The c15 ring of the Spirulina platensis F-ATP synthase: F1/F0 symmetry mismatch is not obligatory

The oligomeric c ring of the F-ATP synthase from the alkaliphilic cyanobacterium Spirulina platensis was isolated and characterized. Mass spectroscopy analysis indicated a mass of 8,210 Da, reflecting that of a c monomer. The mass increased by 206 Da after treatment with the c-subunit-specific inhibitor dicyclohexylcarbodiimide (DCCD), which indicated modification of the ion-binding carboxylate by DCCD. Atomic force microscopy topographs of c rings from S. platensis showed 15 symmetrically assembled subunits. The c15-mer reported here is the largest c ring that is isolated and does not show the classical c-ring mismatch to the three-fold symmetry of the F1 domain.     

Structural evidence for a constant c11 ring stoichiometry in the sodium F-ATP synthase

The Na+-dependent F-ATP synthases of Ilyobacter tartaricus and Propionigenium modestum contain membrane-embedded ring-shaped c subunit assemblies with a stoichiometry of 11. Subunit c from either organism was overexpressed in Escherichia coli using a plasmid containing the corresponding gene, extracted from the membrane using detergent and then purified. Subsequent analyses by SDS/PAGE revealed that only a minor portion of the c subunits had assembled into stable rings, while the majority migrated as monomers. The population of rings consisted mainly of c11, but more slowly migrating assemblies were also found, which might reflect other c ring stoichiometries. We show that they consisted of higher aggregates of homogeneous c11 rings and/or assemblies of c11 rings and single c monomers. Atomic force microscopy topographs of c rings reconstituted into lipid bilayers showed that the c ring assemblies had identical diameters and that stoichiometries throughout all rings resolved at high resolution. This finding did not depend on whether the rings were assembled into crystalline or densely packed assemblies. Most of these rings represented completely assembled undecameric complexes. Occasionally, rings lacking a few subunits or hosting additional subunits in their cavity were observed. The latter rings may represent the aggregates between c11 and c1, as observed by SDS/PAGE. Our results are congruent with a stable c11 ring stoichiometry that seems to not be influenced by the expression level of subunit c in the bacteria.     

Evidence for structural integrity in the undecameric c-rings isolated from sodium ATP synthases

The Na(+)-translocating ATP synthases from Ilyobacter tartaricus and Propionigenium modestum contain undecameric c subunit rings of unusual stability. These c(11) rings have been isolated from both ATP synthases and crystallized in two dimensions. Cryo-transmission electron microscopy projection maps of the c-rings from both organisms were identical at 7A resolution. Different crystal contacts were induced after treatment of the crystals with dicyclohexylcarbodiimide (DCCD), which is consistent with the binding of the inhibitor to glutamate 65 in the C-terminal helix on the outside of the ring. The c subunits of the isolated c(11) ring of I.tartaricus were modified specifically by incubation with DCCD with kinetics that were indistinguishable from those of the F(1)F(o) holoenzyme. The reaction rate increased with decreasing pH but was lower in the presence of Na(+). From the pH profile of the second-order rate constants, the pK of glutamate 65 was deduced to be 6.6 or 6.2 in the absence or presence of 0.5mM NaCl, respectively. These pK values are identical with those determined for the F(1)F(o) complex. The results indicate that the isolated c-ring retains its native structure, and that the glutamate 65, including binding sites near the middle of the membrane, are accessible to Na(+) from the cytoplasm through access channels within the c-ring itself.     

The c13 Ring from a Thermoalkaliphilic ATP Synthase Reveals an Extended Diameter Due to a Special Structural Region

We have structurally characterized the c-ring from the thermoalkaliphilic Bacillus sp. strain TA2.A1 F₁F_o-ATP synthase. Atomic force microscopy imaging and cryo-electron microscopy analyses confirm previous mass spectrometric data indicating that this c-ring contains 13 c-subunits. The cryo-electron microscopy map obtained from two-dimensional crystals shows less closely packed helices in the inner ring compared to those of Na⁺-binding c₁₁ rings. The inner ring of α-helices in c₁₁ rings harbors a conserved GxGxGxGxG motif, with glycines located at the interface between c-subunits, which is responsible for the close packing of these helices. This glycine motif is altered in the c₁₃ ring of Bacillus sp. strain TA2.A1 to AxGxSxGxS, leading to a change in c-c subunit contacts and thereby enlarging the c-ring diameter to host a greater number of c-subunits. An altered glycine motif is a typical feature of c-subunit sequences in alkaliphilic Bacillus species. We propose that enlarged c-rings in proton-dependent F-ATP synthases may represent an adaptation to facilitate ATP synthesis at low overall proton-motive force, as occurs in bacteria that grow at alkaline pH.     

A new solution structure of ATP synthase subunit c from thermophilic Bacillus PS3, suggesting a local conformational change for H+-translocation

In F(o)F(1)-ATP synthase, an oligomer ring of F(o)c subunits acts as a rotary proton channel of the F(o)-proton motor. On the basis of the solution structure of the Escherichia coli F(o)c (EF(o)c) monomer, the rotation of the C-terminal helix coupled with the reorientation of the essential Asp61 side-chain on deprotonation was proposed to drive rotation of the whole c-ring. We have determined the NMR structure of F(o)c from thermophilic Bacillus PS3, TF(o)c, in an organic solvent mixture (chloroform/methanol (3:1, v/v)). Our results showed that, independent of pH, the carboxyl group of the essential Glu56 of TF(o)c protrudes toward the outside of the hairpin, a third orientation that differs from either of the two orientations in EF(o)c. Therefore, it would be inappropriate to draw conclusions about the mechanism of c-ring rotation on the basis of the conformations observed only for EF(o)c. The appearance of different hairpin structures shows that there are multiple energy minima for the hairpin structure in terms of helix rotation and axial displacement. The multiple energy minima may also provide a base for the different oligomeric states in the c-ring structure. A rotation mechanism of the F(o) motor coupled with H(+)-translocation is discussed on the basis of these results and the recently reported crystal structure of the c-ring from Ilyobacter tartaricus Na(+)-ATPase.     

Structural investigations of the membrane-embedded rotor ring of the F-ATPase from Clostridium paradoxum

The Na(+)-translocating F-ATPase of the thermoalkaliphilic bacterium Clostridium paradoxum harbors an oligomeric ring of c subunits that resists dissociation by sodium dodecyl sulfate. The c ring has been isolated and crystallized in two dimensions. From electron microscopy of these c-ring crystals, a projection map was calculated to 7 A resolution. In the projection map, each c ring consists of two concentric, slightly staggered, packed rings, each composed of 11 densities representing the alpha-helices. On the basis of these results, it was determined that the F-ATPase from C. paradoxum contains an undecameric c ring.     

Mutations in a helix-1 motif of the ATP synthase c-subunit of Bacillus pseudofirmus OF4 cause functional deficits and changes in the c-ring stability and mobility on sodium dodecyl sulfate-polyacrylamide gel electrophoresis

The ATP synthase of the alkaliphile Bacillus pseudofirmus OF4 has a tridecameric c-subunit rotor ring. Each c-subunit has an AxAxAxA motif near the center of the inner helix, where neutralophilic bacteria generally have a GxGxGxG motif. Here, we studied the impact of four single and six multiple Ala-to-Gly chromosomal mutations in the A16xAxAxA22 motif on the capacity for nonfermentative growth and, for most of the mutants, on ATP synthesis by ADP- and P(i)-loaded membrane vesicles at pH 7.5 and 10.5. Sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) analyses of the holo-ATP synthases were used to probe stability of the mutant c-rotors and mobility properties of the c-rotors as well as the monomeric c-subunits that are released from them by trichloroacetic acid treatment. Mutants containing an Ala16-to-Gly mutation exhibited the most severe functional defects. Via SDS-PAGE, most of the mutant c-monomers exhibited increased mobility relative to the wild-type (WT) c-subunit, but among the intact c-rings, only Ala16-to-Gly mutants exhibited significantly increased mobility relative to that of the WT c-ring. The hypothesis that these c-rings have a decreased c-subunit stoichiometry is still untested, but the functional impact of an Ala16-to-Gly mutation clearly depended upon additional Ala-to-Gly mutation(s) and their positions. The A16/20G double mutant exhibited a larger functional deficit than both the A16G and A16/18G mutants. Most of the mutant c-rings showed in vitro instability relative to that of the WT c-ring. However, the functional deficits of mutants did not correlate well with the extent of c-ring stability loss, so this property is unlikely to be a major factor in vivo.     

Microscopic rotary mechanism of ion translocation in the F(o) complex of ATP synthases

The microscopic mechanism of coupled c-ring rotation and ion translocation in F(1)F(o)-ATP synthases is unknown. Here we present conclusive evidence supporting the notion that the ability of c-rings to rotate within the F(o) complex derives from the interplay between the ion-binding sites and their nonhomogenous microenvironment. This evidence rests on three atomic structures of the c(15) rotor from crystals grown at low pH, soaked at high pH and, after N,N'-dicyclohexylcarbodiimide (DCCD) modification, resolved at 1.8, 3.0 and 2.2 ?, respectively. Alongside a quantitative DCCD-labeling assay and free-energy molecular dynamics calculations, these data demonstrate how the thermodynamic stability of the so-called proton-locked state is maximized by the lipid membrane. By contrast, a hydrophilic environment at the a-subunit-c-ring interface appears to unlock the binding-site conformation and promotes proton exchange with the surrounding solution. Rotation thus occurs as c-subunits stochastically alternate between these environments, directionally biased by the electrochemical transmembrane gradient.     

F(0) of ATP synthase is a rotary proton channel. Obligatory coupling of proton translocation with rotation of c-subunit ring

Coupling of proton flow and rotation in the F(0) motor of ATP synthase was investigated using the thermophilic Bacillus PS3 enzyme expressed functionally in Escherichia coli cells. Cysteine residues introduced into the N-terminal regions of subunits b and c of ATP synthase (bL2C/cS2C) were readily oxidized by treating the expressing cells with CuCl(2) to form predominantly a b-c cross-link with b-b and c-c cross-links being minor products. The oxidized ATP synthases, either in the inverted membrane vesicles or in the reconstituted proteoliposomes, showed drastically decreased proton pumping and ATPase activities compared with the reduced ones. Also, the oxidized F(0), either in the F(1)-stripped inverted vesicles or in the reconstituted F(0)-proteoliposomes, hardly mediated passive proton translocation through F(0). Careful analysis using single mutants (bL2C or cS2C) as controls indicated that the b-c cross-link was responsible for these defects. Thus, rotation of the c-oligomer ring relative to subunit b is obligatory for proton translocation; if there is no rotation of the c-ring there is no proton flow through F(0).     

Purification, characterization and reconstitution into membranes of the oligomeric c-subunit ring of thermophilic F(o)F(1)-ATP synthase expressed in Escherichia coli

F(o)F(1)-ATP synthase catalyzes ATP synthesis coupled with proton-translocation across the membrane. The membrane-embedded F(o) portion is responsible for the H(+) translocation coupled with rotation of the oligomeric c-subunit ring, which induces rotation of the γ subunit of F(1). For solid-state NMR measurements, F(o)F(1) of thermophilic Bacillus PS3 (TF(o)F(1)) was overexpressed in Escherichia coli and the intact c-subunit ring (TF(o)c-ring) was isolated by new procedures. One of the key improvement in this purification was the introduction of a His residue to each c-subunit that acts as a virtual His(10)-tag of the c-ring. After solubilization from membranes by sodium deoxycholate, the c-ring was purified by Ni-NTA affinity chromatography, followed by anion-exchange chromatography. The intactness of the isolated c-ring was confirmed by high-resolution clear native PAGE, sedimentation analysis, and H(+)-translocation activity. The isotope-labeled intact TF(o)c-ring was successfully purified in such an amount as enough for solid-state NMR measurements. The isolated TF(o)c-rings were reconstituted into lipid membranes. A solid-state NMR spectrum at a high quality was obtained with this membrane sample, revealing that this purification procedure was suitable for the investigation by solid-state NMR. The purification method developed here can also be used for other physicochemical investigations.     

ATP synthase that lacks F0a-subunit: isolation, properties, and indication of F0b2-subunits as an anchor rail of a rotating c-ring

In a rotary motor F1F0-ATP synthase, F0 works as a proton motor; the oligomer ring of F0c-subunits (c-ring) rotates relative to the F0ab2 domain as protons pass through F0 down the gradient. F0ab2 must exert dual functions during rotation, that is, sliding the c-ring (motor drive) while keeping the association with the c-ring (anchor rail). Here we have isolated thermophilic F1F0(-a) which lacks F0a. F1F0(-a) has no proton transport activity, and F0(-a) does not work as a proton channel. Interestingly, ATPase activity of F1F0(-a) is greatly suppressed, even though its F1 sector is intact. Most likely, F0b2 associates with the c-ring as an anchor rail in the intact F1F0; without F0a, this association prevents rotation of the c-ring (and hence the gamma-subunit), which disables ATP hydrolysis at F1. Functional F1F0 is easily reconstituted from purified F0a and F1F0(-a), and thus F0a can bind to its proper location on F1F0(-a) without a large rearrangement of other-subunits.     

Crystallographic structure of the turbine C-ring from spinach chloroplast F-ATP synthase

In eukaryotic and prokaryotic cells, F-ATP synthases provide energy through the synthesis of ATP. The chloroplast F-ATP synthase (CF₁F_O-ATP synthase) of plants is integrated into the thylakoid membrane via its F_O-domain subunits a, b, b’ and c. Subunit c with a stoichiometry of 14 and subunit a form the gate for H⁺-pumping, enabling the coupling of electrochemical energy with ATP synthesis in the F₁ sector.Here we report the crystallization and structure determination of the c14-ring of subunit c of the CF₁F_O-ATP synthase from spinach chloroplasts. The crystals belonged to space group C2, with unit-cell parameters a=144.420, b=99.295, c=123.51 Å, and β=104.34° and diffracted to 4.5 Å resolution. Each c-ring contains 14 monomers in the asymmetric unit. The length of the c-ring is 60.32 Å, with an outer ring diameter 52.30 Å and an inner ring width of 40 Å.     

Insights into the rotary catalytic mechanism of F0F1 ATP synthase from the cross-linking of subunits b and c in the Escherichia coli enzyme

The transmembrane sector of the F(0)F(1) rotary ATP synthase is proposed to organize with an oligomeric ring of c subunits, which function as a rotor, interacting with two b subunits at the periphery of the ring, the b subunits functioning as a stator. In this study, cysteines were introduced into the C-terminal region of subunit c and the N-terminal region of subunit b. Cys of N2C subunit b was cross-linked with Cys at positions 74, 75, and 78 of subunit c. In each case, a maximum of 50% of the b subunit could be cross-linked to subunit c, which suggests that either only one of the two b subunits lie adjacent to the c-ring or that both b subunits interact with a single subunit c. The results support a topological arrangement of these subunits, in which the respective N- and C-terminal ends of subunits b and c extend to the periplasmic surface of the membrane and cAsp-61 lies at the center of the membrane. The cross-linking of Cys between bN2C and cV78C was shown to inhibit ATP-driven proton pumping, as would be predicted from a rotary model for ATP synthase function, but unexpectedly, cross-linking did not lead to inhibition of ATPase activity. ATP hydrolysis and proton pumping are therefore uncoupled in the cross-linked enzyme. The c subunit lying adjacent to subunit b was shown to be mobile and to exchange with c subunits that initially occupied non-neighboring positions. The movement or exchange of subunits at the position adjacent to subunit b was blocked by dicyclohexylcarbodiimide. These experiments provide a biochemical verification that the oligomeric c-ring can move with respect to the b-stator and provide further support for a rotary catalytic mechanism in the ATP synthase.     

Structural model of the transmembrane Fo rotary sector of H+-transporting ATP synthase derived by solution NMR and intersubunit cross-linking in situ

H(+)-transporting, F(1)F(o)-type ATP synthases utilize a transmembrane H(+) potential to drive ATP formation by a rotary catalytic mechanism. ATP is formed in alternating beta subunits of the extramembranous F(1) sector of the enzyme, synthesis being driven by rotation of the gamma subunit in the center of the F(1) molecule between the alternating catalytic sites. The H(+) electrochemical potential is thought to drive gamma subunit rotation by first coupling H(+) transport to rotation of an oligomeric rotor of c subunits within the transmembrane F(o) sector. The gamma subunit is forced to turn with the c-oligomeric rotor due to connections between subunit c and the gamma and epsilon subunits of F(1). In this essay we will review recent studies on the Escherichia coli F(o) sector. The monomeric structure of subunit c, determined by NMR, shows that subunit c folds in a helical hairpin with the proton carrying Asp(61) centered in the second transmembrane helix (TMH). A model for the structural organization of the c(10) oligomer in F(o) was deduced from extensive cross-linking studies and by molecular modeling. The model indicates that the H(+)-carrying carboxyl of subunit c is occluded between neighboring subunits of the c(10) oligomer and that two c subunits pack in a "front-to-back" manner to form the H(+) (cation) binding site. In order for protons to gain access to Asp(61) during the protonation/deprotonation cycle, we propose that the outer, Asp(61)-bearing TMH-2s of the c-ring and TMHs from subunits composing the inlet and outlet channels must turn relative to each other, and that the swiveling motion associated with Asp(61) protonation/deprotonation drives the rotation of the c-ring. The NMR structures of wild-type subunit c differs according to the protonation state of Asp(61). The idea that the conformational state of subunit c changes during the catalytic cycle is supported by the cross-linking evidence in situ, and two recent NMR structures of functional mutant proteins in which critical residues have been switched between TMH-1 and TMH-2. The structural information is considered in the context of the possible mechanism of rotary movement of the c(10) oligomer during coupled synthesis of ATP.     

Induction and Resuscitation of the Viable but Nonculturable State in a Cyanobacteria-Lysing Bacterium Isolated from Cyanobacterial Bloom

The viable but nonculturable (VBNC) state has been found to be a growth strategy used by many aquatic pathogens; however, few studies have focused on VBNC state on other aquatic bacterial groups. The purpose of this study was to explore the VBNC state of cyanobacteria-lysing bacteria and the conditions that regulate their VBNC state transformation. Three cyanobacteria-lysing heterotrophic bacterial strains (F1, F2 and F3) were isolated with liquid infection method from a lake that has experienced a cyanobacterial bloom. According to their morphological, physiological and biochemical characteristics and results of 16SrDNA sequence analysis, F1, F2 and F3 were identified as strains of Staphylococcus sp., Stappia sp. and Microbacterium sp., respectively. After being co-cultured with the axenic cyanobacterium, Microcystis aeruginosa 905, for 7 days, strains F1, F2 and F3 exhibited an inhibition effect on cyanobacterial growth, which was expressed as a reduction in chlorophyll concentration of 96.0%, 94.9% and 84.8%, respectively. Both autoclaved and filtered bacterial cultures still showed lytic effects on cyanobacterial cells while centrifuged pellets were less efficient than other fractions. This indicated that lytic factors were extracelluar and heat-resistant. The environmental conditions that could induce the VBNC state of strain F1 were also studied. Under low temperature (4°C), distilled deionized water (DDW) induced almost 100% of F1 cells to the VBNC state after 6 days while different salinities (1%, 3% and 5% of NaCl solution) and lake water required 18 days. A solution of the cyanobacterial toxin microcystin-LR (MC-LR) crude extract also induced F1 to the VBNC state, and the effect was stronger than DDW. Even the lowest MC-LR concentration (10 μg L⁻¹) could induce 69.7% of F1 cells into VBNC state after 24 h. On the other hand, addition of Microcystis aeruginosa cells caused resuscitation of VBNC state F1 cells within 1 day, expressed as an increase of viable cell number and a decrease of VBNC ratio. Both VBNC state and culturable state F1 cells showed lytic effects on cyanobacteria, with their VBNC ratio varying during co-culturing with cyanobacteria. The findings indicated that VBNC state transformation of cyanobacteria-lysing bacteria could be regulated by cyanobacterial cells or their toxin, and the transformation may play an important role in cyanobacterial termination.     

Arginine-induced conformational change in the c-ring/a-subunit interface of ATP synthase

The rotational mechanism of ATP synthases requires a unique interface between the stator a subunit and the rotating c-ring to accommodate stability and smooth rotation simultaneously. The recently published c-ring crystal structure of the ATP synthase of Ilyobacter tartaricus represents the conformation in the absence of subunit a. However, in order to understand the dynamic structural processes during ion translocation, studies in the presence of subunit a are required. Here, by intersubunit Cys-Cys cross-linking, the relative topography of the interacting helical faces of subunits a and c from the I. tartaricus ATP synthase has been mapped. According to these data, the essential stator arginine (aR226) is located between the c-ring binding pocket and the cytoplasm. Furthermore, the spatially vicinal residues cT67C and cG68C in the isolated c-ring structure yielded largely asymmetric cross-linking products with aN230C of subunit a, suggesting a small, but significant conformational change of binding-site residues upon contact with subunit a. The conformational change was dependent on the positive charge of the stator arginine or the aR226H substitution. Energy-minimization calculations revealed possible modes for the interaction between the stator arginine and the c-ring. These biochemical results and structural restraints support a model in which the stator arginine operates as a pendulum, moving in and out of the binding pocket as the c-ring rotates along the interface with subunit a. This mechanism allows efficient interaction between subunit a and the c-ring and simultaneously allows almost frictionless movement against each other.     

Fluidity of structure and swiveling of helices in the subunit c ring of Escherichia coli ATP synthase as revealed by cysteine-cysteine cross-linking

Subunit c in the membrane-traversing F(0) sector of Escherichia coli ATP synthase is known to fold with two transmembrane helices and form an oligomeric ring of 10 or more subunits in the membrane. Models for the E. coli ring structure have been proposed based upon NMR solution structures and intersubunit cross-linking of Cys residues in the membrane. The E. coli models differ from the recent x-ray diffraction structure of the isolated Ilyobacter tartaricus c-ring. Furthermore, key cross-linking results supporting the E. coli model prove to be incompatible with the I. tartaricus structure. To test the applicability of the I. tartaricus model to the E. coli c-ring, we compared the cross-linking of a pair of doubly Cys substituted c-subunits, each of which was compatible with one model but not the other. The key finding of this study is that both A21C/M65C and A21C/I66C doubly substituted c-subunits form high yield oligomeric structures, c(2), c(3)... c(10), via intersubunit disulfide bond formation. The results indicate that helical swiveling, with resultant interconversion of the two conformers predicted by the E. coli and I. tartaricus models, must be occurring over the time course of the cross-linking experiment. In the additional experiments reported here, we tried to ascertain the preferred conformation in the membrane to help define the most likely structural model. We conclude that both structures must be able to form in the membrane, but that the helical swiveling that promotes their interconversion may not be necessary during rotary function.     

Alternative proton binding mode in ATP synthases

ATP synthases are rotary engines which use the energy stored in a transmembrane electrochemical gradient of protons or sodium ions to catalyze the formation of ATP by ADP and inorganic phosphate. Current models predict that protonation/deprotonation of specific amino acids of the rotating c-ring, extracting protons from one side and delivering them to the other side of the membrane, are at the core of the proton translocation mechanism of these enzymes. In this minireview, an alternative proton binding mechanism is presented, considering hydronium ion coordination as proposed earlier. Biochemical data and structural considerations provide evidence for two different proton binding modes in the c-ring of H⁺-translocating ATP synthases. Recent investigations in several other proton translocating membrane proteins suggest, that hydronium ion coordination by proteins might display a general principle which was so far underestimated in ATP synthases.     

Anomalous behavior of human leukocyte interferon subtypes on polyacrylamide gel electrophoresis in the presence of dodecyl sulfate

35S-labeled human leukocyte interferon (IFN) subtypes produced in a cell-free system derived from Escherichia coli were analyzed by polyacrylamide gel electrophoresis in the presence of SDS (SDS-PAGE). Some IFN subtypes anomalously showed lower electrophoretic mobilities than those expected from their formula molecular masses. The results with hybrid IFNs and esterification suggest that this anomaly of IFN subtypes on SDS-PAGE is due to the introduction of one or two negative charges in the middle of the molecule.     

Structure and Flexibility of the C-Ring in the Electromotor of Rotary FoF1-ATPase of Pea Chloroplasts

A ring of 8–15 identical c-subunits is essential for ion-translocation by the rotary electromotor of the ubiquitous F_OF₁-ATPase. Here we present the crystal structure at 3.4Å resolution of the c-ring from chloroplasts of a higher plant (Pisum sativum), determined using a native preparation. The crystal structure was found to resemble that of an (ancestral) cyanobacterium. Using elastic network modeling to investigate the ring''s eigen-modes, we found five dominant modes of motion that fell into three classes. They revealed the following deformations of the ring: (I) ellipsoidal, (II) opposite twisting of the luminal circular surface of the ring against the stromal surface, and (III) kinking of the hairpin-shaped monomers in the middle, resulting in bending/stretching of the ring. Extension of the elastic network analysis to rings of different c_n-symmetry revealed the same classes of dominant modes as in P. sativum (c₁₄). We suggest the following functional roles for these classes: The first and third classes of modes affect the interaction of the c-ring with its counterparts in F_O, namely subunits a and bb''. These modes are likely to be involved in ion-translocation and torque generation. The second class of deformation, along with deformations of subunits γ and ε might serve to elastically buffer the torque transmission between F_O and F₁.