Determinants of Directionality and Efficiency of the ATP Synthase Fo Motor at Atomic Resolution

Fo subcomplex of ATP synthase is a membrane-embedded rotary motor that converts proton motive force into mechanical energy. Despite a rapid increase in the number of high-resolution structures, the mechanism of tight coupling between proton transport and motion of the rotary c-ring remains elusive. Here, using extensive all-atom free energy simulations, we show how the motor’s directionality naturally arises from the interplay between intraprotein interactions and energetics of protonation of the c-ring. Notably, our calculations reveal that the strictly conserved arginine in the a-subunit (R176) serves as a jack-of-all-trades: it dictates the direction of rotation, controls the protonation state of the proton-release site, and separates the two proton-access half-channels. Therefore, arginine is necessary to avoid slippage between the proton flux and the mechanical output and guarantees highly efficient energy conversion. We also provide mechanistic explanations for the reported defective mutations of R176, reconciling the structural information on the Fo motor with previous functional and single-molecule data.

also supports the notion that the difference in pKa between the B and R site carboxylates arises from the strikingly different degree of hydration (see Fig S8,S7). For E162 we found pKa to be shifted considerably (by 1.9±0.2 units) to 6.0. Difference of 4 units between R site carboxylate and E162 suggests that E162 may participate in shuttling protons released into the half-channel from the c-ring R site.
We were also interested in the effect of the central (R176) and secondary (R169) arginine residues on the proton affinity of the R site carboxylate. As described in the main text, by comparing pKa of the wild type and R176K mutant with the R176A mutant, we found that both positively charged residues, arginine and lysine, stabilize the deprotonated state of the carboxylate to a similar extent, lowering its pKa by ∼5 units from a value of 6.9±0.1 calculated for the R176A mutant to 1.9±0.2 (WT) and 2.2±0.4 (R176K). In contrast, the secondary arginine shifts the pKa of the R site only by ∼1 unit, as the pKa of the R169A mutant was computed to be 2.8±0.2. Since the effect of R169 on the protonation behavior of the R site carboxylate is weak and the rotation free energy profile of the R169A mutant remains asymmetric around 0 • (Fig. S16), we conclude that the presence of the secondary arginine in the yeast F o does not qualitatively affects the general rotary mechanism.

System preparation
The cryo-EM structure (PDB Id: 6B2Z) 2 of yeast mitochondrial ATP synthase (isolated F o monomer) was taken as an initial configuration. As e-and g-subunit, located far from the S2 crucial a/c-ring interface, were modeled in the cryo-EM structure as poly-Ala chains, they were completely omitted. Using the CHARMM-GUI Membrane Builder, 3-5 the protein was embedded in a lipid bilayer oriented perpendicularly with respect to the z-axis and composed of 151 POPC, 118 POPE, and 55 TOCL −2 (tetraoleoyl cardiolipin) molecules (46.6, 36.4 and yeast. 6 The system was solvated with 25201 TIP3P water molecules in a 123.85 × 123.85 × 91.422Å rectangular box and the number of K + and Cl − ions was adjusted to maintain a physiological salt concentration of 0.15 M and neutralize the net charge of the system. One POPC and one POPE molecule per leaflet were manually inserted inside the c-ring, to seal its central channel, similarly to the previous treatment. 7 System was subjected to two-step minimization (first keeping all protein atoms fixed and then without any constraints) followed by preliminary relaxation of the protein using CHARMM-GUI protocol (short MD runs with progressively weaker restraints on protein atoms). Next, the system was simulated with the protein backbone atoms harmonically restrained to their initial positions with a force-constant of 1000 kJ/(mol·nm 2 ) for 500 ns, and only then equilibrated without restraints for another 700 ns. Random frames from the last 100 ns of this restraint-free run were picked as initial coordinates for five independent unbiased MD simulations of the wild type F o , each lasting 1 µs. The mutants of F o , R176A, R176K, R169A and E223A, were prepared by substituting R176, R169 or E223 residues with alanine or lysine, and subject to 2 µs of unbiased MD simulations, using random frames from the WT equilibrium trajectory as initial coordinates. In the systems where changes in protonation states or mutations created non-zero net charge, the number of ions in aqueous phase was adjusted to neutralize the system.

Simulation parameters
All molecular dynamics (MD) simulations were performed using GROMACS 8 and the CHARMM36m force field. 9 The simulations were carried out in the isothermal-isobaric S3 (NPT) ensemble using periodic boundary conditions in 3D. The constant temperature was kept at 310 K using the Nose-Hoover thermostat 10 and the pressure was maintained at 1 bar semi-isotropically (separately in the plane of the bilayer and perpendicular to the bilayer) using Parrinello-Rahman algorithm. 11 Long-range electrostatic interactions were evaluated using the Particle Mesh Ewald (PME) 12 method with a real-space cut-off of 1.2 nm. Van der Waals interactions were evaluated using a smooth cut-off of 1.2 nm with a switching distance of 1 nm. Bond lengths were constrained using the SHAKE 13 (for water) or P-LINCS 14 (for protein and lipids) algorithm. The equations of motion were integrated using a leap-frog algorithm with a time step of 2 fs. pK a calculations To determine pKa values of the c-ring carboxylates as well as two glutamate residues located in the proton-binding and proton-release half-channels (E223 and E162, respectively), we used alchemical free energy calculations. To this end, a free glutamic acid molecule capped with N-methyl (NME) and acetyl (ACE) termini was added to the F o system as a reference, and kept in bulk solution, at a minimal distance of 3 nm from the membrane center with the use of a one-sided harmonic potential applied to the z component of the vector connecting the centers of mass of the reference glutmate and the c-ring using PLUMED (topologies were generated using our in-house script (https://gitlab.com/KomBioMol/proton_alchemist). 15 To predict the pKa shift for a given c-ring carboxylate with respect to the reference glutamate, the system was transformed, using a switching parameter λ, from the initial state with the c-ring carboxylate protonated and the reference glutamate deprotonated (state A) to the final state with the reversed protonation states (state B), and vice versa. Due to this treatment the simulated system was neutral at all λ-points and the obtained ∆∆G values, describing the difference in the proton affinity between both environments, could be used directly to compute the pKa shift with respect to the experimental pKa in aqueous solution (4.1 for the glutamic acid side chain). The number of λ-points (or windows) was chosen to be 20 S4 and the system was simulated in these windows using Hamiltonian replica-exchange molecular dynamics until the convergence of ∆∆G was reached (up to ∼200 ns). To optimize λ values, we used our in-house script (https://gitlab.com/KomBioMol/converge_lambdas) that iteratively restarts short replica-exchange runs until λ-values yielding equal exchange rates between neighboring windows (here ∼20%)) are found. 16 ∆∆G values were determined using Bennett acceptance ratio, 17 as implemented in the Gromacs package and the pK a shifts were then calculated according to the formula ∆pK a = log 10 exp

Conformational free energy profiles of Arg176
To determine the conformational preference of the guanidine moiety of R176 to locate in one of the two proton-access half-channels, we performed well-tempered metadynamics simulations 20 of the above described

Interaction analysis
To evaluate the individual enthalpic contributions to the rotation free energies, we calculated electrostatic and van der Waals (vdW) interaction energies between the key residues present at the interface between the c-ring and a-subunit, the remaining protein residues, solvent including ions, and lipids. The binding and release site glutamates and the a-subunit residues within 1 nm from the R site carboxylate forming the interface were selected for S6 the residue-wise analysis (for a complete list of residues and their location at the c-ring/a interface, see Fig. S18). Using Boltzmann-reweighted umbrella sampling data, we computed the average electrostatic and vdW interaction energies between all the pairs considered as a function of the rotation angle. After adding electrostatic and vdW energies, the average slope of the resulting angle-dependence in the 0-18 • range was determined by linear fitting, and was used as measure of a given pairwise contribution (Fig. S9, Fig. S10, Fig. S11 and Fig. S12). To extract contributions responsible for the F o directionality the slopes in the hydrolysis direction were subtracted from those in the synthesis direction and shown in  1-75 S10 Figure S1: Top and side view of the average water densities (transparent red surfaces) at the interface between a-subunit and the c-ring in the wild type F o protein, as well as in its R176A and R176K mutants. S11 Figure S2: Subunit composition of the simulated F o complex (top -side view, bottom -view from the mitochondrial matrix). Consistently with Fig. 1., the two c-subunits located in the proton-binding and proton-release half-channels are shown in yellow and red, respectively. The F o complex was stable throughout the simulation, as reflected in RMSD over time for individual subunits (see Fig. S19). S12 Figure S3: Lipid electron densities around the F o complex with the c-ring at its initial position (0 • , left) and rotated by 10 • (right), averaged over 600 ns MD trajectories. The top view shows the density of the membrane hydrocarbon core at the average position of the proton-carrying glutamate residues (E59), indicated by the green dash lines in the side view. The side view panels show the selected electron density isosurfaces (0.1) from the perspective of the c-ring/a-subunit interface. The binding and release site c-subunits are shown in yellow and dark orange, respectively. As can be seen, lipids do not directly interact with the binding and release site glutamates, neither at 0 • nor at 10 • . S13 Figure S4: Convergence of the free energy profiles for the rotation of the wild type F o (R − B 0 ) in the synthesis and hydrolysis direction, with the length of umbrella sampling trajectories taken for analysis.  The arginine adopts a single stable conformation, to the extent that its density reflects the sidechain shape. In contrast, the lysine sidechain is highly mobile such that its average density has a roughly spherical shape, meaning it samples multiple conformations at the c-ring/a-subunit interface, possibly accounting for the increased flux of water between the two half-channels.
S25 Figure S18: Residues in the a-subunit included explicitly in the analysis of pairwise enthalpic contributions to interaction free energies (Fig. S9, Fig. S10, Fig. S11 and Fig. S12).
The selected residues are shown as seen from the mitochondrial matrix (top) and from the perspective of the c-ring (bottom).
S26 Figure S19: Root mean square deviation (RMSD) for the C α atoms of each of the subunits comprising the simulated F o complex as function of the simulation time (see Fig. S2). Since the conformationally flexible b-subunit and f-subunit undergo relaxation when embedded in a model of the inner mitochondrial membrane, their RMSDs reach plateau at significantly higher values than for the remaining more rigid subunits. . The closed conformation is clearly preferred by the protonated glutamates both at the B site and exposed to the lipid environment, while the open one is adopted by both protonated and unprotonated glutamates at the R site. S28