Fig. 3. The F_o motor is observed in four discrete rotational positions.

a Simple schematic to describe c-ring positions observed in this study. Arrows show rotation of the c-ring between each step in the ATP synthesis direction (same c subunit colored in cyan and all others in gray) with colored radii (black in Sub-state 1’ and 1”, blue in Sub-state 3 and red in Sub-state 2) describing relative position to the subunit a colored orange (see Supplementary Fig. 6 for assignment of the rotational position of the c-ring). Each schematic is accompanied by a cryo-EM map representative for the state discussed. Sub-state 1’: Sub-state 1A, Sub-state 1”: Sub-state 1C, Sub-state 3: Sub-state 3A and Sub-state 2: Sub-state 2B. b Simple schematic to describe the stored elastic energy (E) versus F_o rotation angle, assuming a linear (Hookean) spring with a zero-point that rotates 1/3 of a revolution between each of F₁ states 1-3. The parabolic curves represent the energy stored in this spring in each F₁ state, as a function of the rotation angle of F_o: E = ½κx², where κ is the spring constant and x the displacement of the spring from its minimum. The minima for the three F₁ states were assumed to be equally spaced, 120° apart, and the stiffness of the spring was assumed to be the same in all three states. The angles of these minima relative to the 10 F_o dwells (vertical lines) were adjusted by hand to set the energy of Sub-state 1” lower than that of Sub-state 1’ (as required if the 3-fold higher count of particles classified as Sub-state 1” relative to Sub-state 1’ is representative of the equilibrium occupancy of these states), while at the same time setting the energies of Sub-states 2 and 3 close to their minima. The four observed sub-states are those with elastic energy low enough to be accessed thermally, shown as black filled squares. Sub-states that were not observed in this study and cannot be accessed thermally under these conditions are shown as empty boxes. F₁ dwells State 2 (red) and State 3 (blue) align close the c-ring dwells and therefore we were only able to observe F₁F_o in single c-ring positions. F₁ dwell State 1 (black) aligns mid-way between two c-ring dwells, so we were able to observe F₁F_o in two separate c-ring positions.