In Fig. , the possible quaternary structure of the dimeric bovine F
0F
1I complex is depicted according to the structural data available from crystallographic [
20], 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 IF
1 in the F
1F
0 dimer? We assumed a crossed IF
1 structure at the dimer interface, given that we also resolved by high-resolution electron microscopy the dimeric F
1F
0 and found a conical homodimeric molecule containing a protein bridge at the F
1–F
1 interface [
54]. In this model, the IF
1 N-terminal side is located at the rotor–stator interface in inhibitory position, whereas the C-terminal side of IF
1 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 [
65]. This model explains both the inhibitory and dimerizing roles of IF
1; however, both functions of IF
1 would require some further distortion from the fully extended helix observed in the isolated IF
1 to a bent or random coil conformation. This distortion is necessary to introduce the N-terminal side of IF
1 into the β
DP–γ interface as shown by the crystal structures [
21,
22]. In the F
1F
0 dimer model, we used a crystal IF
1 conformer that is bent in the middle of the IF
1 protein, and this fits better at this interface than the extended IF
1 dimer conformers [
68]. Similar crossed IF
1 dimeric structures have been observed in the IF
1 crystal [
68]; this arrangement would be different from the observed antiparallel coiled-coil dimer of isolated IF
1 [
68]. It was necessary to invoke this crossed structure because the distance between the N-terminal inhibitory domains in the IF
1–IF
1 extended dimer is about 60 Å [
68], whereas the F
1–F
1 distance observed in the soluble F
1–IF
1 dimer [
22] or in the (F
1F
0I)
2 dimer is ≤10 Å [
54]. This implies that the IF
1 dimer must bend or cross somehow to be accommodated at the F
1–F
1 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 [
54], 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 [
69]; however, in both cases, the dimeric structure adopted two angles of about 40° and 70° [
69]. Dudkina and colleagues [
70] 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 F
1-portions, showing that their preparation is largely unstable compared to our preparation, which contains mostly complete F
1F
0 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 F
1 and F
0; in contrast, our dimer enriched at lower detergent concentrations preserves essentially full oligomycin sensitivity, i.e., F
1F
0 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 F
0 inhibition. (3) There is emerging evidence from others [
73] and from our recent studies with the yeast F
1F
0 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 IF
1 is not essential for IF
1 dimerization in yeast [
52], the possibility remains that the shift from an extended to a compact conformation of the IF
1 dimer could participate in determining the angle of dimeric F
1F
0. 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” (
![[congruent with]](/corehtml/pmc/pmcents/cong.gif)
70°) and “closed” (
![[congruent with]](/corehtml/pmc/pmcents/cong.gif)
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 F
0 side that have been found in yeast F
1F
0 [
74]; these two interfaces would build a helical polymer of dimers that wraps and gives shape to the tubular cristae of mitochondria [
75], as it is currently proposed (Fig. ).
In summary, the dimeric structure of the F
1F
0 ATP synthase is stabilized by the so-called inhibitor protein (IF
1) in the mitochondria of complex organisms such as rat or cow. Literally, on the other hand, the conserved N-terminal side of IF
1 inhibits the F
1F
0-ATPase activity by entering through the open catalytic α
E–β
E interface in a cleft formed by β–γ–ε subunits. With the IF
1 bound at this interface, the F
1-ATPase carries out two 120° gyrations of the central stalk and the N-terminal side of IF
1 locks at the β
DP–α
DP–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 IF
1 with the rotor–stator interface of F
1 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 IF
1 becomes exposed to the media upon membrane energization, whereas the C-terminal side of IF
1 becomes shielded to proteolysis, indicating that it hides behind another F
1F
0 subunit (García-Trejo et al., unpublished). We propose here how this might happen in the dimeric F
1F
0 structure of bovine heart mitochondria. Upon membrane energization, the C-terminal side of IF
1 might become occluded between OSCP or second-stalk subunits at the dimer interface, whereas the N-terminal inhibitory domain is released from the α
DP–β
DP–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 F
1 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 [
75]). 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. ). 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 F
0–F
0 interactions in the dimer as observed by atomic force microscopy in the dimeric enzyme [
71]. 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 [
30] and of a thermoalkaliphilic bacterium [
31]. 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 F
1 portion undergoes slippage from the proton conduction through F
0 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 F
1F
0-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. ).