Rotary properties of hybrid F1-ATPases consisting of subunits from different species

Summary F1-ATPase (F1) is an ATP-driven rotary motor protein ubiquitously found in many species as the catalytic portion of FoF1-ATP synthase. Despite the highly conserved amino acid sequence of the catalytic core subunits: α and β, F1 shows diversity in the maximum catalytic turnover rate Vmax and the number of rotary steps per turn. To study the design principle of F1, we prepared eight hybrid F1s composed of subunits from two of three genuine F1s: thermophilic Bacillus PS3 (TF1), bovine mitochondria (bMF1), and Paracoccus denitrificans (PdF1), differing in the Vmax and the number of rotary steps. The Vmax of the hybrids can be well fitted by a quadratic model highlighting the dominant roles of β and the couplings between α-β. Although there exist no simple rules on which subunit dominantly determines the number of steps, our findings show that the stepping behavior is characterized by the combination of all subunits.


INTRODUCTION
F o F 1 -ATP synthase (F o F 1 ) is the enzyme responsible for the terminal reaction of oxidative phosphorylation, ATP synthesis coupled with proton translocation along proton motive force (pmf) across biological membranes. 1,2 As indicated in the name, F o F 1 is the complex of two distinctive portions, F o and F 1 , both of which work as rotary molecular motors. F o undergoes rotation of its oligomeric rotor ring driven by proton translocation along pmf. F 1 is an ATP-driven rotary motor whose central shaft rotor rotates against the surrounding catalytic stator ring. F o and F 1 work together to interconvert pmf to the free energy of ATP hydrolysis.
The a 3 b 3 g subcomplex of F 1 is the minimum ATP-driven rotary complex in which the rotor shaft, the g subunit, is rotated against the catalytic a 3 b 3 stator ring upon ATP hydrolysis. 3,4 The a 3 b 3 stator ring possesses six ATP binding sites at the a-b interfaces, three of which are catalytic while the other three are non-catalytic. Catalytic residues are almost all on the b subunit, [5][6][7] while the a subunit has one arginine residue critical for catalysis, termed the arginine finger, 8 which stabilizes the transition state of ATP hydrolysis. 9 The g subunit consists of a coiled coil of the N-and C-terminal helices that is held in the central cavity of the a 3 b 3ring, and a globular domain that protrudes from the a 3 b 3 -ring. In a whole complex of F o F 1 , the globular domain of the g subunit binds to the rotor ring of the F o motor, forming the rotor complex. F 1 has other minor subunits. In bacterial systems, F 1 has the d and ε subunits, while in mitochondrial systems, F 1 (MF 1 ) has a different composition of the minor subunits ( Figure S1). In both systems, the minor subunits are structural proteins to build the whole complex of F o F 1 and are not directly involved in the catalysis. 10 An exception is the bacterial ε subunit that acts as a suppressive regulator in some species by modulating the duration time of catalytically inactive state of F 1 . 11 Nevertheless, the ε subunit has only minor effect on catalysis and rotary behaviors when F 1 is active for catalysis. [12][13][14] Therefore, we only focus on the roles of a, b, and g subunits and simply refer to the a 3 b 3 g, the a 3 b 3 gdε subcomplexes as well as the whole F 1 complex as F 1 hereafter.
Chemo-mechanical pathways of F 1 have been well characterized by single-molecule rotary assay, 3,[15][16][17][18][19][20] together with biochemical and structural studies, which set the groundwork for theoretical studies. 21,22 In a standard rotary assay, F 1 is immobilized on a glass surface functionalized with nickel-nitrilotriacetic acid (NTA) through histidine-tags of the a 3 b 3 stator ring. To visualize the rotation of the rotor g subunit, a rotary marker probe, such as polystyrene beads, magnetic beads, gold colloid, or nanorod, is attached to the protruding domain of the g subunit and observed under optical microscopes. The principal approach in elucidating the reaction scheme is to resolve the rotations into discrete rotary steps, each intervened by pauses due to rate-determining catalytic states. Under ATP-limiting conditions, F 1 shows 120 steps intervened by ATP-waiting pause (binding dwell). When the ATP hydrolysis step is retarded by mutations of a catalytic residue or by the use of hydrolyzable ATP analog, such as the ATPgS, F 1 shows 120 steps with catalysis-waiting pauses (catalytic dwell). By analyzing both the binding and catalytic dwell in single F 1 molecules, one can then determine the angular positions of the catalytic dwells relative to the binding dwells, to determine the size of substeps triggered by ATP binding and catalysis, respectively. F 1 from thermophilic Bacillus PS3 (TF 1 ), the best characterized F 1 in rotary assay, shows 2 substeps of 80 and 40 in a 120 rotation, 5,16 initiated after the binding and the catalytic dwell, respectively. The middle panel in Figure 1A shows the reaction scheme of TF 1 . Each catalytic site hydrolyzes one ATP molecule and couples with one turn of the g subunit. Although each catalytic site follows exactly the same reaction process, the phase of reaction states differs by 120 among the three catalytic sites. Specifically, each catalytic site cleaves bound ATP into ADP and P i (inorganic phosphate) after a 200 rotation from the angle where the ATP is bound to the catalytic site. 18 The catalytic site then releases the ADP and the P i at 240 19 and 320 , 20 respectively ( Figure 1A middle panel, Table S1). Although the angular position of each elementary reaction remains to be determined, the reaction schemes of the F 1 's from Escherichia coli (EF 1 ) 23 and the yeast mitochondria (yMF 1 ) 24 are shared with TF 1 . Nonetheless, recent studies revealed Figure 1. Concept of this study (A) Rotation schemes of genuine F 1 s as previously determined. Each circle and black arrow represent one b subunit and angular position of the g. 0 is defined as the ATP-binding position at the highlighted b. ATP* represents pre-or posthydrolysis state of bound ATP. (B) Construction of representative hybrid F 1 s. The plasmid was expressed in Escherichia coli and the purification of the target protein was performed in the same manner as previously described 26 for TF 1 -bMF 1 hybrids, 27 26 has an extra pause, termed the ''short dwell'', in addition to the binding and catalytic dwells ( Figure 1A left panel). On the other hand, F 1 from Paracoccus denitrificans (PdF 1 ) has its binding and catalytic dwells at the same angles, showing that PdF 1 has only 3 steps regardless of the ATP concentration, [ATP] ( Figure 1A right panel). 27 Although theoretical studies indicate that the number and the size of substeps are not directly relevant to the chemo-mechanical coupling efficiency of F 1 , 28 a clear negative correlation was found between the number of steps per turn in F 1 and the number of steps per turn in F o motor. 29 This may provide some implications on the physiological demands or mechanistic constraints on the stepping behaviors of the F 1 and F o motors.
The crystal structures of F 1 show that the g subunit has principally two distinctive interactions with the a 3 b 3 stator ring: the hydrophobic sleeve formed by the N-terminal domains of the a and b subunits, and the near-orifice region which is formed by the C-terminal domains of the b subunit. 4,30 The hydrophobic sleeve is almost rotationally symmetric and has a smooth interface to the g subunit that seemingly acts as an axis holder. In contrast, the near-orifice region shows a distinctively asymmetric interface. The three b subunits adopt different conformational states by swinging its C-terminal domain, forming the asymmetric interface with the g subunit, which is believed to principally determine the rotary potential for the g subunit in the a 3 b 3 -ring. The latest structural analysis of TF 1 31 revealed the atomic structure of F 1 at the binding dwell state in which the g subunit is at 40 in the rotational direction from the hydrolysis-waiting dwell structure. In these structures, two b subunits adopt new conformational states: half-closed and half-opened while the a subunits are in almost the same conformation as those found in previous structures of F 1 in the catalytic dwell states. Thus, the structural features of F 1 seemingly imply that the geometry of rotational potential for the g subunit is dominantly determined by the b subunits. 32 Considering the dominant role of the b subunits in the rotary potential and the catalysis, it is reasonable to consider that the fundamental features of F 1 are principally determined by the b subunits. However, sequence homology analysis shows that the b subunit has the highest sequence identity among species (70% or more), whereas the a subunit is the second (60% or more) and the g subunit is the lowest (40%) (Figure S2), implying that species-specific features stem more from the a and g subunits with lower sequence identity. This raises a question regarding the design principle of F 1 , ''which subunit or which combination of subunits is the most dominant for the rotary behaviors and kinetics?''.
In this study, we constructed several hybrid F 1 s composed of subunits from different origins, aiming to reveal the correlation between the origin of the subunit and the fundamental rotary properties of F 1 , namely, the rotational velocity and the number of steps per turn. As representatives of 3-stepper, 6-stepper, and 9-stepper motors, we employed PdF 1 , TF 1 , and bMF 1 , respectively, and prepared hybrid F 1 s composed of subunits from two of these origins ( Figure 1B). The maximum rotational velocity of the hybrids was determined from the Michaelis-Menten analysis. On the other hand, the number of rotary steps per turn was analyzed as follows (Table S2). To resolve stepping rotation with discrete dwells, rotation was observed in the presence of ATPgS, an ATP analog that significantly retards the catalytic dwell and other dwells in some cases. To discriminate 3-stepper from 6-or 9-stepper motor, rotation was observed at [ATPgS] (or [ATP]) near K m where duration times of binding and catalytic dwells are comparable. Motors showing pauses for binding and catalytic dwells at the same angles at K m are identified as 3-stepper motors, while 6-or 9-stepper motors should show at least 6 pauses at K m . To further discriminate between the 6-and 9-stepper motors, rotation was analyzed at ATPgS (or ATP)-saturating conditions where the 9-stepper motors show the extra pause, i.e., the short dwell. 26 Finally, by structural comparison of the genuine F 1 s, the structural similarities among F 1 s that could affect the rotary properties of hybrid F 1 s are discussed.

Preparation of hybrid F 1
Hybrid F 1 s were prepared from expression plasmids in which one of the constituting genes was replaced with one from another origin as shown in Figure 1B. We introduce triplet characters in labeling the hybrids to indicate the origins (P, T, and b for PdF 1 , TF 1 , and bMF 1 , respectively) of the three subunits, a, b, and g, e.g., ''bbT'' represents the hybrid with a-b from bMF 1 and g from TF 1 . We constructed 12 combinations of hybrids from two origins among the possible 18 combinations. Although Tbb and PPb were not successfully expressed, the hybrids of other 10 combinations were obtained as F 1 complexes. Among them, TbT and PPb did not show detectable ATP hydrolysis activity and did not show rotation ( iScience Article we investigate 8 hybrids with the three original F 1 s for comparison. Note that SDS-PAGE analysis shows that PTT and TTb have apparently lower stoichiometry of the g subunit, compared with other F 1 s, suggesting that the samples contained significant fraction of the a 3 b 3 subcomplex or a/b monomers. However, this does not interfere rotation assay that selectively observes rotation via a probe attached to the g subunit. The lower stoichiometry is probably due to lower expression, instability, or less efficient incorporation of the g subunit into the a 3 b 3 subcomplex. It should also be noted that the hybrid F 1 s were co-expressed with the d and ε subunits originated from PdF 1 or bMF 1 , to enhance the expression yield and stability. These minor subunits were incorporated in hybrid F 1 complexes only when the g subunit has the same origin. Exceptions were PPT and PTT, in which the ε subunit from PdF 1 was incorporated in the hybrids, suggesting the association with the g subunit from TF 1 . It should be noted that the minor subunits from PdF 1 or bMF 1 do not significantly affect rotation in catalysis of ATP hydrolysis, 10,11,13 although the ε subunits from some of other bacterial F 1 s including TF 1 is known to inhibit ATP hydrolysis and enhance the efficiency of ATP synthesis. 33,34 Because the ε subunit from such F 1 s was not used in the present study, the hybrids were principally analyzed based on their composition of a, b, and g subunits. The rotation of hybrid F 1 s was visualized using a laser-dark field imaging system with 40 nm gold nanoparticle as rotary marker ( Figure S4) and recorded at 250-10k fps (frames per second) as in previous studies. 26,27 The rotation rate was determined under various [ATP] by Michaelis-Menten kinetics analysis ( Figures S5A  and S5B). The V max and K m values of genuine F 1 s are found as follows: 786 rps (rotations per second) and 67 mM for bMF 1 , 338 rps and 77 mM for PdF 1 , 189 rps and 17 mM for TF 1 . These values largely agree with previous studies. 9,26,27 The Michaelis-Menten parameters of the 8 hybrids are shown in Table 1. As expected, hybrids whose b originated from bMF 1 or PdF 1 showed fast rotation over 200 rps, whereas hybrids with b from TF 1 showed slow rotation. In the following, we analyze which subunit is the dominant factor for V max . On the other hand, the catalytic efficiencies k on , estimated from 3 3 V max =K m , (Table 1) did not show significant differences among F 1 s. Thereby, these were not subject to further investigation.

Quadratic model
As shown in Table 1, V max values differed among F 1 s, with no clear dependence on subunit origin. Nevertheless, we employed a simple quadratic model as a generic function with three variables that represent the origins of each subunit constituting hybrid F 1 s, as below; where V a , V b , and V g denote the explanatory variables for the a, b, and g subunits, respectively. V a , V b , and V g can take one of the three values, 189rps∕V , 338rps∕V or 786rps∕V , if the corresponding subunit is from the TF 1 , PdF 1 , or bMF 1 . The division by the average rotation rate, z438ðrpsÞ, is to render  iScience Article the explanatory variables and the coefficients of the model dimensionless. For example, the hybrid PbP, with both the a and g subunits from PdF 1 and the b subunit from bMF 1 , has V a = V g = 338ðrpsÞ∕V and V b = 786ðrpsÞ∕V . The 9 coefficients a a ; a b ; a g ; /; a gg characterizing both the linear and coupling strengths of the subunits on the rotation rate are least-squared fitted by the 11 genuine and hybrid F 1 s in Table 1.
Their fitted values are summarized in Table 2. The quadratic model fits the data well with very small fitting residuals (defined as the difference between the observed and predicted V max (see supplemental information ''quadratic model of the dependence of rotation rate on subunits'' and Figure S6). We also note that a model with any single term deleted from V max ðV a ; V b ; V g Þ increases the fitting residuals significantly, indicating that our quadratic model is minimal in explaining the data.
A lattice representation of the predicted V max for the observed hybrids (red dots) and some of the unobserved ones (blue dots) is shown in Figure 2. From the amount of changes of V max in Figure 2 along the a-, b-and g-axis, one can see that the b subunit has a dominant role in controlling the rotational velocity. Specifically, the change of V max along the b-axis (see e.g., bTT/bPT/bbT that varies from 5.2 rps to 608 rps) is often much larger than those along the a-axis (see e.g., TTP/PTP/bTP that varies from 288 rps to 138 rps) and along the g-axis (see e.g., bbT/bbP/bbb that varies from 608 rps to 786 rps). These findings are consistent with the previous structural analysis 32 suggesting the dominant roles played by the b subunit in the rotary potential and catalysis.
In addition to the range of V max that can vary when a subunit with different origins is altered, the fitted coefficients (Table 2) also summarize the nonlinear dependence of V max on the composition of the subunits. In particular, a aa > 0 means that V max is a convex function of V a when V b and V g are fixed, i.e., the curve of V max bends upward when the a subunit changes from TF 1 /PdF 1 /bMF 1 with the b and g subunits fixed (see e.g., TTT/PTT/bTT and TTP/PTP/bTP along the a-axis in Figure 2). Likewise, a bb < 0 ða gg < 0Þ indicates that the curve of V max is concave (bends downward) in V b ðV g Þ when V a and V g (V a and V b ) are fixed (see e.g., PTP/PPP/PbP and PTT/PPT/PbT along the b-axis in Figure 2).
On the other hand, the quadratic model characterizes the coupling effects between subunits. More precisely, the coefficients a ab , a bg , and a ag are all positive, meaning that having faster F 1 parts in two of the subunits, i.e., ab, bg, or ag, always increases V max . Furthermore, the fact that a ab is around 2 to 3 times larger than a bg and a ag ( Table 2) implies that having faster F 1 parts in the ab subunits simultaneously enhances V max the most. As a result, our results show that, in addition to the importance of the b subunit, the ab subunits together further provide a synergistic effect controlling of V max . Accordingly, our model predicts that the unobserved hybrid bbP (see Figure 2) should have large V max since both of its a and b subunits are derived from the fast-rotating bMF 1 (due to the large a ab ).

Number of pauses
The number of steps per turn of the hybrids was then analyzed in order to classify the hybrids into 3-steppers (PdF 1 -type), 6-steppers (TF 1 -type), or 9-steppers (bMF 1 -type). 3-steppers showing 3 steps per  We first distinguish the 3-stepper hybrids from the others in the rotary assay with [ATPgS] around K m (Figure S7A). For hybrids with slow catalytic rates, ATP was used as a substrate in the rotary assay. Michaelis-Menten parameters of the ATP-or ATPgS-driven rotation of hybrids were determined in the rotary assay and listed in Tables 1 and S4, respectively. Figure 3A shows the x-y plots and angular histograms of rotation of bMF 1 or PdF 1 as references for the 6-stepper or 3-stepper at [ATPgS] around K m . All 8 hybrids clearly showed 6 or 3 pauses per turn, allowing for classification of the hybrids. Figure 3B shows the x-y plots and angular histograms of TTb and PbP as representatives of the 6-steppers and 3-steppers at [ATP] or [ATPgS] around K m (Tables 1 and S4). Other hybrids can also be identified as 6/9-stepper or 3-stepper (Figure S8). Surprisingly, all tested hybrids having a subunit with PdF 1 origin (PbP, PTP, PPT, and PTT) showed 3 stepping rotations. This goes against our initial expectation that these hybrids showed 3 steps even if the b subunit is not PdF 1 origin. A significant example is PTT that was identified as a 3-stepper although only the a subunit has PdF 1 origin, probably suggesting the specific role of PdF 1 -a in controlling the stepping pattern.
On the other hand, hybrids from the 6-and 9-stepper motors, bbT, bTb, TTb, and bTT, showed 6 steps at the K m condition without exception (Figures 3 and S8). The results of Pd-hybrid F 1 s (PPT, PTP, PTT, and PbP) suggested that the substep is not programmed in a particular subunit but in all of the subunits.  Next, we classify the non-3-stepper hybrids, which are composed of subunits with bMF 1 -and TF 1 -origins, into 6-steppers or 9-steppers ( Figure S7B). As mentioned previously, the principal barometer is the existence of short dwells that are found in the rotation of bMF 1 . The difficulty is that these short dwells are very short-lived; the mean duration of short dwells of bMF 1 is estimated to be less than 0.1 ms in ATP-driven rotation. These short dwells are extended to around 1.0 ms when bMF 1 hydrolyzes ATPgS. 26 For reliable classification, the hybrids of bMF 1 and TF 1 , as well as the genuine bMF 1 and TF 1 , were investigated under the substrate (ATP or ATPgS) saturating conditions. To objectively detect short dwells without the need to assume any noise models, we employed a nonparametric change-point (CP) analysis 35  The method has already been applied to identify angular changes in the single F 1 rotary traces. 26,35 The detection of the number of pauses was then performed by identifying the number of significant peaks in the angular histogram of the CP intervals without the need to refer to the time constants (see supplemental information ''determining the number of pauses''). Note that CP analysis was introduced into this study to classify bM-T Hybrids into 9-stepper (bMF 1 -type) or 6-stepper type (TF 1 -type) by the number of pauses under substrate saturated-condition. The classification is based on the hypothesis that under substrate saturated-condition, 9-stepper F 1 s show 6 steps whereas 6-stepper F 1 s show only 3 steps due to overlapping of rotation phase of long dwells and short dwells.
Consistent with the previous study, 26 CP analysis successfully detected the short dwells of bMF 1 around the middle in between two successive catalytic dwells ( Figure S9). The histograms of other hybrids, as well as iScience Article bMF 1 and TF 1 are provided in Figures S10 and S11. Figure 4A shows a sample segment of rotary trace of bbT at saturated [ATPgS] condition with the identified dwells detected by the CP analysis. Figure 4B shows the histogram of CP from the rotation of a bbT molecule, showing the distinctive 3 major and 3 minor peaks. Even though TF 1 was expected to show only 3 catalytic dwells, TF 1 showed 3 minor peaks, i.e., 3 extra short pauses at binding angles, besides the catalytic dwells ( Figure S10). It is known that TF 1 conducts ATP binding and temperature-sensitive (TS) reaction at binding angles. According to our previous study, 36 the mean duration time for TS pause is around 0.6 ms, significantly longer than the expected time constant of substrate binding at 1 mM, (<0.1 ms). Thus, it is most likely that the detected extra short pauses are TS reaction dwells. Supporting this contention, when the rotation of TF 1 was observed at 1 mM [ATPgS] at 16 C, the pause time was extended to give a Q 10 factor of 8.0 ( Figure S12) that is close to the reported value for Q 10 factor of TS reaction (7.0). The reason why TS dwell is detected in the present study is that CP analysis is sufficiently sensitive to detect short pauses that have not been identified with conventional angle histogram analysis or manually screening with eye.
In addition to TF 1 , CP analysis shows that all hybrid F 1 s that do not involve a subunit with PdF 1 origin showed 3 extra minor dwells in between the major ones ( Figure S10). In some hybrids, the 3 extra minor dwells were not clear in conventional angle histogram. This is due to the same reason for the detection of TS dwells in TF 1 . Next, we investigate the position of the extra short pauses relative to the major ones by analyzing the angular distance ratio, defined as a/b in Figure 4A where a (b) is the angular distance from a main (sub-) pause to the next sub-(main) pause (see supplemental information ''step size comparison''). In this analysis, the bMF 1 gives the angular distance ratio close to 1.0 (60 o :60 o ) while the TF 1 gives the ratio close to 0.5 (40 o :80 o ) (Table S5). Figure 4C shows the average values of the angular distance ratios determined for the hybrid F 1 s, bMF 1 , and TF 1 . The ratios for the hybrids do not show simple classification into the bMF 1 -type or TF 1 -type. To gain more insights, we investigated the similarities between all 6-and This way to construct the histogram is able to reveal the existence of short dwells in the rotary traces. 26 (C) The mean of angular distance ratios a=b between main and sub-pauses for each hybrid. Short horizontal and vertical lines show the mean values and the standard errors of angular distance ratios after the outliers were removed. The number of sampling steps for the estimation of angular distance ratios is given in Table S5.
(D) Hierarchical clustering (dendrogram) of the 6-and 9-steppers according to the angular distance ratio. iScience Article 9-steppers by hierarchical clustering according to the mean of the angular distance ratios. Figure 4D shows the resultant dendrogram representing the hierarchical similarities among the F 1 s. The dendrogram suggests that TF 1 and bbT are similar to each other, whereas bMF 1 and TTb form another group, and these four form a group with bTb later which means less similarity with them whereas bTT stands alone by itself. These groupings suggest that a simple and explicit rule on which factor determines the number of rotary pauses may not be present. However, the analysis indicates that the angular distance ratio is larger when the g subunit originates from bMF 1 than those with TF 1 origin.

High robustness against interspecies subunit substitution
In this study, we constructed the expression vectors for 12 hybrid F 1 s. Eight out of the 12 hybrids form F 1 complexes that exhibit active catalysis and rotation (Tables S3 and S6). Considering the separation of the 3 genuine F 1 s (TF 1 , PdF 1 , and bMF 1 ) in phylogenetic trees, the high success rate of forming active hybrids indicates that the subunit-subunit interfaces are structurally conserved. The highly permissive recognition by the a 3 b 3 subcomplex to accommodate an exogenous rotor protein in the a 3 b 3 ring was reported in previous studies. Grü ber et al. succeeded in construction of an artificial protein from a 3 b 3 of TF 1 and a rotor subunit E of V 1 -ATPase from yeast, which showed 56% of the ATPase activity of the genuine F 1 . 37 We also demonstrated in a previous study that it is possible to substitute the g subunit with a completely exogenous rod protein FliJ of the S. enterica flagella. 38 The rotary catalysis of that artificial motor protein was experimentally confirmed although the artificial motor showed evidently slow rotation rate, exerting low torque. These results show the structural and functional robustness of the a 3 b 3 subcomplex against exogenous rotor protein. The high success rate to obtain active hybrid F 1 s with the g subunit from a different species is consistent with the previous reports.
An unexpected result to us was the robustness of F 1 against interspecies substitution of the a and b subunits. One reasonable expectation is that although the evolutional constrain on the a and the b subunits is high to retain the fundamental rotational catalytic mechanism, the molecular mechanisms for allosteric interplay among subunits and torque transmission have been diversified in course of evolution, as seen in the diversification of the number of substeps. The observed robustness implies that the fundamental molecular architecture for the allosteric interplay and torque transmission among subunits are more highly conserved than we thought. The higher conservation of amino acid sequence of the a and b subunits would reflect this.
The unraveled robustness of F 1 against interspecies substitution would open a novel experimental strategy for the study on F 1 s that are experimentally difficult to obtain for biochemical/biophysical studies, such as F 1 s derived from species that are difficult to culture and/or have low structural stability. Recent innovation in structural analysis of F o F 1 has been revealing that F o F 1 has wide variety of regulation mechanisms, evolving species-specific regulatory subunit or structural elements. 13,39 However, the types of F 1 suitable for biochemical and biophysical analysis are still limited. In many cases, species-specific regulation mechanisms are based only a few subunits or structural elements. By introducing the necessary subunits and structural elements into F 1 suitable for biochemical/biophysical research, it will be possible to create easy-tohandle hybrid F 1 with the species-specific regulation mechanism. This will enable detailed biochemical/ biophysical analyses, which have been difficult with native F 1 .

Rotation rate
In terms of the lattice representation (Figure 2), we showed the maximum turnover rates V max of the hybrid F 1 s determined from the Michaelis-Menten analysis and predicted from the quadratic model. The V max values vary the most with respect to the exchange of b subunits, showing that the b subunit is a determining factor of V max . We further scrutinize how the subunit dependences of V max are characterized by the quadratic model. In particular, the coefficients for the subunit combinations (a ab , a bg , and a ag ) are all positive with a ab the biggest, indicating that the a and b subunits together provide a synergistic effect on the rotational velocity. This synergistic effect of a and b subunits is consistent with the fact that the catalytic sites reside on the a-b interfaces, and with the crucial roles of their conformational transitions associated with the hydrolysis and phosphate releasing steps that determine the catalytic rate. iScience Article which bound ATP is cleaved into ADP and P i . While the conformation of the b subunit itself is almost identical to that of b TP , the ab DP interface is more closed than the ab TP interface. The closure of ab DP interface accompanies the positional shift of the arginine finger on the a subunit toward the bound ATP that is thought to trigger the hydrolysis of bound ATP. 8,9 Therefore, it would be natural to expect that the difference in V max is represented in the structural arrangement of catalytic residues including arginine finger on ab DP . The atomic structure model of PdF 1 and TF 1 in catalytic dwell state as well as bMF 1 are now available. 31,40 To investigate possible conformational differences of the catalytic residues among the 3 genuine F 1 s, we investigated the structural similarity of catalytic residues by performing structural alignment (Figure S14). However, the atomic coordinates of catalytic residues are so identical that we observed negligibly small RMSD (root-mean-square deviation), around 0.1 nm. Thus, the coordinates of catalytic residues do not provide clues on which structural feature determines V max . Based on QM/MM (Quantum Mechanics/ Molecular Mechanics) study, Hayashi et al. showed that post-hydrolysis proton transfer process mediated by water molecules coordinated in catalytic site is the rate-limiting step of overall hydrolysis step process that was verified with rotation experiments. 9 Taking this into account, it is possible that the coordinates of water molecules and/or those of residues involved in water molecule coordination determine V max .
In addition to hydrolysis step, the P i release step is also another determining factor of duration time of catalytic dwell. It was proposed that the a-b interface loosens to facilitate the phosphate release in the final stage of the ATP-hydrolysis. 32,35 This contention is well consistent with the synergistic effect of a and b subunits for V max . Therefore, it is also possible that structural features involved in P i -releasing step determine the species-specific V max . Regarding this point, further structural studies are required because it remains elusive which type of conformational transition is accompanied with P i release.

Number of substeps
We also investigated the correlation between the origin of the subunit and the number of steps per turn of the F 1 s. TF 1 makes 6 steps per turn, pausing at 0 , 80 , 120 , 200 , 240 , and 320 . Here, 0 , 120 , and 240 are the binding dwells and 80 , 200 , and 320 are the catalytic dwells. Recently, the structure of TF 1 in the binding state was established in addition to that of the catalytic state. 31 While the conformation of a and g subunits does not significantly change in all the binding and catalytic states, the b subunit adopts distinctive conformational states at different angles: half-closed form (HC) at 0 , closed form (C) at 80 , 120 , and 200 , half-opened form (HO) at 240 , and opened form (O) at 320 . These structural features of the b subunit seemingly suggest the b-dictator model stating that the conformational substates of F 1 found as intervening pauses are principally determined by the b subunit. However, the results in the present study do not support this model. Remarkable examples are the 3-stepper hybrids, PbP, PTP, and PTT, with the b subunit originated from TF 1 (6-stepper) or bMF 1 (9-stepper). These hybrids show that the incorporation of PdF 1 subunit results in a 3-stepper motor even if the b subunit has a different origin. The reason for apparently PdF 1 -dictator mechanism remains elusive.
Similarly, the hybrids originated from TF 1 and bMF 1 are also inconsistent with the b-dictator model. The analysis of the angular distance ratios ( Figure 4D) suggests that TF 1 and bbT are similar to each other, while bMF 1 and TTb form another group. bTb and bTT stand relatively alone by themselves. Although a universal rule is yet to be found, our results suggested that the g and b subunits may have a larger effect on the number of substeps than the a subunit. Instead of the b-dictator model, our analysis shows that the number of steps per turn is determined not by a single factor, but by the nontrivial interplays among all subunits.
With aim to investigate which rotor-stator interface is responsible for the number of substeps, we compared the rotor-stator interfaces of 3 genuine F 1 s ( Figure S15). The stator interface against the rotor can be categorized into hydrophobic sleeve, switch II, and DELSEED regions. The highest differences among the three species are found in DELSEED region; higher RMSD values for DELSEED interface, in comparison with those for switch II or hydrophobic sleeve. This result implies that DELSEED interface has a principal role to determine the number and size of substeps. Interestingly, amino acid sequences of interface between DELSEED and g is highly identical among species. This suggests that the scaffold structures behind DELSEED region in addition to the rotor structure are responsible for the diversification of the rotation scheme of F 1 . This idea would be testable by ''chimera approach'' where a certain distinctive structural domain, such as C-terminal helical domain of the b subunit including DELSEED region, is substituted with the corresponding part from another origin. In particular, the analysis on F 1 having a chimera subunit with ll OPEN ACCESS iScience 26, 106626, May 19, 2023 iScience Article PdF 1 subunit could give more detailed insights on which structural element or which part of stator-rotor interfaces are responsible for the number and/or angles of substeps of F 1 .

Conclusions
In summary, this study analyzed hybrid F 1 s which are composed of subunits with different origins (Table S6). Kinetic analysis of the hybrids revealed that the principal factors to determine the maximum turnover rate are the b subunit and the synergistic combination of a and b subunits, which is consistent with the structural features of F 1 . 32,41,42 The step analysis of the hybrids showed that the number of steps per turn is not determined by a single factor but by nontrivial interplays among all subunits. For further understanding of how the number of steps and step-size are determined, detailed analyses of the kinetics and rotary behaviors are required. Structural analysis of the hybrid F 1 s could also give crucial clues on which structural features are responsible for the catalytic rate and the number of steps per turn. We also propose that our subunit exchange strategy would be effective not only for the understanding of the design principle of molecular motors, but also for the engineering of novel motors.

Limitations of the study
In the present study, we focus on the rotary behaviors of hybrid F 1 s utilizing single-molecule rotation assays.
To obtain further insight on the hybrid F 1 s, the structural analysis is required in future. In particular, the structural information of a 3 b 3 -ring and g could provide us with more insights on the regions determining the V max and the complicated interplays among all the subunits determining the number of pauses per turn. Nevertheless, our study can provide phenomenological and dynamical information for the rotary behaviors of F 1 s that complements comprehensive structural analyses. It also enables us to design novel hybrid F 1 s with predictable rotary behaviors by replacing the dominant regions among genuine F 1 s.

STAR+METHODS
Detailed methods are provided in the online version of this paper and include the following:

METHOD DETAILS
Preparation of hybrid F 1 s Genuine TF 1 and bMF 1 were prepared as described. 26,47 As an example, a detailed process of the preparation of bbT is as follows. The plasmid of bbT was constructed from the bMF 1 plasmid as a vector and PCR product coding TF 1 -g as an insert DNA. The primers for PCR reactions are summarized in Table S7. The PCR fragment consists of TF 1 -g and the upstream/downstream of bMF 1 -g. After ligation of the vector and the fragment, the plasmid of bbT was introduced into the F o F 1 -deficient Escherichia coli strain, BL21. The protein purification of TF 1 -bMF 1 hybrids were performed based on the purification method for bMF 1 . 26 The hybrid F 1 s consisting of subunits from PdF 1 were expressed and purified as described previously. 27 PdF 1 plasmid was used as a vector. The primers for PdF 1 -hybrids are summarized in Table S8. After purification of the target proteins, conformation of a 3 b 3 g 1 was confirmed with SDS-PAGE analysis. Note that the process of the size exclusion chromatography was omitted in the purification process of the samples of hybrid F 1 s consisting of subunits from PdF 1 for rotation assay.

Single-molecule rotary assay
To visualize the rotation of F 1 s, two cysteine residues on the g subunit of bMF 1 (gA99C, gS191C), TF 1 (gS109C, gI212C), and PdF 1 (gQ115C, gD214C) were introduced and biotinylated to attach 40 nm diameter gold nanoparticles as an optical probe. The processes are as follows. The flow cell was constructed from 2 cover glasses (18 3 18 mm 2 and 24 3 32 mm 2 ; Matsunami Glass) using double-sided tape as a spacer. The surface of the bottom glass was coated with Ni-NTA. The basal buffer for the assay of bMF 1 or TF 1 -bMF 1 hybrid F 1 s contained 50 mM Hepes-KOH (pH 7.5), 50 mM KCl, and 3 mM MgCl 2 . The basal buffer for the assay of TF 1 contained 50 mM MOPS-KOH (pH 7.0), 50 mM KCl, and 3 mM MgCl 2 . When ATP was used, an ATP-regenerating system (1 mM phosphoenolpyruvate and 50 mg/mL pyruvate kinase) was added to the basal buffer. First, the flow cell was incubated with BSA buffer, the basal buffer containing 5 mg/mL BSA, for 5 min. Next, F 1 molecules of 0.3-10 nM in the BSA buffer were infused and incubated for 10 min. Then, unbound F 1 molecules were washed out by the BSA buffer and 40 nm gold nanoparticles were infused and incubated for 10 min. Unbound particles were washed out with the basal buffer containing substrate. The rotary assay was conducted with a dark-field microscope 46 (OLYMPUS IX-71) with a 603 objective lens at the recording rate of 250-10k fps (FASTCAM-1024PCI or FASTCAM NOVA s-16, Photron, Japan) ( Figure S4). Recorded movies were processed by a custom software. 48 The localization precision and signal-to-noise ratio ranges were the same as the previous studies. 26,46 When it is hard to find rotating particles, the F 1 concentration was increased up to 300 nM. When no rotating particle was observed analyzing typically over 1500 particles showing tethered rotary Brownian motion, we concluded that the hybrid F 1 does not rotate. To determine the number of pauses, ATPgS was used as a substrate in the rotary assay of the hybrid F 1 s, except for whose V ATPgS max values were more than 5 rps. For PdF 1 and its hybrids, the procedures were performed as described in. 27 Note that the basal buffer for PdF 1 and Pd-hybrids contained 50 mM Tris-acetate (pH 8.0), 30 mM CH 3 COOK, and 250 mM Sucrose, and 0.1% LDAO (lauryldimethylamine oxide). Methods for the kinetic and statistical analysis of the stepping behavior are described in the Supplemental text.

Quadratic model of the dependence of rotation rate on subunits
The fitting of the quadratic model for the V max values was performed by least square fitting. To confirm if all 9 terms, especially the nonlinear terms, in the quadratic model were needed, the fitting residuals were checked if any one of the terms was dropped. It was found that the fitting residuals increased significantly by dropping any one of the terms, indicating that our quadratic model is minimal in describing the observed rotation rates. On the other hand, including a constant term in the quadratic model resulted in an almost zero constant without visible improvement of the fitting residual, the constant term was therefore dropped in our quadratic model. A nonparametric change-point (CP) analysis 26 was used to detect changes in the traces. We wanted to find the points where a sudden change happened in the trace. The steps of CP analysis were as follows. A permutation test was used to check if there existed a CP in a segment of trace. In this test, the null hypothesis was that there was no CP and the alternative hypothesis was that there was at least one CP. As a test statistic, cumulative sum (CUSUM) was used, which was defined as CUSUMðtÞ = P t t 0 = 1 ðx t 0 À xÞ where t = 1; $$$; n is time point for the segment ðx 1 ; x 2 ; .; x n Þ and x is the mean angle of the segment. It is the sum of differences between the angles of points and the mean of the segment. This means that if there exists a change point, the fluctuation of CUSUM will be larger. Therefore, it is better to use D = ðCUSUMðtÞÞ À minðCUSUMðtÞÞ as a test statistic since it shows the total fluctuation of the CUSUM. Following the permutation test, if the null hypothesis is rejected, then the probable location of CP should be found. It is the point which has the smallest total squared error from fitted mean values of left and right segments of the point under consideration.
These steps were repeated for each segment to find multiple CPs in the trace. First, CP with the largest D was detected and segments were divided into two parts. Then the permutation test was applied again to new segments and they were divided if a new CP was detected. The process was repeated until no new CP could be detected.
Then, a histogram was constructed for CP intervals ( Figure S9, Second row, Left). Mean angular value of each CP interval was counted only once for this histogram. Therefore, even short pauses can be observed in it.

Cleaning up procedure
Besides true change points, several extra CPs could be detected due to some undesired fluctuations in the trace. Thus, after the detection of CPs, a cleanup procedure was performed. For i-th CP interval with n data points, the median x i $ and the median absolute deviation MAD i = medianðjx 1 À x i $ j; .; jx n À x i $ jÞ were obtained. Mean and standard deviation were not used since they are not robust to outliers. Then, for every consecutive CP interval, we checked if the CP between them could be removed by comparing the difference of their median angles and the sum of their MADs multiplied by a constant A. If jx i $ À x i + 1 $ j < A 3 ðMAD i + MAD i + 1 Þ, then CP between i-th and (i+1)-th CP intervals were removed. If a larger A was chosen, more CPs would be removed. Therefore, it is better to start with a small A. Then, the squared error between the trace before the cleanup procedure and the denoized trace was estimated. This process was repeated by increasing A, we obtained a plot of squared error and A factor ( Figure S9, First row, Right). In this plot, there is a rapid increase in squared error as A increases. Before this rapid increase of the squared error, undesired CPs due to fluctuations are removed; however, after the rapid increase, the true CPs start to be removed. Therefore, a good choice of A factor is just before the sudden increase in the plot. After the cleanup procedure, the peaks in the histogram for CP intervals became sharper ( Figure S9, Second row, Right).

Determining the number of pauses
After the CP analysis and the cleanup procedures, the histogram of CP intervals was constructed for each molecule of a given hybrid. In some cases, the number of peaks in the histogram may still not be easy to determine visually. Therefore, further clean-up procedure was implemented to sharpen the histogram. First, too short CP intervals, whose length was shorter than 7 points, were dropped. There also exists a few CP intervals corresponding to backward steps in the rotary trace or undesired small angular fluctuations from the measurement. To identify these undesired CP intervals, we compared the median angles of each CP interval to its previous and next CP intervals. If the difference between them was smaller than 40 and the medians do not progressively increase, the CP interval under consideration was removed from the histogram. Following these procedures, the visual detection of the number of peaks in the histogram became much easier. Two histograms for each hybrid are shown in Figure S10 for the 6-(or 9-) steppers and Figure S11 for the 3-steppers.
Step size comparison After the number of peaks were determined, it can be seen that some molecules show 6 distinct pauses, suggesting that there is a sub-pause between each pair of main pauses. Boundaries were then placed between the pauses in the histogram (see e.g., Figure S13) so that each CP interval can be uniquely assigned ll OPEN ACCESS iScience 26, 106626, May 19, 2023 iScience Article to one of the 6 pauses. We note that there exist some fluctuations in the angle separations between consecutive main pauses, i.e., the separations do not exactly equal to 120 o , due to, e.g., the titling of the motor rotary plane relative to the imaging axis, etc. To take into account these fluctuations, we considered the ratio of the distance between median angles of a main pause and the following sub-pause (''a'', Figure S13), and the distance between the median angles of the same sub-pause and the following main pause (''b'', in Figure S13). The angular distance ratio is smaller when the sub-pause is closer to the main pause before that. Finally, hierarchical clustering was used to compare the mean angular distance ratios of six hybrids with 6 pauses ( Figure 4D).

QUANTIFICATION AND STATISTICAL ANALYSIS
All details regarding statistical analyses are described in the Methods, Figure legends,