The unbinding of ATP from F1-ATPase

Abstract

Using molecular dynamics, we study the unbinding of ATP in F(1)-ATPase from its tight binding state to its weak binding state. The calculations are made feasible through use of interpolated atomic structures from Wang and Oster [Nature 1998, 396: 279-282]. These structures are applied to atoms distant from the catalytic site. The forces from these distant atoms gradually drive a large primary region through a series of sixteen equilibrated steps that trace the hinge bending conformational change in the beta-subunit that drives rotation of gamma-subunit. As the rotation progresses, we find a sequential weakening and breaking of the hydrogen bonds between the ATP molecule and the alpha- and beta-subunits of the ATPase. This finding agrees with the "binding-zipper" model [Oster and Wang, BIOCHIM: Biophys. Acta 2000, 1458: 482-510.] In this model, the progressive formation of the hydrogen bonds is the energy source driving the rotation of the gamma-shaft during hydrolysis. Conversely, the corresponding sequential breaking of these bonds is driven by rotation of the shaft during ATP synthesis. Our results for the energetics during rotation suggest that the nucleotide's coordination with Mg(2+) during binding and release is necessary to account for the observed high efficiency of the motor.

FIGURE 1

(a) Side view of the F₀F₁-ATPase. (b) Top view of the F₁-ATPase, the β-subunits are colored red, the α-subunits yellow, the γ-shaft blue and cyan. ATP and ADP are shown in space-filling mode. (c) Closed and (d) open configurations of the α/β-subunits. (e) Our setup division of the α/β-subunits, the binding pocket region is colored green, its surrounding red and the outer region gray. (f) The three hydrogen binding regions around ATP in the closed state and the location of Mg. The pictures were created with RASMOL (Sayle and Milnerwhite, 1995), VMD (Humphrey et al., 1996), and MOLSCRIPT (Kraulis, 1991).

FIGURE 2

Total potential energy of our system (coarse grained over 10 ps) for the 4th, 8th, 12th, and 16th steps, (a–d) with respect to the simulation time.

FIGURE 3

Total kinetic energy of our system for the 4th, 8th, 12th, and 16th steps, (a–d) with respect to the simulation time. The horizontal lines show the expected kinetic energy according to equipartition of the energy.

FIGURE 4

Stereo pictures of the hydrogen binding region and ATP. (a) Closed state, (b) 8th step, (c) 13th step, (d) open state. The orientation is the same as in Fig. 1 f. The pictures were created with VMD (Humphrey et al., 1996).

FIGURE 5

Hydrogen bond populations for every other step, starting at the 2nd step (5 a, top left) and ending at the open state (5 h, bottom right). The data are averaged over the last 1 ns of our equilibration runs and show the fraction of the structures in which the specific hydrogen bond is present. Dark spots correspond to high (i.e., the hydrogen bond is present in all structures) and light spots to low populations. A hydrogen bond was defined to exist if its H-A bond length is shorter than 3.0 Å and its D-H-A angle larger than 120°. The Y axis corresponds to the ATP oxygen atoms, starting with the α-phosphate oxygens at the top and ending with the γ-phosphate oxygens at the bottom. Along the X axis the hydrogen bound residues are shown, starting at β-Val-164 and proceeding along the P-loop to β-Arg-189 and α-Arg-373 (see Fig. 4), the last column shows the hydrogen bonds with the solvent.

FIGURE 6

Solid line with -X- markers: average number of hydrogen bonds between ATP and its surrounding residues for each step averaged over 1 ns for the 2nd to 16th step (2500 structures) and over 250 ps for the 1st step (625 structures). Solid lines: the total number of hydrogen bonds, which was found for the largest group of analyzed structures for each step, averaged over 25 structures saved every 10 ps for the last 250 ps of the runs. The hydrogen binding sites were divided into three groups: the P-loop (green), α-Arg-373 (yellow) and β-Arg-189 (brown). A hydrogen bond was defined to exist if its H-A bond length is shorter than 3.0 Å and its D-H-A angle larger then 120°.

FIGURE 7

Coordination number of the Mg²⁺ cation with the F1-ATPase/ATP and the solvent. Atoms are defined to be coordinated if their separation is less than 2.5 Å. The coordination number corresponds to the most often occurring coordination number during the last 250 ps of our equilibration runs, analyzing 25 snapshots, taken every 10ps. The snapshots (left to right) show the first coordination shell around the Mg²⁺ cation at the 1st, 8th, and 13th step.

FIGURE 8

Different components of the interaction energies between ATP, the F1-ATPase, Mg²⁺, and the solvent. The components were calculated for each step as the sum of the van der Waals and Coulomb interactions between the regions considered. The values were averaged over the last 1 ns of the simulation for the 2nd to 16th steps and over the last 250 ps for the 1st step. (a) Interaction energies between ATP and the F1-ATPase + solvent starting at the closed and ending at the open ATP binding pocket (steps 1–16). (b) Interaction energies between ATP and the F1-ATPase + solvent + Mg. (c) Interaction energies of (ATP with ATPase) + (ATP with solvent) + (ATP with Mg) + (Mg with ATPase) + (Mg with solvent). The interaction energy of ATPase with solvent was not calculated because we did not enclose the entire ATPase with solvent. (d) Interaction energies between ATP and Mg. (e) Interaction energies between Mg and the F1-ATPase + solvent. The energies are therefore added together in the following way: 8(a) + 8(d) = 8(b), 8(b) + 8(e) = 8(c). The error bars were obtained using the blocking method (Jaccucci and Rahman, 1984), within a confidence level of 68.3%.