The F₁F_O ATP synthase (Figure 1) that is found in all animals, plants, and eubacteria is comprised of two molecular motors that are attached by their rotors and by their stators (Kühlbrandt, 2019; Spetzler et al., 2012). The F_O motor, which is embedded in bioenergetic membranes, uses a non-equilibrium transmembrane chemiosmotic proton gradient also known as a proton-motive force (pmf) to power clockwise (CW) rotation of its ring of c-subunits relative to the subunit-a and -b stator proteins as viewed from the Escherichia coli periplasm. These subunits contribute to the peripheral stalk bound to one side of the F₁ (αβ)₃-subunit ring where each αβ-heterodimer comprises a catalytic site that synthesizes ATP from ADP and Pi. Subunit-γ, which docks to the c-ring along with subunit-ε, extends into the core of the (αβ)₃-ring (Figure 1B). The rotary position of subunit-γ within the (αβ)₃-ring causes the conformations of the three catalytic sites to differ such that one site contains ADP and Pi, a second site contains ATP, and the third site is empty. Pmf-powered CW rotation of subunit-γ forces conformational changes to all catalytic sites in the (αβ)₃-ring, which releases ATP from one catalytic site with each 120° rotational step (Kühlbrandt, 2019; Spetzler et al., 2012). In this manner, F₁F_O converts the energy from the pmf (Δμ_H+) into energy in the form of a non-equilibrium chemical gradient (Δμ_ATP) where the ATP/ADP•Pi concentration ratio is far in excess of that found at equilibrium.

Figure 1

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When ΔG_ATP is significantly higher than n*pmf, the F₁-ATPase motor can overpower the F_O motor and catalyze net ATP hydrolysis (Steigmiller et al., 2008; Fischer et al., 2000). This results in ATPase-dependent power strokes that rotate continuously CCW for 120° at saturating ATP concentrations (Yasuda et al., 2001; Spetzler et al., 2006), and pump protons across the membrane to the periplasm in E. coli (Spetzler et al., 2012). Power strokes are separated by catalytic dwells that last a few ms, during which ATP is hydrolyzed (Yasuda et al., 2001; Spetzler et al., 2006; Spetzler et al., 2009). At rate-limiting ATP concentrations, an ATP-binding dwell can interrupt the E. coli F₁ power stroke ~34° after the catalytic dwell (Yasuda et al., 2001; Martin et al., 2014). At this same rotary position, high ADP concentrations can compete with ATP to bind to the empty catalytic site resulting in ADP inhibition (Martin et al., 2014). All ATP synthases can catalyze ATP hydrolysis to some extent, although many have evolved regulatory mechanisms to minimize this energy wasteful process (Kühlbrandt, 2019). Under some circumstances, E. coli employs F₁F_O as an ATPase-driven H⁺ pump to maintain a pmf as an energy source for other metabolic processes (Spetzler et al., 2012).

The means by which H⁺ translocation from the periplasm generates CW rotational torque on the c-ring is poorly understood. Molecular motors are believed to operate by either power stroke or by a Brownian ratchet mechanism, which has been postulated for F_O (Hwang and Karplus, 2019; Oster et al., 2000). Although evidence clearly supports a power stroke mechanism for F₁-ATPase-dependent rotation (Martin et al., 2014; Martin et al., 2018; Pu and Karplus, 2008), there is little direct evidence in support of either mechanism for F_O-driven rotation in the ATP synthase direction. Protons enter and exit F_O via half-channels in stator subunit-a. Two c-subunits in the ring contact subunit-a at a time where the leading cD61 during CW rotation (synthase direction) accepts a proton from the input channel, while the lagging cD61 donates its proton to the output channel.

The half-channels are separated by the highly conserved subunit-a arginine (aR210 in E. coli), which has long been thought to be responsible for displacing the H⁺ from cD61 into the output channel during ATP synthesis (Lightowlers et al., 1987; Cain and Simoni, 1989; Cain and Simoni, 1988; Vik et al., 1988). As the result of mutations of E. coli subunit-a residues aN214, aE219, aH245, aQ252, and aE196 to other groups including leucine that decreased ATP synthase activity, ATPase-dependent H⁺ pumping, and altered the ATP hydrolysis activity, these residues were proposed to translocate protons directly along the half-channels (Lightowlers et al., 1988; Howitt et al., 1990; Eya et al., 1991; Hartzog and Cain, 1994; Hatch et al., 1995; Hahn et al., 2018). Cryo-EM F₁F_O structures that reveal details of subunit-a confirmed that these residues are positioned along possible half-channels that are separated by aR210 (Hahn et al., 2018; Zhou et al., 2015; Pinke et al., 2020; Sobti et al., 2020; Martin et al., 2015).

Alternatively, H⁺ translocation through F_O has also been postulated to occur via a Grotthuss mechanism (Cukierman, 2006) where a column of single water molecules that are hydrogen-bonded to specific protein groups behave in a coherent manner to transfer protonic charge over long distances via rapid exchange of H⁺ between H₃O and H₂O (Cukierman, 2006; Wraight, 2006). A recent F₁F_O structure from bovine mitochondria was of sufficient resolution to observe density near the input channel residues consistent with Grotthuss-type water molecules in this half-channel (Spikes et al., 2020). A consequence of this coherent behavior of a Grotthuss water column is that the rate of H⁺ transfer can be much faster than the rate via free diffusion (Cukierman, 2006). The possibility that F_O operates via a Grotthuss mechanism was first suggested from the observation of an astounding H⁺ translocation rate of 6240 H⁺ s^–1 from a driving force of 100 mV across Rhodobacter capsulatus vesicles containing F_O that lacked F₁ (Feniouk et al., 2004). The R. capsulatus F_O rates of H⁺ transfer exceed the rate of delivery of protons by free diffusion from the bulk aqueous solution at a concentration of 10^–8 M (pH 8) such that the ability to supply protons to a Grotthuss water column should be rate-limiting (Wraight, 2006). To achieve this rate of H⁺ translocation, the existence of a H⁺ antenna at the entrance to the F_O input channel has been postulated (Wraight, 2006), which in R. capsulatus, was calculated to consist of a hemispherical Coulomb cage with a H⁺ capture radius of ~40 Å surrounding the entrance to the input channel.

Single-molecule studies of F₁F_O molecules embedded in lipid bilayer nanodiscs (Figure 1C) revealed that the 120° CCW ATPase power strokes can be interrupted by transient dwells (TDs) at ~36° intervals with a duration of ~150 μs (Martin et al., 2015; Ishmukhametov et al., 2010; Yanagisawa and Frasch, 2017). In more than 70% of TDs, the F_O motor not only halted F₁-ATPase CCW rotation, but the c-ring rotated CW in synthase-direction steps (Martin et al., 2015; Yanagisawa and Frasch, 2017). Complete assembly of F₁F_O nanodisc complexes from the membrane scaffold protein (MSP), lipids, and detergent-solubilized F₁F_O was verified by 2D electrophoresis where the first nondenaturing gel dimension contained a single band, which after the second denaturing dimension, contained bands corresponding to MSP and all F₁F_O subunits (Ishmukhametov et al., 2010). The ATPase activity of nanodisc preparations is DCCD-sensitive, remains unchanged after 8 hr at room temperature, and is 1.5-fold higher than the initial activity of detergent-solubilized F₁F_O, which loses all activity in <4 hr. The observation that a subunit-a insertion mutation, which disrupts the interface between subunit-a and the c-ring, retained ATPase activity but lost the ability to form TDs indicates that these dwells result from an interaction between subunit-a and successive c-subunits in the c-ring (Ishmukhametov et al., 2010).

The occurrence of TDs was found to increase at pH 8 when viscous drag on the nanorod is sufficient to slow the angular velocity of the F₁ ATPase-driven power stroke (Martin et al., 2015; Ishmukhametov et al., 2010). These results showed that there is a kinetic component that affects the probability that the interaction between subunit-a and the c-ring will occur relative to the F₁-ATPase power stroke. A kinetic dependence for F₁F_O-catalyzed ATP synthesis versus hydrolysis has been theorized based on energetic calculations (Gao et al., 2005). Occurrence of TDs, including those with synthase-direction steps, is also known to increase inversely with pH between pH 5 and pH 7 (Yanagisawa and Frasch, 2017). This suggests that synthase-direction steps depend on H⁺ transfer from the protonated groups with a low pKa from the subunit-a input channel to the c-ring, and from the c-ring to unprotonated groups with a high pKa in subunit-a output channel.

Maximal ATP synthase rates in membrane vesicles where E. coli F₁F_O is oriented with F₁ on the outer surface are typically achieved with inner and outer pH values of 5.0 and 8.5, respectively (Fischer et al., 2000; Fischer et al., 1994). The pmf can be derived from non-equilibrium differences in pH (ΔpH) or membrane potential (Δψ). Although the energy from ΔpH and Δψ to drive ATP synthesis are interconvertible, the latter is the dominant energy source for E. coli in vivo.

Each of the three successive 120° F₁-ATPase power strokes required for a full revolution of the F₁F_O rotor is unique because the rotary positions of subunit-γ differ relative to the peripheral stalk that includes subunit-a (Figure 1A–C). These power strokes also differ because the 36° stepping of the c₁₀-ring and the 120° power strokes can only be aligned during one of the three catalytic dwells. As a result, the three power strokes require the translocation of 4 H⁺, 3 H⁺, and 3 H⁺ that result in net c-ring rotations of 144°, 108°, and 108°, respectively. Consequently, the c-ring and subunit-γ become misaligned by +14° and −14° during two of the catalytic dwells. The elasticities of the peripheral stalk, subunit-δ, and to some extent, subunit-γ accommodate these rotary differences (Sobti et al., 2020; Murphy et al., 2019).

The positive and negative torsion on the c₁₀-ring from the elastic energy needed to accommodate the +14° and −14° misalignments during rotation affects the ability to form TDs and their associated synthase-direction steps (Yanagisawa and Frasch, 2017), which along with their pH dependence and occurrence every 36°, indicate that they correspond to single c-subunit stepping relative to subunit-a. To determine the percentage of power strokes in which TDs were observed, data sets were collected from one of the three 120° power strokes from each single-molecule of nanodisc-embedded E. coli F₁F_O examined. For each data set that comprised ~300 power strokes, the percent of power strokes that contained TDs was determined. For each molecule examined there was an equal chance that the c-ring and catalytic dwell was aligned, or subject to the positive or negative torsion from misalignment. The distribution of data sets collected from many molecules versus the percent of power strokes containing TDs fit to the sum of three Gaussians that corresponded to low, medium, and high probabilities of TD formation. The high and low TD percentages were consistent with the torsion from misalignment that provides additional energy to promote TD formation, or to inhibit it when torsion is in the opposite direction (Yanagisawa and Frasch, 2017). Similar effects of the c₁₀-ring and catalytic dwell misalignments have also been observed in other single-molecule F₁F_O measurements (Sielaff et al., 2019).

We have now examined mutations of residues in the putative subunit-a half-channels that have been implicated to participate in H⁺ transfer events in both the input and output channels with the goal of distinguishing whether F_O rotation occurs via a Brownian ratchet versus a power stroke mechanism, and whether the half-channel residues transfer protons individually or act together to support water column that transfers protons via a Grotthuss mechanism.

The ability to form ATP synthase-direction steps as a function of pH during ATP hydrolysis-driven CCW power strokes was characterized in single-molecule studies of F₁F_O molecules embedded in lipid bilayer nanodiscs. Formation of synthase-direction steps during a TD was maximal at the pH value when unprotonated and protonated forms of the input and output channels were optimal such that synthase-direction steps required H⁺ transfer both from the input channel to the leading c-subunit and from the lagging c-subunit to the output channel. Mutation of a residue from either the input or output channel altered both the low and high pKa values of TD formation indicating that input and output channels communicate. This is consistent with a Grotthuss mechanism where a water column in each of the two channels is connected by rotation-dependent H⁺ transfer to and from the leading and lagging c-subunits in the c-ring, which is also supported by features from a variety of F₁F_O structures.

The extent of rotation during ATP synthase-direction steps was unexpectedly found to rotate 11° in the WT and all mutants. Cryo-EM structures of sub-states with subunit-a:c-ring differences of 11° that position the lagging c-subunit cD61 adjacent to output residues aS199 and aE196 (Sobti et al., 2020) are consistent with the synthase-direction steps observed here. When combined with structural information, the results do not support the hypothesis that the role of aR210 is to displace the H⁺ from cD61, but are consistent with a Grotthuss H⁺ translocation mechanism involving both half-channels for sustained ATP synthase-direction c-ring rotation that results from successive alternating 11° and 25° synthase-direction sub-steps for each c-subunit in the c₁₀-ring. Direct evidence of a mixed model was observed in which some synthase-direction steps show characteristics of a power stroke while others exhibit oscillations consistent with a Brownian ratchet mechanism.

Contributions of subunit-a residues putatively involved in the ATP synthase H⁺ half-channels were assessed by the effects on TD formation caused by mutations that converted charged or polar groups in subunit-a to hydrophobic leucine. Changes in rotational position were measured by a 35 × 75 nm gold nanorod (AuNR) bound to the biotinylated c-ring of individual E. coli F_OF₁ molecules embedded in lipid bilayer nanodiscs (Ishmukhametov et al., 2010), hereafter F₁F_O (Figure 1C). Changes in rotational position during F₁-ATPase power strokes in the presence of saturating 1 mM MgATP were monitored by the intensity of polarized red light scattered from the AuNR (Spetzler et al., 2006; Hornung et al., 2011). Prior to data collection, the polarizer was adjusted so that the scattered red light intensity was at a minimum during one of the three F₁ catalytic dwells (Figures 1D and 2A). The subsequent power stroke caused an increase in light intensity to a maximum when the AuNR had rotated 90° (Ragunathan et al., 2017). Rotational data sets of each F₁F_O molecule examined were collected for 5 s, which included ~300 of these power strokes (Yanagisawa and Frasch, 2017). Ten data sets were collected for each molecule. The number of F₁F_O molecules examined at each pH for WT and mutants is indicated in Figure 2—figure supplement 3. Using WT at pH 5.0 as an example where data from 103 F₁F_O molecules were collected, this was equivalent to 1030 data sets, and ~309,000 power strokes examined. For each molecule examined, rotational position versus time was calculated from scattered light intensity versus time using an arcsine^1/2 function from which the number of TDs observed during the first 90° of rotation were determined (Ragunathan et al., 2017).

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Example power strokes from WT and mutant F₁F_O molecules at pH 5.0 where TDs were present (black dots) and absent (blue dots) are shown in Figure 2A and Figure 2—figure supplement 1, respectively. When present, TDs either stopped F₁-ATPase CCW rotation momentarily (green dots) or exhibited CW rotation in the ATP synthase direction, hereafter synthase-direction steps (red dots). None of the mutations examined eliminated the ability of F₁F_O to form TDs. Power strokes typically contained two to three TDs, when present. These were separated by an average of ~36°, consistent with an interaction between subunit-a and successive c-subunits in the c₁₀-ring of E. coli F₁F_O.

A power stroke mechanism has been defined as the generation of a large free energy gradient over a distance comparable to the step size of the molecular motion so that transition to the forward position occurs nearly irreversibly (Hwang and Karplus, 2019). By contrast, in a Brownian ratchet mechanism the motor is thought to visit previous and forward positions through thermal motion, where stabilization in the forward position results by conformational changes triggered by the fuel processing event. While some synthase-direction steps shown of Figure 2A and Figure 2—figure supplement 1 rotated CW in a concerted, and apparently irreversible manner characteristic of a power stroke, others indicated by brackets were observed to oscillate back and forth during the TD. These oscillations most commonly occurred late in the F₁ power stroke (~70–80°) and were more pronounced in all mutations examined except aN214L (Figure 2—figure supplement 1). Such oscillations are direct evidence of a Brownian ratchet mechanism and are likely the result of a close balance between the energy that powers the F₁-ATPases power stroke with the energy that powers synthase-direction rotation, which suggests that these mutations cause a decrease in the energy to power synthase-direction rotation.

Subunit-a mutations affect TD formation efficiency

The percent of TDs observed per data set was fit to three Gaussian distributions with low (blue), medium (orange), and high (green) efficiencies as shown at pH 6.0 (Figure 2C), and at all pH values examined (Figure 2—figure supplement 3). These efficiency differences were proposed to result from elastic energy resulting from the 14° rotational mismatch between two of the three catalytic dwells and the c₁₀-ring that supplements or subtracts from the binding energy required for subunit-a to stop F₁-ATPase-driven rotation momentarily, resulting in a TD. If TDs result from H⁺ translocation-dependent interactions between subunit-a and the c-ring, mutations that impact H⁺ translocation should alter the TD formation efficiency.

Subunit-a mutations affected the percent of TDs formed per data set during power strokes in each of these efficiencies, which correlate to the three rotary positions of the central stalk relative to the peripheral stalk (Yanagisawa and Frasch, 2017; Sielaff et al., 2019). The proportional differences of efficiencies of TD formation are shown relative to the average low efficiency for WT (Figure 3). Medium and high efficiency distributions of TDs in WT increased 1.5-fold and 2.2-fold, respectively, relative to low efficiency. The aN214L mutation increased the percent of TDs per data set for high, medium, and low efficiencies by 3-fold, 2-fold, and 1.2-fold, respectively, from the WT low efficiency. Mutations aQ252L and aE219L also increased TDs per data set for the high (2.7-fold and 2.5-fold) and medium (1.7-fold and 1.6-fold), but not the low efficiency distributions. Mutations aH245L and aE196L either did not increase the efficiency or slightly decreased the efficiency of the distributions of TD formation per data set.

Figure 3

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Synthase-direction steps rotate CW an average of ~11°

The proportion of TDs with and without a synthase-direction step for WT and mutants are shown in Figure 4A at the pH values when the proportion of synthase-direction steps was minimum (black bars) and maximum (red bars), and at all pH values examined in Figure 4—figure supplement 1. The minimum proportion of synthase-direction steps was observed at pH 5.5 for WT and all mutants except aN214L that occurred at pH 6.0. Even at these low pH values, synthase-direction steps accounted for 62–68% of all TDs. In WT, a maximum of ~80% of TDs contained synthase-direction steps at pH 7.0, which was an increase of 13% from the minimum. These plots also show the distributions of the extent of CW rotation during a synthase-direction step, for which the 11° and 9° average and median values of CW rotation, respectively, were not changed significantly by the mutations (Figure 4B).

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After subtracting the occurrence of the extent of synthase-direction step CW rotation at the pH when it was at a minimum (black bars) from that observed at other pH values (Figure 4—figure supplement 1) including that at its maximum (red bars), a Gaussian distribution of the increase in the extent of synthase-direction step CW rotation was observed (Figure 4C). During a synthase-direction step, the mean and standard deviations in the extent of CW rotation (Figure 4—figure supplement 2) was 12° ± 3° for WT, with little variation resulting from the mutations including: 11° ± 3° (aN214L), 11° ± 4° (aQ252L), 11° ± 3° (aH245L), 10° ± 3° (aE219L), and 11° ± 3° (aE196L) . In all cases, the distributions were truncated with minimum CW rotational steps of 6°. At their maxima, the extents of CW c-ring rotation during synthase events rotated 25° and 36° about 1% and 0.1% of the time, respectively.

The results presented here provide new insight into the mechanism by which the F_O motor uses the energy from H⁺ translocation to generate CW rotational torque on the c-ring to catalyze ATP synthesis. These studies support the hypothesis that residues associated with the half-channels work together to support a water column that transfers protons across the membrane in a coherent manner coupled to c-ring rotation in lieu of transferring protons directly and independently. These single-molecule investigations also tested the hypothesis that c-rotation operates via a Brownian ratchet versus a power stroke mechanism, and the results provide the first direct evidence that synthase-direction steps can occur by both mechanisms. Finally, the results presented here show that the proton translocation-dependent synthase-direction rotation occurs in 11° steps. These results do not support the hypothesis that the function of the essential aR210 is to deprotonate cD61 because recent F_O structures show that the unprotonated lagging cD61 carboxyl is still 7.3 Å away from aR210 after an 11° c-ring rotation. Alternatively, an alternating two-step mechanism is proposed below to resolve this discrepancy.

F_O uses a Grotthuss mechanism to translocate protons through both half-channels

The results presented here support a Grotthuss mechanism in F_O where water columns in each half-channel communicate via rotation-dependent H⁺ transfer to and from the leading and lagging c-ring cD61 carboxyls. The coherent behavior of the water columns enables the release of a H⁺ to the cytoplasm concurrent with each H⁺ that enters the subunit-a input channel from the periplasm. This conclusion is supported by observations that: (i) ATP synthase-direction steps were maximal in WT and mutants when the fractions of protonated groups and unprotonated groups with low and high pKa values, respectively, were optimal for H⁺ transfer both from the lagging cD61 to the output channel and from the leading cD61 to the input channel; (ii) mutation of a residue from either the input or output channel altered both the low and high pKa values of TDs indicating that the channels communicate; (iii) all mutations changed the ability to form TDs, indicating all the groups examined participate; and (iv) none of the mutations completely eliminated the ability to form TDs.

This conclusion is also consistent with the fact that participating residues aS199, aN214, and aQ252 are polar but not ionizable, and distances between channel residues that are too far apart for direct H⁺ transfer but are positioned at distances able to support a water column. Although aQ252 is highly conserved (Figure 5—figure supplement 1), glycine or hydrophobic groups are naturally substituted: (i) for aN214 (Toxoplasma gondii, Thermus thermophilus); (ii) for aH245 (Mycobacterium phlei, Tetrahymena thermophila, Acetobacter woodii, Toxoplasma gondii, Ilyobacter tartaricus, Fusobacterium nucleatum, Thermus thermophilus); and (iii) for aE219 (Tetrahymena thermophila, Euglena gracilis, Bacillus pseudofirmus OF4, Pichia angusta, Saccharomyces cerevisiae, Arthrospira platensis PCC9438). Such mutations can be tolerated if the primary role of these groups was to support a water column that transferred protons.

A recent F₁F_O structure from bovine mitochondria was of sufficient resolution to observe density near the input channel residues consistent with Grotthuss-type water molecules in this half-channel (Spikes et al., 2020). Unidentified electron densities near subunit-a input channel residues in F₁F_O structures from E. coli (Sobti et al., 2020) and from Polytomella (Murphy et al., 2019) also suggest the presence of bound waters. The observation of a water column in both half-channels of the V_O complex (Roh et al., 2020) suggests that Grotthuss-based H⁺ translocation is a commonly shared trait among the greater family of rotary ATPases.

Additional structural evidence that supports the existence of a Grotthuss H⁺ translocation mechanism (Figure 5) is the presence of an ~30 Å diameter funnel that is lined with carboxylate and imidazole residues as the funnel narrows (Figure 5). The aE219-carboxyl examined here, which we propose to be the start of the Grotthuss column is positioned at the apex of this funnel. A Grotthuss mechanism was first proposed to explain extremely high rates of F_O-dependent H⁺ translocation across R. capsulatus membranes (Feniouk et al., 2004). The rates were so fast that an ~40 Å diameter Coulomb cage of charged and polar groups was proposed to be required to serve as a H⁺ ‘antenna’ to increase the delivery rate of protons from the aqueous solution to the entrance of the input channel water column (Wraight, 2006).

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The results presented here indicate that multiple residues contribute to the pKa values that enable synthase-direction steps. The funnel extends the input channel from the residues investigated here that are located near the middle of the membrane to the periplasm, which provides the ultimate supply of protons to the c-ring. The charged and polar residues in the funnel are likely to contribute to the pKa value, and may also facilitate the protonation of the input channel relative to the output channel even though both half-channels are exposed to the same buffer as the result of the lipid bilayer nanodiscs employed. More work is necessary to address this issue.

F_O undergoes H⁺ translocation-dependent 11° c-ring synthase-direction rotation steps

The extent of rotation during ATP synthase-direction steps was unexpectedly found to rotate CW by 11° in the WT and all mutants. Evidence presented here supports the conclusion that synthase-direction steps result from protonation of the leading cD61 from the input channel and from deprotonation of the lagging cD61 to the output channel to rotate the c-ring relative to subunit-a. These results include that: (i) synthase-direction steps depend on a group of residues with a low pKa that must be protonated, and a second group with a high pKa that must be unprotonated; (ii) formation of synthase-direction steps reached a maximum at the pH when the fractions of protonated groups with the low pKa and unprotonated groups with the high pKa were optimal; and (iii) mutating subunit-a residues in either the input or output half-channels altered both high and low pKa values, and altered the extent and pH dependence of synthase-direction step formation. The effects of the subunit-a mutants on the synthase-direction steps rule out the possibility that these steps result from twisting the entire F_O relative to F₁.

During a CCW F₁-ATPase power stroke, TDs occur every 36°, which is equivalent to an interaction between subunit-a and each successive c-subunit in the E. coli c₁₀-ring. Since synthase-direction steps rotate by 11°, rotation by an additional 25° is required to advance the c-ring by one full c-subunit, which we observed in only 0.1% of the synthase-direction steps. Rotational sub-state structures (pdb-IDs 6OQR and 6OQS) of E. coli F₁F_O that differ by a 25° rotation of the c-ring relative to subunit-a were obtained by cryo-EM (Sobti et al., 2020). Since advancing the c-ring by one c-subunit involves rotation by 36°, the difference between these sub-state structures also reveals information relevant to the 11° sub-step reported here.

The E. coli F₁F_O rotational sub-state structures that differ by the 25° rotation of the c-ring relative to subunit-a were obtained when the complex was inhibited by ADP (Sobti et al., 2020). Similar 11° and 25° rotational sub-states have also been observed with ADP-inhibited F₁F_O from B. taurus (Zhou et al., 2015) and from M. smegmatis (Guo et al., 2021). In M. smegmatis F₁F_O, the binding of bedaquiline stabilizes a rotational sub-state that is either 25° CW or 8° CCW from the equivalent rotational state in the absence of the drug (Guo et al., 2021). The rotational position of the c-ring in the cryo-EM structure of S. cerevisiae F₁F_O is also changed by ~9° when the inhibitor oligomycin is bound to F_O (Srivastava et al., 2018).

Several structural features of E. coli F_O (Sobti et al., 2020) are relevant to its ability to undergo synthase-direction steps, and in combination with the results presented here, they provide insight into the mechanism of sustained CW rotation to power ATP synthesis. A transmembrane view of subunit-a (Figure 5) shows that aE196, aS199, aR201, aN214, and aQ252 are aligned along the plane of cD61 rotation. This plane is surrounded by hydrophobic residues that form a vestibule. Between aS199 and aR210, polar groups line the vestibule above (aS202 and aS206) and below (aK203 and aY263) the cD61 rotation plane. Although these polar groups do not directly participate in H⁺ translocation (Eya et al., 1991), they enable water to access the vestibule (Angevine and Fillingame, 2003; Angevine et al., 2003) to make it less hydrophobic than the lipid phase of the membrane. Residues that provide a possible path for the output channel from aE196 to the cytoplasm include aQ181, aE177, and the subunit-a C-terminal carboxyl, which span this distance at ~4 Å intervals (Sobti et al., 2020), consistent with that needed to stabilize a Grotthuss water channel. More work is required to characterize this channel, especially since aE196 and aS199 are the only output channel residues conserved among other species (Figure 5—figure supplement 1).

A mechanism where F_O uses alternating 11° (Figure 6A,B) and 25° (Figure 6B,C) sub-steps to power c-ring rotation that drives ATP synthesis is consistent with the data presented here, and with E. coli F₁F_O structures 6OQR and 6OQS (Sobti et al., 2020). In 6OQS (Figure 6A), the lagging cD61 (orange) is 3.5 Å from aS199, which enables H⁺ transfer to aS199 and aE196 via bound water. The leading cD61 (pink) is 3.8 Å from the aR210-guanidinium, consistent with intervening water. This cD61 is also proximal to aN214 and aQ252, which positions it for protonation from the input channel via bound water. In our model, the pH-dependent 11° sub-step (Figure 6A) occurs upon H⁺ transfer from water bound to aN214 and aQ252 to the leading cD61, and H⁺ transfer from the lagging cD61 to aS199 and aE196.

Figure 6

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The low, medium, and high efficiencies of TD formation reported here (Figure 2B) were attributed to torsional strain resulting from the asymmetry between 36° c₁₀-ring stepping, and the 120 ° F₁ power strokes (Yanagisawa and Frasch, 2017; Sielaff et al., 2019). Based on this asymmetry observed in ADP-inhibited F₁F_O structures (Sobti et al., 2016), high efficiency TD formation was proposed to occur (Sielaff et al., 2019) in the rotary state comparable to that in which rotary sub-state structures PDB-IDs 6OQR and 6OQS were subsequently observed at 3.1 Å resolution (Sobti et al., 2020). Sobti et al., 2020, concurred that torsional strain contributed to their ability to resolve the 6OQR and 6OQS sub-state structures. However, in results presented here, catalytically active F₁F_o in lipid bilayer nanodiscs show successive 11° ATP synthase-direction steps every 36° including at the rotary position of the ATPase power stroke where ADP inhibits rotation (Figure 2A, dashed line). Because ATP synthase-direction steps can also occur with low efficiency when torsional strain decreases the probability of forming a synthase-direction step, it is clear that torsional strain is not the primary contributing factor to the ability of F_O to undergo 11° ATP synthase-direction steps.

After the 11° sub-step (Figure 6B), the distance of the now unprotonated lagging cD61 to the aR210-guanidinium decreased from ~11.5 to ~7.5 Å. These distances are inconsistent with the long-held belief that the role of aR210 is to displace the proton from the lagging cD61. Instead, we postulate that the electrostatic attraction between the negatively charged lagging cD61 and aR210 is sufficient to induce the 25° sub-step. As the result of this sub-step, the distance between these groups decreases from 7.5 to 3.8 Å (Figure 6C). As the 11° sub-step repeats, the subsequent loss of negative charge when the lagging cD61 is protonated by aN214 and aQ252 then allows this c-subunit to rotate away from aR210 into the lipid bilayer.

The probability that a TD occurs may appear to be stochastic. However, its occurrence depends on the kinetics and the energetics of the system. Slowing the angular velocity of the F₁ ATPase-driven power stroke increases TD occurrence at pH 8.0 (shown here to be suboptimal) indicating that the ability to form a TD depends on the rate that an interaction can form between subunit-a and each c-subunit relative to the angular velocity of F₁-ATPase-driven rotation (Ishmukhametov et al., 2010).

Evidence supports the hypothesis that the energy for F₁-ATPase power strokes is derived from ATP binding-dependent closure of the β-subunit lever domain upon subunit-γ, which is initiated at ~36° after the catalytic dwell in E. coli F₁ (Martin et al., 2014). Based on the K_D of ATP at 36° measured in Geobacillus stearothermophilus F₁, the energy available for the power stroke from ATP binding is ~13.5 k_BT (Adachi et al., 2012).

The results here suggest that the energy required to power the 11° synthase-direction step is close to that of the F₁-ATPase power stroke including: (i) that some synthase-direction steps oscillate consistent with a Brownian ratchet, especially those steps that occur late in the F₁ power stroke when the affinity for ATP is the highest; and (ii) that TD formation efficiency is increased or decreased (high and low efficiencies) by the 0.4 k_BT of torsional energy from the ±14° rotary mismatch between F₁ and F_O calculated from Equation 4, where θ is the rotational displacement in radians using the spring constant, κ, of 12.6 k_BT radian^–2 measured for E. coli F₁F_O(Sielaff et al., 2008).

(4) $\mathrm{U}=0.5\kappa {\theta }^2$

Consequently, the F_O motor must have at least 13.5 k_BT available to cause a TD. Possible sources of energy for TDs in addition to the 0.4 k_BT of torsional energy include: (i) as much as 4.4 k_BT from the difference of pKa values between the input and output channels; (ii) 5.9 k_BT from the exclusion of the lagging charged cD61 carboxyl from the lipid bilayer into the aqueous vestibule, based on its measured desolvation energy (White and Wimley, 1999). The energy penalty of 0.8 k_BT to insert the leading protonated cD61 carboxyl into the lipid bilayer is avoided by its conversion to the closed and locked position in the c-ring (Pogoryelov et al., 2010); and (iii) as much as 38.1 k_BT from the electrostatic attraction of aR210 to unprotonated lagging cD61 at a distance of 11.5 Å when it is exposed directly to the lipid bilayer. The energy of this attractive force, which is highly dependent on the hydrophobicity of its environment, is calculated by the modified Coulomb equation (Equation 5), where q_i and q_j are elementary charges, r_ij is the interatomic distance (in Ångstroms), and e is the dielectric constant, which is a measure of the hydrophobicity of the environment that ranges from 2 (lipid bilayer) to 80 (aqueous solvent). Although we do not yet know how wet the vestibule is, a dielectric constant of 13 and an 11.5 Å aR210-cD61 distance results in 3.8 k_BT, which when summed with the other energy sources totals 14.1 k_BT without input of torsional energy. Since F₁-ATPase rotation from the catalytic dwell to the point that ATP binds is powered by no more than 4 k_BT (Martin et al., 2018), this explains why synthase-direction rotation at these rotational positions typically has power stroke characteristics.

(5) $U=\frac{1}{e}\left(\frac{q_i{q}_j}{r_{ij}}\right)561{\kappa }_{B}T$

After the 25° rotation step when the unprotonated cD61-aR210 distance is 3.8 Å, the electrostatic force is 11.4 k_BT or 73.8 k_BT when the dielectric constant is 13 or 2, respectively. Thus, the electrostatic interaction in a hydrophobic environment would be far too strong for any rotation to occur. More work is required to quantify the energetics of these sub-steps in the ATP synthesis mechanism because, when understood in combination with the steady-state pmf values and the dissociation constants of ATP, ADP, and Pi versus rotary position, these energy contributions will determine the non-equilibrium ATP/ADP•Pi concentration ratio that can be maintained by F₁F_O at steady-state in vivo.

All data generated or analyzed during this study are included in the manuscript and supporting files. Data source files for all figures have been uploaded to DRYAD and can be located at: https://doi.org/10.5061/dryad.9cnp5hqhw.

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Author details

1. Seiga Yanagisawa

   School of Life Sciences, Arizona State University, Tempe, United States

   Contribution

   Data curation, Formal analysis, Investigation, Visualization, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

2. Wayne D Frasch

   School of Life Sciences, Arizona State University, Tempe, United States

   Contribution

   Conceptualization, Formal analysis, Funding acquisition, Methodology, Project administration, Supervision, Writing - original draft, Writing - review and editing

   For correspondence

   frasch@asu.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-6590-7437

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