Phosphate release coupled to rotary motion
of F1-ATPase
Kei-ichi Okazakia,b,c and Gerhard Hummera,b,1
a
Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany; bLaboratory of Chemical Physics, National
Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892; and cDepartment of Pure and Applied Physics,
Waseda University, Tokyo 169-8555, Japan
F1-ATPase, the catalytic domain of ATP synthase, synthesizes most
of the ATP in living organisms. Running in reverse powered by ATP
hydrolysis, this hexameric ring-shaped molecular motor formed by
three αβ-dimers creates torque on its central γ-subunit. This reverse operation enables detailed explorations of the mechanochemical coupling mechanisms in experiment and simulation.
Here, we use molecular dynamics simulations to construct a first
atomistic conformation of the intermediate state following the 40°
substep of rotary motion, and to study the timing and molecular
mechanism of inorganic phosphate (Pi) release coupled to the rotation. In response to torque-driven rotation of the γ-subunit in
the hydrolysis direction, the nucleotide-free αβE interface forming
the “empty” E site loosens and singly charged Pi readily escapes
to the P loop. By contrast, the interface stays closed with doubly
charged Pi. The γ-rotation tightens the ATP-bound αβTP interface,
as required for hydrolysis. The calculated rate for the outward release of doubly charged Pi from the αβE interface 120° after ATP
hydrolysis closely matches the ∼1-ms functional timescale. Conversely, Pi release from the ADP-bound αβDP interface postulated
in earlier models would occur through a kinetically infeasible inward-directed pathway. Our simulations help reconcile conflicting
interpretations of single-molecule experiments and crystallographic
studies by clarifying the timing of Pi exit, its pathway and kinetics,
associated changes in Pi protonation, and changes of the F1-ATPase
structure in the 40° substep. Important elements of the molecular
mechanism of Pi release emerging from our simulations appear to
be conserved in myosin despite the different functional motions.
F
1-ATPase (F1), the catalytic domain of FoF1-ATP synthase, is
a rotary molecular motor that reversibly interconverts ATP
hydrolysis free energy and mechanical work associated with the
rotation of the central stalk (1). The minimal functional F1
consists of a hexameric ring formed by three αβ-subunit dimers,
with the rod-like γ-subunit located at its center (2). The rotation
of the γ-subunit is tightly coupled to the reactions in the three
catalytic sites located at the αβ interfaces and hosted mainly by
the β-subunits. As a result, F1 is a unique reversible motor that
rotates γ by converting ATP hydrolysis energy at high efficiency
(3–5) and, conversely, synthesizes ATP from ADP and inorganic
phosphate (Pi) by forced rotation of γ in the reverse direction (6,
7). The three nucleotide-binding sites are in different phases of
catalysis, reflecting the asymmetric structure of the γ-subunit.
Correspondingly, the αβ-subunits hosting the catalytic interfaces
are in different conformational states, empty (E), ATP-bound
(TP), and ADP+Pi-bound (DP), as seen in crystal structures (2).
They communicate through the γ-subunit or directly within
the α3 β3 ring (8, 9) and cooperatively drive the rotation of
the γ-subunit.
Single-molecule experiments have shown that the γ-subunit
rotates in 120° steps (4). Distinct substeps of 80° and 40° (10) are
driven by ATP binding plus ADP release, and ATP hydrolysis
plus Pi release, respectively (10–13). We thus expect two metastable conformations of F1, one before the 80° substep (binding
dwell) and the other before the 40° substep (catalytic dwell) (14,
15) (Fig. 1A). Most crystal structures correspond to the catalytic
www.pnas.org/cgi/doi/10.1073/pnas.1305497110
dwell state (1, 14–19), with the F1 conformation of the binding
dwell state still elusive (16).
The transition from the catalytic dwell to the binding dwell
involves Pi release, but the release site and the exact timing in the
full cycle remain controversial. In most kinetic models of F1 (1),
but not all (20), Pi is assumed to exit first, followed by ADP
release. This order appears to be consistent with kinetic (21) and
structural studies (22) showing all three sites occupied by nucleotide (22); by contrast, the single-molecule experiments of
Watanabe et al. (13) and structural studies of yeast F1 (23)
suggest that ADP is released before Pi. With γ-rotation stalled in
the catalytic dwell state by magnetic tweezers, the hydrolysis
reaction was found to be reversible without excess Pi in solution
(13), suggesting that Pi is released at 320°, i.e., from the E site
(13, 24) (where ATP binding defines 0°; Fig. 1A).
Here, we reconcile these conflicting interpretations by determining the kinetics of Pi release from the E site and the DP
site with atomistic molecular dynamics simulations. These simulations also allow us to explore the coupling between the 40°
substep and Pi release, and to examine the underlying molecular
mechanisms. F1 has been studied by molecular simulations at
various levels of resolution, including quantum chemical calculations of ATP hydrolysis (25–27), all-atom simulations of conformational changes in the β-subunit (28, 29), of ATP release
(30), of fluctuations in the complex (31, 32), and of γ-rotation
(33, 34), as well as coarse-grained simulations of γ-rotation (35–
37). As in experiment and in earlier simulations (33), we apply
external torque to modulate the rates of the functional processes,
including Pi release.
We first characterize the molecular motions of F1 during the
40° substep in atomically detailed simulations. By rotating the
Significance
F1-ATPase is the catalytic domain of FoF1-ATP synthase, the
rotary molecular motor at the core of the energy transduction
machinery in all of life. We use atomistic molecular dynamics
simulations to study a key event in its catalytic cycle, the release of inorganic phosphate (Pi) produced by the hydrolysis of
ATP. We determine the timing, kinetics, and molecular mechanism of Pi release and clarify its role in torque generation.
We also obtain an atomically detailed structure of a crystallographically unresolved intermediate formed after the 40°
substep. Our results help reconcile conflicting interpretations
of earlier biochemical, crystallographic, and single-molecule
studies; shed light on the functional requirements of efficient
ATP synthesis; and establish connections to other motors such
as myosin.
Author contributions: K.-i.O. and G.H. designed research; K.-i.O. performed research; K.-i.O.
contributed new reagents/analytic tools; K.-i.O. and G.H. analyzed data; and K.-i.O. and G.H.
wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1
To whom correspondence should be addressed. E-mail: [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1305497110/-/DCSupplemental.
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Edited by J. Andrew McCammon, University of California, San Diego, La Jolla, CA, and approved August 28, 2013 (received for review March 21, 2013)
A
B
C
Fig. 1. Mechanochemical coupling scheme and Pi release of F1-ATPase. (A)
Mechanochemical coupling scheme deduced from recent single-molecule
experiments (13). ATP hydrolysis reaction steps in one of the three catalytic
sites (yellow circles) as a function of the γ-rotation (red arrow). T, D−P, D+P,
and P stand for ATP bound, hydrolyzing ATP, ADP+Pi bound, and Pi bound,
respectively. At an angle of 0°, ATP is bound. States differing by integer
multiples of 120° are functionally equivalent. The timing and pathway of Pi
release (purple) has been controversial. (B) Crystal structure (PDB ID code
2jdi) of F1-ATPase that represents the ∼80° catalytic dwell state, with α-, β-,
γ-subunits colored in blue, orange, and red, respectively. (C) Tightly bound Pi
in the E site modeled on the basis of yeast structures (SI Text). The blue and
orange ribbon backbones correspond to the αE- and βE-subunit, respectively.
The five residues that participate in Pi binding are shown with thick bonds.
VMD was used to prepare structural figures (64).
γ-subunit with the help of a newly developed flexible rotor
method, we show how the γ-angle and the protonation state of Pi
(i.e., HPO42− or H2PO4−) affect the conformation of αβ-dimers
and the stability of Pi binding in the E site. We then estimate
rates of Pi release from the E site and from the DP site with the
help of metadynamics simulations (38). From the simulations
and by relating the calculated rates to experiment, we determine
the timing, pathway, and charge state dependence of Pi release.
Finally, we show that key elements of Pi release appear to be
conserved in myosin, despite the different functional motions.
Results
Rotation of γ and Conformational Response of αβ-Dimers. In all-
atom explicit-solvent simulations of the F1 motor, the γ-angle
was rotated in the hydrolysis direction with an angular velocity of
1°/ns by the newly developed flexible rotor method (Methods,
Fig. S1, and Movie S1). The angular velocity may seem higher
than in experiment. However, the millisecond timescale of F1
rotation in experiment mainly reflects the catalytic dwell waiting
for hydrolysis and Pi release. The rotary motion during the 40°
substep transition should thus be much faster, yet it has not been
measured without load to the best of our knowledge. For
structurally more complex transitions like protein and RNA
folding, transition path times have been measured in the lowmicrosecond range, many orders of magnitude faster than the
corresponding mean first-passage times of (un)folding (39, 40).
With the γ-subunit allowed to twist freely in our simulations, the
angle of its core lagged behind the average, while the protruded
part moved ahead (Fig. 2B). This twisting in response to torque
reflects both on the torsional stiffness of γ and on the friction
experienced by the core part due to its tight interactions with the
α3β3 ring. The enhanced rotation of the protruded part (or
“foot”) seen here is consistent with large variations in its rotational angle in crystal structures (22, 41) and the low torsional
stiffness of the γ-rotor (42). Importantly, despite the twisting the
γ-subunit remains structurally intact, as indicated by root-meansquare deviations (RMSDs) of <3.5 Å (Fig. S2A). The bottom
part of the C-terminal helix of γ resists rotation, which seems to
be a main source of the twisting (Fig. S2B). The elastic energy
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stored in this region may contribute to the reversibility and efficiency of the F1 motor (32).
Rotation of the γ-subunit induces conformational changes in
all three αβ dimers, αβE, αβTP, and αβDP. We monitor their
conformational responses by projection onto the principal
component axes PC1 and PC2 obtained previously from the
analysis of X-ray structures (43). PC1 reports on the hinge closing motion of the β-subunit, and PC2 on the tightening motion of
the αβ interface in response to ligand binding and γ-rotation. PC1
and PC2 are in units of Ångstroms. During the γ-rotation, the
αβDP interface remained close to the X-ray structures (Fig. 3A).
By contrast, the interface structure of αβTP tightened in both
simulations, moving toward αβDP already after ∼20° γ-rotation
(Fig. 3A, green points; and difference ΔDRMSD of the RMSD
with respect to the initial αβTP and αβDP structures in Fig. S2C).
αβTP thus indeed moved in the direction expected for hydrolysis.
This motion is concentrated mainly in αTP (Fig. 3B, blue), with
rotation of γ in the hydrolysis direction pushing a protruded
β-hairpin of γ (γ165–173) away from the helix-turn-helix motif of
the C-terminal domain of αTP, and αTP occupying the vacated
space (Fig. 3B and Movie S1). We note that this conformational
change was not observed in free simulations without torque
(Fig. S3B).
The αβE-subunit motions induced by γ-subunit rotation depend sensitively on the protonation state of Pi in the E site. To
account for the near-neutral pKa2 of 7.2, we studied HPO42− and
H2PO4− in separate simulations. The interface of αβE loosened
after a few degrees of rotation with H2PO4−, as reflected in the
large change of PC2 to negative values (Fig. 3A, Left). The
loosening of the αβE interface with γ-rotation in the hydrolysis
direction is consistent with a yeast structure at a 12° γ-angle (23),
as indicated by their PC2 values of −10 ± 5 Å (molecular
dynamics at γ= 12°) and −7.9 Å (X-ray) (43). By contrast, the
αβE interface remained relatively tight with HPO42− (Fig. 3A,
Right). The doubly charged Pi locks the interface, forcing α- and
β-subunits to move together in response to γ-rotation (Fig. S2D).
By comparison, with the singly charged Pi, the motion is concentrated in the α-subunit, reflecting the weaker interactions of
Pi with the αβE dimer. Thus, the motion of αE, pushed by the
N-terminal helix of γ, is primarily responsible for the loosening of
the E-site interface (Fig. 3C), which in turn weakens Pi binding
to the E site, as studied below.
Protonation State of Pi, Interface Conformation, and Direction of
γ-Rotation Affect Binding Stability in the E Site. Pi moves in the E
site as the γ-subunit is rotated. To cancel out the overall rotational
motion, we superimposed the binding site on the initial structure,
using residues within 10 Å from Pi in the initial structure. Fig. 4A
shows the resulting Pi distance from the initial position as a
function of time, with γ rotated in the hydrolysis direction by 1°/ns.
H2PO4− and HPO42− in the E site responded quite differently to
γ-rotation. The singly charged Pi readily moved toward the P-loop
A
B
Fig. 2. Rotation of γ-subunit in the hydrolysis direction. (A) Rotation of γ
against α3β3 ring in the hydrolysis direction. The N- and C-terminal helices
(γ1–33, 224–273), colored in purple, form the core that penetrates the center
of the α3β3 ring. The protruded part is colored in red. (B) Rotational angle for
the whole (blue), the core (purple), and the protruded parts of γ (red) as
a function of time for F1 with H2PO4− in the E site.
Okazaki and Hummer
Fig. 3. Conformational response
w/ HPO420-25ns w/ H2PO4X-ray structures
 E
 TP
60
of αβ-dimers to γ-rotation in the
 DP
40
hydrolysis direction. (A) Projections of αβ-dimer structures
20
onto the principal component
0
axes PC1 and PC2 obtained from
-20
E
 TP
the analysis of X-ray structures
-40
(43) during the (Upper) first and
-60
(Lower) second half of the sim25-50ns
60
ulations with H2PO4− (Left) and
2−
HPO4 (Right) in the E site. Red,
40
green, and blue points corre20
spond to αβ that starts from αβE,
0
αβTP, and αβDP, respectively,
-20
and purple points correspond
-40
to X-ray crystal structures (43).
-60
The arrows indicate directions
-80 -60 -40 -20
0
20
40
60
-80 -60 -40 -20
0
20
40
60
open
close
PC1
PC1
of αβ-motion in response to
γ-subunit rotation in the hydrolysis direction. (B) Conformational change of αβTP in response to 30° rotation of the γ-subunit during the trajectory with HPO42−.
The snapshot at 30 ns is colored as in Fig. 1B, and the reference structure at 0 ns is colored in cyan. Only the C-terminal domains of αβ are shown for the 0-ns
conformation, and the β-hairpin and the C-terminal helix are shown for the γ-subunit. (C) Conformational change of αβE in response to 30° rotation of the
γ-subunit during the trajectory with H2PO4−. The snapshots at 30 and 0 ns are shown as in B.
A
C
region. This motion of Pi was tightly coupled to the loosening of
the interface conformation of αβE (Fig. 5A) and was not observed
in the free simulation without torque (Fig. S3C). The observed
coupling supports the earlier suggestion that Pi binding is regulated by the αβE interface conformation, as inferred from a comparison of different F1 structures (43). The transient structure at
3.5 ns is shown in Fig. 4B, with αARG373 and βLYS162 coordinating Pi. The so-called Arg-finger, αARG373, seems to play
a role of guiding Pi to the P loop. In fact, αARG373 remained
coordinated to Pi even as Pi moved toward the P loop (Fig. 4A,
green line). Pi stayed at the P loop for the rest of the trajectory,
frequently interacting with αARG373. The rapid escape of Pi from
the E site to the P loop during the 40° substep, as probed in the
torque simulations, is consistent with the dramatic increase in the
rate of Pi release between 320° and 360° reported from experiment (24). By contrast, the doubly charged Pi remained quite
A
B
80
Rotational angle [deg.]
90
100
110
120
12 Escape
H2PO4-
3.5ns
H2PO4-
toward P-loop
Pi distance [Å]
130
10
8
6
H2PO4-- Arg373
HPO42-
4
2
0
C
0
10
20
30
Time [ns]
HPO42-
20ns
40
50
39ns
P-loop
stably bound in the initial position and maintained interactions
with its coordinating residues throughout the trajectory (Fig. 4C).
With two negative charges, the doubly charged Pi was, in effect,
trapped by the four positively charged residues in its immediate surrounding, holding the interface tight during the torque
simulations.
We also studied the dependence of the Pi binding stability in
the E site on the direction of γ-rotation. The singly charged Pi,
with the γ-subunit rotated in the synthesis direction, stayed at the
initial position for the first ∼30 ns (Fig. 5C, Left). After moving
transiently to the P loop, Pi returned back to the initial position
at around 70 ns and remained there. These motions suggest that
Pi binding in the E site is more stable when γ is rotated in the
synthesis direction than in the hydrolysis direction. This increased stability would be important for ATP synthesis, where
ADP should bind into the E site already occupied by Pi (see
below). The loosening of the αβ interface in response to
γ-rotation in the hydrolysis direction, and the tightening in the
synthesis direction (Fig. 5B), are likely the main factors changing
the Pi binding stability. The doubly charged Pi (Fig. 5C, Right)
stayed at the initial position, independent of the direction of the
γ-rotation, and maintained tight interactions with the αβE residues.
As a direct demonstration of the coupling between Pi release
and γ-rotation, three independent 40-ns free simulations without
torque were conducted: (i) without Pi, and with (ii) singly and
(iii) doubly charged Pi in the E site (Fig. S3D). The resulting
γ-angles are distributed narrowly around 85° with doubly charged
Pi, with a wider distribution for singly charged Pi indicating
a looser γ-shaft. Importantly, after doubly charged Pi was released, γ indeed rotated by ∼10° in the hydrolysis direction (Fig.
S3E). These free simulations thus further support the hypothesis
that release of doubly charged Pi from the E site drives γ-rotation
in the hydrolysis direction.
Metadynamics Simulation of Pi Release from the E Site and DP Site. Pi
Fig. 4. Pi motion in the E site during rotation of γ in the hydrolysis direction.
(A) Pi distance from the initial position during the torque simulations. The
trajectories with H2PO4− and HPO42− are shown in red and blue, respectively.
The distance between H2PO4− and the Cζ atom of αARG373 is plotted in
green. (B) Pi (H2PO4−) migration toward the P loop at 3.5 ns (Upper) and 39
ns (Lower). (C) Tightly bound Pi (HPO42−) at 20 ns (details as in Fig. 1C).
Okazaki and Hummer
exits the E site (at 320°) and DP site (at 200°) on entirely different pathways according to the metadynamics (38) simulations
(Fig. 6A). From the E site, singly and doubly charged Pi both
escaped outward via a transient intermediate at the P loop,
consistent with the escape route of H2PO4− in the torque simulations. In the DP site, this outward path is blocked by ADP,
forcing Pi instead to escape inward and exit at the central hole of
the ring subunits (Table S1). This alternate pathway was confirmed by separate simulations with a different metadynamics
hill height (0.2 kcal/mol) and for a different F1 structure with
a slightly open DP site [Protein Data Bank (PDB) ID code 4asu;
Fig. S4].
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loose
PC2
tight
PC2
B
PC2
25
B
Pi
12
10
8
5
6
0
4
-5
-10
-20
0
2
C
8
0
-40
-60
0
8
6
4
2
80
60
40
20
100
Time [ns]
120
w/ HPO42hyd. direct.
syn. direct.
14
10
0
syn. direct.
-20
16
hyd. direct.
syn. direct.
Pi distance [Å]
12
6
Time [ns]
40
w/ H2PO4-
16
14
4
0
10
loose
2
-15
hyd. direct.
20
PC2 of E-site
15
10
Pi distance [Å]
PC2 of E-site
20
Pi distance [Å]
tight
A
12
10
8
6
4
2
0
20
40
60
80
100
120
0
0
10
20
Time [ns]
30
40
50
Time [ns]
Fig. 5. Interface conformation and γ-rotational–direction dependence of Pi
binding stability. (A) PC2 of the E site (left scale; blue) reporting on αβ interface tightening, and Pi distance relative to starting conformation (right
scale; red) during the first 10 ns of the hydrolytic torque simulation with
H2PO4−. (B) PC2 of the E site in the hydrolytic (blue) and synthetic (purple)
torque simulations with H2PO4−. (C) (Left) Distance of the singly charged Pi
from its starting point for the hydrolytic (red) and synthetic (green) torque
simulations. (Right) Distance of the doubly charged Pi for the hydrolytic (red)
and synthetic (green) torque simulations.
These two exit pathways have drastically different free-energy
barriers (Fig. 6B). Escaping from the E site in the z direction,
singly and doubly charged Pi face free-energy barriers of ∼5 and
∼10 kcal/mol, respectively, to transition from the tightly bound
state to the P loop. The free-energy barrier for Pi to be released
from the P loop into solution is ∼5 kcal/mol in both cases. By
contrast, the free-energy barrier for Pi to be released from the
DP site, moving along the x direction, is almost ∼30 kcal/mol in
total, and thus insurmountable on the functional timescale. This
high barrier is a result of the tight interface of the DP site, and of
ADP blocking the pathway to the P loop, which effectively
A
Free energy [kcal/mol]
B
-5
X coord. [Å]
5
10
0
15
20
0
release
-10
z
x
prevent Pi escape to the outside (Fig. 6C). Our results are consistent with the interpretation of recent single-molecule experiments (13) of Pi being released from the E site, i.e., at 320° in
Fig. 1A during the catalytic dwell. The free-energy barriers were
confirmed by additional long simulations with a different protocol (SI Text and Fig. S5).
As listed in Table 1, the calculated timescale of ∼2 ms for the
release of doubly charged Pi agrees well with the ∼1-ms estimate
from experiment (10, 12, 13). The mean first-passage times were
calculated from the free-energy profiles and diffusion coefficients (SI Text, Fig. S6, and Table S2). As described above, the
Pi movement from the tightly bound state to the P loop is coupled to the global interface motion that occurred within a few
nanoseconds (Fig. 5A). This rapid conformational change prevents backtransfer of Pi, which is thus ignored in our timescale
estimates. Overall, our simulations suggest that doubly charged
Pi is released from the E site at 320° before the 40° substep.
P-loop
-20
-30
tightly
bound
0
4
8
12
Z coord. [Å]
16
C
blocked
Fig. 6. Pi release from the E site and DP site. (A) Pathways and (B) freeenergy profiles of Pi release determined from metadynamics simulations of
singly charged Pi (brown) and doubly charged Pi (yellow) from the E site, and
of singly charged Pi from the DP site (green). In A, βE (cyan cartoon) is
superimposed on βDP (orange cartoon), and the P loops are colored in purple.
ADP, Mg2+, and Pi in the DP site are shown as sticks. (C) Cut through the
binding site in the DP state, with arrows indicating exit pathways.
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Discussion
We found that Pi release from the E site is kinetically realistic
and that release from the DP site is not. The calculated time of
∼2 ms for the release of doubly charged Pi from the E site
matches the rate of Pi release during the catalytic dwell reported
from experiment (13). With this timescale matching also the
catalytic dwell time, Pi release could thus be rate-limiting. Our
results suggest the need to correct earlier models in which Pi was
assumed to exit first from the DP site, just after the hydrolysis
reaction, followed by ADP release. Instead, Pi is likely released
from the E site at 320° (Fig. 1A), 120° after the hydrolysis reaction, and after ADP release.
Our simulation results help reconcile conflicting interpretations
of earlier experiments. Shimo-Kon et al. (21) showed that Pi
binding from solution inhibits ATP binding, concluding that the E
site must be devoid of Pi. However, at 320°, Pi could have escaped
with a ∼1/ms rate and ATP rebound with an estimated on rate of
∼1/ms at 1 mM concentration (24), making the empty E site shortlived in the cycle. Nucleotide binding to all three sites at ∼1 mM
concentration (21) could also explain the presence of three ADPs
in a recent F1 crystal structure (22). With these ADPs not produced during turnover, but likely taken up from solution (1), Pi
would not be kinetically trapped in the DP and E sites. By contrast, tightly bound Pi observed in the E site of some structures
(23, 44) likely mimics a product Pi of hydrolysis before release in
the catalytic dwell. Gao et al. (20), on the basis of kinetic data on
the inhibition of ATP hydrolysis by ADP and Pi, concluded that Pi
is released after ADP, consistent with our calculations. We also
note that, in the synthesis direction, preferential binding of Pi in
the empty E site is advantageous by favoring the subsequent
binding of substrate ADP (45) over the abundant but inhibitory
product ATP. The ADP/ATP preference with Pi bound could be
probed in experiment (21).
The combination of experiment (13) and simulation suggests
that Pi is released as HPO42−. According to quantum chemical
calculations, Pi is doubly protonated (singly charged) just after
hydrolysis (25). However, after ADP and Mg2+ (net charge is −1)
leave the site, four positively charged residues surround Pi,
shifting its pKa. This electrostatic environment would indeed
favor the loss of one proton, resulting in a singly protonated
(doubly charged) Pi in the E site. Probing the pH dependence of
the dwell time of the Pi release (or the 40° substep) could test
this hypothesis, assuming protonic equilibrium with the solvent.
We also investigated the conformational changes of F1 in response to the 40° rotation step of the γ-subunit, and their coupling to Pi release. γ was rotated both in the hydrolysis and
synthesis directions, for two possible protonation states of Pi in
the E site. By rotating for 40° in the hydrolysis direction relative
to the available crystal structures, we obtained a first fully atomistic conformation of the intermediate state following the 40°
substep. We found that the structure of the ATP-bound αβTP
interface became as tight as that of ADP+Pi-bound αβDP interface, thus facilitating hydrolysis. By comparison, the αβE
Okazaki and Hummer
Table 1. Estimated mean first-passage times of Pi release from the E site
H2PO4−
HPO42−
Tightly bound to P loop
P loop to tightly bound
P loop to release
2.4 μs
2.0 ms
0.11 μs
0.014 μs
0.34 μs
41 μs
interface became looser, and Pi escaped to the P loop. We expect
these structures to be representative of the conformations of the
two sites in the binding dwell state. The αβDP site remains relatively tight and shows only a slight opening, as indicated by the
displacement of purple and blue points in Fig. 3A. We conclude
that αβDP motions in response to γ-rotation are considerably
slower than those of αβE and αβTP (16). The salt bridges between
γ and α3β3 formed in the intermediate state are listed in SI Text.
To test whether the intermediate state is stable without torque
applied to γ, two 40-ns free simulations were conducted with the
torque switched off at 40° and 50° from the catalytic dwell, respectively. In both simulations, the γ-angle settled around 110°
(30° from the catalytic dwell), indicating the formation of a metastable state (Fig. S7A). Importantly, the torque simulations drive
the system out-of-equilibrium (as would the Fo motor in intact
ATP synthase). In such a nonequilibrium process, the γ-rotor will
be slightly over-twisted. Releasing the torque that drives the rotation is thus expected to result in a fast relaxation of the angle.
We indeed observed a relaxation on a ∼5-ns timescale after releasing the torque at 120°, close to the presumed metastable
minimum (Fig. S7A, green curve). When we released the torque at
130°, beyond the minimum, we again saw this fast recoil, and in
addition a more gradual relaxation to a state at ∼110°, consistent
with an overdamped, weakly driven motion in a metastable minimum at ∼110°. The interface conformations of αβE and αβTP
relaxed partially, but importantly in a reversible way (Fig. S7B).
These interfacial motions are coupled to torque generation,
which should make it possible to probe our results by mutation.
Torque generation as a result of nucleotide binding/dissociation has
been probed extensively by mutations of β–γ interactions (46). By
contrast, relatively little is known about the specific mechanisms of
torque generation as a result of Pi release. The interfacial motions
seen in our simulations suggest that torque generation by Pi release
should be sensitive to the hydrophobic interactions between
αPHE403/αPHE406 and γILE16/γILE19/γLEU77, and the electrostatic interactions between αASP409 and γARG133, αASP411
and γLYS30, αGLU355 and γLYS11, and αGLU399 and γLYS18.
Perturbations of these interactions by mutation should affect the
coupling between the αβE interface and the γ-subunit, and should
thus report directly on torque generation as a result of Pi release.
Remarkably, the two Pi exit pathways observed in this study
appear to be conserved in myosin, and possibly other members of
the large family of P-loop ATPases. In particular, a so-called
“back door” exit pathway for Pi release has been proposed for
myosin, to circumvent the “front door” pathway blocked by ADP
in the binding pocket (47). Molecular dynamics simulations
showed that the Pi release pathway is tightly linked to the cleftclosing motion of myosin upon binding to actin (48, 49). The
back door route dominated for an open cleft and a closed
binding site, whereas the front door and a variant of the back
door route dominated for a closed cleft and an open binding site
(49). We have a similar situation in F1, although the global
motions are quite different. With the binding site closed (DP
site), Pi escaped via an inward route that corresponds to the back
door in myosin (toward switch II). By contrast, with the binding
site open (E site), we observed the outward route corresponding
to the front door in myosin (Fig. S8). Despite large differences in
the global functional motions of different P-loop ATPases, local
motions during the hydrolysis cycle thus appear to be conserved.
Functional requirements then dictate the dominant route of Pi
exit in different ATPases, and possibly also GTPases. Myosin
uses both back and front doors, whereas F1 takes the front door
exclusively, as shown here.
Okazaki and Hummer
Methods
Initial Structures. The initial structures of F1 were taken from the azide-free
crystal structure (PDB ID code 2jdi) (50). Residues 24–510 were used for the
α-subunits, 9–478 were used for the β-subunits, and all residues were used
for the γ-subunit. MODELER (51) was used to model structures of missing
residues. Missing residues in the γ-subunit were modeled according to the
dicyclohexylcarbodiimide-inhibited structure (PDB ID code 1e79) (52). In the
azide-free structure, the TP site and DP site bind an ATP analog (AMPPNP)
and Mg2+, and the E site is empty. For the simulation system, the ATP analog
in the TP site was replaced with ATP, and that in the DP site was replaced
with ADP and Pi (H2PO4−). Pi (HPO42− or H2PO4−) was modeled in the E site,
representing the catalytic dwell state just after ATP hydrolysis (SI Text). A
variety of analyses (1, 14–19) consistently indicate that the initial crystal
structure represents the catalytic dwell, which corresponds to a γ-angle of
80° by definition (Fig. 1A). The half-closed structure by Menz et al. (44) was
not used here because it possibly corresponds to an E site occupied by ADP
rebound from solution at high ADP concentration, and thus would not be
part of the actual sequence of product release. Pi in the DP site was modeled
as doubly protonated following the quantum chemical studies of ATP hydrolysis in this site (25). Crystal water molecules were retained unless they
clearly overlap with replaced ligands.
Simulation Setups. The modeled F1 with crystal waters was solvated with
TIP3P water (53) in a rectangular box such that the minimum distance to
the edge of the box is 11 Å, and neutralized with potassium ions. Then, ∼100 mM
KCl was added to the system. The total number of atoms is ∼313,000 (Fig. S1). The
Amber ff99SB force field was used for the protein (54), with modified parameters
for KCl (55), and for ATP and ADP (56). The point charges for singly and doubly
protonated Pi were determined using Gaussian 03 (57) and the Antechamber
module of Amber (58) (SI Text). The system was energy minimized and equilibrated at isothermal–isobaric (NPT) conditions with Ewald electrostatics and
restraints on all heavy atoms in the protein for 500 ps, and subsequently, with
restraints on only Cα atoms for 1 ns. After the equilibration, production runs were
conducted with restraints on the Cα atoms of the 10 N-terminal residues of each
of the three β-subunits, mimicking the role of His-tag anchoring in singlemolecule experiments. NAMD 2.8 was used for the molecular dynamics simulations with periodic boundary condition (59). Langevin dynamics with
1 ps−1 damping coefficient was used for temperature control at 310 K, and
the Nose–Hoover Langevin piston was used for pressure control at 1 atm (60).
Flexible Rotor Simulation. In the torque simulations, only the average rotational angle of the γ-subunit was restrained. As in an earlier method (61), the
γ-subunit is allowed to twist freely, but here without arbitrary subdivision
into slabs. We also allow free translation of its center of mass. Details of the
method and explicit expressions for the restraint forces are in SI Text.
Metadynamics Simulation of Pi Release. To enhance the sampling and estimate
free-energy profiles for Pi release, metadynamics (38) simulations were
conducted using the PLUMED 1.3 plugin with NAMD (62). The relative Cartesian coordinates x, y, and z of Pi from the binding site were used as collective variables (63), where the binding site was defined by the Cα atoms of
β-subunit residues 188, 256, 257, 259, and 309–312, which are within 8 Å
from Pi in the DP site. Flexible α and P-loop residues are excluded. Repulsive
Gaussian potentials with heights of 0.1 kcal/mol and widths of 0.6 Å were
deposited every 1 ps during the metadynamics simulations. The free-energy
profiles were calculated by a PLUMED utility, sum_hills.
ACKNOWLEDGMENTS. We thank Drs. Kazuhiko Kinosita and Hiroyuki Noji
for insightful discussions, and Drs. Edina Rosta, Fangqiang Zhu, Jürgen
Köfinger, Pilar Cossio, and Ikuo Kurisaki for technical help. This work was
supported by the Intramural Research Program of the National Institute of
Diabetes and Digestive and Kidney Diseases, National Institutes of Health and
by the Max Planck Society. K.-i.O. is supported by research fellowship for
young scientists and postdoctoral fellowship for research abroad of the Japan
Society for the Promotion of Science. The research used the high-performance
computational capabilities of the Biowulf Linux cluster at the National Institutes of Health (http://biowulf.nih.gov).
PNAS Early Edition | 5 of 6
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Okazaki and Hummer
Supporting Information
Okazaki and Hummer 10.1073/pnas.1305497110
P
P
rotational angle is calculated as Δϕ = i j→
si jðϕi − ϕ0i Þ= i j→
si j.
The resulting force on atom j at time t is
SI Text
Modeling Tightly Bound Pi in the E Site. Several crystal structures of
F1 from yeast mitochondria show inorganic phosphate (Pi) in the
empty (E) site (1, 2) interacting tightly with the biochemically
identified Pi-binding residues (3). In one bovine structure, Pi
binds partly to these residues in the E site (4); however, the
interface structure is slightly more open than in the tightly bound
8
9
P →
>
>
<
=
0
→c
i j si jcos ϕi − ϕi
− cos ωt
P →
Fj = − K
>
>
:
;
i j si j
8
9
P →
>
>
<
=
0
→s
i j si jsin ϕi − ϕi
− sin ωt
P →
Fj = − K
>
>
:
;
i j si j
P
→
i j si j
P
→
i j si j
with
!
P ∂j→
si jcos ϕi − ϕ0i
X ∂j→
si j
−
i ∂→
rj
P → 2
i j si j
rj
∂→
i
!
P ∂j→
si jsin ϕi − ϕ0i
structures (5). By contrast, the bovine azide-free structure has
a similarly tight interface and a nearly identical side chain arrangement at the Pi site, even without Pi bound (5, 6). Therefore,
we modeled Pi into the E site of the azide-free bovine structure
on the basis of the yeast structure [Protein Data Bank (PDB) ID
code 2hld; second structure]. As shown in Fig. 1C, Pi is surrounded by four positively charged residues αARG373, βLYS162,
βARG189, and βARG260, and one neutral residue βASN257.
i
∂→
rj
X ∂j→
si j
−
i ∂→
rj
P → 2
i j si j
γ-subunit (represented by its Cα atom) is defined through a displacement vector that is projected on a surface perpendicular to
the rotation axis →
v, →
si = →
ri − →
r CM − ½ð→
ri − →
r CM Þ · →
v →
v, where →
r i is the
→
positional vector of residue i, and rCM is center of mass of the
Cα atoms. The principal axis of the ring subunits was used as
the rotation axis. Then, the rotational angle satisfies ϕi − ϕ0i =
→0 →
cos−1 j→ssi0 jj· →ssi j , where the superscript 0 indicates the initial state.
!
!
X
j→
s jcos ϕi
i i
X
j→
s jsin ϕi
i i
− ϕ0i
− ϕ0i
!
!
with
∂j→
si j
=
rj
∂→
8
>
>
>
<
Flexible Rotor Simulation. A rotational angle for each residue of the
i
∂Vr →c →s
= Fj + Fj
∂→
rj
→
Fj = −
∂ cos
ϕi − ϕ0i
→
∂ rj
=
8
>
<
−1 →
si
si j
Nj→
>
: 1 − 1 →1 →sj
N j sj j
ði ≠ jÞ
ði = jÞ
8
→0 → 9
si · si =
−1 < 1 →0
− →3 →
si
→0 : → si
;
j si j
Nj si j j si j
ði ≠ jÞ
9
8
→0 → =
>
<1
sj · sj
>
1
1
→0
>
−
: 1 − N j→sj0 j :j→sj j sj j→sj j3 →sj ;
ði = jÞ
i
→
By subtracting r CM , we allow free overall translations of the
γ-subunit. In the simulations, the distance-weighted averages
of the cosine and sine of the rotational angle were harmonically restrained, Vr = K2 ðcosΔϕ − cosωtÞ2 + K2 ðsinΔϕ − sinωtÞ2
with K = 105 kcal/mol, where ω is the angular velocity
P
P
of the rotation, cosΔϕ = i j→si jcosðϕi − ϕ0i Þ= i j→si j and
→0 →
P
P
·s
sinΔϕ = i j→
si jsinðϕi − ϕ0i Þ= i j→
si j, with cosðϕi − ϕ0i Þ = j→ssi0 jj→si j,
i
i
→ →
→
ð v × si0 Þ · si
0
sinðϕi − ϕi Þ =
. For the analysis, the distance-weighted
→
j s 0 jj→
sj
i
∂ sin ϕi − ϕ0i
∂→
rj
8
>
>
>
<
=
8
<
−1
1 → →0
v × si −
Nj→
si0 j :j→
si j
→
→ →0
v × si · si
si j3
j→
8
>
<
>
>
: 1 − N1 j s1 j :j 1s j v × s
→0
j
→
j
→
→0
j
−
→
si
9
=
→
→ →0
v × sj · sj
→
j sj j3
ði ≠ jÞ
;
→
sj
9
=
;
ði = jÞ
i
Okazaki and Hummer www.pnas.org/cgi/content/short/1305497110
1 of 7
for the derivatives; we obtain
→c
Fj
=−
K
P
i
j→
si j
2
98
1
!0
>
→
→0
=< X
0
j
s
jcos
ϕ
−
ϕ
sj A
1 X →
si0
i
→
i i
i
@
−
− cos ωt
+ 0 −
js j
P →
i i
i j→
>
N
si0 j j→
sj j
;:
i j si j
8
>
<P
>
:
98
8
1
!0
P →
>
>
→0
→0
=< X
<
0
X →
v
×
s
K
1
v
×
s
→s
j
i
→
i j si jsin ϕi − ϕi
− sin ωt
+ →0 A −
j s j @−
P →
Fj = − i i
i j→
>
N
P → 2>
si0 j
j sj j
;:
:
i j si j
j
s
j
i
i
for the two components of the force acting on atom j as a result of
the flexible rotor potential. This method was implemented using
the Tcl Forces interface in NAMD (7).
Force Field for Pi. The force fields for the two relevant protonation
states of Pi, HPO42− and H2PO4−, were determined from
quantum chemical calculations in a similar way as in previous
work (8). For each protonation state, the geometry optimization
and electrostatic potential (ESP) calculation were conducted at
the HF/6–31+g* level of theory with Gaussian03. Then, the ESP
was fitted using restrained ESP charge fitting with the antechamber module of Amber. For H atoms, Lennard–Jones of SH
groups were used.
Free-Energy Profile of Pi Release from Metadynamics Simulations. We
tested our free-energy surface for the release of Pi in Fig. 6B by
performing additional metadynamics simulations. To assess the
statistical convergence, we performed long simulations with
multiple reversible Pi binding and unbinding events. To test for
possible systematic errors, we used a different biasing protocol
than in the simulations of Fig. 6B. We focused on the free-energy
barrier governing escape of Pi from the E site to the P loop, with
γ at 80°. To sample the free-energy surface, we defined an axis
connecting the tightly bound site (represented by Cζ of βARG189,
Nδ of βASN257, Cζ of βARG260, and Cγ of βTYR311) and the
P-loop site (represented by Cα atoms of βGLY156-βLYS162).
The projection xτ of the Pi position on this axis was used as the
first collective variable, keeping the distance from the axis <7 Å.
The distance yτ from the arginine finger (αARG373) was used as
a second collective variable. The γ-angle was weakly restrained at
80° during the simulation. After the simulation, free-energy profiles were calculated along the distance q of Pi from the tightly
bound site (represented by Cζ of βARG189, Nδ of βASN257, and
Cζ of βARG260) by a reweighting procedure (9, 10),
Z
Fðq; tÞ = − kB T ln
0
t
δðq − qτ ÞeβV ðxτ ;yτ Þ dτ
Z t
bias
eβV ðxτ ;yτ Þ dτ
bias
!
;
0
bias
where t is the simulation time, V (xτ,yτ) is the biasing potential
added at the position of collective variables (xτ,yτ) up to time τ,
and β = 1/kBT.
The trajectories of the Pi distance from the tightly bound site
show that Pi goes back and forth at least four times between
the two states (Fig. S5A). The resulting free-energy profiles for
release of singly and doubly charged Pi calculated at t = 4 and
∼40 ns are shown in Fig. S5B. As shown in Fig. S5C, the barrier
Okazaki and Hummer www.pnas.org/cgi/content/short/1305497110
X
j→
s jcos ϕi
i i
− ϕ0i
X
j→
s jsin ϕi
i i
!
− ϕ0i
!9
→
sj =
1 X →
si
+
−
i j→
N
s i j j→
sj j ;
!
!9
→
sj =
1 X →
si
+
−
i j→
N
si j j→
sj j ;
heights converge to ∼5 and ∼10 kcal/mol for singly and doubly
charged Pi, respectively, which is consistent with the metadynamics simulations in Fig. 6 of the main text.
We monitored the γ-angle during the ∼40-ns metadynamics
simulation and calculated probability distributions for bound
(q ≤ 8 Å) and unbound (q > 8 Å) states. These distributions are
in good agreement with the corresponding distributions from
free simulations, after appropriate reweighting the by Boltzmann
factor expð−βVr Þ of the weak restraint potential Vr with K = 80
kcal/mol restraining the γ-angle near 80° in the metadynamics
simulation (Fig. S5D). Small differences between the angle distributions in free and metadynamics simulations likely reflect
the nonequilibrium character of the latter, with Pi driven to
sample both bound and unbound states. Importantly, release
of Pi induces rotation of the γ-subunit also in the metadynamics simulations, with direction and magnitude both fully
consistent with the free simulation results, after appropriate
corrections for the weak restraints applied in the metadynamics run.
Estimation of Mean First-Passage Time. The mean first-passage time
from position a to b along the reaction coordinate is estimated
from the following equation (11) for one-dimensional diffusion,
Zb
τða → bÞ =
dx
a
eβGðxÞ
D
Zx
dye−βGðyÞ ;
x0
where GðzÞ is free-energy profile along the reaction coordinate z,
D is the diffusion coefficient, and x0 is the position of a reflecting
barrier. The diffusion coefficient is estimated as D = varðzÞ=τ for a
harmonically trapped Pi, where the numerator is the variance
of
R∞
the reaction coordinate, and the denominator is τ = 0 CðtÞdt,
with CðtÞ = hδzðtÞδzð0Þi=varðzÞ the normalized time correlation
function of the reaction coordinate (12). To estimate τ, the time
correlation functions were fitted with double exponentials (Fig.
S6) and analytically integrated. The parameters used are listed
in Table S2.
Salt Bridges in the Intermediate State. In earlier molecular dynamics simulations, the dynamic coupling between α3β3 and γ was
found to be mediated by the ionic track on the protruded part of
the γ-subunit (13). During the rotation of γ in the hydrolysis
direction, existing salt bridges dissociated and new ones formed.
Following is a list of notable salt bridge exchanges for individual α3β3-subunits during formation of the intermediate state:
αEASP409 breaks interaction with γARG133; αTPASP409 switches
interaction partner from γARG166 to γLYS87; αDPASP409
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switches interaction partner from γARG113/118 to γLYS129/
ARG133 transiently; βDPASP394 switches interaction partner
from γLYS111/LYS129 to γARG133; βEGLU395/398/399 forms
interactions with γARG166; βTPGLU398-γLYS87/90 interaction
breaks and βTPASP394/GLU395/398/399-γLYS111/ARG113/
ARG118 interaction forms. These salt bridge exchanges were
observed consistently in the two simulations with different protonation states of Pi.
1. Kabaleeswaran V, Puri N, Walker JE, Leslie AG, Mueller DM (2006) Novel features
of the rotary catalytic mechanism revealed in the structure of yeast F1 ATPase. EMBO
J 25(22):5433–5442.
2. Kabaleeswaran V, et al. (2009) Asymmetric structure of the yeast F1 ATPase in the
absence of bound nucleotides. J Biol Chem 284(16):10546–10551.
3. Ahmad Z, Senior AE (2005) Identification of phosphate binding residues of Escherichia
coli ATP synthase. J Bioenerg Biomembr 37(6):437–440.
4. Gibbons C, Montgomery MG, Leslie AG, Walker JE (2000) The structure of the central
stalk in bovine F(1)-ATPase at 2.4 A resolution. Nat Struct Biol 7(11):1055–1061.
5. Okazaki K, Takada S (2011) Structural comparison of F1-ATPase: Interplay among
enzyme structures, catalysis, and rotations. Structure 19(4):588–598.
6. Bowler MW, Montgomery MG, Leslie AG, Walker JE (2007) Ground state structure of
F1-ATPase from bovine heart mitochondria at 1.9 A resolution. J Biol Chem 282(19):
14238–14242.
7. Phillips JC, et al. (2005) Scalable molecular dynamics with NAMD. J Comput Chem
26(16):1781–1802.
8. Pfaendtner J, Branduardi D, Parrinello M, Pollard TD, Voth GA (2009) Nucleotidedependent conformational states of actin. Proc Natl Acad Sci USA 106(31):12723–12728.
9. Marsili S, Barducci A, Chelli R, Procacci P, Schettino V (2006) Self-healing umbrella
sampling: A non-equilibrium approach for quantitative free energy calculations. J
Phys Chem B 110(29):14011–14013.
10. Dickson BM, Legoll F, Lelièvre T, Stoltz G, Fleurat-Lessard P (2010) Free energy
calculations: An efficient adaptive biasing potential method. J Phys Chem B 114(17):
5823–5830.
11. Zwanzig R (1988) Diffusion in a rough potential. Proc Natl Acad Sci USA 85(7):
2029–2030.
12. Hummer G (2005) Position-dependent diffusion coefficients and free energies from
Bayesian analysis of equilibrium and replica molecular dynamics simulations. New J
Phys 7(1):34.
13. Ma J, et al. (2002) A dynamic analysis of the rotation mechanism for conformational
change in F(1)-ATPase. Structure 10(7):921–931.
14. Rees DM, Montgomery MG, Leslie AGW, Walker JE (2012) Structural evidence of
a new catalytic intermediate in the pathway of ATP hydrolysis by F1-ATPase from
bovine heart mitochondria. Proc Natl Acad Sci USA 109(28):11139–11143.
Fig. S1. Simulation system of F1-ATPase in water box. The α- (blue), β- (orange), and γ-subunits (red) are shown in cartoon representation. Potassium and
chloride ions are shown as blue and red spheres, respectively.
Okazaki and Hummer www.pnas.org/cgi/content/short/1305497110
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a
b
4
RMSD [Å]
3
2
1
0
0
10
20
30
40
50
Time [ns]
d
c
w/ HPO42-
w/ HPO42-
w/ H2PO4-
2
E
DP
DRMSD [Å]
1
TP
0
-1
-2
0
10
20
30
Time [ns]
40
50 0
10
20
30
Time [ns]
40
50
Fig. S2. Torque simulations. (A) Root-mean-square deviation (RMSD) plot of γ-subunit during hydrolytic torque simulation with H2PO4− in the E site. (B)
γ-Structure after 50° rotation (red) superimposed on the initial structure (cyan) from the same simulation. The ellipse highlights the twisted bottom part of the
C-terminal helix. (C) Conformational response of αβTP and αβDP monitored by ΔDRMSD. ΔDRMSD = RMSDðXt ,XTP Þ − RMSDðXt ,XDP Þ is plotted for αβTP (red) and αβDP
(green) conformations during the simulations with singly charged Pi (Left) and doubly charged Pi (Right) in the E site, where RMSDðXt ,XTP=DP Þ means RMSD of
corresponding αβ-dimers at time t from the initial αβTP/DP. (D) Conformational motion of αβE. The conformational change observed in the torque simulations in
the hydrolysis direction is shown for the doubly charged Pi in the E site. The conformations of αE, βE, and γ at 30 ns are shown in blue, orange, and red,
respectively, whereas the conformations of the C-terminal domain of αβE at 0 ns are shown in cyan.
whole
w/ H2PO4
w/ HPO4
2-
Pi distance [Å]
100
c
protruded
core
-
90
80
14
w/ H2PO4-
12
w/ HPO42-
10
8
6
2
10
b
60
20
30
40 0
10
20
30
Time [ns]
Time [ns]
w/ H2PO4-
w/ HPO42DP
20
0

E
-40
-60
-100 -80
-40
-20
PC1
0
20
40
60
-80
-60
-40
-20
PC1
0
10
15
20
25
30
35
40
e
TP
105
20
40
60
w/o Pi
w/ H2PO4-
w/ HPO42-
100
95
90
85
80
75
-60
5
d


0
Time [ns]
40
-20
0
40
0
5
10
15
20
25
Time [ns]
30
35
40
w/o Pi
0.2
Probability distribution
0
PC2
16
4
70
Rotational angle [deg.]
Rotational angle [deg.]
a
w/ H2PO4-
w/ HPO42-
0.15
0.1
0.05
0
70
80
90
angle [deg.]
100
110
Fig. S3. Free simulations without external torque acting on γ-subunit. (A) Rotational angles of the whole, core, and protruded parts of γ as a function of time.
(B) Conformational fluctuations of the three αβ-dimers as a function of time, projected onto the plane of the first two principal component axes. The color
scheme is the same as in Fig. 3A of the main text. (C) Pi distances in the E site during the free simulations with the singly (orange) and doubly (purple) charged Pi
are shown. (D) Trajectories and (E) histograms of the γ-angle without Pi, and with singly and doubly charged Pi in the E site are shown in cyan, orange, and
purple, respectively. Data were collected after a 5-ns equilibration during 40-ns unrestrained simulation runs.
Okazaki and Hummer www.pnas.org/cgi/content/short/1305497110
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a
Free energy [kcal/mol]
b
release
0
-10
-20
-30
-10
0
10
X coord. [Å]
20
Pi distance to binding site [Å]
a
w/ H2PO4-
20
16
12
8
4
0
0
5
10
15
20
25
30
35
Pi distance to binding site [Å]
Fig. S4. (A) Pi pathway and (B) free-energy profile from the metadynamics simulation with the slightly open DP site [PDB ID code 4asu (14)], with Pi added.
w/ HPO42-
20
16
12
8
4
0
5
10
15
Free energy [kcal/mol]
up to 4ns
up to 36ns
12
10
8
6
4
2
0
2
4
6
8
10
12
14
16
18
40
5
0
2
6
5
4
3
2
1
0
5
10
15
20
Time [ns]
25
30
4
6
8
10
12
14
16
18
20
Pi distance to binding site [Å]
Barrier height [kcal/mol]
Barrier height [kcal/mol]
35
10
20
7
0
30
up to 4ns
up to 44ns
15
Pi distance to binding site [Å]
c
25
20
14
Free energy [kcal/mol]
b
20
Time [ns]
Time [ns]
35
14
12
10
8
6
4
2
0
0
5
10
15
20
25
30
Time [ns]
35
40
45
d
Probability distribution
0.2
HPO42- bound from metadynamics
unbound from metadynamics
biased from free simulation w/ HPO42biased from free simulation w/o Pi
0.1
0
70
80
90
angle [deg.]
100
110
Fig. S5. Free-energy profile of Pi release from metadynamics simulation with several (un)binding transitions for singly charged Pi (Left) and doubly charged Pi
(Right). (A) Trajectories of the distance between Pi and the binding site. (B) Free-energy profiles along this distance calculated after 4- and ∼40-ns simulation times.
Whereas the barrier relevant for Pi escape to the P loop appears converged, the relative stability of the P-loop state (distance > 10 Å) increases because entropic
contributions to this less structured interaction require additional sampling. (C) Simulation-time dependence of free-energy barrier of Pi release from binding site
(distance < 5 Å) to the P loop (distance > 10 Å). (D) Distributions of γ-angles for bound and unbound states from the metadynamics simulation with doubly charged Pi
are plotted in purple and cyan solid lines, respectively. For comparison, distributions from free simulations with doubly charged Pi and without Pi, reweighted by the
Boltzmann factor of the weak restraint potential acting on the γ-angle used in the metadynamics simulation, are plotted as purple and cyan dotted lines, respectively.
Okazaki and Hummer www.pnas.org/cgi/content/short/1305497110
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a
b
1
1
C(t)
0.215*exp(-t/0.069)+
(1-0.215)*exp(-t/0.848)
0.8
C(t)
0.624*exp(-t/0.002)+
(1-0.624)*exp(-t/0.127)
0.8
C(t)
C(t)
0.6
0.6
0.4
0.2
0.4
0
0.2
0
0.2
0.6
0.4
t [ns]
0.8
1
-0.2
0
0.1
0.2
0.3
0.4
0.5
t [ns]
c
1
C(t)
0.443*exp(-t/0.00406)+
(1-0.443)*exp(-t/0.0858)
C(t)
0.8
0.6
0.4
0.2
0
0.02
0.04
0.06
0.08
0.1
t [ns]
Fig. S6. Estimation of diffusion coefficients. Time correlation functions of relative z coordinate of Pi and fitted double-exponential curves are shown for the
single charged Pi in the tightly bound state (A), the doubly charged Pi in the tightly bound state (B), and the singly charged Pi in the P-loop bound state (C).
b
60
140
from 130deg.
130
40
from 120deg.
120
20
PC2
Rotational angle [deg.]
a
110
0
100
-20
90
-40
80
0
10 20 30 40 50 60 70 80 90
-60
-100 -80 -60 -40 -20
0
20
40
60
PC1
Time [ns]
Fig. S7. Stability of the intermediate state in the absence of external torque. (A) Rotational angles of the γ-subunit as a function of time. The external torque
was switched off at 120° and 130°, and free 40-ns trajectories from these points are plotted in green and blue, respectively. (B) Conformational changes of
αβ-dimers after switching off the external torque. The color code is as in Fig. 3A. The arrows and circles represent the directions of the conformational changes,
and metastable positions of αβE and αβTP.
a
b
outward
front door
inward
back door
cleft
Fig. S8. Pi pathways in F1-ATPase and myosin. (A) βDP of F1-ATPase is shown. (B) The postrigor structure of myosin is shown (PDB ID code 1MMD). The P loop,
switch I, and switch II are colored in blue, red, and orange, respectively. The blue arrow indicates the direction of P-loop movement in the open conformation.
Okazaki and Hummer www.pnas.org/cgi/content/short/1305497110
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Table S1. Residues involved in metastable states of Pi release
from the DP site
M1
αGln349
αArg373
βGly159
βLys162
βAsn257
βArg260
βTyr311
βArg337
M2
M3
αAsn341
αSer344
βArg260
βGln263
βTyr311
αArg291
αTyr337
αAsn341
The three metastable states M1, M2, and M3 are labeled in the order of
decreasing relative populations.
Table S2.
Parameters used in rate calculations
Pi
H2PO4−
HPO42−
Tight ➔ P loop
P loop ➔ tight
P loop ➔ out
2.6 Å
10.2 Å
0.5 Å
1.50 Å2/ns
2.0 Å
8.4 Å
0.5 Å
1.61 Å2/ns
10.2 Å
2.6 Å
11.4 Å
1.50 Å2/ns
8.4 Å
2.0 Å
9.3 Å
1.61 Å2/ns
10.1 Å
14.1 Å
8.0 Å
5.16 Å2/ns
8.3 Å
14.1 Å
6.2 Å
5.16 Å2/ns
a
b
x0
D
a
b
x0
D
Movie S1. γ-Rotation in the hydrolysis direction with HPO42− in the E site. The γ-angle goes from 80° to 130°. The trajectory is time-reversed in the middle,
to return from 130° back to 80°. The α-, β-, and γ-subunits are shown in blue, orange, and red, respectively.
Movie S1
Okazaki and Hummer www.pnas.org/cgi/content/short/1305497110
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