Figure 1.
Side view of F1FO ATP synthase, oriented with high-potential side on top, showing the half-channels in the stator a-subunit, c-ring rotor of FO (c10 for E. coli), and F1 complex, within which the γ-subunit rotates to release three ATP molecules per cycle [adapted from Fillingame [5] with permission].
Figure 2.
Top view of the c-ring (yellow) and stator a-subunit (green) of FO, showing equipotential surface cross-sections (curved lines) perpendicular to the electric field emanating from the half-channels (blue and red circles) in the a-subunit.
Black arrows represent forces due to tangential field components (red arrows) acting on protonated (blue circles) and deprotonated (light circle) sites on the c-ring. (Equipotentials computed using QuickField.)
Figure 3.
Gravity-driven mechanical model of FO, where the ball rolling down the ramp depicts a proton moving to lower potential energy, driving the blue “c-ring” to rotate, before emerging from the “exit channel” hole.
Figure 4.
Torque from the c-ring drives rotation and ATP production by overcoming the periodic energy barrier in F1 with the aid of thermal fluctuations. (a)
Tilted washboard potential as the driving torque τ from FO works against the opposing torque
from F1. Top: Torque exceeds the critical value (
) needed to release ATP from F1 with the aid of thermally activated hopping. Bottom: Plot shows the case where F1 uses energy from ATP hydrolysis to drive the c-ring backwards and pump protons across the membrane. (b) Computed thermally assisted ATP production (rotation) rates f vs. pmf Δp, using the tilted washboard potential in Fig. 4(a), at various temperatures and (inset) f vs. temperature for two different pmf’s, using the values n = 8, τc = 40 pN·nm, and τ1 = 20 pN·nm.
Figure 5.
Plots show the predicted c-ring rotation rates vs. proton motive force for various values of n, τc, and τ1. (a)
Predicted rotation rate f (see text) vs. pmf, Δp, taking τc = 40 pN-nm and τ1 = 20 pN-nm, for various numbers n of proton binding sites on the c-ring. Positive and negative rotation rates correspond to ATP synthesis and ATP hydrolysis, respectively. (b) Theoretical rotation rate f vs. Δp, assuming τc = 40 pN-nm and n = 8, for various values of τ1. (c) Predicted rotation rate f vs. Δp, assuming τ1 = 20 pN·nm and n = 8, for two values of τc. (d) Theoretical ATP production rate (dashed line) vs. Δp (using τc = 31 pN·nm and τ1 = 17 pN·nm), as compared to maximum intracellular ATP/ADP ratios (squares) reported by Nicholls [38].
Figure 6.
Geometry of c-ring and stator half channels, showing the geometrical parameters used to express the tangential field component in Eq. (M-1).