Physical pictures of rotation mechanisms of F1- and V1-ATPases: Leading roles of translational, configurational entropy of water

Abstract

We aim to develop a theory based on a concept other than the chemo-mechanical coupling (transduction of chemical free energy of ATP to mechanical work) for an ATP-driven protein complex. Experimental results conflicting with the chemo-mechanical coupling have recently emerged. We claim that the system comprises not only the protein complex but also the aqueous solution in which the protein complex is immersed and the system performs essentially no mechanical work. We perform statistical-mechanical analyses on V₁-ATPase (the A₃B₃DF complex) for which crystal structures in more different states are experimentally known than for F₁-ATPase (the α₃β₃γ complex). Molecular and atomistic models are employed for water and the structure of V₁-ATPase, respectively. The entropy originating from the translational displacement of water molecules in the system is treated as a pivotal factor. We find that the packing structure of the catalytic dwell state of V₁-ATPase is constructed by the interplay of ATP bindings to two of the A subunits and incorporation of the DF subunit. The packing structure represents the nonuniformity with respect to the closeness of packing of the atoms in constituent proteins and protein interfaces. The physical picture of rotation mechanism of F₁-ATPase recently constructed by Kinoshita is examined, and common points and differences between F₁- and V₁-ATPases are revealed. An ATP hydrolysis cycle comprises binding of ATP to the protein complex, hydrolysis of ATP into ADP and Pi in it, and dissociation of ADP and Pi from it. During each cycle, the chemical compounds bound to the three A or β subunits and the packing structure of the A₃B₃ or α₃β₃ complex are sequentially changed, which induces the unidirectional rotation of the central shaft for retaining the packing structure of the A₃B₃DF or α₃β₃γ complex stabilized for almost maximizing the water entropy. The torque driving the rotation is generated by water with no input of chemical free energy. The presence of ATP is indispensable as a trigger of the torque generation. The ATP hydrolysis or synthesis reaction is tightly coupled to the rotation of the central shaft in the normal or inverse direction through the water-entropy effect.

Keywords: ATP hydrolysis; ATP synthesis; ATP-driven protein; linear molecular motor; protein structure; rotary molecular motor; statistical mechanics; water entropy.

FIGURE 1

Basal processes in protein folding. (A) Formation of α-helix or β-sheet. (B) Close packing of side chains.

FIGURE 2

(A) State of F₁-ATPase, α₃β₃γ complex, in which two nucleotides are bound to two of the three β subunits, respectively. “Nucleotides” signifies ATP, ADP, and related chemical compounds. Following the works of Walker and coworkers (Bowler et al., 2007), the three β subunits are named β_DP, β_TP, and β_E, respectively, and the three α subunits are named α_DP, α_TP, and α_E, respectively. In aqueous solution of AMP-PNP and ADP, the nucleotides bound to β_DP and β_TP are AMP-PNP and AMP-PNP, respectively. In aqueous solution of AMP-PNP, ADP, and azide, the nucleotides bound to β_DP and β_TP are ADP and AMP-PNP, respectively. Azide stabilizes the β subunit with ADP bound (Bowler et al., 2007). The structure of a β subunit with a nucleotide bound is closed whereas that without a nucleotide bound is open. (B) Top view of ribbon representation of α₃β₃γ-complex structure stabilized in aqueous solution of AMP-PNP and ADP (the Protein Data Bank (PDB) Code is 2JDI) (Bowler et al., 2007). The β subunits, α subunits, and γ subunit are colored yellow, green, and gray, respectively. AMP-PNP is represented by the red fused spheres. (AMP-PNP bound to each of the three α subunits is not shown.)

FIGURE 3

(A) Definition of subcomplexes 1, 2, and 3 for F₁-ATPase. The three subcomplexes are named in respect of their positions. Two nucleotides are bound to β_DP and β_TP, respectively. (B) Subcomplexes 1, 2, and 3 after 120° rotation of γ subunit. (C) Definition of subcomplexes 1, 2, and 3 for V₁-ATPase. The three subcomplexes are named in respect of their positions. Two nucleotides are bound to A_DP and A_TP, respectively. (D) Subcomplexes 1, 2, and 3 after 120° rotation of DF subunit.

FIGURE 4

Top view of ribbon representation of A₃B₃DF-complex structure stabilized in aqueous solution of AMP-PNP and ADP. The A subunits, B subunits, and DF subunit are colored yellow, green, and gray, respectively. AMP-PNP is represented by the red fused spheres. (Unlike in the case of F₁-ATPase, AMP-PNP bindings to the three B subunits do not occur.)

FIGURE 5

Packing structures of (A) A₃B₃DF⋅2ATP, (B) A₃B₃, (C) A₃B₃⋅2ATP, and (D) A₃B₃DF. A yellow circle denotes ATP. A number colored red quantifies ΔS _IJ /k _B (subunit I is an A subunit and subunit J is a B subunit; see Eq. 8). For example, ΔS _IJ /k _B in (A) for which subunits I and J denote A_DP and B_DP, respectively, is 438.0. A number colored blue quantifies ΔS _IJ /k _B (subunit I is an A subunit or a B subunit and subunit J is the DF subunit). For example, ΔS _IJ /k _B in (A) for which subunits I and J denote B_E and the DF subunit, respectively, is 60.9. Larger ΔS _IJ /k _B implies closer packing of the interface of subunit pair I-J. In (A), for example, a number colored in black within parentheses denotes S ₁/k _B (S ₁/k _B<0) of an A subunit relative to S ₁/k _B of A_TP. For example, “S ₁/k _B of A_E”−“S ₁/k _B of A_TP” is −185.4. Smaller | S ₁/k _B | implies closer packing or higher PE of an A subunit. The PE follows the order, A_TP>A_DP>A_E. Relatively large numbers are surrounded by rectangles. (In (B), a number colored in black within parentheses denotes S ₁/k _B (S ₁/k _B<0) of an A subunit relative to S ₁/k _B of A_E. For example, “S ₁/k _B of A_TP”−“S ₁/k _B of A_E” is −162.5.) S ₁/k _B of the A subunit which is the most closely packed among the three A subunits is also given. (E) Packing structures of catalytic dwell states for F₁-ATPase (α₃β₃γ complex with two ATPs bound). S ₁/k _B of the A or β subunit which is the most closely packed among the three A or β subunits is also given. (F) Packing structure of A₃B₃DF⋅2ADP. A right-blue circle denotes ADP. S ₁/k _B of the A subunit which is the most closely packed among the three A subunits is also given.

FIGURE 6

(A) Packing structure of catalytic dwell state of α₃β₃γ complex (F₁-ATPase) stabilized in aqueous solution of ATP, ADP, and Pi. ATP-H₂O and ATP are bound to β_DP and β_TP, respectively, and Pi remains in β_E. ATP-H₂O denotes ATP just before the ATP hydrolysis reaction (ATP-H₂O is an activated complex). The packings of backbones and side chains in subcomplexes 1, 2, and 3 are relatively loose, moderate, and close, respectively: The packing efficiencies (PEs) of subcomplexes 1, 2, and 3 are relatively low, moderate, and high, respectively. (B) Packing structure of catalytic dwell state of A₃B₃DF complex (V₁-ATPase) stabilized in aqueous solution of ATP, ADP, and Pi. ATP-H₂O and ATP are bound to A_DP and A_TP, respectively, and nothing is bound to A_E. The packings of backbones and side chains in subcomplexes 1, 2, and 3 are relatively loose, close, and moderate, respectively.

FIGURE 7

Physical picture of unidirectional rotation of γ subunit in F₁-ATPase during one ATP hydrolysis cycle. In state (A), Pi, ATP, and ATP-H₂O are bound to β_E, β_TP, and β_DP, respectively. In (B), ATP(ATP-H₂O) and ADP+Pi are bound to β′_TP and β_DP ^HO, respectively. The packings of β_E and subcomplex 1 are loose in state (A) but they become closer in state change (A)→(B). Those of β′_E and subcomplex 1 become further closer in (B)→(C). Those of β_TP and subcomplex 1 are moderate in (C). Those of β_TP and subcomplex 2 are moderate in (A) but they become closer in (A)→(B). Those of β′_TP and subcomplex 2 become further closer in (B)→(C). Those of β_DP and subcomplex 2 are close in (C). Those of β_DP and subcomplex 3 are close in (A) but they become looser in (A)→(B). Those of β_DP ^HO and subcomplex 3 become further looser in (B)→(C). Those of β_E and subcomplex 3 are loose in (C). As mentioned in Section 4.3, even without the γ subunit, the α₃β₃ complex exhibits the structural rotation (Uchihashi et al., 2011; Yoshidome et al., 2011) illustrated in this figure.

FIGURE 8

Physical picture of unidirectional rotation of DF subunit in V₁-ATPase during one ATP hydrolysis cycle. In state (A), ATP and ATP-H₂O are bound to A_TP and A_DP, respectively. In (B), ATP(ATP-H₂O) and ADP+Pi are bound to A’_TP and A’_DP, respectively. ATP-H₂O denotes ATP just before the ATP hydrolysis reaction, and ATP(ATP-H₂O) is an intermediate between ATP and ATP-H₂O (ATP(ATP-H₂O) and ATP-H₂O are the activated complexes). The packings of A_E and subcomplex 1 are loose in state (A) but they become closer in state change (A)→(B). Those of A’_E and subcomplex 1 become further closer in (B)→(C). Those of A_TP and subcomplex 1 are close in (C). Those of A_TP and subcomplex 2 are close in (A) but they become looser in (A)→(B). Those of A’_TP and subcomplex 2 become further looser in (B)→(C). Those of A_DP and subcomplex 2 are moderate in (C). Those of A_DP and subcomplex 3 are moderate in (A) but they become looser in (A)→(B). Those of A’_DP and subcomplex 3 become further looser in (B)→(C). Those of A_E and subcomplex 3 are loose in (C).

FIGURE 9

Physical picture of unidirectional rotation of γ subunit in F₁-ATPase during one ATP synthesis cycle. In state (A), Pi, ATP, and ATP-H₂O are bound to β_E, β_TP, and β_DP, respectively. In (B), ADP+Pi and ATP(ATP-H₂O) are bound to β′_E and β′_DP, respectively. The packings of β_E and subcomplex 1 are loose in state (A) but they become closer in state change (A)→(B). Those of β′_E and subcomplex 1 become further closer in (B)→(C). Those of β_DP and subcomplex 1 are close in (C). Those of β_TP and subcomplex 2 are moderate in (A) but they become looser in (A)→(B). Those of β′_TP and subcomplex 2 become further looser in (B)→(C). Those of β_E and subcomplex 2 are loose in (C). Those of β_DP and subcomplex 3 are close in (A) but they become looser in (A)→(B). Those of β′_DP and subcomplex 3 become further looser in (B)→(C). Those of β_TP and subcomplex 3 are moderate in (C).

FIGURE 10

Three different state changes per cycle, (A)→(B), (A)→(C), and (A)→(D). The aqueous solution is under the condition that the ATP hydrolysis reaction should occur. However, the γ subunit is forcibly rotated it in the inverse direction by a sufficiently strong external torque imposed on it. The α₃β₃γ complex in state (B) corresponds to that in state (C) shown in Figure 9. The α₃β₃ complex in state (C) corresponds to that in state (C) shown in Figure 7.