PNAS PLUS
Catalytic strategy used by the myosin motor to
hydrolyze ATP
Farooq Ahmad Kiani and Stefan Fischer1
Computational Biochemistry, Interdisciplinary Center for Scientific Computing, University of Heidelberg, D-69120 Heidelberg, Germany
Myosin is a molecular motor responsible for biological motions
such as muscle contraction and intracellular cargo transport, for
which it hydrolyzes adenosine 5’-triphosphate (ATP). Early steps of
the mechanism by which myosin catalyzes ATP hydrolysis have
been investigated, but still missing are the structure of the final
ADP·inorganic phosphate (Pi) product and the complete pathway
leading to it. Here, a comprehensive description of the catalytic
strategy of myosin is formulated, based on combined quantum–
classical molecular mechanics calculations. A full exploration of
catalytic pathways was performed and a final product structure
was found that is consistent with all experiments. Molecular movies
of the relevant pathways show the different reorganizations of
the H-bond network that lead to the final product, whose
γ-phosphate is not in the previously reported HPγO42− state, but
in the H2PγO4− state. The simulations reveal that the catalytic strategy of myosin employs a three-pronged tactic: (i) Stabilization of
the γ-phosphate of ATP in a dissociated metaphosphate (PγO3−)
state. (ii) Polarization of the attacking water molecule, to abstract
a proton from that water. (iii) Formation of multiple proton wires
in the active site, for efficient transfer of the abstracted proton to
various product precursors. The specific role played in this strategy
by each of the three loops enclosing ATP is identified unambiguously. It explains how the precise timing of the ATPase activation
during the force generating cycle is achieved in myosin. The catalytic strategy described here for myosin is likely to be very similar
in most nucleotide hydrolyzing enzymes.
T
he molecular motor myosin cyclically interacts with the actin
filament to generate the mechanical force that is used in
living cells to achieve muscle contraction (1), cytokinesis (2, 3),
and intracellular cargo transport (4). Hydrolysis of one ATP
molecule per cycle provides the free energy that drives the acto–
myosin interaction cycle, as originally described by Lymn and
Taylor (5). ATP is the common energy currency in biology, and is
extremely stable in aqueous solution (6, 7). ATPases, the
enzymes that catalyze the hydrolysis of the Pβ–O–Pγ anhydride
linkage in ATP, are ubiquitous in biology because they are
needed to accelerate the release of free energy stored in ATP.
Myosin manages to speed up the hydrolysis by a factor of 107 over
the uncatalyzed rate in solution. The experimental uncatalyzed
energy barrier is 29 kcal mol−1 (7, 8), and the catalyzed barrier has
been determined experimentally between 14.4 kcal mol−1 (9) and
14.8 kcal mol−1 (10). Understanding how myosin achieves its
ATPase function is necessary to understand how myosin works as
a motor, but also helps one to understand the functioning of the
multitude of other nucleotide hydrolyzing enzymes. The catalytic mechanism of ATP hydrolysis in myosin has been studied extensively with methods such as protein crystallography
(11–14), mutagenesis (15, 16), photochemical kinetics (10), and
quantum-mechanical simulations of the active site (9, 17–21).
This has yielded structures of analogs of the reactant and
transition states, a list of residues affecting the catalytic process, and a number of proposed catalytic pathways. A reactant
(ATP-bound) structure of the catalytically competent state
of the Lymn–Taylor cycle, such as the one shown in Fig. 1A,
can be derived from the crystals. In that state, three loops (called
the Switch 1, the Switch 2, and the P loop) are closed over the
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triphosphate4−/Mg2+ moiety of ATP. A structure of myosin
bound to the dissociated product (ADP/Pi) has not been
available so far. This product state is important, because the
inorganic phosphate (Pi) and ADP products are only released
later by myosin, upon rebinding to the actin filament during the
power stroke. This rebinding can only take place when the nucleotide is in the ADP/Pi product state. Some residues thought
to be catalytically relevant are Glu459 (22), Ser181 (23), Ser236
(24–25), and Gly457 (26) (using the residue numbering of Dictyostelium discoideum), which are all strictly conserved. Whereas
Glu459 has been proposed to act as a general base in the catalysis,
the exact role played by the other residues remained unclear. Both
associative (9, 17, 21) and dissociative (18, 19) pathways in myosin
have been investigated by combined quantum-classical (QM/MM)
simulations. In an associative mechanism, the breaking of the
Pβ–Oβγ bond is concerted with the attack of water onto the
γ-phosphate (Fig. 2A), whereas in a dissociative mechanism
they are sequential (Fig. 2B). The simulations have shown that
only dissociative pathways have transition barriers that are low
enough to be consistent with the experimental rates (9, 18, 19).
Recently, we have explained how myosin achieves the stabilization of the metaphosphate (PγO3−) that is generated by the
dissociative mechanism (20). Furthermore, Nemukhin and coworkers have shown that Glu459 can promote the abstraction of
a proton from a close-by water (Wa in Fig. 1A) to produce the
attacking OH− hydroxyl (Fig. 2B) (18, 19). However, the fate of
the abstracted proton in the final myosin-bound ADP/Pi product
has not been elucidated. Without this knowledge the catalytic
pathway remains incomplete.
Here we address the open questions about the catalytic
mechanism and present a comprehensive view of the strategy
used by myosin to catalyze ATP hydrolysis. In particular: (i)
Significance
Biomolecular motor proteins like myosin generate mechanical
force from the chemical energy of ATP. Like gas engines, they
have different parts (protein domains) that run through a welldefined cycle of motions, consuming one ATP per cycle. Because ATP is very stable, motor proteins catalyze its breakdown
(hydrolysis). The catalytic mechanism is at the core of understanding how these motors work, because the activation of
the catalytic ATPase-function coordinates the motion of the
different domains. Identifying which protein groups are essential for catalysis allows one to understand how the precise
coupling between ATPase activation and mechanical motion is
achieved. Moreover, ATPases are involved in most biochemical
processes and are expected to have a catalytic strategy very
similar to the one reported here.
Author contributions: S.F. designed research; F.A.K. performed research; F.A.K. and S.F.
analyzed data; and F.A.K. and S.F. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1
To whom correspondence should be addressed. Email: stefan.fischer@iwr.uni-heidelberg.de.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1401862111/-/DCSupplemental.
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Edited by Donald G. Truhlar, University of Minnesota, Minneapolis, MN, and approved June 6, 2014 (received for review January 30, 2014)
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Fig. 1. End states of ATP hydrolysis in myosin. (A) ATP4− reactant state R. (B)
Final ADP3−/H2PγO4− product state P. The phosphorus atoms of ATP are
colored gold. The adenosine and the two waters coordinating the Mg2+ are
not displayed. Interatomic distances are in Å. All hydrogen bonds of less than
2.8 Å length (between the heavy atoms) are shown as dotted lines.
Where are the protons positioned in the final ADP/Pi product
(before F-actin binding)? (ii) How is the abstracted proton
transferred from the attacking water to its final position in the
product state? (iii) What are the respective roles of the residues
in active site? To answer these questions, we have used QM/MM
calculations to find the most stable ADP/Pi product structure
in the active site. Then, we computed minimum energy paths
(MEPs) of all of the substeps from the reactant (ATP) to this
final product state (MEPs and how they are computed is described in SI Methods), trying different reaction mechanisms. We
find that in the final product (Fig. 1B), the inorganic γ-phosphate
is doubly protonated and can be formally written as H2PγO4−. Its
calculated energy is –2(±1) kcal mol−1 relative to the ATP reactant, in very good agreement with the experimental values
between –1.5 kcal mol−1(9) and −2.6 kcal mol−1(10) for the reaction energy in prepower stroke myosin. We show how this
product structure is consistent with the well-known reversibility
of the hydrolysis reaction in myosin (27–30). The most favorable
MEP transition has four stable intermediates between the ATP
reactant state and the final ADP/Pi product state, separated by
five transition states (MEP1 in Fig. 3). Unlike often assumed,
there is no dominant rate-limiting step. Instead, three of the five
substeps have similarly high barriers (in the 8.7–10.4-kcal mol−1
range, consistent with experimental rates), and jointly contribute
in limiting the overall reaction rate. The present calculations
confirm that the reaction is dissociative. The catalytic mechanism
is found to have three main phases: (i) Dissociation of the
γ-phosphate as a stable PγO3− metaphosphate (as in Fig. 2B), to
provide a better target for the subsequent attack by an OH−
group. (ii) Abstraction of a proton from the attacking water (Wa
in Fig. 1A) and attack of the resulting OaH− onto the PγO3−. (iii)
Transfer of the abstracted proton to the inorganic γ-phosphate
via a proton wire and rearrangement of the H-bond network
to yield the final H2PγO4− product (Fig. 1B). Accordingly, the
E2948 | www.pnas.org/cgi/doi/10.1073/pnas.1401862111
catalytic strategy of myosin combines three tactics, and the role
of the protein residues that are specifically involved in each tactic
can now be identified: The initial metaphosphate intermediate is
stabilized by interactions with the P-loop backbone and the
Lys185+ side chain (Fig. 1A), which pull negative charge from
the γ-phosphate to the α- and β-phosphate groups, thereby favoring the dissociation (compare the charge distribution in Fig.
2 A and B). The backbone carbonyl of Ser237 activates the
attacking water Wa by polarizing it with a H-bond (Fig. 1A). We
find that the role of the Glu459 carboxylic side chain is to polarize a “helping” water molecule (Wh in Fig. 1A), rather than
serving as a general base itself and accepting a proton as previously proposed (18, 19). Water Wh accepts the proton abstracted from the attacking water and transiently becomes a
H3O+ hydronium. The precise positioning of this helping water
is achieved by Gly457. The abstracted proton is then transferred
from the helping water to the inorganic γ-phosphate group via
a proton wire through the side chain of Ser181. Thus, the specific
role of the residues involved in the catalytic strategy is now
identified for myosin. Significantly, residues that are central to
the strategy are located on each of the three active-site loops, so
that a primary role can be assigned to each loop: The P loop, the
Switch 1, and the Switch 2 are, respectively, responsible for
metaphosphate stabilization, polarization of water Wa, and polarization of water Wh. An overlap of the crystal structures of
different myosins in the ATPase competent conformation (listed
in Table 1) shows that they all have identical configurations of
the active site, indicating that probably all myosins use the same
catalytic strategy. Analogous active sites are found in other
motors and ATPases (20), and a similar catalytic strategy is seen
in enzymes catalyzing the hydrolysis of other types of P–O bonds,
such as DNA restriction endonucleases (31).
Results
The Reactant and Product Structures. The energy-optimized structure of the ATP4−–Mg2+-bound reactant state (R) is shown in Fig.
1A. There are no significant changes in the positions of the
protein atoms compared with the crystal structure of myosin
bound to either vanadate/ADP (12) or to beryllium fluoride/ADP
(32). The length of the Pγ–Oβγ bond is 1.78 Å, which is significantly longer than the 1.6 Å typical of the phospho–ester bonds in
isolated ATP. This shows that the enzyme is using some of the
Fig. 2. Associative versus dissociative mechanisms. (A) Associative mechanism: ATP4− dissociation is concerted with the attack by water Wa. (B)
Dissociative mechanism: the P γO 3− metaphosphate dissociates before
water attack.
Kiani and Fischer
binding energy of ATP to destabilize the reactant ground-state
structure, distorting it in the direction of the subsequent reaction
step (i.e., Pγ–Oβγ bond dissociation). The attacking water (Wa in
Fig. 1A) is in apical position relative to Oβγ and 3.04 Å distant
from the Pγ.
In the final product state (P), of ADP/Pi bound to myosin
protein, the two protons from the attacking water Wa need to be
placed somewhere to account for the proton stoichiometry in the
active site. Several proton positions and orientations were tried,
on either the phosphate groups or the Glu459− side chain. The
structure with the lowest energy is shown in Fig. 1B. Its computed energy is −3.0 kcal mol−1 (unless mentioned otherwise,
all energies are given here relative to the ATP reactant structure
R), consistent with the experimental reaction energy (9, 10). In
Table 1. Crystal structures of myosin in the ATPase-competent conformation
PDB ID code
1VOM
2JJ9
3MKD
1MND
2V26
4ANJ
4BYF
1DFL
Organism
Myosin type
Bound nucleotide analog†
Water Wa‡
Water Wh§
Water W3¶
Dictyostelium discoideum
Dictyostelium discoideum
Dictyostelium discoideum
Dictyostelium discoideum
Sus scrofa
Sus scrofa
Homo sapiens
Argopectin irradians
II
II
II
II
VI
VI
1c
II
ADP-VO4
ADP-VO4
ADP-VO4
ADP-AlF4
ADP-VO4
ADP-AlF4
ADP-VO4
ADP-VO4
+
+
+
n.a.
+
n.a.
+
+
+
+
+
+
+
+
+
k
+
+
+
+
+
+
—
k
Entries in the PDB having a structure with the Converter domain (which carries the lever arm) in the postrecovery–prepower stroke
conformation. All have the Switch 1 and Switch 2 loops in the same closed–closed configuration over the P loop. n.a., not applicable.
†
Nucleotide analog makes the same H-bonds to the protein and the Mg2+ as those shown for ATP in Fig. 1A.
‡
“+” means that the apical oxygen of the vanadate is positioned like water Wa in Fig. 1A.
§
“+” means that a crystal water molecule is present in the same position as water Wh in Fig. 1A.
¶
“+” means that a crystal water molecule is present in the same position as water W3 in Fig. 1A.
k
1DFL does not show any water positions.
Kiani and Fischer
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Fig. 3. Transition network of the ATP hydrolysis in myosin. The names of
stable states and their energies are shown inside circles (their structures are
shown in Figs. 4 and 5). R is the ATP reactant state (shown in Fig. 1A). P is the
most stable ADP/Pi product state (shown in Fig. 1B). Intermediates m1, m2,
and m3 are metaphosphate states (i.e., with a dissociated PγO3−). Intermediates e1, e2, and e3 are states where the side chain of E459 is protonated. g1 to g4 are product precursors, with two protons on the inorganic
γ-phosphate (H2PγO4−). The computed MEPs are shown as lines connecting
the circles, the corresponding transition state energy labeling each line. The
most favorable transition from R to P is shown in bold and named MEP1. All
energies (in kcal mol−1) are given relative to the reactant R. Values in parentheses are energies obtained when water W3 is treated quantummechanically instead of classically (Methods).
this structure, the inorganic γ-phosphate is doubly protonated,
H2PγO4−. One of the two protons is bound to oxygen atom Oa
(which was the oxygen of the attacking water, Wa), where it
retains its H-bond to the backbone carbonyl of Ser237 (compare
with Fig. 1A). The second proton is bound to the oxygen that
receives a H-bond from the Ser181 side chain (Fig. 4F), and
makes a H-bond to the β-phosphate group of the ADP3− (to the
oxygen labeled Oβγ in Fig. 2B). This H-bond is important, because it keeps the inorganic H2PγO4− in close proximity to the
β-phosphate group, despite the strong electrostatic repulsion
with the negative charges on the β-phosphates of ADP3−. As a
result, the H-bond network in the active site of the product is
identical to that of the reactant state (except for water Wh, which
accepts a H-bond from the NH of Gly457 in P instead from water
Wa in R). In particular, the groups involved in the sixfold coordination sphere of the Mg2+ ion are the same as in the reactant
(unlike previously speculated) (9). The implication of this similarity between reactant and product conformations with respect
to the reversibility of ATP hydrolysis is addressed below (see
Discussion).
A very similar product structure (g2, not displayed), with
similar energy (−2.6 kcal mol−1), is found when water Wh is
turned to make a H-bond with the Oa oxygen of the inorganic
γ-phosphate instead of Gly457 (Fig. 6E). Another low-energy
product state (−1.5 kcal mol−1), labeled here g1, is shown in Figs.
4E and 6C. It is like g2, except that one of the protons of the
H2PγO4− is turned toward the Ser181 side chain (instead of toward the β-phosphate), which itself is turned toward the oxygen
of water Wh. In the present calculations, the g1 and g2 states appear as precursors of the P structure (Fig. 3). However, the energies of these three structures are within a narrow (1.5 kcal mol−1)
range, so that they might easily interchange in nature (for
example, the H-bond distances in a crystal structure of the
product would reflect an average of their H-bond networks). In
contrast, all configurations (states e1, e2, e3, in Fig. 3) with one
proton placed on the Glu459− side chain (i.e., the nucleotide is
in the ADP3−/HPγO42− state) have significantly higher energies. Structure e1 (Fig. 5D) starts at 6.8 kcal mol−1, which is much
higher than found experimentally for the hydrolysis product.
Therefore, none of the states with a protonated Glu459 can be
considered to be the final product state of the ATP hydrolysis
(before myosin binds F-actin). Finally, a P-like structure was tried
in which the proton between the γ- and the β-phosphates is bonded
to the β-oxygen rather than to the γ-oxygen (not displayed).
The formula for this P′ structure is then ADPH2−.HPγO42− .
It has an energy of +2.1 kcal mol−1 and is unstable, the proton
tending to jump back onto the γ-oxygen.
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a protonated Glu459 side chain and the γ-phosphate in the
HPγO42− state. The other transition, MEP2, is shown on the left
side of Fig. 3 and proceeds via the intermediates m3, e1, e2,
and g4. The highest energy along the MEP1 transition is 10.4
kcal mol−1 relative to the reactant R, which is consistent with the
experimental barrier. Along MEP2, the highest energy is 18.5
kcal mol−1. It follows that the MEP1 transition is significantly
more likely than the MEP2 transition. The events along the
MEP1 and MEP2 transitions are shown in molecular movies
(Movies S1 and S2), as well as schematically illustrated in Figs. 6
and 7, respectively, and are described in the next sections.
Fig. 4. Structures along the MEP1 transition. (A) ATP 4− reactant state
(R, same as Fig. 1A). (B) Stable metaphosphate (ATP 3− /P γO 3− ) intermediate m2. (C ) Transition state m2-g3: a proton wire ring composed of
6 atoms is formed by water Wa , water Wh (in H 3O+ hydronium state), and
PγO 3− . (D) Transition state m2-g1: a proton-wire ring composed of
8 atoms is formed by water Wa , water Wh (H3O+ ), the Ser181 side chain
and PγO3−. (E) ADP3−/H2PO4− product precursor g1. (F) Final ADP·Pi product
state (P, same as Fig. 1B). Atoms that are not displayed have essentially the
same positions as in the reactant R (Fig. 1A). See Figs. 1 and 3 for display and
naming conventions.
Reaction Pathways. We had previously explored a variety of pathways for the associative mechanism of catalysis (9), and had found
that they all have much higher energy barriers (30–40 kcal mol−1)
than the experimental barrier. Recently, Nemukhin and coworkers
(18, 19) have shown that the early dissociation of the γ-phosphate
(leading to a product precursor with the abstracted proton on
Glu459) has a barrier on the order of 10 kcal mol−1. Therefore,
we focused on further exploring and extending the pathways of
the dissociative mechanism. Several MEPs and their transition
state barriers were computed, varying the positions of the waters,
trying proton transfer from Lys185+ to the phosphates, changing
the configurations of the hydrogen-bond network in the active
site, and using alternative proton wires for the reshuffling of
protons from the reactant to the product configuration. This was
done in particular for (i) transitions in which the side chain of
Glu459− never gets protonated, and (ii) transitions in which the
side chain of Glu459 gets protonated in some intermediates. The
best of each of these two sorts of transitions are shown in Fig. 3
and are labeled, respectively, as MEP1 and MEP2.
The substates and energy levels along the MEP1 transition are
shown on the right side of Fig. 3. They connect the reactant state
R to the final product P via intermediates called here m1, m2, g1,
and g2, which are local minima of the potential energy. The
intermediates were named according to their chemical state: m1,
m2, and m3 have a metaphosphate PγO3−; g1 to g4 have a doubly
protonated inorganic γ-phosphate H2PγO42− ; e1 to e3 have
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Metaphosphate Formation. The first step in both the MEP1 and
MEP2 transitions (R→m1) is the cleavage of the Pγ–Oβγ bond
which produces a PγO3− metaphosphate (Fig. 6A). The resulting
structure m1 (shown in Fig. 5A) has an energy of 2.7 kcal mol−1 and
is nearly identical to the reactant R except for a small (1.1 Å)
motion of the γ-phosphate toward the oxygen of the attacking
water Wa (Movie S1). Nevertheless, an 8.7-kcal mol−1 barrier
clearly separates m1 from R (Fig. 3). m1 is also separated by
significant barriers from the ensuing intermediate along the two
transition pathways (10.4 kcal mol−1 and 10.9 kcal mol−1 from
states m2 and m3, respectively, Fig. 3). Consequently, the m1
state constitutes a distinctive intermediate of the catalytic
mechanism. Using a basis set [B3LYP/6–31+G(d,p)] of even
higher quality than was used for Fig. 3 (Methods), the energy of
m1 drops further to 2.3 kcal mol−1.
The energy of the m1 metaphosphate state is remarkably low.
Indeed, when the surrounding protein is removed, then the
vacuum energy of the nucleotide (including the Mg2+ and its
coordination shell) is calculated to be very much higher (by 44.3
kcal mol−1) in the ADP3−·PγO3− conformation of m1 than in the
ATP4− conformation of R. This means that myosin stabilizes the
metaphosphate state of the nucleotide by more than 40 kcal mol−1.
We have recently shown how myosin combines two strategies to
achieve this stabilization (20): (i) Myosin exploits the charge
shift of 1e from the γ- to the α–β-phosphates when metaphosphate is formed (compare Fig. 2 A and B). The backbone
NH groups of residues 182–187 of the P loop and the side chain
of Lys185+ preferentially interact with the α- and β-phosphate
groups (Fig. 1A), thus contributing 52% (P-loop backbone)
and 25% (Lys185) of the overall stabilization of the m1 state,
respectively. (ii) Myosin promotes the formation of hydrate
complex between the attacking water Wa and the PγO3− metaphosphate (the distance between them is only 1.84 Å, Fig. 5A). It
does so by polarizing Wa with a H-bond to the backbone C = O
of Ser237 (Fig. 5A), which contributes 16% of further stabilization. A detailed description of the contribution from the other
protein residues to the stabilization of the m1 metaphosphate
state is given in ref. 20.
The formation of the metaphosphate intermediate is one of
the crucial features of the catalytic strategy of myosin (and of
other ATPases as well) (20). Indeed, the PγO3− metaphosphate
has a planar geometry and a single negative charge, which both
make the metaphosphate a much better target for the attack
by an OH− ion later in the reaction (Fig. 2B) than the tetrahedral and doubly negative PγO42− moiety of ATP (Fig. 2A).
This is one of the reasons for the remarkably low transition
barrier (10.3 kcal mol−1 in MEP1 and 10.7 kcal mol−1 in MEP2)
of the subsequent attack by water Wa onto the metaphosphate
(see Discussion, Catalytic Strategy I). The MEP1 and MEP2
transitions diverge after m1 (Fig. 3). The essential difference
between these two transitions is the way one of the protons of
water Wa is transferred to the γ-phosphate in the final product:
In MEP2, this transfer involves stable intermediates (e1, e2) in
which the side chain of Glu459 is protonated, whereas in MEP1
this side chain never gets stably protonated. The two transitions
are described in the next sections.
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Fig. 5. Structures along MEP2 transition (starting from m1 in Fig. 3). (A) m1 metaphosphate (ADP3− ·PγO3− ) intermediate. (B) m3 metaphosphate intermediate. (C ) m3-e1 transition state: a proton wire is formed along Wa→ Wh→Glu459. (D) e1, an ADP3− /HPγO42− intermediate with a protonated
Glu459. (E ) e2-g4 transition state: a proton wire is formed along Glu459→W3→Ser181→γ-phosphate. (F ) g4, an ADP3− /H2PγO4− product precursor with
unprotonated Glu459.
The MEP1 transition. The transfer of the proton from Wa to the
γ-phosphate proceeds via a proton wire through the helping
water Wh. This first requires reorientation of Wh to form the
proton wire: In the reactant, water Wh makes a H-bond with the
C = O of Gly457 (Fig. 1A) which is still present in m1 (Fig. 5A).
In step m1→m2, water Wh breaks this H-bond and moves (see
the white-headed arrow in Fig. 6B and Movie S1) to form a
H-bond with the side chain of Ser181. This involves the crossing
of a 10.4-kcal mol−1 energy barrier (7.7 kcal mol−1 relative to m1).
The key feature of the resulting m2 metaphosphate state is
its extreme polarization of water Wa, which is due to the two
H-bonds Wa makes with the C = O of Ser237 and with water Wh
(itself polarized by Glu459− ), Fig. 4B. This tightens the
Wa·PγO3− hydrate (the distance between Pγ and Oa is only 1.87
Å), and weakens the Oa–H-bonds of water Wa.
All this sets the stage for the hydrolysis of water Wa, its simultaneous attack on the γ-phosphorus, and proton transfer
along a proton wire Wa→Wh→Ser181→Pγ. They happen in step
m2→g1 (Fig. 6D): Because water Wh is highly polarized by the
H-bond with the -COO− side chain of Glu459, it can act as
a proton acceptor and abstract one proton from water Wa.
Water Wa breaks up (i.e., undergoes hydrolysis) into OaH− and
Kiani and Fischer
Ha+, the OaH− binding to Pγ and the Ha+ binding to Oh of water
Wh, which transiently becomes a hydronium H3Oh+. Simultaneously, the protons in the eight-membered H-bond ring
P γ. . .O a –Ha. . .Oh–Hh. . .OSer181–H. . .O–Pγ (where . . . denotes a
H-bond) switch to Pγ–Oa. . .Ha–Oh. . .Hh–OSer181. . .H–O–Pγ,
which results in the net transfer of one proton from Wa to the
γ-phosphate (see the black-headed arrows in Fig. 6D). The
corresponding transition state structure (m2–g1) is shown in
Fig. 4D and has an energy of 10.3 kcal mol−1. It is noteworthy
that the energy barrier taken relative to m2 is only 2.6 kcal mol−1
(=10.3–7.7). This is remarkably low for a reaction step involving
the breakup of a water molecule. Myosin achieves this by simultaneously presenting a good electrophile (i.e., the phosphorus of
the PγO3− metaphosphate) and a good base (i.e., the polarized
water Wh), respectively, to the OaH− and the Ha+ moieties of
water Wa. Water Wa readily breaks up into these two moieties
because of the strong polarization of Wa in the m2 state (described above). The resulting structure g1 is shown in Fig. 4E
and has an energy of −1.5 kcal mol−1.
An alternative route to go from m2 to g1 is via g3 (Fig. 3). In
that case, water Wh breaks its H-bond with Ser181 and instead
makes a H-bond with the γ-phosphate (Movie S3). This forms
PNAS | Published online July 8, 2014 | E2951
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Fig. 6. Events along the MEP1 transition of Fig. 3. The actions occurring from one panel to the next are represented as curved arrows: Arrows with a black
arrowhead indicate bond breaking and -making; white arrowheads indicate motions leading to switches in the H-bond network (i.e., without changes in the
covalent bond structure). These events can be watched in Movie S1. Values in parentheses give the energy of the state; values next to the arrows between
panels (which indicate the order of events) give the energy of the corresponding transition state. All energies (in kcal mol−1) are relative to the reactant state
R. Hydrogen bonds are indicated by broken lines. (A) state R, (B) state m1, (C) state g1, (D) m2, (E) state g2, and (F) state P.
a six-membered H-bond ring (as opposed to the eight-membered
H-bond ring described above), Pγ. . .Oa–H. . .Oh–Hh. . .O–Pγ,
which undergoes a proton wire switch to Pγ-Oa. . .H–Oh. . .Hh–O–Pγ.
The corresponding transition state structure m2-g3 is shown in
Fig. 4C and has an energy barrier of 12.6 kcal mol−1. In step g3→g1,
Ser181 reforms a H-bond with water Wh (not displayed), over a
9.1-kcal mol−1 barrier (Fig. 3). The barriers of the direct m2→g1
route and of the m2→g3→g1 route differ by only 2.6 kcal mol−1,
which is within the accuracy range of the calculations, so that
both routes may occur.
In g1, the nucleotide is already in the same ADP3−/H2PO4−
state as the final product, but the H-bond network is not yet fully
optimal. The next two steps, g1→g2 and g2→P, involve only
rearrangements of the H-bond network (Movie S1). First, the
Ser181 side chain breaks its H-bond with Oh and rotates to donate a H-bond to the γ-phosphate, which itself switches from
donating a H-bond to Ser181 to donating this H-bond to the
β-phosphate (white-headed arrows in Fig. 6C). This involves
a 0.1-kcal mol−1 barrier. The energy of the resulting structure g2
is −2.6 kcal mol−1. Finally, water Wh moves back to the position
it had in R (see the white-headed arrows in Fig. 6E), which
involves a 0.7-kcal mol−1 barrier relative to g2, thereby reforming
the H-bond with the C = O of Gly457 and reaching the final
product P.
The MEP2 transition. As mentioned, it had been proposed that after
reaching the metaphosphate state, the hydrolysis in myosin would
proceed by stably transferring a proton from water Wa onto the
E2952 | www.pnas.org/cgi/doi/10.1073/pnas.1401862111
side chain of Glu459− via the proton wire Wa→Wh→Glu459
(Fig. 1A) (18, 19). However, when this transfer is performed in
the m1 conformation, the resulting structure (e3) is unstable
(Fig. 3): The proton only remains on the Glu459 side chain with
the help of an artificial restraining force. The energy of e3 is
quite high at 9.2 kcal mol−1 (without counting the restraining
energy). This is because there is another water molecule (labeled
here W3 ) in the crystal structure (Methods) that donates a
H-bond to the Glu459 side chain (Fig. 5A). Moreover, Glu459− is
engaged in a salt bridge with Arg238+ (Fig. 1A). Altogether, this
makes the Glu459− side chain a poorer proton acceptor. Nevertheless, we found that the side chain can get stably protonated
if water W3 breaks its H-bond to Glu459− and rotates to make
a H-bond with the side chain of Thr230 (Movie S2), which itself
switches from water W3 to the backbone carbonyl of Asn233 (see
the white-headed arrows in Fig. 7A). This transition has a barrier
of 10.9 kcal mol−1. The resulting structure m3 (shown in Fig. 5B)
has an energy of 9.9 kcal mol−1. From m3, the hydrolysis of water
Wa and the concerted transfer of one proton along the proton
wire from Wa to Glu459 (black-headed arrows in Fig. 7B) has
only a small barrier of 0.8 kcal mol−1 relative to m3. This easy
breakup of water Wa results from its high polarization by Ser237
and Wh (Fig. 5B), just as described above for state m2. The
transition state, m3-e1, is shown in Fig. 5C.
This then yields a stable structure (e1, shown in Fig. 5D)
with a protonated Glu459 side chain and the nucleotide in an
ADP3− /HPO42− state. Its energy is 6.8 kcal mol−1, significantly
Kiani and Fischer
PNAS PLUS
higher than the reactant R, which is inconsistent with the experimental data (9, 10) showing that the energy of the final
product is clearly lower than the reactant. Because the product
P (in the ADP3−/H2PγO4− state, described above) does fulfill this
condition, we searched for transition routes between state e1 and
the product P. The route of lowest energy is shown on the left
side of Fig. 3. First (e1→e2), the proton on the Glu459 side chain
rotates to form a H-bond with water W3 (white-headed arrow in
Fig. 7D). This involves the crossing of a high barrier of 16.6
kcal mol−1. Then (e2→g4), a proton wire transfers one proton from
the Glu459 side chain to the γ-phosphate, by switching the
H-bond network from Glu459–H. . .O3–H3. . .OSer181–H. . .O–PγO3H2−
to Glu459−. . .H–O3. . .H3–OSer181. . .H–O–PγO3H− (Fig. 7C). The
corresponding transition state e2-g4 is shown in Fig. 5E and has
an energy of 18.5 kcal mol−1. The resulting structure g4 has the
nucleotide in the ADP3−/H2PO4− state (Fig. 5F) and an energy
of 5.5 kcal mol−1. Finally, proton reorientations (see the whiteheaded arrows in Fig. 7E) convert g4 into the final product
P over a 15.5-kcal mol−1 barrier. All steps of the second part
of the MEP2 transition (e1→e2→g4→P) involve high transition
states (with energies in a range 15.5–18.5 kcal mol−1 above R).
We tried to find alternative e1→P routes with lower energy
barriers, for example, involving proton wires via water Wh, but
without success. Therefore, unless lower e1→P pathway can
be found, a hydrolysis mechanism with intermediates having a
protonated Glu459 side chain appears unlikely. The whole
MEP2 transition is shown in Movie S2.
Kiani and Fischer
Discussion
What Are the Reactant and Product Structures? Only cocrystals of
myosin with analogs of ATP, not actual ATP, have been available so far in the postrecovery–prepower stroke conformation (in
which catalysis takes place). By using a high-level quantum
method for the ATP and the relevant active site residues
(Methods), we find a catalytically competent structure of myosin/
ATP (R) from which the hydrolysis reaction can proceed over
low-energy barriers (MEP1, Fig. 3) that are consistent with the
experimental rate. This already is a very good indication that it is
the correct reactant structure. Moreover, the energy difference
between R and the final product state P again matches the experimental reaction energy. This simultaneous consistency of
energy barrier and reaction energy is strong evidence that the
correct pair of reactant–product structures has been found here.
Note that the H-bond networks displayed in Fig. 1 are also
compelling by their perfection, every H-bond having a nearideal geometry. This is important, because the above description
of the transition pathways has made it clear that the positioning
of the protons in the active site is determinant for the catalytic
pathway.
The protonation state of ADP·Pi in the final product structure is
found to be ADP3−·H2PO4−. The most remarkable thing is the
similarity between the product (P, Fig. 1B) and the reactant
structures (R, Fig. 1A). This is achieved by the H-bond between
the β- and the γ-phosphate groups that keeps these two groups in
close contact, even though the covalent Pγ–Oβγ–Pβ linkage is
broken after the hydrolysis. This explains the much-studied reversibility of ATP hydrolysis in myosin (27–30): Isotope exchange
PNAS | Published online July 8, 2014 | E2953
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COMPUTATIONAL BIOLOGY
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Fig. 7. Events along the MEP2 transition (starting from state m1 in Fig. 3). See legend of Fig. 6 for the meaning of numbers and arrows. The events shown in
this figure can be observed in Movie S2. (A) state m1, (B) state m3, (C) state e2, (D) state e1, (E) state g4, and (F) state P.
experiments have shown that, by reversal of the hydrolysis reaction in the absence of F-actin, oxygen atoms of the solvent
become incorporated into the γ-phosphate of ATP. For this to
happen, it is necessary that the ADP and Pi products of hydrolysis remain in close contact in the product state, as is the case in
the present P structure.
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Catalytic Strategy I: Why is the Dissociative Mechanism Preferred?
The energy barrier of ATP hydrolysis in myosin calculated for
associative mechanisms (38–42 kcal mol−1) (9) has a similar
value as the barrier for uncatalyzed hydrolysis of ATP in gas
phase (40–42 kcal mol−1) (20). This means that the catalytic
machinery of myosin is definitely not laid out to hydrolyze ATP
via an associative mechanism. On the other hand and as found
previously (18, 19), the catalytic barrier via a dissociative mechanism is found here to be significantly lower (10.4 kcal mol−1).
The key to this lowering is twofold: First, a dissociative mechanism uncouples the energy barrier due to the breaking of the
Pγ–Oβγ from the barrier due to the breaking of the attacking
water into OaH− and H+. Secondly, the dissociated metaphosphate (PγO3−) is a much better target for the attack by
a negatively charged OaH− than the undissociated γ-phosphate
group of ATP (–O–PγO32−), both in terms of geometry and of
charge (Fig. 2). The PγO3− is planar, allowing a closer approach
of the OaH− than the tetrahedral –OPγO32−. Moreover, the
former is singly negative, creating less repulsion with the OaH−
than the double-negative charge of the latter.
Experimental testing for the presence of the metaphosphate
state could be envisioned by spectroscopic methods, taking advantage of the spectral differences between the tetrahedral PO4
and the planar PO3 species. Rather than in solution, where the
signals from ATP and ADP would be overwhelming, this might
be done with myosin in the crystalline state, because the hydrolysis reaction is known to be reversible as long as the protein
remains in the postrecovery–prepower stroke conformation.
Detecting the metaphosphate intermediate in kinetic experiments will be difficult because, based on the energies calculated
here, that state is ∼100 times less populated than the ATP reactant and 4,000 times less populated than the final ADP/
Pi state.
Catalytic Strategy II: What Are the Roles of the Protein Residues?
From the MEP1 transition (Fig. 6), it can be seen that myosin
facilitates the dissociative hydrolysis mechanism by using a threepronged tactic:
i) Stabilization of a metaphosphate state, in which the γ-phosphate of ATP dissociates as PγO3−.
ii) Activation of the attacking water Wa by a composite base, to
promote the breaking of water Wa into an OaH− hydroxyl
and Ha+ proton.
iii) Transfer of the abstracted proton Ha+ via a proton wire to
the HPγO42− formed by the attack of the OaH− onto
the PγO3−.
The protein residues specifically involved in each tactic can be
identified:
i) Metaphosphate stabilization. As mentioned above, Pγ–Oβγ
bond cleavage is accompanied by a charge shift of 1e from
the γ-phosphate of ATP to the β-phosphate of ADP (Fig.
2B). The protein promotes this charge shift by placing
H-bond donors of the P-loop backbone (residues 182–187)
and the side chain of Lys185+ in such a way that they interact
preferentially with the α-and β-phosphate groups (Fig. 1A),
thereby pulling negative charge toward the ADP moiety and
favoring the ADP3− + PγO3− state.
ii) Activation of the attacking water. In the standard textbook
case, a general base B− in direct contact with the attacking
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water Wa has the role of polarizing water Wa, splitting it into
OaH− and Ha+, and then accepting the abstracted proton
(BHa). Examples of P–O bond cleaving enzymes where this
is the case are EcoRV (31) and RAS-GAP (33). In myosin,
the role of the general base is shared by water Wh, the
Glu459− side chain, and the PγO3− metaphosphate itself.
Indeed, as illustrated in the transition state m2-g1 (Fig.
4D), the polarization of water Wa is performed by water
Wh, itself polarized by Glu459−. Whereas the direct acceptor
of the Ha+ proton is Wh (transiently becoming a H3O+ hydronium), the final acceptor of the abstracted proton is the
γ-phosphate (after transfer through a proton wire, Fig. 6D).
This complex situation makes it difficult to pin the role of
general base to any single residue in myosin. It is not uncommon in hydrolase enzymes that a helping water intercalates between the “general base” and the attacking water,
this then resulting in the transient formation of a hydronium
(H3O+) ion. Such a hydronium has been directly observed in
some enzymatic pockets by joint X-ray–neutron diffraction
(34), and the possible involvement of a hydronium in the
catalytic mechanism of ATP hydrolysis had been inferred
from the crystal structures of myosin (35) and kinesin (36).
The H-bond of water Wa with the backbone C = O of Ser237
on loop Switch 1 polarizes Wa further, and thereby contributes to the weakening of its Oa–H-bonds. Moreover, polarization of Glu459− also plays a role. This can be seen when
the Glu459 side chain is not treated quantum-mechanically,
but classically. In that case, the barrier of the m2-g1 step
increases slightly. Mutagenesis studies confirm that hydrolysis is abolished when neither residue of the 238/459 salt
bridge has a carboxylic acid side chain (22, 26, 37). However,
the high barriers along the MEP2 transition (Fig. 3) show
that Glu459− is not the final acceptor of the proton, which
instead gets shuttled to the γ-phosphate (see g1 in Fig. 4E).
iii) Transfer of the abstracted proton along proton wires. The
most likely proton wire that shuttles a proton away from
the Wh+ hydronium proceeds via the side chain of Ser181
(Wa→Wh→Ser181→PγO3− , Figs. 6D and 4D). However,
the point mutant Ser181Ala has been shown to have
a nearly normal ATPase rate (38). In that mutant, the
proton transfer may occur along the more direct proton
wire (Wa→Wh→PγO3− , Fig. 4C), whose energy barrier
is not significantly higher. In m2, the Ser236 side chain
is H-bonded to the PγO3− (2.66 Å, not displayed). Therefore, a proton wire involving the side chain of Ser236 (via
Wa→Ser236→PγO3− ) might be envisioned. However, this is
not likely, because it is now clear that the proton transfer from
Wa must first get through water Wh, which is the primary
proton acceptor as described above. A proton wire along
Wa→Wh→Ser236→PγO3− is just as unlikely, due to the large
distance between Wh and Ser236 (3.5 Å between the oxygen
atoms in m2) that makes a proton jump difficult. Thus, Ser236
is probably not involved in the proton transfers. To verify this,
it would be necessary to test the double mutant Ser181/
Ser236, in which the proton transfer is predicted to still be
possible along the direct proton wire (which does only involve
water Wh, Fig. 4C).
Why is Protonation of Glu459− Unlikely? When, during the MEP2
transition, one proton is stably transferred from the Wh+ hydronium to the Glu459− side chain (m3→e1, Fig. 7B), the energy of
the resulting structure e1 (Fig. 5D) is 6.8 kcal mol−1 higher than
the reactant. A similar structure reported by Nemukhin et al. was
also 3.2 kcal mol−1 higher than the reactant (18, 19). Because it is
known that the experimental product is –1.5 kcal mol−1 to –2.5
kcal mol−1 lower than the reactant (9, 10), the protonated state of
Glu459 is not the final product state.
Kiani and Fischer
Conclusions
A comprehensive description of the catalytic strategy of the
ATPase in myosin has been formulated. The role of the key
residues has been identified for each of the three tactics used by
myosin: (i) Stabilization of the charge shift occurring during the
initial dissociation of the PγO3− metaphosphate. (ii) Activation
of the attacking water by a composite base composed of a protein
side chain (Glu459), a helping water, and the γ-phosphate. (iii)
Formation of a H-bond network that allows the efficient transfer
of protons along proton wires. This description can serve as
a blueprint for the interpretation of mutational and kinetic
experiments in myosins in general: Crystal structures of myosins
from different organisms and of different myosin types having
the “Converter” domain (which carries the lever arm) in the
postrecovery–prepower stroke conformation (i.e., in the ATPase
competent stage of the Lymn–Taylor cycle) are listed in Table 1.
They all have the Switch 1 and Switch 2 loops in the same
closed–closed configuration over the P loop. An overlap of their
active site shows that these independently refined crystal structures have water molecules in the exact same positions (relative
to the surrounding protein) as do waters Wa, Wh, and W3 shown
in Fig. 1. Moreover, in all structures of Table 1, the Mg2+ ion is
in the same position and has the same coordination partners as
shown in Fig. 1. This great similarity suggests that the same
catalytic strategy is used by all myosins. Given the similarity of
their active sites, the catalytic strategy presented here will most
likely be similar in the kinesin motor (36, 39), in the F1-ATPase
(40, 41,) and in other ATPase and GTPase enzymes, (33, 42, 43,)
most of which have been shown to involve the formation of
a metaphosphate intermediate as well. Even the strategy used by
the EcoRV restriction enzyme to cleave the P–O bond in the
P–O–C phosphodiester linkage of the DNA backbone (as opposed to the P–O–P anhydride linkage in ATP) has great
similarity (31): EcoRV cleaves the P–O bond before the water
activation, thus generating a planar phosphate intermediate of
the form R–O–PO2 (equivalent to the PγO3− metaphosphate in
myosin). The nearby Asp90 then acts as general base (similarly
to the Glu459–Wh complex in myosin) and activates the
attacking water to generate an OH−, whose attack onto the
phosphorus atom completes the reaction.
For myosin to function efficiently as a motor, the ATP hydrolysis must take place at a very well-defined point along the
Lymn–Taylor motor cycle (5): just after the recovery stroke that
primes the lever arm and just before the power stroke that swings
Kiani and Fischer
Methods
The setups of the protein and of the energy function are identical to those
recently described in ref. 20 and are summarized here (see also SI Methods):
Atomic coordinates were taken from crystal structures of myosin bound to
the ATP analogs ADP·Be·F3 (32) and ADP·VO4 (12). In the so-called reactant
state, the ATP atoms were positioned as in the vanadate analog. The
γ-phosphate group of ATP was placed so as to make the same H-bonds as the
vanadate group, and water Wa was positioned where the apical oxygen of
the vanadate is located. The density functional theory method with B3LYP
functional and a 6–31G(d,p) basis set was used to treat 84 atoms in the active
site, which include the triphosphate, Mg2+ and its two coordinating waters,
waters Wa and Wh, all of the side chains shown in Fig. 1A (except Lys185 and
Asn233), and the backbone peptide group 181/182. For the calculation of
some MEP2 subpathways, water molecule W3 [water number 103 in the
Protein Data Bank (PDB) ID code 1VOM] (12) was also included in this
quantum-mechanical region. All of the remaining atoms of the myosin head
were included explicitly in the simulation, using a classical energy that was
computed with the CHARMM force field and parameters described previously. (46, 47,) The link atom approach (48) was used to treat the QM/MM
boundary. The strong polarization of some active site peptide groups by the
charge on the triphosphate moiety was accounted for by individually
−4e
up-scaling the atomic point charges of these peptide groups, as described in
detail in ref. 20. Nonuniform charge scaling (49), an implicit solvent model,
was used to account for the solvent screening effects.
The conjugate peak refinement (CPR) algorithm (50) as implemented in
CHARMM (51) was used to determine the MEPs and their transition state
structures. CPR finds the exact transition state structure and the whole
path (consisting of a series of structures, which are used to make the
frames of the molecular movie) that connects the desired reactant to the
desired product structures, thus making sure that the relevant energy
barrier is identified. The method allows determination of the mechanism
of complex reactions in proteins. CPR has been used successfully in conjunction with QM/MM energy functions, for example to study proton
PNAS | Published online July 8, 2014 | E2955
PNAS PLUS
the lever arm while myosin rebinds to the actin filament. To
ensure this precise timing in activating the ATPase function, the
closing of the Switch 2 loop is mechanically coupled to the leverarm swing (44), whereas the closing of the Switch 1 is mechanically coupled to the opening of the actin-binding cleft (45).
However, why does the ATPase only become active when both
Switch 1 and Switch 2 loops are closed onto the P loop? The
catalytic strategy presented here explains how this is achieved:
Each of the three loops carries at least one of the groups that are
essential to the ATPase function. Indeed, the groups that promote the dissociation of the γ-phosphate are mainly on the P
loop (backbone NH and Lys185), the group that directly polarizes water Wa is on Switch 1 (C = O of Ser237), and the group
that turns water Wh into a proton acceptor is on Switch 2
(Glu459 side chain). This means that the closing of any two loops
is still not sufficient to activate the ATPase. Only when all three
loops come together are all essential groups in place. In this way,
the protein ensures that ATP will not be hydrolyzed at the wrong
point in the motor cycle, which would be a wasteful loss of energy
for the cell. This nicely shows how the catalytic machinery of
an ATPase enzyme has been evolved in myosin to become the
control center that coordinates the motion of the force-generating
domains, thereby making it an efficient motor.
A structure of the final ADP·Pi product (P) that is consistent
with biochemical (reversibility of ATP hydrolysis) and kinetic
(reaction and barrier energies) data is now available. This
product structure is important for a functional understanding
of the myosin motor cycle. Indeed, the rebinding of myosin to
the actin filament and the subsequent power stroke requires
the separation of the Switch 1 loop from the P loop (45). This
opening of the active site can only occur when the nucleotide
is in the ADP·Pi state, not in the ATP state. How the state of
the nucleotide controls Switch 1–P-loop separation is still
completely unknown. Having structures now for both the ATP
and the ADP·Pi states will allow a comparative study of the
interaction forces in the active site that may explain this
control mechanism.
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Moreover, the energy barriers for shuttling the proton from
Glu459 to the γ-phosphate (i.e., the remaining of the MEP2
transition) are too high (Fig. 3). There are two reasons for that:
(i) Water W3 is strongly held by three H-bonds, donating two
to Glu459 and to Ser181 (Fig. 1A), and accepting one from
Thr230 (Fig. 5A). This stabilizes the position of the Glu459
side chain during the catalytic transition by forming a bridge
between Glu459 and Ser181 (Fig. 1A). When W 3 breaks its
H-bond to Glu459 in step m1→m3 of MEP2 (Fig. 7A), this
results in a poorer geometry of this salt bridge from states m3
to g4 (Movie S2). This is one of the reasons for the higher
energies along the MEP2. (ii) The distance between the excess
H+ (that is shuttled around the active site) and the negatively
charged HPγO42− becomes much larger during the MEP2 than
during the MEP1 transition: In MEP1 transition state m2-g1
(Fig. 4D), the Wh+ ··· HPγO42− distance is 3.6 Å (between Oh
and Pγ), whereas in MEP2 transition state e2-g4 (Fig. 5E), the
W3+ ··· HPγO42− distance is 5.1 Å (between O3 and Pγ). This
larger separation between two groups of opposite charge is
unfavorable, and is the other reason for the high transition
barriers along MEP2. All this indicates that a state with
a protonated Glu459 is unlikely to be a necessary intermediate
of the catalytic mechanism.
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transfer along proton wires (52, 53), the cleavage of P ̶O bonds (9, 31), or
isomerization reactions (54–56). Unlike molecular dynamics simulations,
the MEP shows only the motions that are essential for the reaction, but
gives no information on the time needed to get from one movie frame to
the next. MEPs and the CPR method are described in more detail in SI
Methods. The CPR criterion for deciding that a transition state has been
found was that a gradient of less than 10−2 kcal mol−1·Å−1 is obtained for
55 successive line minimizations.
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E2956 | www.pnas.org/cgi/doi/10.1073/pnas.1401862111
ACKNOWLEDGMENTS. Financial support by the German Science Foundation
through the module SFB 623, Molecular Catalysts: Structure and Functional
Design is gratefully acknowledged.
Kiani and Fischer