Correlation between the numbers of rotation steps in the ATPase and proton-conducting domains of F- and V-ATPases.

This letter reports the correlation in the number of distinct rotation steps between the F1/V1 and Fo/Vo domains that constitute common rotary F- and V-ATP synthases/ATPases. Recent single-molecule studies on the F1-ATPase revealed differences in the number of discrete steps in rotary catalysis between different organisms—6 steps per turn in bacterial types and mitochondrial F1 from yeast, and 9 steps in the mammalian mitochondrial F1 domains. The number of rotational steps that Fo domain makes is thought to correspond to that of proteolipid subunits within the rotating c-ring present in Fo. Structural studies on Fo and in the whole ATP synthase complex have shown a large diversity in the number of proteolipid subunits. Interestingly, 6 steps in F1 are always paired with 10 steps in Fo, whereas 9 steps in F1 are paired with 8 steps in Fo. The correlation in the number of steps has also been revealed for two types of V-ATPases: one having 6 steps in V1 paired with 10 steps in Vo, and the other one having 3 steps in V1 paired with 12 steps in Vo. Although the abovementioned correlations await further confirmation, the results suggest a clear trend; ATPase motors with more steps have proton-conducting motors with less steps. In addition, ATPases with 6 steps are always paired with proton-conducting domains with 10 steps.


ATP synthase
The ATP synthase, also known as F o F 1 ATPase or F-ATPase, mediates the energy interconversion between the proton motive force (pmf) across membranes and the free energy of ATP hydrolysis via a rotary catalysis mechanism (Abrahams et al. 1994;Yoshida et al. 2001;Noji et al. 2017). The ATP synthase is composed of two rotary motors, F 1 and F o ( Fig. 1) (Junge et al. 1997). F 1 is the catalytic core domain responsible for ATP synthesis, showing an active ATPase activity when isolated (Yasuda et al. 2001;Spetzler et al. 2006;Bilyard et al. 2012;McMillan et al. 2016). Upon ATP hydrolysis, F 1 rotates the inner subunit (γε) against the catalytic stator ring (α 3 β 3 ). F o is the membrane-embedded domain and conducts proton translocation across the membrane. Upon proton translocation, F o rotates the oligomeric ring formed by the protoncarrying c-subunits against the stator complex (ab 2 ). In the whole ATP synthase complex, the rotor parts of F 1 and F o are bound together, forming the common rotary shaft (Junge et al. 1997;Oster and Wang 2000;Yasuda et al. 2001). The stator parts of F 1 and F o are connected via the peripheral stalk to transmit the torque without slippage. When pmf is sufficient, F o generates a larger torque than F 1 , reversing the rotation of the rotor shaft in F 1 to induce ATP synthesis. In contrast, when pmf is low, F 1 reverses the rotation of the rotor ring in F o , forcing F o to actively pump protons and generate pmf.
Stepping rotation of F 1 The minimum F 1 complex as a rotary motor is the α 3 β 3 γ subcomplex, which rotates the rod-shaped γ subunit against the α 3 β 3 stator ring in a counterclockwise direction when viewed from the F o side. The catalytic reaction centers for ATP hydrolysis reside at the three pairs of α−β, with the main catalytic residues harbored in each of the β subunits (Weber and Senior 1997). The three β subunits conduct the catalytic reaction in a highly sequential manner, resulting in a sequential power-stroking conformational change that rotates the γ subunit unidirectionally.
As expected from the pseudo threefold symmetry of F 1 , the unitary rotational step is 120°rotation, coupled with a single turnover of ATP hydrolysis (Yasuda et al. 1998). The rotation dynamics of the γ subunit in F 1 from thermophilic Bacillus PS3 (TF 1 ) has been intensively characterized to establish a standard reaction scheme for bacterial F 1 domains. TF 1 makes 80°and 40°sub-steps in a single 120°rotation, which means that TF 1 makes rotational steps intervened with 6 pauses per turn (Yasuda et al. 2001;Shimabukuro et al. 2003;Nishizaka et al. 2004;Adachi et al. 2007). Other F 1 domains from bacteria and mitochondrial F 1 from yeast (yMF 1 ) were reported to make 6 pauses per turn (Steel et al. 2015). Thus, a 6-step rotation is widely conserved across microorganism species.
On the other hand, rotation assays in mammalian F 1 domains have found an additional pause in 120°rotation, which translates into 9 steps per turn (e.g., three step rotations at 65°, 25°, and 30°) in human mitochondrial F 1 (hMF 1 ) (Suzuki et al. 2014). Similarly, bovine mitochondrial F 1 (bMF 1 ), the gold standard model for structural analysis of F 1 , was studied in the rotation assay and found to have an additional pause in 120°rotation (Kobayashi et al. 2020). However, the position in bMF 1 is different from hMF 1 , making three step rotations of 10-20°, 60-70°, and 40°. These observations suggest that a 9step rotation is conserved in mammalian mitochondrial F 1 domains.
We should be able to progressively detect smaller substeps by improving the spatiotemporal imaging resolution and the data analysis methods. In fact, we analyzed the data of rotation trajectories with elaborated mathematical methods and found that TF 1 makes an additional small step of 10°between the 80°and 40°sub-steps (Li et al. 2015). In this review, we aimed at a coarse-grained classification of the rotation behavior of F 1 . Therefore, we only considered the experimentally distinctive steps: the step size must be over 10°, and/or the intervening pause must be long enough to set the pace of the overall rotation rate under a certain condition, typically in the range of sub-or milliseconds.

Stoichiometry of H + per turn of F o
F o is a membrane-embedded motor with the minimum subunit composition of a 1 b 2 c n . The stoichiometry (n) of the c-subunits varies from 8 to 15 among species (Meier et al. 2005;Pogoryelov et al. 2009;Watt et al. 2010;Saroussi et al. 2012;Preiss et al. 2014Preiss et al. , 2015Morales-Rios et al. 2015;Guo et al. 2019). The c-subunits form an oligomer ring that is rotated against the ab 2 stator complex upon proton translocation across the membrane. According to the two half-channel model (Vik and Antonio 1994;Junge et al. 1997), which is well supported by the recent cryoEM studies, the a-subunit has two halfchannels, one exposed on each side of the membrane (Allegretti et al. 2015). Each proton enters through one of the half-channels and is transferred to one of the csubunits. After one turn of the c-ring against the ab 2 stator, the proton is transferred to the other half-channel of the a-subunit facing the opposite side of the membrane. Thus, a proton is translocated by a c-subunit, and therefore, the total number of protons translocated per turn is determined by n, the number of c-subunits in the oligomer c-ring.
Currently, there are not enough reports on the stepping rotation of F o to discuss the experimental data in a comprehensive manner. Our working assumption is that the number of steps in F o is determined by n. Fig. 1 The two rotary motors of ATP synthase, F 1 and F o . The subunit composition of F 1 and F o in bacterial types is α 3 β 3 γδε and ab 2 c n , respectively, where n varies among species. F 1 rotates the rotary shaft, composed of the γ and ε subunits (red) against the α 3 β 3 stator ring (blue). F o rotates the oligomer ring of the c-subunits (red) against the ab 2 stator complex (blue) during proton translocation across the membrane. In the whole ATP synthase complex, the rotor complexes F 1 and F o form the common rotary shaft (red) and stator complexes (blue), which are connected via the peripheral stalk formed by the b 2 and δ subunits Number of steps in F 1 versus F o We analyzed the data on the following ATP synthases: thermophilic Bacillus PS3 TF, Escherichia coli EF, yeast yMF, and bovine bMF. We chose these ATP synthases because both single-molecule rotation assays on F 1 (Watanabe et al. 2010;Bilyard et al. 2012;Steel et al. 2015;Kobayashi et al. 2020) and the structural data on the c-ring of F o (Stock et al. 1999;Ballhausen et al. 2009;Watt et al. 2010;Guo et al. 2019) are available. Considering the evolutionary distance and the highsequence homology of the c-subunits, it is highly likely that the ATP synthase from human mitochondria (hMF) also contains 8 c-subunits. Therefore, we added the data on hMF. The correlation between the number of steps in F 1 and F o is shown in Fig. 2. Clearly, a 6-step F 1 is always paired with a 10-step F o , whereas a 9-step F 1 is paired with an 8-step F o .
To gain more data points, we added information gained from the studies on V-ATPases, which are evolutionarily highly related rotary ATPases. V-ATPases are also composed of two distinctive domains, V 1 and V o , corresponding to F 1 and F o , respectively. To date, there are only two wellcharacterized V-ATPases for which the number of rotational steps in V 1 and number of proton-carrying units in V o is known. One of them is the Enterococcus hirae V-ATPase (EhV), with a 6-step V 1 (Iida et al. 2019) and a V o with 10 proton-carrying units (Murata et al. 2005), providing support for the abovementioned correlation. The other one is the V-ATPase from Thermus thermophilus (ThV), which consists of a 3-step V 1 (Furuike et al. 2011) and a V o with 12 proton-carrying units (Toei et al. 2007). This data point from ThV appears to expand the correlation map to include 3-step ATPases paired with 12-step proton-conducting domains.
Implications and perspective Figure 2 shows an obvious trend: ATPase motors with more steps have proton-conducting motors with less steps. Although the total number of steps varies from 15 to 17, this trend appears to be relevant in the design principle of rotary ATPases. One possibility is that rotary ATPases are designed to have potential minima around 16. It is highly likely that some angular pause positions in F 1 /V 1 overlap with the pause positions in F o /V o . In that case, the above numbers should indicate the maximum numbers of rotary potential minima per turn in the ATPase complex.
In this letter, we only consider the data points of F/V-ATPases, of which the number of the proteolipid is 8, 10, or 12, due to the limited information. On the other hand, some ATPase's have different numbers of proteolipids: 9, 11, 13, 14, or 15 (Meier et al. 2005;Pogoryelov et al. 2009;Saroussi et al. 2012;Preiss et al. 2014Preiss et al. , 2015. Therefore, it is important to analyze other ATPases to investigate the universality and limitation of the found correlation between the step numbers of F 1 and F o . At least, the correlation line in Fig. 2 should be kinked or broken for F o /V o with proteolipids more than 12, because the number of rotational steps in F 1 /V 1 should not be 2 or less, considering the conservation of the threefold symmetry of F 1 without exception. A simple expectation is that when the number of proteolipids is 12 or more, F 1 /V 1 is a 3-step motor. In this regard, F o F 1 from Caldalkalibacillus thermarum TA2.A1 (CtF) could be along this contention: CtF o has 13 proteolipids in the c-ring (Matthies et al. 2009), and the single-molecule rotation assay of CtF 1 found only 3 distinctive pauses per turn. It should be mentioned that a few rotation trajectories of CtF 1 seem to show a sign of the additional pauses in a turn. A more conclusive analysis is awaited. It Fig. 2 The number of steps in F 1 versus the number of steps in F o . TF represents data on ATP synthase from thermophilic Bacillus PS3, EF from Escherichia coli, yMF from yeast, bMF from bovine, hMF from human, EhV from Enterococcus hirae, and ThV from Thermus thermophilus. Structures of c 8ring of bMF (orange), c 10 -ring of TF (red), c 12 -ring of ThV (cyan), and c 14 -ring of Pisum sativum ATP synthase (brown) are shown would be also interesting to characterize the rotary catalysis of the F-ATPases from Paracoccus denitrificans (Morales-Rios et al. 2015), Pisum sativum (chloroplast) (Saroussi et al. 2012), and cyanobacteria bacteria species (Pogoryelov et al. 2007), in which the F o contains 12, 14, and 13-15 c-subunits, respectively. It should be noted that the deviance from the found correlation may come from ATPases isolated from cyanobacteria species: the single-molecule rotation assay on a thermophilic cyanobacteria species shows the ADPinhibition pause at a difference position from ATP-binding pause found in active rotation (Konno et al. 2006), suggesting cyanobacterial F 1 make more than 3 steps per turn.

Summary
Recent progress in single-molecule rotation analysis and structural analysis on rotary ATPases has revealed a variety of functions and structures among species. This allows for comprehensive analyses. Here, we report a correlation between the number of steps in F 1 /V 1 and that in F o /V o . There is a clear trend showing that ATPase motors with more steps have proton-conducting motors with less steps. In addition, ATPases with 6 steps are always paired with protonconducting domains with 10 steps. To confirm the universality of these findings, we need more data on the rotation and structure of rotary ATPases. A theoretical approach is also needed to investigate the mechanism behind these rules.
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