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The F1F0-adenosine triphosphate (ATP) synthase rotational motor synthesizes most of the ATP required for living from adenosine diphosphate, Pi, and a proton electrochemical gradient across energy-transducing membranes of bacteria, chloroplasts, and mitochondria. However, as a reversible nanomotor, it also hydrolyzes ATP during de-energized conditions in all energy-transducing systems. Thus, different subunits and mechanisms have emerged in nature to control the intrinsic rotation of the enzyme to favor the ATP synthase activity over its opposite and commonly wasteful ATPase turnover. Recent advances in the structural analysis of the bacterial and mitochondrial ATP synthases are summarized to review the distribution and mechanism of the subunits that are part of the central rotor and regulate its gyration. In eubacteria, the ε subunit works as a ratchet to favor the rotation of the central stalk in the ATP synthase direction by extending and contracting two α-helixes of its C-terminal side and also by binding ATP with low affinity in thermophilic bacteria. On the other hand, in bovine heart mitochondria, the so-called inhibitor protein (IF1) interferes with the intrinsic rotational mechanism of the central γ subunit and with the opening and closing of the catalytic β-subunits to inhibit its ATPase activity. Besides its inhibitory role, the IF1 protein also promotes the dimerization of the bovine and rat mitochondrial enzymes, albeit it is not essential for dimerization of the yeast F1F0 mitochondrial complex. High-resolution electron microscopy of the dimeric enzyme in its bovine and yeast forms shows a conical shape that is compatible with the role of the ATP synthase dimer in the formation of tubular the cristae membrane of mitochondria after further oligomerization. Dimerization of the mitochondrial ATP synthase diminishes the rotational drag of the central rotor that would decrease the coupling efficiency between rotation of the central stalk and ATP synthesis taking place at the F1 portion. In addition, F1F0 dimerization and its further oligomerization also increase the stability of the enzyme to natural or experimentally induced destabilizing conditions.
The mitochondrial adenosine triphosphate (ATP) synthase is a ubiquitous motor enzyme that provides most of the cellular chemical energy in the form of ATP to fuel all kinds of work in biological nature. This motor functions as a coupling factor between the condensation of adenosine diphosphate (ADP) and Pi that takes place at its catalytic F1-ATPase portion and proton flow through the transmembranous F0-proton channel that consumes energy from electrochemical proton gradients. According to the well-established chemiosmotic theory, this proton gradient is established by oxidative or photosynthetic electron transfer chains of the plasma membrane of bacteria, the inner mitochondrial membrane, and the thylakoid membranes of chloroplasts. Because of thermodynamic and mechanical reversibility, the F1F0-ATP synthase becomes a proton-pumping F1F0-ATPase under conditions of partial or total collapse of the proton gradient; for instance, during anoxia in bacteria where it works as a primary pump to drive secondary transporters, during ischemia in mitochondria, or under dark conditions in chloroplasts. In all these systems, different subunit structures control gyration of the central stalk by favoring rotation in the ATP synthase turnover direction. Chloroplast ATP synthase possesses a unique disulfide bridge in the γ subunit that controls rotation of the central stalk; however, only the structures of the bacterial and the bovine enzymes are reviewed here.
Important new information such as the dimerization of the ATP synthase and the role of the inhibitor protein (IF1) in this process are also reviewed and used to propose a model of the structure of the ATP synthase dimmer that explains the inhibitory and dimerizing roles of IF1. This model also explains how dimerization of the ATP synthase may confer a higher stability and efficiency of the dimeric enzyme to synthesize ATP. This also sheds light on how F1F0 dimerization promotes formation of tubular cristae membrane structures in mitochondria after further polymerization.
The catalytic part of the enzyme is a water-soluble portion (F1) that can be released in vitro from the membrane, retaining its capacity to hydrolyze ATP (F1-ATPase) . ATP synthesis occurs in the whole F1F0 when the energy derived from proton conduction through the F0 membrane channel is combined with the nucleotide (Mg-ADP) and Pi binding energies [2–5] to drive the release of newly synthesized ATP from each of the three alternating catalytic sites of F1. The coupling between F1 and F0 is critical for efficient ATP synthesis to occur and major progress in the understanding of this coupling mechanism has been achieved. Several approaches at different laboratories showed that a central rotor actually gyrates relative to a stator that holds the catalytic subunits; this rotation induces the alternating binding, catalysis, and product release from three catalytic sites of F1 (for reviews, see [5–9]). These studies also indicated that the γ subunit, together with ε and the ring of 9–15 c subunits of F0, form the rotor in the central part of the enzyme. The more direct evidence demonstrating this rotational movement was the observation by fluorescence microscopy of rotation of a fluorescent actin filament attached to the γ, ε, or c subunits of immobilized F1 and F1F0 complexes [10–13]. These experiments established that the rotor of the enzyme is formed by the central γ–ε–c9−15 domain. This core rotor–stator structure is preserved in bacterial and mitochondrial ATP synthases and is shown in Fig. 1 indicating the reversible rotational mechanism of the enzyme.
The rotary mechanism of the enzyme implies that, in the central stalk, the γ subunit (together with ε and c9−15 subunits) rotates relative to a stator where the catalytic α–β interfaces are held. Therefore, this stator must be somehow anchored to an F0 subunit at the lipid bilayer. A peripheral second stalk was literally “invoked” and found by means of high-resolution electron microscopy studies [14, 15] and by cross-linking of α, δ, b, and a subunits along this peripheral second stalk . The anchoring part of the second stalk with the α subunit of F1 has been solved by nuclear magnetic resonance (NMR) for the Escherichia coli enzyme , whereas most of the structure of the second stalk of the bovine mitochondrial enzyme has been resolved by X-ray crystallography . Thus, the whole picture of the simplest ATP synthase of E. coli involves a stator formed by (α–β)3, δ, b2, and a subunits and a central rotor formed by the γ–ε–c9−15 domain. This core rotor–stator structure of bacterial ATP synthase becomes more complex with about twice as many different subunits present in chloroplasts and mitochondria. Besides the core subunits and structure of the EF1F0 motor, there are six to eight additional or “supernumerary” subunits that are well described in mitochondrial yeast and bovine ATP synthases. These subunits are d, e, f, g, F6 (h in yeast), A6L (8 in yeast), the inhibitor protein (IF1), and mitochondrial subunit ε which does not have a bacterial counterpart (see below and Table 1). Three additional F0 proteins are also found in the yeast enzyme (see legend of Table 1). The roles of these additional subunits are related to regulation and oligomerization of the ATP synthase as will be described below.
Crystallographic studies have solved most of the central stalk structure in E. coli (EF1)  and bovine mitochondrial (MF1) F1-ATPases [19–22]. The tertiary structure and orientation of the globular domain of the γ subunit is very similar in both species (Fig. 2), and it is in agreement with previous cross-linking data obtained with the enzyme from E. coli. However, the ε subunit of E. coli (bovine δ) was found far away from the cross-linking distance to the α or β subunits but closer to the F0 subunit c in the crystals of the yeast  and bovine [20–22] enzymes. It was therefore unclear how ε could cross-link with α or β subunits in the native enzyme as found before, until another X-Ray diffraction analysis was made with a soluble γ–ε complex from E. coli . In this study, the structure of soluble ε was very different from the bovine δ subunit F1. The soluble ε subunit associated with γ was found rotated in relation to the vertical axis of the central stalk and extending its two C-terminal helices toward the C-termini of α and β. This position placed the appropriate residues in cross-linking distance  (Fig. 2). The conclusion is therefore that ε experiences dramatic changes in conformation that are important for its role as an inhibitor of the ATPase activity of the enzyme, controlling the rate of rotation of the central stalk. Engineered cross-linking in the E. coli F1F0 complex entrapped these two conformations of the ε subunit . Interestingly, when the C-terminus of ε is compacted as an antiparallel α-helix coil with its N-terminal β-sheet domain, the F1F0-ATPase activity is enhanced and the enzyme is coupled during ATP hydrolysis and synthesis. However, when the C-terminus of ε extends toward F1 (as shown in Fig. 2), ATP hydrolysis is inhibited but ATP synthesis remains unaffected . In agreement with this work, the structure of the γ–ε domain in the E. coli F1-ATP synthase  was found very similar to that of the isolated subunits . Furthermore, it has been found that the ratchet mechanism of ε can be regulated by ATP binding in some bacteria [9, 26]. When ATP is bound, the closed conformation is stabilized, thus favoring rotation of the central stalk in the ATPase direction; conversely, at low ATP concentrations, ε is unable to bind ATP, and therefore the extended conformation is favored, thus leaving the enzyme prone to rotate into the ATP synthase turnover. This model is supported with the recent crystal structure of the Bacillus PS3 subunit ε with ATP associated to the C-terminus of this subunit . In summary, these studies show that ε works as an ATP sensor in bacteria that posses a novel ATP-binding motif in this subunit [26–29].
Besides the control of rotation described so far for the bacterial enzymes by the ε subunit, it is important to introduce a novel inhibitory 11-kDa protein that we recently found in the ATP synthase of the α-proteobacteria Paracoccus denitrificans (Morales-Ríos et al. 2008, submitted). The ATP synthase from P. denitrificans has been only described functionally as the fastest ATP synthase and the slowest ATPase found to date ; however, it has never been isolated until we addressed this issue. This novel inhibitory 11-kDa protein is present in F1-ATPase and F1F0-ATPase preparations obtained from P. denitrificans membranes, and it will likely add a novel control and inhibitory mechanism to the α-proteobacteria family where the open reading frame exists. Importantly, the ε subunit of this enzyme does not inhibit the ATPase activity of the F1-ATPase or F1F0-ATPase complexes in P. denitrificans (Morales-Ríos et al. 2008, submitted). Thus, the 11-kDa protein will add a novel control mechanism to the ATP synthases, in addition to the classical inhibitory mechanisms of bacterial, chloroplast, and mitochondrial F1F0 complexes. Unidirectional functioning of ATP synthase turnover has been also described for another bacterial enzyme of the thermoalkaliphilic type, Bacillus sp. TA2.A1 . However, instead of additional regulatory proteins, unique polar interactions at the rotor–stator interface of the F1 subunits allow almost exclusively unidirectional rotation in the ATP synthase direction for this enzyme . To our knowledge, only two other bacterial proteins have been found encoded in the atp operon in addition to the eight core subunits of bacterial F1F0 (α, β, γ, δ, ε, a, b, c); these two proteins are encoded by the unc-I and urf-6 genes that correspond, respectively, to an assembly factor of the c-ring  and to majastridin, a cytosolic protein nonassociated with the Rhodospirillum blasticus ATP synthase . In contrast, the gene encoding the 11-kDa protein of P. denitrificans is located upstream to both atp operons (one for F0 and another for F1 subunits) already sequenced on chromosome II of P. denitrificans (see Morales-Ríos et al. 2008, submitted, and the following link: http://genome.jgi-psf.org/finished_microbes/parde/parde.home.htm). Therefore, it seems that the 11-kDa regulatory protein that we found in the F1F0 complex of P. denitrificans is one of the first, if not the first, supernumerary subunit added to bacterial ATP synthases as an exogenous gene of the atp operon (formerly known as the unc operon). This 11-kDa protein therefore emerged during α-proteobacterial evolution and previous to the endosymbiotic event from which mitochondria emerged.
Most of the supernumerary subunits in the mitochondrial enzyme correspond to membrane proteins associated with the F0 proton channel. These additional subunits are d, e, f, g, F6, and A6L. Subunits d and F6 are part of the second stalk, and A6L is a membrane protein of F0 that is essential for the assembly of subunit 6, the one that forms the proton-conducting interface with the c9−15 ring. On the other hand, the roles of some of these subunits were recently unveiled by studies in yeast showing that subunits e and g are needed to form F1F0 dimers in situ [34, 35]. However, an unexpected result was the finding that genetic removal of these e and g subunits deformed the inner mitochondrial membrane and the classical cristae transformed into concentric membrane layers inside enlarged mitochondria . This demonstrated that dimerization of the ATP synthase is not an artifact of detergent extraction as suspected but a natural and important biological process that improves the ATP synthase activity and the stability of the enzyme. Thus, besides dimerizing to improve somehow the ATP synthesis reaction, the dimeric enzyme also promotes mitochondrial cristae formation, thus optimizing the overall process of oxidative phosphorylation.
Two supernumerary subunits are part of the mitochondrial F1, namely ε and the so-called inhibitor protein (IF1). Bovine ε is different with its bacterial homonym; it is a 5.7-kDa protein, whereas that of E. coli is 15 kDa in size (Table 1 and Fig. 2). Bovine ε stabilizes the structure of the central stalk by interacting with the globular part of γ (Figs. 2, ,3,3, and and4).4). Closely interacting with ε, bovine subunit δ has a similar structure to that of its homologous E. coli ε. However, neither bovine δ or ε subunits inhibit the ATPase activity of bovine F1F0; together, they form a compact and noninhibitory structure at the central stalk, in contrast to the flexible structure of E. coli ε (Fig. 2) . The bovine and E. coli δ subunits also correspond to different proteins. E. coli δ does not form part of the central stalk as the bovine δ does (Table 1, Fig. 2). E. coli δ is the connection between the “tip” of the F1 subunit α and the “top” of the peripheral second stalk (reviewed in ). It is homologous to bovine oligomycin sensitivity conferring protein (OSCP) which also interacts with subunits of the second stalk (see Fig. 4, and [17, 36–38]). As mentioned above, the connection between E. coli δ and α subunits has been resolved by NMR .
A key regulatory subunit absent in bacterial or chloroplast F1F0 is the mitochondrial inhibitor protein (IF1). Since its first isolation in 1963 by Pullman and Monroy , this protein was shown to inhibit the ATPase activity of the catalytic F1 part. This protein is therefore crucial to preventing the hydrolysis of newly synthesized ATP in conditions of low membrane potential in mitochondria. Upon membrane energization, IF1 is believed to be relocated from its inhibitory site into an unknown position within [40, 41] or outside the F1F0 complex [42, 43], therefore allowing ATP synthesis to occur. In de-energized or uncoupled conditions, such as ischemia, the bovine IF1 is productively associated with the enzyme, inhibiting the ATPase turnover of the F1I or F1F0I complexes. However, this protein allows the rotational ATP synthesis turnover during energization of mitochondrial membranes. Therefore, IF1 is an important physiological regulator of the functioning of the ATP synthase.
Although the location of the endogenous IF1 in the whole F1F0I-ATP synthase remains unknown, on the basis of the available structural studies, we proposed a model of the binding site for the IF1 that would explain the inhibitory role of IF1 . It is well known that the inhibitory domain of IF1 lies on the N-terminal side of the molecule [45–47]; thus, according to our cross-linking data showing for the first time a relatively short distance (12 Å) between IF1 and the γ and ε subunits, we placed the N-terminal inhibitory side in a cross-linking position of about 12 Å from the γ and ε subunits . Figure 3 (top panels) shows this position of the N-terminal side on a cleft formed by the βE catalytic subunit and the γ–ε part of the central rotor; lysine residues that are at 12-Å cross-linking distance are shown in purple. This β E–γ–ε cleft was the wider binding site available for entrance of the IF1 N-terminal side into the rotor–stator interface. It is clearly demonstrated from different perspectives that the binding of the N-terminal side of IF1 in this position interferes not only with the conformational changes of the β subunits, as proposed before [19, 48], but also with the intrinsic rotation of the central stalk. Thus, we supported and proposed a novel mechanism of action for this protein that was later confirmed by the elegant crystal structure of the reconstituted dimeric F1–IF1 complex . In the latter complex, the central coiled α-helixes of the γ subunit that extend along the central pseudosymmetry axis of the F1-ATPase particle were found not only in proximity but in actual close contact with the its N-terminal side of IF1 [21, 22] (see Fig. 3, bottom panels). The IF1 was found locked into a βDP–γ cleft rather than in a βE–γ–ε interface, as we originally proposed . This shows that what we found by cross-linking and model building was the entrance site of IF1 into the F1-ATPase particle and that two further angular movements of the γ subunit of 120° lock the IF1 into the βDP form of the catalytic subunit that previously received the IF1 in its open βE conformation (see Fig. 3 and ). Thus, the mechanism of action of IF1 as inhibitor involves blocking the rotation of the central stalk and inhibiting the opening–closing conformational changes of the catalytic β subunit that leads to substrate binding, catalysis, and product release from F1.
Besides showing the close-up view of the IF1–γ interaction, the isolation and resolution of the F1–IF1 crystal structure also showed that reconstitution of recombinant IF1 induces dimerization of the soluble F1-ATPase particles in the expected 1:1 IF1–F1 stoichiometry [22, 49]. Earlier blue native polyacrylamide gel electrophoresis analyses of mitochondria showed a dimeric ATP synthase species that appears after mitochondrial solubilization with several detergents  and that some F0 subunits such as e and g are essential for ATP synthase dimerization [34, 35]. Thus, the question emerged of whether the IF1 participates in the dimerization of the whole F1F0-ATP synthase in mitochondria, besides dimerizing the soluble F1-ATPase in vitro . Initially, several groups found that genetic or physical removal of the yeast or bovine IF1, respectively, did not prevent F1F0 dimerization; thus, it was concluded that IF1 does not participate in the homodimerization of the whole F1F0 [51, 52]. However, because the yeast IF1 protein lacks most of the C-terminal dimerizing domain and it is much less prone to dimerize , it was conceivable that the role of IF1 in dimerization of the ATP synthase might be excluded from the yeast enzyme but present in the bovine and rat mitochondrial enzymes. Besides, the results where IF1 removal did not change the dimer to monomer ratio of the bovine ATP synthase were obtained in the presence of triton X-110 where the F1F0-ATPase is inactive . Therefore, we reassessed the role of IF1 as a dimerizing factor of the bovine and rat mitochondrial enzymes in digitonin-extraction conditions where the dimeric and monomeric forms of the F1F0 complex are functional . Besides, instead of looking to the decrease in the dimeric ATP synthase after IF1 removal, we looked for the recovery or promotion of the dimeric species after reconstitution of increasing amounts of IF1 into submitochondrial particles. With this approach, we demonstrated that removal of IF1 dissociated the whole ATP synthase into monomers of high ATPase activity, and the reconstitution of IF1 into SMP brought a partial recovery of the dimer content of the SMP extract accompanied by an overall inhibition of the ATPase activity . Interestingly, the larger ATP synthase oligomers were also partially recovered by IF1 reconstitution , suggesting that IF1 participates in the formation of aggregation states of the ATP synthase larger than the ATP synthase dimer. Thus, it seems that yeast IF1 is not essential for F1F0 dimerization in Saccharomyces cerevisiae simply because it is much less prone to dimerize since it lacks most of the C-terminal coiled-coil dimerizing domain . The latter seems therefore essential for bovine and rat IF1 to promote and/or stabilize the dimer and higher oligomer structures of the mitochondrial ATP synthase. This is consistent with previous findings where it has been shown that IF1 confers structural stability to the F1F0I and F1I complexes during high-pressure denaturation that leads to dissociation of oligomeric species . In line with the dimerizing role of IF1, it has been recently shown that, among other metabolic effects, the overexpression of IF1 increases the amount of mitochondrial cristae, and its downregulation decreases the number of cristae in mitochondria of cultured cells . Taken together, these studies confirm that, besides the inhibitory role of IF1, it is also an important factor that stabilizes dimerization and further oligomerization of the mitochondrial ATP synthase, thus promoting formation of mitochondrial cristae as detailed below.
In Fig. 4, the possible quaternary structure of the dimeric bovine F0F1I complex is depicted according to the structural data available from crystallographic , genetic [58–60], subunit association [36, 37], cross-linking [38, 44, 61–65], and protease accessibility [38, 66, 67] evidence. How does this model accommodate the inhibitory and dimerizing functions of IF1 in the F1F0 dimer? We assumed a crossed IF1 structure at the dimer interface, given that we also resolved by high-resolution electron microscopy the dimeric F1F0 and found a conical homodimeric molecule containing a protein bridge at the F1–F1 interface . In this model, the IF1 N-terminal side is located at the rotor–stator interface in inhibitory position, whereas the C-terminal side of IF1 crosses the dimer interface and interacts with the opposite monomer probably through the OSCP subunit at the top of the side stalk as found by cross-linking evidence . This model explains both the inhibitory and dimerizing roles of IF1; however, both functions of IF1 would require some further distortion from the fully extended helix observed in the isolated IF1 to a bent or random coil conformation. This distortion is necessary to introduce the N-terminal side of IF1 into the βDP–γ interface as shown by the crystal structures [21, 22]. In the F1F0 dimer model, we used a crystal IF1 conformer that is bent in the middle of the IF1 protein, and this fits better at this interface than the extended IF1 dimer conformers . Similar crossed IF1 dimeric structures have been observed in the IF1 crystal ; this arrangement would be different from the observed antiparallel coiled-coil dimer of isolated IF1 . It was necessary to invoke this crossed structure because the distance between the N-terminal inhibitory domains in the IF1–IF1 extended dimer is about 60 Å , whereas the F1–F1 distance observed in the soluble F1–IF1 dimer  or in the (F1F0I)2 dimer is ≤10 Å . This implies that the IF1 dimer must bend or cross somehow to be accommodated at the F1–F1 interface of the ATP synthase dimer that had an angle of about 40° which gives its conical shape.
On the other hand, it is also noted that, besides the bovine dimeric ATP synthase , other similar dimeric structures have been subsequently observed by electron microscopy in S. cerevisiae and Polytomella sp mitochondria. The latter species has a unique second-stalk composition and is therefore nonrepresentative of other mitochondrial ATP synthases ; however, in both cases, the dimeric structure adopted two angles of about 40° and 70° . Dudkina and colleagues  named their open (70°) structure as the “true dimer”, and our compact (40°) structure as a “pseudo-dimer”; furthermore, they also suggest that, in line with other reports, only their open “true” dimer actually participates in cristae formation [71, 72]. However, their dimer structures have several drawbacks: (1) their image averages are collected not by hand but automatically by image analysis software; in consequence, a large proportion of their dimer particles lack one or both of the F1-portions, showing that their preparation is largely unstable compared to our preparation, which contains mostly complete F1F0 structures. (2) The larger detergent concentration used to isolate the enriched open dimers [69, 70] decreases the dimer yield and stability, and, importantly, it also decreases the functional coupling between F1 and F0; in contrast, our dimer enriched at lower detergent concentrations preserves essentially full oligomycin sensitivity, i.e., F1F0 functional coupling (Minauro-Sanmiguel and García-Trejo, unpublished results). This parameter has not been reported in the preparations enriched with the open (70°) and unstable dimer; it would not be surprising to find there a decreased F0 inhibition. (3) There is emerging evidence from others  and from our recent studies with the yeast F1F0 dimer (not shown) indicating that both structures (open and closed) coexist with a wide distribution of dimers showing different angles after detergent extraction, but there is no clear evidence indicating which protein or factor is controlling the opening or closing of the dimer angle. Although IF1 is not essential for IF1 dimerization in yeast , the possibility remains that the shift from an extended to a compact conformation of the IF1 dimer could participate in determining the angle of dimeric F1F0. Therefore, we conclude that there is no reason to name arbitrarily the open or closed conformations as “pseudo” or “true” dimers; instead, we propose to refer to them just as “open” (70°) and “closed” (40°) dimers, with the understanding that the dimer population actually spreads through all angles between these values. Regardless of the observed angle values after detergent extraction, two major dimeric species correlate well with two distinct dimeric interfaces at the F0 side that have been found in yeast F1F0 ; these two interfaces would build a helical polymer of dimers that wraps and gives shape to the tubular cristae of mitochondria , as it is currently proposed (Fig. 5).
In summary, the dimeric structure of the F1F0 ATP synthase is stabilized by the so-called inhibitor protein (IF1) in the mitochondria of complex organisms such as rat or cow. Literally, on the other hand, the conserved N-terminal side of IF1 inhibits the F1F0-ATPase activity by entering through the open catalytic αE–βE interface in a cleft formed by β–γ–ε subunits. With the IF1 bound at this interface, the F1-ATPase carries out two 120° gyrations of the central stalk and the N-terminal side of IF1 locks at the βDP–αDP–γ interface, completely blocking rotation of the central stalk and the opening and closing of the catalytic sites. A further question that emerges is, how this deep inhibitory interaction of IF1 with the rotor–stator interface of F1 is reversed in the presence of the mitochondrial electrochemical proton gradient to allow ATP synthesis turnover? We are currently addressing this question by limited proteolysis experiments; interestingly, we observed that the N-terminal side of IF1 becomes exposed to the media upon membrane energization, whereas the C-terminal side of IF1 becomes shielded to proteolysis, indicating that it hides behind another F1F0 subunit (García-Trejo et al., unpublished). We propose here how this might happen in the dimeric F1F0 structure of bovine heart mitochondria. Upon membrane energization, the C-terminal side of IF1 might become occluded between OSCP or second-stalk subunits at the dimer interface, whereas the N-terminal inhibitory domain is released from the αDP–βDP–γ cleft where it is bound, thus restoring rotation of the central stalk and the opening–closing conformational changes of the β subunits that are essential for F1 catalysis. In this model, second-stalk subunits are not depicted for clarity, but they should contribute significantly to the dimer interface, as shown for the yeast H subunit (bovine subunit F6, see ). Once formed, the dimer structure seems more stable and in better shape to resist the rotational drag of the continuous gyration of the central stalk than its dimeric form (Fig. 4). In other words, the monomeric enzyme could lose coupling energy by rotating as a rigid body following the angular drag of the rotor; this would hardly occur in a dimerized or oligomerized ATP synthase. Indeed, it has been proposed that the rotational drag of each monomer promotes closer F0–F0 interactions in the dimer as observed by atomic force microscopy in the dimeric enzyme . It can also be questioned whether dimerization actually increases the coupling efficiency of the enzyme, given that the monomeric bacterial enzyme is already highly efficient as a coupling factor; indeed, the most efficient and practically unidirectional ATP synthases described so far are those of P. denitrificans  and of a thermoalkaliphilic bacterium . However, it is also recalled that, in α-proteobacteria and even in eubacteria such as E. coli, it has been described that the rotary turnover of the F1 portion undergoes slippage from the proton conduction through F0 under conditions of low ADP and Pi concentrations [76, 77]. This slipping has not been observed for the mitochondrial enzyme, probably because the rotor and stator interfaces of each monomer interact more efficiently in the dimeric or oligomeric forms of the enzyme. In this line, we are currently collecting evidence to respond to the question of whether the dimeric enzyme possesses a higher stability and better efficiency as ATP synthase in comparison with its monomeric species; preliminary results indicate that it is actually the case. Together with its role in formation of the mitochondrial cristae, these studies and models shed light on the mechanisms by which the F1F0-ATP synthase becomes not only the most efficient nanomotor in nature by its regulation in bacteria and by its dimerization in mitochondria, but also becomes a dimeric building block of a hypothetical helical polymer that wraps and gives shape to the mitochondrial cristae (Fig. 5).
This work and our work reviewed here were supported by the CONACyT grants No. I32903-N, J34744-N, and V43814-M.