The ATP-waiting conformation of rotating F₁-ATPase revealed by single-pair fluorescence resonance energy transfer

Abstract

F₁-ATPase is an ATP-driven rotary motor in which a rod-shaped γ subunit rotates inside a cylinder made of α₃β₃ subunits. To elucidate the conformations of rotating F₁, we measured fluorescence resonance energy transfer (FRET) between a donor on one of the three βs and an acceptor on γ in single F₁ molecules. The yield of FRET changed stepwise at low ATP concentrations, reflecting the stepwise rotation of γ. In the ATP-waiting state, the FRET yields indicated a γ position ≈40° counterclockwise (= direction of rotation) from that in the crystal structures of mitochondrial F₁, suggesting that the crystal structures mimic a metastable state before product release.

The F₁-ATPase is a part of F_oF₁-ATP synthase that synthesizes ATP in F₁, the water-soluble portion of the ATP synthase, from ADP and inorganic phosphate (P_i) when protons pass through F_o, the membrane-embedded portion. Isolated F₁, consisting of α₃β₃γδε subunits, hydrolyzes ATP as the reverse reaction. The minimum ATPase unit, α₃β₃γ (hereafter referred to as F₁), is pseudo 3-fold symmetric: a rod-shaped, asymmetric γ subunit is surrounded by an α₃β₃ cylinder (1). Rotation of γ inside the α₃β₃ cylinder has been suggested (2–5) and confirmed by chemical (6) and optical (7, 8) methods. Direct observation under an optical microscope (8–11) has shown that F₁ rotates in discrete 120° steps, each fueled by a single ATP molecule.

Several kinds of high-resolution crystal structures of mitochondrial F₁ (MF₁) have been solved (1, 12, 13), but it is unknown which rotation states these crystal structures correspond to or how closely these are related to the structure of actively rotating F₁. To investigate the transient structures in rotating F₁, we applied a single-pair fluorescence resonance energy transfer (FRET) technique (14). We measured FRET between a donor (Cy3) on one of three βs and an acceptor (Cy5) on γ in single thermophilic F₁ molecules fixed on a glass surface (Fig. 1). Because the FRET yield strongly depends on the distance between the two fluorophores, the FRET yield will change cyclically as the γ subunit rotates (15). The distance between labeled residues were estimated from the FRET yield and used to analyze the transient conformation of F₁.

Fig. 1.

Visualization of the rotation of F₁ through single-pair FRET: principle of the experiment.

Materials and Methods

Proteins. Cy5-maleimide was prepared as in ref. 16. The sole cysteine of a mutant subcomplex of F₁, α(C193S)₃β(His-10 tag at N terminus)₃γ(S107C) derived from thermophilic Bacillus PS3, was labeled with Cy5-maleimide (molar ratio 1:2) in 20 mM Mops-KOH (pH 7.0), 100 mM KCl, and 5 mM glycine at 23°C for 30 min. The cysteine of a mutant β(S205C) (without His tag) was labeled with Cy3-maleimide at 1:2 in the same buffer excluding glycine at 23°C for 30 min. Free dyes were removed on a PD10 column (Amersham Pharmacia). The (Cy5-γ)F₁ was incubated with Cy3-β at 1:10 at 45°C for 2 days, and free β subunit was removed on a size exclusion column (Superdex 200, Amersham Pharmacia). The final preparation contained 0.7–1 mol Cy5 and 0.05–0.2 mol Cy3 per mol F₁ (estimated from absorption spectra, using ,,,,, and . A solution of 0.05–0.5 nM labeled F₁ in 50 mM KCl, 2 mM MgCl₂, 10 mM Mops-KOH (pH 7.0), 0.06–1 μM ATP, 70 mM 2-mercaptoethanol, 200 μg/ml glucose oxidase, 20 μg/ml catalase, and 4.5 mg/ml glucose was sandwiched between two KOH-cleaned quartz coverslips for microscopic observation. Resulting thickness of the solution was ≈3 μm. Previously, we found that His-tagged F₁ rotates on a clean glass surface (11), presumably bound by the negatively charged surface. To determine the activity of labeled β, a construct α(C193S)₃β(S205C)₃γ(S107C) was expressed and labeled with Cy3 at 1:8–20, resulting in 0.5–1.0 mol of Cy3 per cysteine. ATPase activity was measured as described (9).

Microscope. A laser beam (532 nm, DPSS 532–200, Coherent Radiation, Palo Alto, CA) was introduced into an inverted microscope (IX70, Olympus) through a water-immersion objective (PlanApo ×60, numerical aperture 1.2, Olympus). Fluorescence was divided into <620-nm (Cy3) and >620-nm (Cy5) components (17) and focused onto an intensified (VS4–1845, Videoscope, Dallas) charge-coupled device (CCD-300T-IFG, Dage-MTI, Michigan City, IN) camera. Bandpass filters (Chroma Technology, Brattleboro, VT) reduced the cross talk between Cy3 and Cy5 channels to <3%. The excitation efficiency of Cy5 at 532 nm was <0.03 times that of Cy3. Images recorded on a videotape were captured in a personal computer (LG3, Scion, Frederick, MD) and analyzed off-line with custom software. Because only Cy5 close to a donor emitted fluorescence, we could find FRET pairs (F₁ having both Cy3 and Cy5) by looking for fluorescence of Cy5. Most FRET pairs (>99%) did not show time-dependent change of the FRET yield, presumably because of surface denaturation (18). In the Cy3 channel, we observed many more fluorescent spots that lack companion spots in the Cy5 channel. Most of them photo-bleached in a single step. These presumably represent F₁ carrying a single Cy3 fluorophore without Cy5 acceptor.

Calculation of Distance Between FRET Pairs. The FRET yield f was obtained experimentally as f = aCy5/(Cy3 + aCy5), where Cy5 and Cy3 denote the fluorescence intensities above the background and a is the ratio of the intensity change of two dyes, ΔCy3/ΔCy5 (see Fig. 3E). The distance between the donor and acceptor was calculated as R = R_o(1/f – 1)^1/6, where f is the experimental FRET yield and R_o is the Förster distance (19). R_o was determined as [(8.79 × 10¹⁷)·n^–4·κ²·Q_D·J]^1/6 (nm), where J, the overlap integral, was calculated from measured emission spectrum of (Cy5-γ)F₁ and absorption spectrum of (Cy3-β)F₁ to be 8.85 × 10^–13 M^–1·cm³, Q_D = 0.25 is the quantum yield of the donor measured with rhodamine-B (quantum yield = 0.49; ref. 20) as reference, n = 1.33 is the refractive index of water, and κ² = 0.667 ± 0.524 (see below) is the orientation factor. The error in R_o was mainly from κ² and was estimated as δR_o = R_o·δ(κ²)/(6κ²). Resulting R_o was 5.9 ± 0.8 nm. The error in R was estimated as (, where δf is the standard error for f.

Fig. 3.

Changes in the FRET yield accompanying rotation. (A–C) Time courses of Cy3 (red) and Cy5 (black) fluorescence at different [ATP]. Arrows indicate photobleaching of Cy5 (A) or Cy3 (B and C). (D–F) Correlation between Cy3 and Cy5 intensities in A–C (data up to the arrow are scored). Straight lines in A–F represent the background intensities for Cy3 (red) and Cy5 (black) channels measured near the FRET pair.

Calculation of Orientation Factor. The orientation factor κ² is defined as κ² = 〈(cosθ_T – 3 cosθ_D cosθ_A)²〉, where θ_T is the angle between μ_D and μ_A, the donor emission and acceptor absorption transition moments, and θ_D is the angle between μ_D and d and θ_A between μ_A and d, where d is the vector connecting the donor and acceptor (19). Because none of these angles are known, we assigned arbitrary orientations to μ_D, μ_A, and d and calculated average κ² for that combination while allowing μ_D and μ_A to wobble within a cone around the assigned axis. This calculation was repeated for all combinations of μ_D, μ_A, and d, giving the average and standard deviation for κ². The cone angle ϕ_X (X = A or D) for the subnanosecond wobble of the fluorophore is related to the limiting and residual fluorescence anisotropy r_o and r_inf (21) by r_inf = r_o·[cosϕ_X(1 + cosϕ_X)/2]². r_o and r_inf in turn are related with the steady-state anisotropy r_s (21) by r_s = (r_o – r_inf)/(1 + τ/τ_r) + r_inf, in which τ is the fluorescence lifetime and τ_r the rotation correlation time of the dye. τ/τ_r was estimated, by assuming that τ_r is not much different from the correlation time of free dye in water, as (τ/τ_r)_waterQ_protein/Q_water, where Q_protein and Q_water are the quantum yields of the dye on protein and in water, and (τ/τ_r)_water is the quantity for free dye in water that was measured as (τ/τ_r)_water = (r_o/r_water – 1), where r_water is the steady-state anisotropy of the free dye in water. The steady-state fluorescence anisotropy r_s was measured in a cuvette by using a spectrofluorometer (F-4500, Hitachi, Tokyo) to be 0.29, 0.30, 0.26, and 0.17 for (Cy3-β)F₁ (some proteins contain multiple Cy3), (Cy5-γ)F₁, free Cy3, and free Cy5, respectively (λ_ex = 550 and 650 nm, λ_em = 590 and 690 nm, respectively for Cy3 and Cy5). Lower limit of r_o (giving lower limit of the cone angle) was measured as the steady-state anisotropy of the dyes in glycerol at 0°C to be 0.36 for Cy3 and 0.39 for Cy5. The quantum yield Q was measured as 0.25, 0.26, 0.03, and 0.25, respectively, for Cy3-F₁, Cy5-F₁, free Cy3, and free Cy5, using rhodamine-B as a reference. From measured r_s, r_o, and Q, the wobble cone semiangles were obtained as ϕ_D >25° and ϕ_A >33° for Cy3 and Cy5 on F₁.

Derivation of Possible Positions of FRET Pair. The linker length from the dye center to the labeled cysteine sulfur was estimated to be 1.2 and 1.7 nm for Cy3 and Cy5, respectively, from the bond angles and lengths. The donor and acceptor were assumed to be within the linker lengths of the labeled cysteines (β205 and γ107; β203 and γ99 in the MF₁ sequence). Because γ97–100 in MF₁ are unresolved in the crystals, possible positions of γ99-S (mutated to cysteine) were calculated as follows: the peptide backbone was extended from the visible γ101 to γ99 by assigning standard bond lengths and angles while allowing arbitrary rotations around N—C_α (Φ) and C—C_α (Ψ) bonds. If resultant γ99-C is not within 1.0 nm (maximum possible length between γ99-C and γ96-C) from γ96-C, the structure was discarded. Carbonyl oxygens and amino nitrotgens and γ99-C_β were modeled automatically assuming the standard l-amino acid configuration (no need to model a side chain for γ100 glycine). Finally, C_α—C_β bond in γ99 was rotated into an arbitrary angle to locale γ99S. During the construction, if an added atom (excluding hydrogen) was within 0.15 nm of the visible atoms in the crystal, that structure was also discarded. After 5,000 trials, we obtained 562, 462, and 2,323 possible γ99S locations for native MF₁, , and MF₁-dicyclohexylcarbodiimide (DCCD). For each location, we assigned a sphere of radius 1.7 nm and assumed that the acceptor could be anywhere in the sphere with the same probability. The acceptor spheres seen in Fig. 5 show the outermost circumference enclosing all possible acceptor position. In the native MF₁ (1), γ91–96 and γ101 are also missing, and we adopted the structure (12) for this part.

Fig. 5.

(A) Side (Left) and top (Right) views of the backbone trace of the structure of MF₁ (13), color-coded as in Fig. 1 A. Small and large spheres represent geometrically allowed positions of the donor (Cy3) and acceptor (Cy5), respectively, on the native MF₁, , and MF₁-DCCD structures (blue, black, and pink); the degree of twist in γ varies among the three structures, resulting in the slight deviations of large circles. Red dots indicate possible acceptor positions calculated from the FRET results (see Materials and Methods). The black line indicates the putative rotation axis. (B) The acceptor sphere (and γ) is rotated counterclockwise by 40°.(C) Probability (p) of finding red dots in the acceptor sphere as functions of γ angle (θ) for native MF₁ (blue), MF₁-DCCD (pink), and (black). Larger values between p(θ) and p(θ + 120°) are plotted.

Positions of the acceptor compatible with our FRET results (see Fig. 5 A and B, red dots) were obtained as follows. First, we randomly assigned a donor position from the donor sphere, removing the positions inside the protein by discarding the positions within 0.4 nm of the atoms in the crystal structure. We also chose μ_D and μ_A randomly. Instead of rotating the acceptor, we rotated the donor into three equivalent positions, assuming the same linker vector and μ_D for the three (simple 120° rotations). Then we selected three FRET efficiency values f, one for a high-FRET state and two for low-FRET states, assuming a Gaussian distribution for f with half-width at 1/e maximum equaling the experimental standard error. The remaining task was to find three donor-acceptor vectors d that are compatible with the chosen conditions. This was done in an iterative search for the orientation and absolute value of d by first assigning random orientations to the three vectors d. (i) We calculated three orientation factors from the chosen orientations of d, μ_D, and μ_A, while allowing μ_D and μ_A to wobble in the respective cones. (ii) This gave three distances |d|, from which we determined the acceptor position. Two answers were obtained, above and below F₁, and we always chose the one above. (iii) From the acceptor position, we extracted three orientations of d, disregarding the absolute values, and repeated steps i-iii. We stopped the iteration when the differences in the three orientations between two adjacent iteration cycles all became <0.5°.In ≈10% of trials, the calculation did not converge within 500 iterations and we gave up. For a chosen set from ≈1,800 donor positions, μd and μ_A, we always attempted five independent iterations starting from different and randomly selected orientations of d. These gave consistent results within 0.2 ± 0.04 nm (mean ± SD), when converged. Finally, if the obtained acceptor position was within 0.4 nm of the crystal atoms that position was discarded (to avoid physical conflicts). Red dots seen in Fig. 5 A and B represent results obtained in this way. When we rotated γ for a better fit with the experimental FRET efficiencies (see Fig. 5), the final check of physical conflicts was made for each γ orientation; the number of remaining red dots did not depend significantly on the γ angle, ranging from 1,340 to 1,414, 1,144 to 1,308, and 1,078 to 1,187, respectively, for native MF₁, , and MF₁-DCCD.

The probability of finding a FRET-compatible acceptor position (see red dots in Fig. 5 A and B) among the possible acceptor positions in the crystal structures was estimated by counting the number of red dots within the acceptor-linker length of a possible γ99-S position, averaging this number over all possible γ99-S positions, and dividing the average by the total number of the red dots. We also calculated the probabilities for rotated γ by rotating the acceptor spheres.

Results

Visualization of F₁ Rotation Through Single-Pair FRET. To label one of the three βs with Cy3 (Fig. 1), we expressed β alone with an engineered cysteine and labeled it with Cy3. The labeled β was exchanged into an independently expressed F₁ of which γ had been labeled with Cy5, resulting in 0.05–0.2 mol of labeled β and 0.7–1.0 mol of labeled γ per mol of F₁. The effect of β mutation and labeling was checked in yet another F₁ construct where all three βs had the cysteine and were fully labeled (Fig. 2): at low [ATP] where hydrolysis rate was proportional to [ATP], the apparent rate of ATP binding was estimated as and for the labeled and unlabeled F₁. When only one of three β was labeled, therefore, the rotation at low [ATP] where ATP binding is rate limiting will consist of alternate one slow and two fast steps, as has been demonstrated for an F₁ chimera of normal and slow β subunits (22).

Fig. 2.

Effect of labeling on ATPase activity (11). F₁ with a sole cysteine at γ was labeled with Cy3 (green) or unlabeled (black). F₁ with four cysteines (one each in βs and γ) were fully labeled (red), 50% labeled (pink), or unlabeled (blue). Smooth curves are fits with V_max[ATP]/([ATP] + k_M) (green, red, pink, blue) or with (V_maxk_M + V_max2[ATP]²)/([ATP]² + k_M2[ATP] + k_Mk_M2) (black). The rate of ATP binding, k_on, was estimated as V_max/k_M = (1.1 ± 0.3) × 10⁷ M^–1·s^–1 (green), (5.4 ± 0.9) × 10⁶ M^–1·s^–1 (blue), (1.9 ± 1.1) × 10⁶ M^–1·s^–1 (red), (2.8 ± 1.2) × 10⁶ M^–1·s^–1 (pink), and (1.65 ± 0.32) × 10⁷ M^–1·s^–1 (black).

Under an epi-fluorescence microscope, Cy3 was selectively excited at 532 nm, and emissions from Cy3 and Cy5 were simultaneously imaged. The two showed alternate and stepwise intensity changes in the presence of ATP (Fig. 3 A–C), indicating alternation of the FRET yield between high and low states. The rate of alternation was faster at higher [ATP], as expected for ATP-dependent stepwise rotation of γ. When Cy3 lost its companion acceptor by photobleaching of Cy5, the fluorescence of Cy3 increased (arrow in Fig. 3A). If Cy3 bleaches before Cy5, both are expected to disappear simultaneously, as was indeed observed (arrows in Fig. 3 B and C). There was a clear correlation between Cy3 and Cy5 fluorescence, showing the existence of two FRET states (Fig. 3 D–F).

The transition rates between the high- and low-FRET states, defined as the inverse of the averaged dwell times, (1/〈τ_H〉 and 1/〈τ_L〉), were each proportional to [ATP] (Fig. 4), confirming that the change in the FRET yield represents rotation steps. The rate of rotation, estimated as 1/(〈τ_H〉 + 〈τ_L〉), was also proportional to [ATP] (Fig. 4A).

Fig. 4.

(A) ATP dependence of the transition rate from the high and low FRET states (1/〈τ_H〉 and 1/〈τ_L〉) and the rotation rate estimated as 1/(〈τ_H〉 + 〈τ_L〉) (160 FRET states were analyzed in 15 FRET pairs). For comparison, the rate of ATP hydrolysis in F₁ without the subunit labeling is shown (Fig. 2 A). Lines show linear fits with slopes (± SE) of (4.9 ± 0.7), (10.9 ± 1.3), (3.3 ± 0.4), and (16.5 ± 0.2) × 10⁶ M^–1·s^–1 for 1/〈τ_H〉, 1/〈τ_L〉, rotation, and ATPase, respectively. (B) Histogram of dwells, τ, of the high (black) and low (orange) FRET states. Solid curves show fit for case i in the text: low FRET dwell (red) with constant·τ[ATP]exp(), where is the ATP binding constant of unlabeled F₁ from Fig. 2, and high FRET dwells (black) with constant·exp(), where is for labeled β (χ² = 257, 80 dwells, 15 FRET pairs). Dashed curves show fit for case ii in the text: low FRET dwells (red) with constant·exp(), and high FRET dwells (black) with constant·{exp, where and are fixed to the experimental values above (χ² = 497, 80 dwells, 15 FRET pairs).

For 120° stepping, three FRET states are expected, as observed for a different donor-acceptor pair (15). In our experiments, two of three states were indistinguishable, leading to two possibilities: (i) the high-FRET state with a longer dwell (〈τ_H〉/〈τ_L〉 = 2.3 ± 0.3) involved one slow step associated with the labeled β and the low-FRET state involved two normal steps, or (ii) the high-FRET state involved one normal and one slow steps and the low-FRET state involved one normal step. For each case, the rates of ATP binding, and were calculated from the observed dwell times and compared with the rates estimated from ATP hydrolysis. For case i, is given as 〈τ_H〉^–1[ATP]^–1 = (3.8 ± 0.7) × 10⁶ M^–1·s^–1 and as 2〈τ_L〉^–1[ATP]^–1 = (1.6 ± 0.3) × 10⁷ M^–1·s^–1, both of which agree with and estimated from the ATPase activity. For case ii, and , inconsistent with the ATPase results. Thus, the low-FRET state involved two normal steps, and the high-FRET state involved one slow step. Histograms of dwell times (Fig. 4B) were also better fit with model i.

ATP-Waiting Conformation of F₁. The FRET yields in the high- and low-FRET states were calculated from the observed fluorescence intensities as 0.56 ± 0.06 and 0.15 ± 0.03, respectively, corresponding to the donor-acceptor distances of 5.7 ± 0.9 and 7.9 ± 1.0 nm. Because the low-FRET state involves two rotation steps, the distance between the two dyes will change as 5.7, 7.9, and 7.9 nm during rotation. These values are to be compared with the known crystal structures of F₁.

Three different crystal structures of MF₁ have been solved: a “native MF₁” structure in which AMP-PNP, ADP, and none occupy the three catalytic sites (1), an “MF₁-DCCD” structure that is inhibited with DCCD and has the same nucleotides as the native MF₁ (12), and an “” structure, which is inhibited with aluminum fluoride and has two ADP and one ADP (13). To compare these structures, we adopt the triangle made of three α-carbons of α-GLU26 as the frame of reference (23); a line perpendicular to, and passing through the center of, the triangle is assumed to be the rotation axis. The conformation of γ inside the α₃β₃ cylinder varies little among the three crystal structures, whereas part of γ near the upper orifice of the α₃β₃ cylinder is twisted clockwise (opposite to the rotation direction) up to 20° and 11° in ) and MF₁-DCCD, respectively, compared with the native MF₁ when viewed from above in Figs. 1 and 5 (13).

In these structures, the position of the residue labeled with the acceptor, which is on the protruding portion of γ, varies to some extent, while the donor residues occupy the same positions. Possible positions of the donor and acceptor in the three MF₁ structures are essentially the same (Fig. 5A, small and large spheres for the donor and acceptor, respectively). The acceptor spheres are larger, because several residues around the acceptor site are unresolved in the structures and linker length of the acceptor is longer than that of the donor. Starting with the donor positions that are common to all structures, we calculated acceptor positions that are compatible with the three FRET efficiencies above (red dots in Fig. 5 A and B). The FRET-estimated acceptor positions overlap best with the acceptor sphere (large ones) when γ was rotated counterclockwise by ≈40° in all MF₁ crystals (Fig. 5C). Because FRET measurements were done at low ATP concentrations where binding of ATP limits the rotation rate, this conformation corresponds to the ATP-waiting state of F₁.

Discussion

Rotation Mechanism of F₁-ATPase. Our FRET results suggest that the conformation of γ in the ATP-waiting state of F₁ is ≈40° counterclockwise, or ≈40° in the rotation direction, from that in the MF₁ crystal structures. Then, which kinetic state do the MF₁ structures correspond to? At least one intermediate state during rotation, other than the ATP-waiting state, has so far been resolved: binding of ATP to F₁ in the ATP-waiting state induces a counterclockwise ≈90° substep, and F₁ remains at this intermediate angle for ≈2 ms before undergoing a further ≈30° substep induced by product release (11). When F₁ is inhibited on tight binding of MgADP, the rotation stalls at ≈80° (24), suggesting that the inhibited conformation resembles that of the intermediate state after the ≈90° substep. Naively, crystal structures are expected to be close to the 90°/80° conformation rather than the ATP-waiting conformation, because crystallization involves long incubation with MgADP or MgATP, a condition that favors the formation of the MgADP-inhibited enzyme (25), as has been suggested in cross-linking studies (26). If so, expected acceptor positions in the ATP-waiting state should be 30°/40° ahead the crystal structures (Fig. 5B). Our FRET results (Fig. 5, red dots) indeed point to this position, suggesting that the crystal structures are closer to the 90°/80° conformation rather than the ATP-waiting conformation (0° or 120°).

Whether rotation of F₁-ATPase requires filling of all three catalytic sites with a nucleotide (27) or filling two is sufficient (28) is an important, but unresolved, issue. Because γ orientation in both the 2- and 3-nt crystal structures differ from our results by 40°, the ATP-waiting conformation likely binds a single nucleotide. If so, rotation under our experimental conditions occurs by filling at most two catalytic sites.

The protruding part of γ in crystals of F₁ from Escherichia coli (29) or the thermophilic bacterium (Y. Shirakihara, personal communication) is twisted counterclockwise compared with the MF₁ structures, such that possible acceptor positions in these bacterial crystals are close to the large circles in Fig. 5B. Our FRET results obtained with the thermophilic F₁ are consistent with these positions. In particular, the thermophilic bacterial crystal contained only 1 nt, suggesting again that the ATP-waiting state corresponds to a single-nucleotide state.

Our interpretations above rest on the assumption that the crystal structures closely mimic an active rotation intermediate hosting the same number of nucleotides. However, the lattice packing may have deformed the F₁ structure in the crystals (12, 13). The twist of γ in and MF₁-DCCD, relative to native MF₁, is maximal around the orifice of the α₃β₃ cylinder and is smaller both above and below the orifice, suggesting some distortion. In particular, native MF₁ and MF₁-DCCD both have two catalytic nucleotides, and yet γ in MF₁-DCCD is twisted clockwise up to 11°. Significantly, the MF₁-DCCD crystal is more closely packed than the native MF₁ crystal, and the bacterial crystals in which γ is twisted counterclockwise are less densely packed. A possibility thus exists that 2-nt MF₁ in a relaxed crystal might show a γ orientation similar to the bacterial one. If so, our FRET results might point to the necessity of three-site filling. FRET with different donor-acceptor pairs will help resolve the remaining ambiguity.

Analysis of Protein Conformation Through Single-Pair FRET. FRET is a standard technique for measuring distances in the 1- to 10-nm range and often used for analyzing conformation of proteins and nucleotides in solution (30). For analysis of transient protein conformations, FRET measurement on individual donor-acceptor pairs is essential because protein molecules behave stochastically and their operations cannot be synchronized.

In this study, we have demonstrated that single-pair FRET reveals a transient conformation of F₁-ATPase with nanometer precision. The resolution, limited mainly by the ambiguity in the orientation factor and the relatively large linker length between the fluorophore and target residue, could be improved by synthesizing short-linker fluorophores and searching for a proper fluorophore-residue combination that warrants an extensive wobble of the fluorophore on the protein surface.