8. TA2F₁ and TA2F₁γ2c were extracted from E. coli strain DK8 cytoplasmic fractions and purified via a three-step purification procedure. SDS-PAGE analysis of the purified recombinant mutant enzyme (TA2F₁γ2c) revealed five subunits (viz. α, β, γ, δ, and ϵ) that were identical to those of the native F₁ purified from the overexpressed WT TA2F₁ previously by Keis et al. (51) (Fig. 1B, lane 2). Postpurification, TA2F₁γ2c was specifically biotin-modified via the cysteine residues at positions 107 and 210 in the γ-subunit for attachment of rotation probes (Fig. 1B, lane 1). This was confirmed by Western blotting (Fig. 1B, lane 2), revealing that biotin was specifically incorporated into the γ-subunit of TA2F₁γ2c.

FIGURE 1.

Purification, labeling, and biochemical features of TA2F₁γ2c. A, schematic representation of the TA2F₁ structure (Protein Data Bank code 2QE7 (53)) showing the relative positions of the two introduced cysteine residues (γH107C/γS210C; in yellow Corey-Pauling-Koltun modeling; hence TA2F₁γ2c) located in the γ-subunit (green). The ϵ-subunit is pink, and the α- and β-subunits are shown in blue and red, respectively. This model was constructed and rendered using PyMOL (Schrödinger, LLC). B, lane 1, SDS-PAGE analysis of the purified, biotin-labeled TA2F₁γ2c ATPase resolved on a 12% polyacrylamide gel and stained with Coomassie Brilliant Blue. B, lane 2, prior to Western blotting analysis, biotin-labeled TA2F₁γ2c ATPase was separated by SDS-PAGE (12%). TA2F₁γ2c was subsequently transferred onto a polyvinylidene difluoride membrane and immunoblotted using a streptavidin-alkaline phosphatase conjugate directed against the biotin-modified γ-subunit of TA2F₁γ2c. 10 μg of protein was used in all separations. C and D, representative plots showing the effect of 0.1% LDAO on biotin-labeled TA2F₁γ2c (C) or TA2F₁ WT (D) ATPase activity at 45 °C. E, representative plots showing the effect of 0.1% LDAO on biotin-labeled TA2F₁γ2c ATPase activity at 25 (gray line) and 65 °C (black line). Arrows indicate the points during the time traces where various assay components were added. F, effect of ATP concentration and temperature on biotin-labeled TA2F₁γ2c ATP hydrolysis activity in the presence of 0.1% LDAO. All measurements were at pH 8.0, and three replicates were performed using 5 μg of protein per measurement with the ATP-regenerating assay described under “Experimental Procedures.” mAU, milliabsorbance units. Error bars represent S.E.

ATP Hydrolysis of TA2F₁γ2c-Biotin

A feature of the TA2F₁ enzyme is its specific blockage in ATP hydrolysis activity and that this activity can be stimulated up to 30-fold with 0.05% LDAO (26, 51). Like the recombinantly expressed native TA2F₁, TA2F₁γ2c-biotin was blocked in ATP hydrolysis activity. Neither the WT nor the biotin-modified mutant displayed any measureable ATP hydrolysis activity (Fig. 1, C and D). ATP hydrolysis could be induced in TA2F₁γ2c-biotin at both 25 and 45 °C with 0.1% LDAO (Fig. 1, E and F). Per TA2F₁γ2c-biotin molecule, this resulted in a maximal specific activity of 124.3 (30.4 units/mg of protein), 141.6 (34 units/mg of protein), and 166.2 mol/s (Fig. 1F) at 25, 45, and 65 °C, respectively. The K_m for ATP was 0.27 mm at 25 °C, 0.28 mm at 45 °C, and 0.26 mm at 65 °C. The activities reported here are consistent with those observed previously for TA2F₁ by Keis et al. (51) (28.5 units/mg of protein at 45 °C). We have further optimized the assay by introduction of 50 mm KCl to optimize pyruvate kinase activity (data not shown). In this optimized assay system, upon addition of ATP, we observe a small sharp drop indicative of a small amount of ADP present in the ATP. This is followed by a flat line indicating that the TA2F₁ ATPase has close to zero ATP hydrolysis activity at 25, 45, and 65 °C (see Fig. 1, C–E, upon ATP introduction).

Rotation Velocity Is Dependent on ATP Concentration

Because TA2F₁ does not natively catalyze hydrolysis and we sought to examine TA2F₁ rotational dynamics with ATP hydrolysis-driven rotation, we required a system capable of activating F₁ ATPase activity. Fortunately, we have two methods to achieve this in the form of LDAO and the use of magnetic beads with magnetic tweezers, the latter of which is well documented to aid in relieving the TF₁ ATPase inhibited states (34, 55, 56). Although the use of magnetic beads is a powerful tool, to examine the true maximum rotation speed, a probe with no viscous drag is required. Therefore, to explore the kinetic properties of the TA2F₁, a 40-nm gold nanoparticle was utilized. The hydrodynamic friction on a 40-nm gold nanoparticle is practically negligible, allowing the observation of unloaded rotation of TA2F₁ to be observed provided the bead is unobstructed and free to rotate in the assay solution (42). Considering our low flow chamber volume and requirement for accessibility to the chamber volume, assays at 65 °C present a significant technical problem. However, because ATP hydrolysis at 25 °C is 73% of that possible at 65 °C (see Fig. 1E), we considered it appropriate to conduct all rotation experiments forthwith at 25 °C. To observe single enzyme rotation, TA2F₁γ2c-biotin was immobilized on an NTA-modified glass surface in a flow chamber using hexahistidine tags at the N terminus of the β-subunit, and a 40-nm streptavidin-functionalized gold nanoparticle was attached at the top of the γ-subunit as a rotation probe (Fig. 2A). Initial experiments did not include an ATP regeneration system or LDAO. These experiments revealed very few rotating molecules, each of which only performed two to five revolutions before lapsing into an inactive state. Henceforth, we performed rotation studies using TA2F₁γ2c using a 40-nm gold nanoparticle system in the presence of 0.1% LDAO and an ATP regeneration system. Rotation was observed at a variety of ATP concentrations using total internal reflection dark field microscopy (31) recorded at a rate of 10,000 frames per second (fps). In the presence of LDAO, TA2F₁ rotated counterclockwise for continuous revolutions that decreased in velocity upon decrease in ATP concentration (Fig. 2, B and C). Above 1 mm, rotation rates were essentially constant, and below 200 μm ATP, the rotation rates were proportional to ATP concentration. This suggests that ATP binding may be rate-limiting at ATP concentrations below 200 μm. Rotation velocities at various ATP concentrations collectively followed Michaelis-Menten kinetics with a V_max of 112.4 ± 4.3 revolutions s⁻¹ at 2 mm ATP and an apparent ATP K_m of 46.85 ± 3.69 μm (Fig. 2C). The second-order rate constant (K_on[ATP]) was determined using 3 × V_max/K_m derived from Fig. 2C and was estimated to be (7.20 ± 0.1) × 10⁶ m⁻¹ s⁻¹ assuming that three ATP molecules are hydrolyzed per revolution of the gold nanoparticle attached to the γ-subunit.

FIGURE 2.

Effect of ATP concentration on TA2F₁γ2c rotation rate with a gold nanoparticle. A, schematic representation of the experimental setup for a single molecule rotation assay of the TA2F₁γ2c gold nanoparticle probe. The stator α₃β₃δ subcomplex of TA2F₁γ2c was fixed onto the nickel-NTA glass surface with the hexahistidine tag at the N terminus of each β-subunit. A streptavidin-coated 40-nm gold nanoparticle was attached to biotinylated cysteine residues in the γ-subunit rotor (γH107C/γS210C). B and C, effect of ATP concentration on rotation of TA2F₁γ2c using the system displayed in A. B, displayed are representative rotation traces recorded at 10,000 fps with a variety of ATP concentrations: 2 mm (blue), 200 μm (cyan), 50 μm (green), 20 μm (yellow), and 2 μm (red). C, displayed are the average rotation rates of 15 molecules at the concentrations of ATP indicated on the graph. Error bars represent S.E. C, inset, Lineweaver-Burke plot of data from C used to define the V_max of 112.4 ± 4.3 revolutions s⁻¹ (rps) and K_m of 46.85 ± 3.69 μm.

Stepping Behavior and Dwell Time Analysis of TA2F₁

A feature of F₁ ATP synthases is the 3-fold symmetry of the catalytic domain of the enzyme. Typical examples of rotation at ATP concentrations of 2 mm, 200 μm, and 20 μm ATP are shown in Fig. 3, A–F. At almost all ATP concentrations, it was possible to observe clear 120° stepwise rotation of TA2F₁ under both V_max and low ATP conditions as shown in the x-y trajectories and distribution of rotary angles (Fig. 3, A–C, insets, and D–F). Under V_max conditions, each 120° step was completed within 0.2 ms; however, this time period was highly dependent on ATP concentration, underscoring that rotation rate is directly related to the duration of the intervening 120° pauses. At 2 mm ATP, considerably above the K_m of 46.85 ± 3.69 μm, these pauses are proposed to represent catalytic dwells. To obtain the time constants and kinetic parameters, the duration of these pauses were examined. Unambiguous analysis was achieved by examination of the first 30 s of traces from 10 molecules distributed over 2 orders magnitude of substrate concentration. These were modeled using a three-consecutive reaction scheme representing ATP binding, hydrolysis, and ADP/P_i release. All distributions of the durations showed a convex shape (Fig. 3, G–I). The average time constants at 2 mm, 200 μm, and 20 μm ATP (Fig. 3, G–I) revealed three time constants that were (i) 2.2 ± 0.2, 2.6 ± 0.3, and 6.2 ± 0.9 ms, respectively; (ii) 0.42 ± 0.04, 0.32 ± 0.04, and 0.68 ± 0.07 ms, respectively; and (iii) 0.42 ± 0.24, 0.78 ± 0.27, and 0.7 ± 0.18 ms, respectively. These time constants correspond to (i) ATP-hydrolysis, (ii) ATP binding, and (iii) ADP/phosphate release. It is unclear from this analysis what time constant corresponds to which reaction step. The second-order rate constant (K_on[ATP]) determined from the distribution of the duration of the ATP-waiting dwells was estimated to be (8.3 ± 0.2) × 10⁶ m⁻¹ s⁻¹, consistent with (7.20 ± 0.1) × 10⁶ m⁻¹ s⁻¹ determined by 3 × V_max/K_m derived from Fig. 2C. To resolve what time constant corresponds to which reaction step, we examined the catalytic mechanism to see whether TA2F₁ displayed the same substep behavior as TF₁ (35). This is achieved by closely examining rotational stepping behavior around the K_m value. Unfortunately, we were unable to observe substepping using the full TA2F₁ construct with a gold nanoparticle; however, the 120° steps were clearly broadened at 50 μm ATP (K_m = 46.85 ± 3.69 μm; data not shown).

FIGURE 3.

Rotation of TA2F₁ reveals three distinct dwell states separated by 120°. A–C, representative rotation traces recorded using gold nanoparticle as a rotation probe at a variety of ATP concentrations: 2 mm (A), 200 μm (B), and 20 μm (C). Insets from A–C show the x-y trajectories of the centroid of the rotating gold nanoparticle from the respective traces. D–F are distributions of rotary angles shown in A–C. G–I are distributions of duration times of dwells at each 120° step composed of dwells from 15 molecules from rotation traces analyzed collectively at the same ATP concentrations as in A–C. 1, 2 and 3 are the three dwell positions separated by 120°. The bin width across all plots was 0.5 ms, and the red curves show the fitting with a triple exponential model: m1 × (exp(−1/m2 × m0) − exp(−1/m3 × m0) − exp(−1/m4 × m0)); m1 = 150, m2 = 0.002, m3 = 0.0005, and m4 = 0.0005. For G, τ₁ = 2.2 ± 0.2 ms, τ₂ = 0.42 ± 0.04 ms, and τ₃ =0.42 ± 0.24 ms (n = 1835). For H, τ₁ = 2.6 ± 0.3 ms, τ₂ = 0.32 ± 0.04 ms, and τ₃ = 0.98 ± 0.27 ms (n = 1500). For I, τ₁ = 6.2 ± 0.9 ms, τ₂ = 0.68 ± 0.07 ms, and τ₃ = 0.7 ± 0.18 ms (n = 1500). Fitting was conducted with KaleidaGraph version 4.5.

Rotation of TA2F₁ Using ATP and ATPγS with Magnetic Beads Reveals a Six-dwell Rotation Profile

To avoid using LDAO as an activation method, we replaced the gold nanoparticle with magnetic beads, allowing mechanical activation; this is a well documented method to aid in relieving TF₁ inhibited states (34, 55, 56). In place of a gold nanoparticle, a ∼200-nm streptavidin-functionalized magnetic bead duplex was attached to the γ-subunit as a rotation probe (Fig. 4A). Initially, rotation was observed at a saturating ATP concentration of 2 mm using phase-contrast microscopy at 30 fps. As with the gold nanoparticle rotation system, in the absence of LDAO or any mechanical stimulation, very few rotating molecules were observed. Each molecule in this system only performed two to five revolutions before lapsing into an inactive state. However, upon a single forced counterclockwise rotation using magnetic tweezers, TA2F₁ was capable of ATP hydrolysis (Fig. 4B)-driven rotation at speeds of up to 6.9 revolutions s⁻¹ (Fig. 4, C and D). Rotation was observed at a variety of ATP concentrations that decreased in velocity upon decrease in ATP concentration, obeying Michaelis-Menten kinetics. The maximum rotary velocity measured under V_max conditions was 6.5 ± 0.4 revolutions s⁻¹ with an apparent ATP K_m of 2.72 ± 0.45 μm (Fig. 4, C and D). The suppression of rotation velocity and lowering of apparent K_m are a typical feature of using a large, high viscosity probe for rotation observation (31, 33, 44). The second-order rate constant (K_on[ATP]) was determined using 3 × V_max/K_m derived from Fig. 4D and was estimated to be (9.90 ± 0.1) × 10⁶ m⁻¹ s⁻¹, assuming that three ATP molecules are hydrolyzed per revolution of the γ-subunit. This is very much in agreement with observations with the values for ATP of (7.20 ± 0.1) × 10⁶ m⁻¹ s⁻¹ in the same assay system using a gold nanoparticle. However, in the magnetic bead system, these 120° steps were only clearly observed during rotation at very low ATP concentrations (Fig. 5, A–F). Because this is due to the combined effect of camera and probe response times coupled with the high viscous friction of the probe, we changed to using a fast framing camera at 5000 fps to take advantage of the ability to capture stepping. Initially, ATP was used as substrate; however, the 120° steps were simply broadened at 3 μm ATP. In light of this, we attempted to slow the catalytic steps to clarify the stepping behavior. One such method of achieving this is using the slowly hydrolyzable ATP analogue ATPγS (35); however, using this analogue removes the possibility of harnessing the ATP regeneration assay to remove the buildup of Mg-ADP. To limit this unwanted effect, observation times in the rotation assay were limited to 10 min before flushing the flow cell with fresh ATPγS at the desired concentration. Magnetic bead rotation observations at various ATPγS concentrations revealed a maximum rotation velocity of 4.02 ± 0.3 revolutions s⁻¹ under saturating ATPγS concentrations (2 mm; Fig. 6A). From the various ATPγS concentrations tested, TA2F₁ has an apparent K_m of 5.69 ± 1.33 μm (Fig. 6B). Due to the recording rate being at 5000 fps, discrete 120° steps were observed at most concentrations of ATPγS tested (Fig. 6, C–H). However, at a concentration of 5 μm ATPγS, multistep (six-step) rotary profiles with 50° and 70° substeps were observed (data not shown). Unfortunately, due to the rarity of the events measured and the less than discrete localization, this is a tentative estimate.

FIGURE 4.

Effect of ATP concentration on TA2F₁ rotation rate with magnetic beads. A, schematic representation of the experimental setup for a single molecule rotation assay of TA2F₁γ2c with a magnetic bead as a probe. The stator α₃β₃δ subcomplex of TA2F₁γ2c was fixed onto the nickel-NTA glass surface with the hexahistidine tag at the N terminus of each β-subunit. A streptavidin-coated 200-nm magnetic bead was attached to biotinylated cysteine residues in the γ-subunit rotor (γH107C/γS210C). B, frame-by-frame montage of a single rotating magnetic bead directly showing rotation states. C and D, effect of ATP concentration on rotation of TA2F₁γ2c using the system displayed in A. C, displayed are representative rotation traces recorded at 30 fps with a variety of ATP concentrations: 2 mm (blue), 200 μm (cyan), 20 μm (green), 2 μm (yellow), 200 nm (red), and 150 nm (black). D, displayed are the average rotation rates of 15 molecules at the concentrations of ATP indicated. Error bars represent S.D. D, inset, Lineweaver-Burke plot of data from D used to define the V_max of 6.5 ± 0.4 revolutions s⁻¹ (rps) and K_m of 2.72 ± 0.45 μm. The rotation assay was conducted as described under “Experimental Procedures.”

FIGURE 5.

Effect of ATP concentration on TA2F₁ dwell state distribution with a magnetic bead. A–C, representative rotation traces recorded using a magnetic particle as a rotation probe at a variety of ATP concentrations: 2 mm (A), 20 μm (B), and 200 nm (C). Insets from A–C show the x-y trajectories of the centroid of the rotating particles from the respective traces. D–F show the distributions of rotary angles shown in A–C. 1, 2 and 3 are the three dwell positions separated by 120°. The traces, plots, and trajectories are representative of 15 molecules. The rotation assay was conducted as described under “Experimental Procedures.”

FIGURE 6.

Effect of ATPγS concentration on TA2F₁ rotation rate with a magnetic bead. Shown is the effect of ATPγS concentration on rotation of TA2F₁γ2c using the system displayed in Fig. 4A. A, displayed are representative rotation traces recorded at 1000 fps with a variety of ATPγS concentrations: 2 mm (blue), 200 μm (cyan), 20 μm (green), 2 μm (yellow), and 1 μm (red). B, displayed are the average rotation rates of 15 molecules at the concentrations of ATP indicated. Error bars represent S.D. B, inset, Lineweaver-burke plot of data from B used to define the V_max of 4.02 ± 0.3 revolutions s⁻¹ (rps) and K_m of 5.61 ± 1.33 μm. C–E, representative rotation traces recorded using a magnetic particle as a rotation probe at a variety of ATPγS concentrations: 2 mm (C), 200 μm (D), and 20 μm (E). Insets from C–E show the x-y trajectories of the centroid of the rotating particles from the respective traces. F–H are distributions of rotary angles shown in C–E. 1, 2 and 3 are the three dwell positions separated by 120°. The traces, plots, and trajectories are representative of 15 molecules. The rotation assay was conducted as described under “Experimental Procedures.”

TA2F₁ Torque Is the Highest Estimated Using Fluctuation Theorem

Because the conservation of energy is key to survival at alkaline pH, the stepping torque of TA2F₁ was measured to examine the power required to turn the rotor to drive ATP hydrolysis. One of the most accurate methods for this type of analysis is by utilizing fluctuation theorem (FT) (44). FT describes entropy production in small non-equilibrium systems, various colloidal particle systems, and more recently biological systems such as RNA hairpins and the F₁ ATPase (44). FT is of particular use as it estimates torque by use of steps isolated from the time courses of rotary angles (Fig. 7A) without the need for an accurate measurement of the frictional drag coefficient of the probe itself. Because this analysis requires perfect 120° stepping motion with close to equal dwell time at each step, we used rotational data of TA2F₁ hydrolyzing ATPγS under V_max conditions. Ten TA2F₁ rotation traces recorded in the presence of 2 mm ATPγS were analyzed, revealing a rotary torque of 52.4 ± 4 pNnm (Fig. 7, B and C). For comparison with another ATPase under the same conditions and using the same analysis, we also measured the torque for TF₁. In our hands, TF₁ generated a torque of 41.4 ± 2.2 pNnm, which is quite comparable with that reported previously (Table 1), strongly supporting the reliability of the estimated torque value reported.

FIGURE 7.

Rotary torque of TA2F₁ is the highest determined by fluctuation theorem. A, typical time course of TA2F₁γ2c rotation with 2 mm ATPγS filmed at 5000 fps. Boxed in red are the stepping regions of the trace, θ(t), used to determine the torque. The steps were determined by eye. B and C, 10 TA2F₁ rotation traces were collectively analyzed. B, ln[P(Δθ)/P(−Δθ)] as a function of Δθ/k_BT. The red line shows the average torque of the 10 molecules. The slope revealed a rotary torque of 52.4 ± 4 pNnm/radian (rad) in the case of Δt = 6 ms. C, N_FT as a function of Δt for the recording rate of 5000 fps. Torque from 5 to 10 ms was regarded as consistent enough to judge the rotary torque of TA2F₁. deg, degrees. Error bars represent S.E.

Discussion

Here, we have conducted the first full biophysical interrogation of a thermoalkaliphilic F₁ ATPase in single molecule analysis with simultaneous comparison with biochemical methods. In this study, we comprehensively demonstrate that the TA2F₁ is a unidirectional rotary molecular motor. In previous studies with TA2F₁, the small amount of hydrolysis activity observed was likely due to the presence of α₃β₃ incomplete complex (51). However, the fully intact TA2F₁ used here does not natively hydrolyze ATP. However, in agreement with previous studies (26, 49, 51, 52), TA2F₁ hydrolyzes ATP upon either mechanical or chemical induction. In TF₁ studies, the requirement for mechanical activation was proposed to be due to inhibition from a classical feedback loop of product inhibition by Mg-ADP (57); however, rotation was always observable without activation mechanically or with LDAO. Furthermore, TF₁ biochemically measured ATP hydrolysis activity was only enhanced 3–4-fold with LDAO (58). In contrast, TA2F₁ is activated from an inactive state with LDAO or mechanical activation, the mechanisms by which remain to be fully described. Interestingly, the K_m and K_on values obtained from bulk-phase and rotation experiments do not agree. The estimation of K_m revealed by gold nanoparticle rotation was 5.95-fold lower than that determined by the bulk-phase biochemical assay, and the estimation of K_on reflects this. However, this is unsurprising when considering that single molecule analysis specifically selects active molecules, whereas the bulk-phase assay does not, providing an ensemble measurement. The lowering of K_m is a known hallmark for competitive inhibition, suggesting that inactive molecules are likely due to ADP inhibition. In support of this, it is well known that ATP hydrolysis in TF₁ is regulated by Mg-ADP inhibition to prevent wasteful ATP consumption (57), a phenomenon yet to be explored in TA2F₁. In TF₁ studies, the difference between single molecule results and biochemical results has long been attributed to Mg-ADP inhibition. Under single molecule conditions using a 40-nm gold nanoparticle, TF₁ has a maximal rotation velocity of 200 revolutions s⁻¹; however, in the ATP-regenerating assay under V_max conditions, only 270 ATP/s/molecule were consumed. Because three ATP molecules are consumed per revolution, bulk biochemistry results would imply only 90 revolutions s⁻¹ are possible; however, TF₁ is 55% faster according to single molecule data (59). In line with this, according to TA2F₁ biochemical data, 124.3 ATP/s/molecule are consumed; therefore a maximum velocity of 41.44 revolutions s⁻¹ is expected at 25 °C. However, TA2F₁ single molecule results show a maximal velocity of 112.4 revolutions s⁻¹, a 63% faster V_max velocity than that derived from biochemical data. This observation is strikingly close to the biochemical versus single molecule discrepancies reported for the TF₁ and EhV₁ (24, 44, 59).

At almost all ATP and ATPγS concentrations tested above or below K_m, TA2F₁ rotation profiles exhibited three dwells separated by 120° (Figs. 3 and 6) when recorded at 5000 fps. Upon using the slowly hydrolyzable substrate ATPγS, six substeps were able to be resolved close to ATPγS K_m. This is in close agreement with observations of two other F₁ ATPases, TF₁ and EF₁, that have both been reported to rotate with six dwells per revolution, close to their respective K_m values (35, 40). This observation together with the lack of six-step rotation observed in the EhV₁ ATPases (24) and structural differences between F₁ and V₁ ATPases (60, 61) implies that the interactions between rotor and stator determine the presence or absence of substeps upon enzyme rotation. However, we report the angular spacing of these 50° and 70° substeps conservatively due to insufficient quality and quantity of the molecules observed. In addition, it was observed that in almost all cases, one of the six substeps was masked showing the “six-step profile.”

Conservation of energy is a constant challenge under thermoalkaliphilic conditions. In light of this, it is unsurprising that the stepping torque derived using fluctuation theorem for TA2F₁ is very high (52.4 ± 4 pNnm); however, it was unexpected that it would be 20% higher than that for TF₁ (44). Although TF₁ and other F₁ ATPases studied in rotation studies come from organisms that grow at neutral (E. coli and Bacillus PS3) and acidic (E. hirae) pH, the C. thermarum TA2.A1 F₁F₀ is highly adapted to function at alkaline pH (Fig. 8A) (48, 53, 62). Given the difference in torque between TF₁ and TA2F₁ (Fig. 8B) despite both enzymes originating from organisms that grow optimally at 65 °C and that the internal pH of both organisms is similar at 7.5–8.0 (63, 64), we suggest that the differences in torque across species may be more related to evolutionary adaptation to external pH than temperature (Fig. 8, A and B). It is also noteworthy that both TA2F₁ and TF₁ torque was measured at 25 °C, ruling out temperature as a potential evolutionary pressure on torque. Even if the torque of TF₁ measured at 65 °C was the same as that of EF₁ measured at 25 °C, TA2F₁ has 13 pNnm greater torque than TF₁.

FIGURE 8.

Comparison of bacterial growth conditions in relation to ATPase torque. Shown is a comparison of mild acidophilic (E. hirae), mesophilic (E. coli), thermophilic (Bacillus PS3), and thermoalkaliphilic (C. thermarum TA2.A1) A, optimal temperature and pH of growth conditions (temperature, solid symbols, left y axis; pH, empty circles, right y axis). B, torque of the ATPase. The torque value here for EF₁ was derived using a method similar to that used for TF₁ and TA2F₁ in this study. For methodology details and appropriate references, see Table 1.

Notwithstanding, a higher torque implies a much stiffer rotor. One of the key features of alkaliphilic adaptation is a large c-subunit ring rotor. In the case of C. thermarum TA2.A1, this is a 13-mer (15) with an F₁ torque of 52 pNnm in comparison with the E. coli 10-mer (65) with an F₁ torque of 30 pNnm (40) and the E. hirae 10-mer (46, 66) with a V₁ torque of 20 pNnm (44). This ion coupling ratio is critical in understanding the power of the molecular motor because although velocity and torque are important for determining enzyme efficiency the gearing (i.e. the number of protons coupled to a single revolution event) is also important when considering purpose and efficiency and that C. thermarum TA2.A1 must partially maintain internal pH by synthesis of ATP. However, it is clear that differences in torque cannot be fully ascribed to the number of c-subunits because E. coli and E. hirae both have 10 c-subunits, but E. coli has a 10 pNnm greater torque (40, 44, 65, 66). This strongly suggests that although c-subunit ring size may have a mechanical influence it is the native direction of catalysis (i.e. TA2F₁ is a synthase, and EhF₁ is a hydrolase) that has the greater mechanical influence. This seems logical given that there is no torque without resistance; the greater the resistance, the greater the torque. Because we are examining TA2F₁ in hydrolysis, it is rotating against its native function; hence, one would expect more resistance.

However, in the field of ATPase dynamics, there are several methods by which to estimate torque values for enzymes (Table 1) (28, 40, 44, 67–70). Early EF₁ torque measurements were estimated to be 50 pNnm using the drag on the curvature of an actin filament during rotation (67). However, more recently, when rotation of EF₁ was assessed using gold nanorods and analysis of torque was conducted using a “power stroke” drag force method, the torque was estimated to be 63 pNnm (68). Clearly, different experimental methods and systems can result in different torque estimations. Here, we use a very conservative method of analysis, “fluctuation theorem,” to directly compare TA2F₁ stepping torque with that of TF₁ and other enzymes that have been previously analyzed with similar methodology, thus allowing a very reliable comparison between enzymes. Although the stepping torque measured here reflects the shape of rotation potential, future measurement of stall torque will reflect the thermodynamic efficiency. Interestingly, the complete E. hirae V₁V₀ ATPase has a higher torque than V₁ (44). This could be due to a “tighter” overall structure influenced by V₁-V₀ contacts and/or the influence of specific subunit interactions, i.e. the observation of reinforced torque by genetic fusion of the F-subunit to the D-subunit in T. thermophilus V₁ (70). It remains to be examined whether this is a V-type ATPase feature or applies more generally. Future studies will focus on what features dictate torque, activity of the TA2F₁F₀ complete with the c₁₃-ring, the specific role of ADP inhibition, the substep size, and the mechanical roles of the ϵ- and/or γ-subunits in TA2F₁F₀ regulation of hydrolysis.

Experimental Procedures

Bacterial Strains, Plasmids, and Growth Conditions

E. coli DH5α (71) was used for all cloning experiments, and E. coli DK8 (72) lacking the ATP synthase genes encoding the unc operon (Δatp) was used to overproduce the TA2F₁ (63, 73). For cloning and overexpression of TA2F₁ enzyme, the plasmid pTrc99A (Amersham Biosciences) was used. To overproduce F₁ ATPases, transformants of E. coli DK8 were routinely grown in 2× YT medium (74) containing 2 g/liter glucose and 100 μg/ml ampicillin at 37 °C with shaking at 200 rpm.

Construction of pTA2F₁γ2c (γH107C/γS210C) and TA2F₁ α₃β₃γδϵ Complexes

In a previous study, the genes coding for the C. thermarum TA2.A1 F₁ ATPase were cloned into the expression vector pTrc99A, yielding the plasmid pTrcF1 (75). To substitute the native histidine 107 and serine 210 in the γ-subunit of TA2F₁ to cysteine residues, double site-directed mutagenesis was carried out using the plasmid pTrcF₁ as template with a three-fragment strategy based on the overlap extension PCR method (76). To construct pTA2F₁γ2c, an 837-bp PCR product was generated using primers Tg-cysF and Tg-cysMutR, and a 1492-bp PCR product was generated using primers Tg-cysMutF2 and Tg-cysR. A 331-bp PCR product that overlapped the 3′- and 5′-ends of the 837- and 1492-bp PCR products, respectively, was generated using primers Tg-cysMutF1 and Tg-cysMutR2. The 837- and 331-bp PCR products were then joined by overlap PCR to generate a 1145-bp PCR product using primers Tg-cysF and Tg-cysMutR2. Lastly, the 1145- and 1492-bp PCR products were joined by overlap PCR to generate a 2615-bp fragment using primers Tg-cysF and Tg-cysR and digested with AflII and AfeI, and the resulting 2292-bp fragment was cloned with a 6817-bp fragment from pTrcF1 digested with the same enzymes (75). This new plasmid was designated pDMTA11. All PCRs were conducted with the Phusion high fidelity PCR kit (New England Biosciences) according to the manufacturer's instructions. Mutant inserts in both plasmids were confirmed to be correct by DNA sequencing, and the recombinant plasmid was transformed into E. coli DK8. Primer sequences and specific details are displayed in Table 2.

TABLE 2.

Primers used in this study

Primer	Sequence (5′–3′)a	Description or mutations	Direction
Tg-cysF	ATCTGTTCTACTCCGGTGTGCG	5′ external primer upstream from an AflII restriction site	Forward
Tg-cysR	AGGAAACGCTGGATTTTGCGGG	3′ external primer downstream from an AfeI restriction site	Reverse
Tg-cysMutF	GAGGAGCGttgTCAGTCCAAAGAC	γH107C	Forward
Tg-cysMutR	TGGACTGAcaaCGCTCCTCGATC	γH107C	Reverse
Tg-cysMutF2	CGAACCGGACtGTGAATCGGTC	γS210C	Forward
Tg-cysMutR2	GACCGATTCACaGTCCGGTTCG	γS210C	Reverse

^a Lowercase letters indicate specific changes in the primer for site-directed mutagenesis.

Expression and Purification of TA2F₁ and TA2F₁γ2c

The procedure applied was a modified hybrid of that in McMillan et al. (48) and Keis et al. (51). DK8 harboring plasmid pTrcF1 or pDMTA11 was grown to an A₆₀₀ of 0.4. The culture was induced with 1 mm isopropyl β-d-thiogalactopyranoside, and incubation continued for 4 h. Cells were harvested, washed with precooled resuspension buffer (50 mm Tris (pH 8.0), 5 mm MgCl₂), and resuspended in the same buffer. Phenylmethylsulfonyl fluoride (PMSF) was added to 0.1 mm, and the cells were disrupted by two passages through a French pressure cell at 20,000 p.s.i. Pancreatic DNase I was added to 0.1 mg/ml, and the mixture was kept on ice for 30 min. Lysate was cleared of debris by centrifugation at 8000 × g for 10 min, and the inverted membrane vesicles were pelleted from the supernatant at 180,000 × g for 1 h at 4 °C. To extract TA2F₁ or TA2F₁γ2c, the supernatant was heated to 60 °C for 15 min to precipitate contaminating E. coli proteins, and the precipitate was pelleted from the supernatant at 180,000 × g for 30 min at 4 °C. The supernatant was then adjusted to 500 mm NaCl and 10 mm imidazole before application to a 20-ml column of nickel-Sepharose High Performance (GE Healthcare) that was previously washed with water and equilibrated with buffer A (50 mm Tris (pH 8.0), 2 mm MgCl₂, 10% glycerol, 500 mm NaCl) containing 10 mm imidazole. To remove contaminating proteins, the resin was washed with buffer A containing 30 mm imidazole, and TA2F₁, TA2F₁γ2c, or TA2F₁ϵ2c was eluted with buffer A supplemented with 200 mm imidazole. The eluted TA2F₁, TA2F₁γ2c, or TA2F₁ϵ2c was pooled and concentrated to 10–30 mg/ml using Amicon Ultra centrifugal filter devices (molecular weight cutoff, 50,000). The concentrated sample was then applied to a Superdex 200 10/300 (GE Healthcare) gel filtration column and fractionated with 50 mm Tris-HCl (pH 8.0), 2 mm MgCl₂, 100 mm NaCl buffer. The eluted TA2F₁- or TA2F₁γ2c-containing fractions (a peak between 370 and 380 kDa) were pooled and concentrated to 10 mg/ml using Amicon Ultra centrifugal filter devices (molecular weight cutoff, 50,000) in 50 mm Tris-HCl (pH 8.0) containing 2 mm MgCl₂, 100 mm NaCl, and 10% glycerol.

Labeling

TA2F₁γ2c preparations were treated with a 5-fold molar excess of tris(2-carboxyethyl)phosphine for 2 h at 4 °C to reduce the two cysteines on the γ-subunit. This was then buffer-exchanged by gel filtration through a Nap5 column (GE Healthcare) into a potassium phosphate buffer (pH 7.0) containing 5% (v/v) glycerol, 5 mm MgCl₂, and a 2-fold molar excess of tris(2-carboxyethyl)phosphine. After reduction, a 10-fold molar excess of biotin-PEAC₅-maleimide was added to the reduced TA2F₁ and incubated for 1.5 h at room temperature. Unreacted biotin-PEAC₅-maleimide was removed by gel filtration through a Nap10 column (GE Healthcare) and buffer-exchanged into 50 mm Tris-HCl (pH 8.0) containing 2 mm MgCl₂, 100 mm NaCl, and 10% glycerol.

SDS-PAGE and Immunoblotting

TA2F₁ and TA2F₁γ2c preparations were routinely analyzed on 12% sodium dodecyl sulfate (SDS)-polyacrylamide gels using the buffer system of Laemmli (77). Polypeptide bands were visualized using Coomassie Brilliant Blue. During immunoblotting, proteins were separated by 12% SDS-PAGE followed by blotting onto a polyvinylidene difluoride (PVDF) membrane. Detection was achieved using a streptavidin-alkaline phosphatase conjugate (Roche Applied Science) directed against the biotin-modified γ-subunit of TA2F₁γ2c. The antibody-specific bands were visualized using the 4-nitro blue tetrazolium chloride/5-bromo-4-chloro-3-indolyl phosphate, 4-toluidine detection system (Roche Applied Science).

Protein Assay

Protein concentrations were determined using a bicinchoninic acid (BCA) protein assay kit (Sigma) with bovine serum albumin as the standard.

Biochemical Assays

ATP hydrolysis activity was measured using a spectrophotometric ATP-regenerating assay at 25 and 45 °C similar to that used in McMillan et al. (48, 52). The assay mixture contained 100 mm Tris·Cl (pH 8.0), 1.5 mm MgCl₂, 3 mm phosphoenolpyruvate, 50 mm KCl, 0.25 mm NADH, 5 units/ml pyruvate kinase, 6.4 units/ml lactate dehydrogenase, and variable concentrations of sodium ATP (Sigma) or lithium ATPγS (Roche Applied Science). For measurements at 65 °C, thermophilic enzymes, 10 units/ml pyruvate kinase HI1 and 6.4 units/ml lactate dehydrogenase 2, were used (Funakoshi Ltd.). The reaction was initiated by the addition of enzyme or ATP, as indicated, into 1 ml of assay mixture, and the rate of NADH oxidation was monitored continuously at 340 nm using a Jasco V-660 spectrophotometer. Approximately 5–10 μg (as indicated) of recombinant TA2F₁ or TA2F₁γ2c subunit complexes was used for assays.

Single Molecule Rotation Assays

Single molecule rotation of TA2F₁γ2c was measured as described previously using either a ∼200-nm magnetic bead duplex (high load probe) or a 40-nm gold nanoparticle (low load probe) (33, 44, 55, 78). Briefly, a flow cell was constructed using a Ni²⁺-NTA-modified glass surface and an uncoated cover glass (Matsunami Glass Ltd., Japan), and biotinylated TA2F₁γ2c subunit complexes were immobilized on the Ni²⁺-NTA surface via a hexahistidine tag introduced at the N terminus of the β-subunit. After 5 min, non-immobilized TA2F₁γ2c subunit complexes were removed using buffer A (100 mm Tris (pH 8.0), 1.5 mm MgCl₂, 50 mm KCl) followed by a 5-min incubation in 20 mg/ml bovine serum albumin in buffer A to prevent nonspecific interactions of probes with the surface. Either ∼0.2-μm high load streptavidin-functionalized magnetic bead duplexes (Seradyn Inc., Indianapolis, IN) or a low load 40-nm streptavidin-functionalized gold nanoparticle (British BioCell International, UK) were subsequently attached to the biotinylated cysteine residues in the TA2F₁ γ-subunit in buffer A and incubated for 10 min. Non-bound probe was then removed from the flow cell using buffer A. Observation of TA2F₁γ2c rotation was initiated after the infusion of either buffer A containing ≥0.2 mm sodium ATP/lithium ATPγS or buffer B (100 mm Tris (pH 8.0), 300 μm MgCl₂, 50 mm KCl) containing <0.2 mm ATP/sodium ATP/lithium ATPγS. In line with previous studies, 3 mm phosphoenolpyruvate and 2.5 units/ml pyruvate kinase were used to prevent accumulation of ADP in solution; where necessary, 0.1% LDAO was also included in the assay mixture. When using magnetic beads, the rotation of the duplex attached to the TA2F₁γ2c γ-subunit was observed using bright field or phase-contrast microscopy and, when necessary, manipulated with home-built magnetic tweezers (33) controlled with custom-made software (Celery, Library) for activation of “stalled” enzyme. Images were recorded on an inverted microscope (IX-71, Olympus, Japan) at 30 fps (FC300M, Takenaka Systems, Japan) for all characterization experiments with the exception of the six-step rotation observation that was recorded using a high speed complementary metal oxide semiconductor camera at 5000 fps (FASTCAM-1024PCI, Photron). When using gold nanoparticle, the rotation of the duplex attached to the TA2F₁γ2c γ-subunit was observed using a modified inverted microscope (IX-71) using total internal reflection dark field microscopy (31) with a lens capable of total internal reflection microscopy (APON 60XOTIRF, Olympus) (44). Images were recorded with a high speed complementary metal oxide semiconductor camera at 10,000 fps (FASTCAM-1024PCI).

Torque Measurements

Stepping torque (N) was determined from the rotation trajectories of magnetic duplex beads (∼0.2 μm in diameter) attached to TA2F₁γ2c by using the FT (44). For continuous rotation of TA2F1, the time evolution of θ(t) can be described by the Langevin equation (Equations 1 and 2).

$$\Gamma \text{d}\theta /\text{d}t=N+\xi \left(t\right)$$ (Eq. 1)

$$\left[\xi \left(t\right)\xi \left(t\prime \right)\right]=2\Gamma k_{B}T\delta \left(t-t\prime \right)$$ (Eq. 2)

where Γ is the frictional drag coefficient, ξ is a random force representing thermal noise, k_B is the Boltzmann constant, and T is the room temperature (298 K). N is torque and is assumed to be a constant value as described previously (44). Observation of rotation of TA2F₁γ2c was performed as described above except that observations were recorded at 5000 fps, and 2 mm lithium ATPγS was used (FASTCAM-1024PCI). Only enzymes exhibiting clear and even dwell times of three steps (120°) were used for analysis where the area on each trace used for analysis was the period moving between one 120° step and the next. Because the rotary motor proteins rotate in one direction, the following expression is derived from FT.

$$\ln \left[P\left(\Delta \theta \right)/P\left(-\Delta \theta \right)\right]=N\Delta \theta /K_{B}T$$ (Eq. 3)

where θ(t) is the rotary angle of the bead, Δθ = θ(t + Δt) − θ(t), and P(Δθ) is the probability distribution of Δθ. For molecules continuously rotating for at least 4 s, P(Δθ) was calculated for the case Δt = 5 ms, and then ln[P(Δθ)/P(−Δθ)] versus Δθ/k_BT was plotted. The slope of the resulting plot corresponds to the torque. The torque of each molecule was defined as the maximum value obtained from the FT analysis when using a 4-s moving window with windows starting at 1-ms intervals.

Author Contributions

D. G. G. M. conceived the study, performed the experiments, analyzed the data, and wrote the article. R. W. and H. U. provided critical insight and experimental/analytical knowledge necessary for the magnetic bead and gold rotation assay platforms, respectively. G. M. C. and H. N. provided critical insight into the broader interpretation of results in the view of both physiology and mechanical mechanism.