J. Phys. Chem. B 2007, 111, 13455-13464
13455
Phosphorylation Reaction in cAPK Protein Kinase-Free Energy Quantum Mechanical/
Molecular Mechanics Simulations
Marat Valiev,*,† Jie Yang,‡ Joseph A. Adams,§ Susan S. Taylor,‡ and John H. Weare‡
Molecular Sciences Software Group, EnVironmental Molecular Sciences Laboratory, Pacific Northwest
National Laboratory, Richland, Washington 99352, and Department of Chemistry and Biochemistry and
Department of Pharmacology, UniVersity of California San Diego, La Jolla, California 92093
ReceiVed: June 21, 2007; In Final Form: September 6, 2007
We present results of a theoretical analysis of the phosphorylation reaction in cAMP-dependent protein kinase
using a combined quantum mechanical and molecular mechanics (QM/MM) approach. Detailed analysis of
the reaction pathway is provided using a novel QM/MM implementation of the nudged elastic band method,
finite temperature fluctuations of the protein environment are taken into account using free energy calculations,
and an analysis of hydrogen bond interactions is performed on the basis of calculated frequency shifts. The
late transfer of the substrate proton to the conserved aspartate (D166), the activation free energy of 15 kcal/
mol, and the slight exothermic (-3 kcal/mol) character of the reaction are all consistent with the experimental
data. The near attack conformation of D166 in the reactant state is maintained by interactions with threonine201, asparagine-177, and most notably by a conserved water molecule serving as a strong structural link
between the primary metal ion and the D166. The secondary Mg ion acts as a Lewis acid, attacking the β-γ
bridging oxygen of ATP. This interaction, along with a strong hydrogen bond between the D166 and the
substrate, contributes to the stabilization of the transition state. Lys-168 maintains a hydrogen bond to a
transferring phosphoryl group throughout a reaction process. This interaction increases in the product state
and contributes to its stabilization.
Introduction
Protein kinases catalyze the transfer of the γ-phosphoryl group
of ATP to serine, threonine (Ser/Thr kinases), and tyrosine (Tyr
kinases) residues in target protein substrates, a key regulatory
process governing signaling pathways in eukaryote cells.1-3
There are ∼500 protein kinases encoded in the human genome,
20% of which phosphorylate tyrosine residues and the remaining, serine and threonine residues. Within classes, Ser/Thr or
Tyr kinases, the organization of the residues in the active sites
is highly conserved, implying a common catalytic mechanism.
Because of the tremendous importance of these enzymes in
signaling processes, a vast amount of experimental research1-16
has gone into trying to understand their structure-function
relationships. Extensive mutagenesis and kinetic studies have
been performed on numerous kinases to evaluate not only the
role of individual residues but also the role of larger loops and
secondary structures1 and the presence of conserved waters in
the catalytic site.12 For the cAMP-dependent protein kinase
(cAPK), it has been proposed that the catalytic reaction is
dissociative and the rate-limiting step is the release of ADP
molecule.16,17 The important role of the highly conserved
aspartate residue as a catalytic base has been suggested by its
position in the active site of cAPK. The active site of cAPK
also appears to be largely preformed with many of the key
residues already positioned for catalysis, even in the absence
of ATP and protein substrate.18
Despite important advances provided by experimental approaches, there are many unanswered questions regarding the
†
Pacific Northwest National Laboratory.
Department of Chemistry and Biochemistry, University of California
San Diego.
§ Department of Pharmacology, University of California San Diego.
‡
roles of specific residues in the active site of this enzyme.
Computational modeling based on accurate ab initio methodologies can help to address many of these questions by providing
a molecular level understanding of the reaction process. Such
studies19-22 have already clarified the role of a highly conserved
aspartate (D166) residue in the active site. Our earlier calculations19 based on density-functional theory (DFT) along with
dynamical simulation based on Car-Parrinello methodology
have shown that contrary to earlier semiempirical calculations,23,24 the reaction mechanism in cAPK is dissociative and
characterized by a late transfer of the substrate proton. Clear
theoretical evidence19 was provided that the conserved aspartate
acts as a proton acceptor late in the reaction process. These
findings were consistent with the consensus interpretation of
the data and have now been confirmed by several other
calculations.20-22
Although this initial success of theoretical calculations for
cAPK is encouraging, more questions remain regarding the
phosphoryl transfer mechanism in this enzyme and other
members of the kinase family. As with other enzymatic
systems,3,25-29 the conserved features of the active site (i.e., the
presence of conserved amino acid residues, Mg2+ metal ions,
and water molecules) are expected to play an important role in
stabilization of the transition state and timing of the phosphoryl
transfer reaction. In addition, conformational changes in the
active site facilitating the reaction30 and the focusing of the
substrate in the proper position31 may also play an important
role in catalytic mechanism.
Given the computational complexity of the problem, earlier
calculations of cAPK19,21,22 were limited in their scope and had
to resort to approximations (e.g., neglect of the solvent and
protein backbone fluctuations, limited size of the model of the
10.1021/jp074853q CCC: $37.00 © 2007 American Chemical Society
Published on Web 11/06/2007
13456 J. Phys. Chem. B, Vol. 111, No. 47, 2007
catalytic pocket, etc.) in describing the catalytic mechanism.
Further progress in this area requires a more realistic treatment
of the system that takes into account the dynamics of the native
protein environment while retaining a sufficiently large representation of the catalytic pocket to accurately capture the reactive
mechanism. Combined quantum mechanical molecular mechanics methodologies25,32-34 offer an attractive way to accomplish
this task. Although quantum mechanics and molecular mechanics (QM/MM) calculations for cAPK have previously been
reported, these studies20 were not based on a full characterization
of the reaction pathway, but rather, enforced a simplistic reaction
coordinate. In addition, finite temperature fluctuations of the
protein environment were not taken into account, and the
reaction process was described in terms of total energy differences.20 Total energy is an inappropriate metric for the description of reaction processes for complex systems with many
degrees of freedom because of the rugged nature of the potential
energy landscape.
In the study reported here, a more comprehensive approach
is taken using extensive functionality provided by the recently
developed QM/MM module35 in the NWChem software package.36 The protein environment is fully represented in the
calculations of the reaction pathway using a novel QM/MM
implementation of the nudged elastic band (NEB) method. The
resulting unbiased optimized reaction pathway offers unique
insights into the detailed rearrangements of the active site during
the reaction process. Our method of calculation also takes into
account finite temperature fluctuations of the protein environment by means of free energy simulations along the reaction
coordinate.
The predictions from the calculations presented in this work
expand and differ from earlier studies. We provide the first
reliable theoretical estimate of the activation free energy and
the reaction pathway for the phosphorylation process. In contrast
to prior QM/MM simulations, we find an exothermic phosphoryl
group transfer scheme, which is in line with experimental
findings.37 New insights into the roles of the active site residues
are obtained, including the roles of the metal ions and the
conserved waters.
The approach used in this work leads to a much more realistic
and reliable interpretation of the rich database of experimental
measurements of the catalytic mechanism of cAPK. Therefore,
it provides an excellent reference point for understanding the
catalytic mechanism within the larger kinase family and for
dissociative phosphoryl transfer mechanisms in general.
Setup and Computational Methodology
The starting structure for cAPK kinase was taken from X-ray
data11 (1ATP) as published in the PDB data archive. This is a
ternary complex of kinase with ATP-Mg and the pseudo
substrate inhibitory peptide IP20, composed of residues 5-24
from PKI, an in vivo cAPK inhibitor. To mimic an active
substrate peptide SP20, the inhibitor substrate (PKI) in the
original X-ray structure was modified via P and P-1 site
mutations to Ser and Ala, respectively. On the basis of the
analysis of local hydrogen-bonding environment the protonation
states of histidine, residues were chosen as follows: HIP87,
HID62, HID68, HID260, HIE131, HIE142, HIE158, HIE294,
and HIE(P+2). In this notation, HIE and HID denotes the singly
protonated form at the epsilon position or delta position,
respectively; HIP denotes the doubly protonated form at both
epsilon and delta positions. The structure was solvated in a cubic
box (∼81 Å) of SPC/E waters. Three Cl- counter-ions were
Valiev et al.
added to the system to neutralize the charge. The overall
structure contained 5904 solute and 48 387 solvent particles.
Prior to QM/MM simulations, the entire system was equilibrated
to room temperature via annealing with 40 ps of molecular
dynamics simulation.
QM/MM calculations were performed using the recently
developed QM/MM module in NWChem.35 The quantum (QM)
region consisted of a full representation of the ATP molecule,
two Mg2+ ions, three coordinating waters, and the side chains
of the aspartate-166 (D166), lysine-168 (K168), and substrate
serine residues (a total of 75 atoms). Bonds crossing into the
MM region were capped with hydrogen link atoms. The solution
to the Schrödinger equation for the quantum mechanical region
was based on a local basis implementation of density functional
theory with the B3LYP approximation for the exchangecorrelation functional. Wavefunctions were expanded using the
Ahlrich’s pVDZ basis set.38 The remainder of the protein (MM
region) was described at the molecular mechanics level using
an Amber-type force field.39
Structural Optimizations. Structural optimizations of reactant and product states were performed using the multiregion
optimization algorithm as implemented in the NWChem QM/
MM module. Similar to the iterative procedure suggested by
Zhang et al.,40 this method performs a sequence of alternating
optimization cycles of the QM and MM regions. During the
MM region optimization, the electrostatic field from the QM
region was represented by a set of effective charges in lieu of
resolving the Schrödinger equation at each step, greatly increasing the efficiency. The effective charges were recalculated in
each optimization cycle by fitting the electrostatic field outside
QM region to that produced by the full electron density
representation. To ensure full relaxation of the protein environment, structural optimization was always performed in combination with molecular dynamics equilibrations of the MM region.
During this process, the QM region was represented by effective
charges, which were recalculated periodically.
The initial structure of the reactant state was taken from the
modified X-ray structure of the ternary complex of cAPK as
described above. After the first optimization pass of the full
system, dynamical equilibration of the MM region was performed at room temperature (298.15 K) for ∼35 ps. This was
followed by another round of optimizations of the full system.
The structural parameters for the optimized reactant state are
shown in Table 1 and Figure 2a.
An initial guess for the product state was obtained by starting
with the optimized structure of the reactant state and performing
a sequence of constrained optimizations, wherein harmonic
restraints on Pγ-OpSer and OD166-OpSer distances were imposed
to drive the system over the reaction barrier to the product state
while allowing the MM system (initially equilibrated to the
reactant structure) to adjust to the changes. When a reasonable
estimate of the product structure was obtained, the constraints
were lifted, and the product state was optimized using a
sequence of optimizations and dynamical relaxation steps similar
to those discussed above for the optimization of the reactant
state. The resulting structural data for the optimized product
state is shown in Table 1 and in Figure 2c.
NEB Reaction Pathway. To obtain an unbiased view of the
reactive process, we have used a new implementation of the
NEB approach41 within the NWChem QM/MM module. The
NEB method optimizes the trial reaction pathway between two
fixed points (e.g., reactant and product states) represented by
replicas of the molecular system connected by harmonic spring
forces. In our application, we assumed that the reaction
Phosphorylation Reaction in cAPK Protein
J. Phys. Chem. B, Vol. 111, No. 47, 2007 13457
TABLE 1: Compilation of Structural Parameters of Reactant, Product, and Transition States of PKA from Experimental
Measurements and Computations (This Work)
X-ray datae
structures calculated in this work
distancea
reactant (inhibitor)b
reactant (optimized)c
reactant (dynamical)d
transition
product
1ATP
1L3R
Pγ-Oβ
Pγ-pSerf
OH(pSer)
1.73
n/a
n/a
1.74
3.20
0.98
1.81
2.96
0.99
2.41
2.23
1.09
2.85
1.74
1.75
1.62
3.7
n/a
2.31
2.27
n/a
D166-T201
D166-N171
D166-pSer(O)
D166-pSer(H)
D166-w1
2.77
2.76
n/a
n/a
2.57
2.83
2.88
2.74
1.83
2.57
2.75
3.05
2.67
1.74
2.62
2.72
3.26
2.56
1.48
2.73
2.74
3.50
2.71
1.01
2.84
2.78
2.91
n/a
n/a
2.43
2.76
3.29
2.48
n/a
2.47
K168-T201
K168-Oγ
2.99
2.6
3.01
2.61
3.02
2.62
3.07
2.58
3.04
2.61
3.04
2.44
2.72
n/a
Mg1-Oγ
Mg1-Oβ
Mg1-w1
Mg1-w2
Mg1-D184-1
Mg1-D184-2
2.02
2.03
2.02
2.08
2.01
2.17
2.01
2.03
2.03
2.09
2.01
2.19
2.01
2.02
2.03
2.08
2.01
2.16
2.01
1.97
2.07
2.06
1.98
2.23
2.00
1.98
2.10
2.11
2.04
2.12
2.04
2.18
1.85
2.15
2.36
2.19
n/a
2.13
2.36
2.12
2.32
2.21
Mg2-Obγ
Mg2-OR
Mg2-Oγ
Mg2-N171
Mg2-w3
Mg2-D184
2.41
1.95
2.01
2.07
2.07
2.0
2.48
1.94
1.97
2.06
2.05
2.02
2.35
1.94
1.97
2.10
2.06
2.02
2.09
1.94
2.02
2.35
2.04
1.97
1.99
1.99
2.04
2.52
2.09
2.02
3.00
1.99
2.21
2.09
2.08
2.14
2.06
1.88
n/a
2.11
2.18
2.00
a pSer denotes p-site serine residue. b Reactant (inhibitor) column denotes structure of optimized reactant complex in the presence of inhibitor
substrate. c Reactant (optimized) column denotes structure of optimized reactant complex in the presence of active substrate. d Reactant (dynamics)
column denotes structure of reactant complex in the presence of active substrate at finite temperature as obtained from free energy simulations.
e The experimental X-ray structures were taken from Protein Data Bank (PDB ID 1ATP and 1L3R). f Pγ-pSer distance was estimated on the basis
of AlF3 positions in the 1L3R structure, Cb position of p-site Ala in the inhibitor complex.
Figure 1. Free energy cycle.
coordinate is dominated by movements in the QM region. The
NEB energy functional was, therefore, taken to be
ENB )
k|Rni - Rn-1
|2
∑n E[{Rni }, {RnM}, ψ] + ∑
i
i,n
(1)
In this equation, lower and upper case subscripts signify the
coordinates of QM and MM regions, respectively, and the n
index represents summation over replicas. The initial step in
our NEB approach involved generation of the initial trial
pathway, as well the determination of effective charges for each
of the resulting replicas of the QM region. After this initialization, the self-consistent cycle was carried out, which consisted
of (i) optimization of the MM region in the field of effective
charge representation of the QM region, (ii) calculation of new
forces and effective charges for the QM region through the
solution of the Schrödinger equation, and (iii) evolution of the
QM region according to the NEB methodology.41,42 The cycle
was repeated until convergence was achieved.
In the NEB calculations for this work, a total of 10 beads/
replicas were used for the pathway representation. The initial
guess for the pathway was generated by linear interpolation
between optimized reactant and product states. To ensure full
relaxation of the protein environment, the first NEB optimization
pass was followed by 20 ps of molecular dynamics equilibration
at room temperature of the MM region for each of the 8
intermediate beads along the pathway. After this equilibration,
another round of NEB optimization was performed.
Free Energy Calculations. The free energy profile over the
NEB optimized pathway was obtained by calculating free energy
differences between the consecutive NEB beads. The approach
that we used is similar to the multilevel perturbation methodology43 used previously for reactions in solutions. To efficiently
calculate the free energy change between two QM configurations, an intermediate effective charge representation of the QM
region (Hmm/mm) was introduced, leading to the free energy cycle
shown in Figure 1. As a result, the free energy difference
between two consecutive NEB beads (A and B), characterized
by coordinates RA, RB, and effective charges QA, QB, can be
represented as (see Figure 1)
∆FAB ) ∆FAA - ∆FBB + ∆Fmm
AB
(2)
The first two terms are the free energy differences for changing
the description of the QM region from the quantum mechanical
to the effective charge representation with fixed QM coordinates
(RA or RB) and effective charges (QA, QB). In the spirit of the
QM + MM44 or QM - FEP40 approaches, these can be
approximated as internal energies. For example,
∆FAA ≈ EAqm ) 1
2
∫
1
〈ψRA|∇2|ψRA〉 +
∑
2 R
FA(r)FA(r′)
|r - r′|
∑i ∫
dr dr′ + Exc[FA(r)] +
ZiF(r)
|RAi - r|
dr +
1
∑
2 i*j
ZiZj
|RAi - RAj |
(3)
13458 J. Phys. Chem. B, Vol. 111, No. 47, 2007
Valiev et al.
Figure 3. Analysis of hydrogen bond interactions in cAPK.
Figure 4. Calculated QM/MM free energy profile for the phosphorylation reaction in cAPK.
based on the linear mapping between the A and B configurations:
R(λ) ) (1 - λ)RA + λRB
Q(λ) ) (1 - λ)QA + λQB
(7)
Using the trapezoidal rule, ∆Fmm
AB can then be approximated by
Figure 2. Optimized structures of reactant, transition, and product states
in cAPK. See reactant (optimized) column in Table 1.
The third term, ∆Fmm
AB , represents the free energy difference for
changing the coordinates of the QM region from QA, RA to
QB, RB configurations within the effective charge description
of the QM region.
Ẽ(R , Q , RM) )
A
A
∑
i,M
QMQAi
+
|RM - RAi |
Umm ({RAi },
{RM}) (4)
This quantity was calculated using thermodynamic integration.
∆Fmm
AB )
∫01
∂F(λ)
dλ ≡
∂λ
∫01 F′(λ) dλ
(5)
Here, we have defined the λ-dependent free energy function
F(λ) ) -
1
ln
β
∫ e-βẼ(R(λ),Q(λ),R ) dRM
M
(6)
∆Fmm
AB ≈ 0.5(F′(0) + F′(1))
(8)
The derivatives were calculated using the finite difference
method:
F′(λ) )
(F(λ + δ) - F(λ)) + (F(λ) - F(λ - δ))
2δ
F(λ ( δ) - F(λ) )
1
- ln〈e-βẼ(R(λ(δ),Q(λ(δ),RM)+βẼ(R(λ),Q(λ),RM)〉λ (9)
β
The above procedure was applied to all the consecutive pairs
of NEB beads. The coordinates RA, RB, and effective charges
QA, QB were generated during the NEB optimization procedure
described previously. After a 5 ps pre-equilibration step, the
statistical data was collected over 12 ps of molecular dynamics
simulation at constant temperature (T ) 298.15 K) at both
λ ) 0 and λ ) 1 ends of the interval with δ ) 0.1. This
simulation was performed for each pair of consecutive beads
in the NEB pathway. The resulting free energy profile is shown
in Figure 4.
Phosphorylation Reaction in cAPK Protein
J. Phys. Chem. B, Vol. 111, No. 47, 2007 13459
Figure 5. Evolution of key structural parameters of the cAPK active site during the reaction process.
Results
The Reactant State. The reactant state of cAPK has been
studied extensively in the course of several experimental
investigations,15,45-49 providing a rich source of information
regarding the structure of the active site and the surrounding
protein environment. Given the high catalytic activity of the
enzyme, various inactive structural analogs of substrate, nucleotide, or both were utilized11,14,15,17,46-49 to trap the reactant
complex. The results of the calculations presented below refer
to the native reactant complex of cAPK (see Table 1) and
provide a unique view of the active site interactions prior to
the phosphorylation reaction.
A key structural quantity in the active site of cAPK is the
distance between the γ-phosphorus of ATP and the hydroxyl
oxygen of the substrate serine (see Pγ-pSer entry in Table 1),
which was found to be 3.2 Å in our calculations. The knowledge
of this distance is important because it allows us to make some
predictions3 regarding the fractional associativity of the transition
state. Assuming that only the PO3 group moves from reactant
to a symmetric transition state, the analysis suggested by
Mildvan3 predicts a nearly dissociative (94%) reaction process.
As will be shown in a later section, this simple estimate is in
good agreement with the calculations of the transition state
structure described in this work. The experimental measurements
allow only indirect determination of the γ-phosphate-to-substrate
distance, which leads to significant uncertainties regarding its
exact value. The estimates from NMR measurements47 and the
superposition analysis of X-ray data46,48 are 5.3 and 2.7 Å,
respectively. One potential source of these deviations may come
from the perturbation of the substrate serine side chain position
due to different nucleotide replacements: ADP48 or AMPPNP46 in the X-ray data comparison and Co3+(NH3)4ATP in
the NMR measurements. Indeed, our results indicate (see
discussion later) that the side chain orientation of the substrate
serine is quite sensitive to the position of the γ-phosphoryl group
and changes significantly during the reaction process.
13460 J. Phys. Chem. B, Vol. 111, No. 47, 2007
In the optimized structure of the reactant complex, the ATP
is oriented in the near-attack conformation31 with respect to
substrate serine. The angle formed by the Pγ-Oβ bond of the
ATP and the substrate serine oxygen is close to linear (∠PγOβOpSer ) 160 °), facilitating the inline phosphoryl group transfer
mechanism observed in cAPK. The length of the ATP Pγ-Oβ
bond, 1.74 Å, differs from the X-ray refinement estimates of
1.6211 and 1.65 Å,15 but it is consistent with Pauling’s estimated
value of 1.73 Å,3,50 as well as our original model studies19 and
the subsequent calculations20-22 of other groups. To determine
if lengthening of the Pγ-Oβ bond was induced by the presence
of active substrate, we performed an additional calculation of
the kinase-inhibitor complex. This calculation yielded nearly
the same result (1.73 Å). This indicates that, at least within the
limits of DFT description, the “natural” Pγ-Oβ bond distance
in the ATP-Mg complex in the kinase active site is around
1.73-1.74 Å and suggests that the X-ray data may need
reinterpretation. We must note that there is a significant amount
of uncertainty associated with the restrained refinement procedure utilized in the X-ray measurements on kinase enzyme and
proteins in general. Because the refinement penalizes deviation
from “standard” bond lengths (such as 1.62 A for the PO bond),
obtained as an average of diverse range of compounds, it cannot
fully account for the fine difference in the actual environment.
The average experimental PO bond length is indeed around
1.611 Å, but the actual range spans from 1.512 to 1.742 Å.51 In
any case, these fine differences cannot be distinguished in
standard X-ray measurements. Indeed, the X-ray refinement of
kinase protein works well with both 1.62 and 1.74 Å “standard”
PO bond values. The level of quantum mechanical description
based on DFT is known to produce bond lengths within a 0.010.03 Å error bar. The extensive analysis of DFT accuracy for
ATP compounds has been published recently by Akola and
Jones.52 These authors indicate that the presence of divalent
metal cations (such as Mg) has a tendency to increase the
terminal PO bond length to 1.74 Å, which is what we observe
in the kinase case.
The substrate hydroxyl group is located in close proximity
to the D166 residue. D166 is universally conserved across the
entire kinase family and plays an important role in the catalytic
mechanism of cAPK.19 Its mutation to Ala in yeast enzyme
results in significant loss of catalytic activity,53 with kcat ) 0.05
(∼0.3% of the wild type value). Similar effects are also observed
in mutational studies of the phosphorylase kinase.54 In the
optimized reactant state complex, the distance between the D166
and the substrate hydroxyl is 2.74 Å, which is in good agreement
with the X-ray measurements.48 Despite the short distance, the
interaction between the two residues appears to be small. We
take as a measure of this interaction the shift in the OH bond
stretching frequency of the substrate serine, as compared to its
gas-phase value. Such shifts have been shown to provide a
semiquantitative measure of hydrogen bond strength.55 We find
only a modest 7% change in HOSer stretching frequency, which
indicates a weak hydrogen bond. This is consistent with the
result that D166 does not abstract the substrate proton early in
the reaction process. The weak nature of the interaction between
the D166 and the substrate serine highlights the importance of
other elements of the active site, contributing to stabilization
of the D166 in the near-attack conformation31 with respect to
the substrate serine hydroxyl group at the beginning of the
reaction process. Indeed, the structural analysis of optimized
reactant structure (see Figure 2a) shows that the D166 interacts
with a number of residues in the active site: threonine (T201),
asparagine (N171), and a conserved water molecule. T201
Valiev et al.
coordinates the vacant side of the carboxylic group of the D166
with a hydrogen bond distance of 2.83 Å and is conserved across
the Ser/Thr kinase family. An interesting feature15 of the T201
and D166 interaction is that it is observed only in substratebound complexes of cAPK, raising the possibility that this
interaction may play a role in the substrate recognition process.15
The proton accepting side of D166 is coordinated by a conserved
asparagine residue (N171) and the conserved water molecule
(W1) with hydrogen bond distances 2.88 and 2.57 Å, respectively. The interaction between D166 and N171 was observed
previously in the X-ray measurements of the inhibitor ternary
complex of cAPK,49 and the experimental distance of 2.7 Å is
in good agreement with a calculated value of 2.88 Å. The
interaction between D166 and conserved water (residue id 447
in 1ATP) has not been given much attention, yet it is prominent
in the kinase X-ray structures.15,17,48,49,54 Our calculations
indicate that this is a strong hydrogen bond interaction characterized by a significant shift of OH water bond frequency of
20% (see Figure 3). The reason for such strong interaction comes
from the direct coordination of the same water molecule by the
essential Mg1 ion, which through strong polarization activates
the hydrogen bond donor properties of the water molecule.
K168 is another residue that lies in close proximity to the
phosphoryl transfer site. Its precise role in the catalytic process
is still unclear. Similar to T201, it is conserved across the Ser/
Thr kinase family (it is replaced by Arg in tyrosine kinases).
Its mutation to Ala reduces kcat/Km by ∼3 orders of magnitude.53
In the reactant state, K168 is in contact with several key residues
in the active site: the γ-phosphoryl group (2.61A), substrate
hydroxyl group (2.74 Å), and T201 (3.01 Å). The interaction
with the oxygen on the γ-phosphoryl group is relatively strong,
characterized by a significant shift in NH bond stretching
frequency of 14%. Its interaction with the hydroxyl group of
the serine substrate and T201 seems to be weak; we have found
only 6% shift in the stretching frequency of the NH bond that
participates in these interactions.
There are two metal ions in the active site of cAPK. The
first metal ion (Mg1) is essential for the catalytic activity of
cAPK. The results from our calculations correlate well with the
observed X-ray data,15,48,49 indicating an octahedral coordination
shell of Mg1 consisting of D184 (two contacts), β- and γ-groups
of ATP, and two conserved water molecules. One of these
waters, as mentioned above, forms an extremely strong hydrogen
bond with the essential D166 residue, which highlights the
importance of the Mg1 metal ion as a structural anchor that
facilitates the proper orientation of the ATP with respect to the
substrate hydroxyl group.
As indicated by X-ray49 and kinetic measurements,1,37,56,57
the second metal ion (Mg2) is weakly bound, which correlates
well with its incomplete coordination in the reactant state, as
observed in our calculations as well as experimental X-ray
data.49 Its 5-fold coordination sphere includes D184, the R- and
γ-groups of ATP, N171, and a water molecule. The incomplete
coordination of Mg2 may be advantageous as it provides the
mobility required for the Lewis acid attack of Mg2 on the β-γ
bridging oxygen during the phosphoryl transfer step.
In the discussion presented so far, we have referred to the
optimized structure of the reactant state. This structure does not
include finite temperature protein fluctuations under physiological conditions. The effects of these fluctuations on the structure
of the reactant state in cAPK can be inferred from the
examination of the calculated free energy curve shown in Figure
4 and the finite temperature structure as given in Table 1. The
free energy minimum (corresponding to the reactant complex
Phosphorylation Reaction in cAPK Protein
at room temperature) is different from that of the optimized
reactant complex (the first point on the free energy curve). We
observe a distance reduction between the γ-phosphate group
and substrate (from 3.2 to 2.96 Å). This reduction comes
primarily from the rotation of the serine side chain toward ATP
with a small stretch in PO bond of ATP. A similar motion was
observed in our first principle molecular dynamics simulations19
of the phosphorylation reaction in cAPK. The overall changes
in the two structures indicate that the finite temperature
fluctuations of the protein environment push the reactant
complex along the reaction coordinate toward the product state
complex.
The Transition State. Knowledge of the transition state is
central to the understanding of the catalytic activity of an
enzyme.25 The structure of this state offers insight into the nature
of the reaction mechanism, and its free energy with respect to
the reactant complex can be directly related to the reaction rate.25
Due to its inherent instability, only indirect information about
the transition state structures can be obtained from experimental
studies. These include structural characterizations of transition
state analogs, which are stable complexes designed to mimic
real transition state structure. In the case of cAPK, such a
transition state mimic is given by the substrate ternary complex
in which the γ-phosphoryl group is replaced by AlF3.17
Structural data for this complex is given in Table 1.
Direct characterization of the cAPK transition state complex
and its approach from the reactant state using accurate computational techniques provides detailed molecular information
about the transition state complex and timings of various
structural and bonding changes along the reaction pathway
leading to the transition state. Computational characterization
of the transition state complex is a difficult problem requiring
an accurate description of the electron structure, stable procedures for reaction pathways determination, and consideration
of finite temperature effects. All these components are essential
for a proper description and have not been fully addressed in
the prior QM/MM computational investigations of cAPK.20
In contrast to the prior QM/MM investigation,20 our calculations made no assumptions about the reaction coordinate;
instead, the reaction pathway was determined using the NEB
approach that utilized only the information about the stable
reactant and product states. The calculated free energy profile
(see Figure 4) along the full reaction pathway provided clear
and unambiguous identification of the transition state as a
highest free energy point located 15 kcal/mol higher with respect
to the reactant state. Normal-mode analysis58 of the Hessian
(second derivative) matrix calculated numerically within the
QM/MM description of the system confirmed the presence of
a single negative frequency mode of -170 cm-1.
The major structural changes occurring during the passage
from the reactant to the transition state involve the motion of
the γ-phosphoryl group of ATP, the secondary Mg2 ion, and
side chains of substrate serine and D166. Other than these, there
is little rearrangement of the protein environment; the root-meansquare (rms) deviation between the reactant and transition state
structures (not including ATP and solvent) is only 0.02 Å.
The evolution of the γ-phosphoryl group position with respect
to the β-γ-bridging oxygen and substrate hydroxyl oxygen is
illustrated in Figure 5A. This motion constitutes the major part
of the reaction coordinate between the reactant and the transition
state and is consistent with the nearly in-line mechanism. Similar
to our prior gas-phase calculations,19 in the transition state, the
γ-phosphoryl group adopts a nearly planar configuration located
approximately midway between the ADP and the substrate
J. Phys. Chem. B, Vol. 111, No. 47, 2007 13461
serine. This structure is similar to that observed in the X-ray
structure17 of the transition state mimic with the planar AlF3
(analog of PO3-) group with distances of 2.31 and 2.27 Å to
the ADP and substrate, respectively (87% dissociative with
respect to entering group59). In our calculations, the PO3 group
occupies a slightly asymmetrical position in the transition state
complex. It is pushed closer to the entering substrate hydroxyl
group (2.23 Å) than the leaving ADP group (2.41 Å), which is
opposite to our previous gas phase estimates (2.32 and 2.14
Å). This indicates that the presence and fluctuations of the
protein environment pushes the transition state complex further
along the reaction coordinate. This is consistent with a trend
observed for the finite temperature reactant state. The calculated
Pauling bond orders59 are 0.07 and 0.15 for distances to the
ADP and substrate, respectively. This means that while the
leaving ADP group has lost 93% of its bond to the γ-phosphoryl
group, the entering substrate group acquired only 15% of a bond,
which points to a primarily dissociative reaction mechanism.3
The movement of the γ-phosphoryl group is accompanied
by the simultaneous rotation of the serine substrate side chain
(see the CA-CB-OG-HG dihedral angle evolution in Figure
5C), resulting in the reduction of the total distance between the
β-γ-bridging oxygen of ATP and the substrate serine oxygen
(see Figure 5A). The latter distance contracts by a total of 0.32
Å during the reaction process, with the bulk of the change (0.29
Å) occurring by the time the transition state is reached.
The movement of the secondary Mg2 ion toward the β-γbridging oxygen of the ATP (see Figure 5D) is another important
structural change that accompanies the reaction process. As was
discussed earlier, the coordination of this metal ion is incomplete
(5-fold) in the reactant state, allowing it to attack the oxygen
connecting the β and γ phosphoryl groups of the ATP. This
movement activates the cleavage of this bond stabilizing the
leaving ADP group and the formation of a highly electrophilic
metaphosphate PO3 group in the transition state by screening
the negative charge accumulated on the β-γ-bridging oxygen.
The potential importance of Mg2-Oβ interaction in stabilizing
the leaving group was previously highlighted by Admiraal and
Hershlag27 in the their analysis of homogeneous hydrolysis of
ATP in solution. In the transition state, the secondary Mg2 ion
is 2.09 Å away from the β-γ-bridging oxygen (compare to
2.41 Å in the reactant state). This agrees well with the 2.06 Å
distance observed in the experimental transition state mimic
structure (1L3R).17 The coordination of the primary metal ion
changes little in moving from the reactant to the transition state.
The role of D166 in the reaction mechanism has been the
subject of considerable debate, and its close proximity to the
substrate serine group had in the past raised suggestions that it
might abstract the substrate proton early in the reaction process.
Consistent with our previous gas-phase results, this behavior
was not observed in this work. As illustrated in Figure 5B, the
substrate OH bond changes little as the system evolves from
the reactant state. However, we observe a considerable reduction
in distance between the substrate proton and the D166. The latter
change is mostly due to the rotation of the D166 side chain
along the CB-CG axis (see evolution of χ2, CA-CB-CGOD1 dihedral angle, in Figure 5C). Similar motion was also
observed in the X-ray measurements of the transition state mimic
1L3R of cAPK17, where an ∼20° change in the χ2 angle of the
D166 was observed, as compared to the ATP/IP20 ternary
complex (1ATP). As a result of this coordinate change, there
is a pronounced shortening in the distance between the D166
and the substrate oxygen, which reaches a minimum (2.56 Å)
in the transition state (see Figure 5F). The close proximity
between the D166 and the substrate hydroxyl group results in
13462 J. Phys. Chem. B, Vol. 111, No. 47, 2007
the 49% shift in the OHSer bond stretching frequency in the
transition state. At this point in the reaction process, the length
of the substrate OH bond reaches 1.09 Å (see Table 1 and Figure
5B), corresponding to a bond order of 68%.59 All this is
indicative of a formation of a low-barrier hydrogen bond
between the D166 and the substrate hydroxyl group, which
contributes to the stabilization of the transition state.55,60-62 This
point in the reaction process marks the beginning of the substrate
proton transfer, with the OH bond at 1.09 Å (bond order of
68%).59 This increases the nucleophilicity of the substrate
oxygen preparing an attack on the electrophilic Pγ. This
describes the role of D166 as a concerted catalytic base.63 The
onset of strong interactions between the D166 and the substrate
hydroxyl group disrupts interactions with the conserved water
and N171 (see Figure 5E), which coordinate the same sidechain oxygen on D166. The OH bond stretching frequency of
W1 decreases to 11% (as compared to 20% in the reactant state),
and contact with N171 is essentially lost (3.26 Å, as compared
to 2.86 in the reactant state). As T201 donates an H-bond to
the opposite side chain oxygen of the D166, interaction with
this residue persists in the transition state (see Table 1).
The distance between the K168 and the γ-phosphoryl group
of the ATP in the transition state remains nearly unchanged in
moving to the reactant state. The calculated NH bond stretching
frequency of 17% is slightly larger than the 14% in the reactant
state (see Figure 3), which is consistent with the slight increase
in the N-H-O bond angle to 149° (from 145°). The distances
of Lys-168 to the substrate hydroxyl group and T201 increase
to 3.0 and 3.07 Å, and the shift in the corresponding NH bond
stretching frequency drops to 3%. On the basis of this information, it is unlikely that K168 plays a direct role in transition
state stabilization, which comes from the strong hydrogen bond
interactions with the D166 and the substrate and the Lewis acid
attack of the secondary Mg2 ion.
Product State. In the product state, the substrate serine
residue is phosphorylated, and the substrate proton is transferred
to the D166 residue, as illustrated in Figure 2c. Unlike prior
QM/MM simulations,20 we find a slightly exothermic reaction
process with a free energy difference between the reactant and
product state of -3 kcal/mol. This conclusion is now in good
agreement with experimental measurements.37
The OH bond on the serine substrate, which remained nearly
intact from the reaction to the transition state complex, is rapidly
broken as the system approaches the product state. The late
transfer of the substrate proton is consistent with our previous
first principles molecular dynamics simulations and experimental
pH data.9,64 As the proton-transfer event takes place, the D166
residue moves away from the substrate hydroxyl oxygen, with
a final distance of 2.7 Å in the product state. Given the 18%
shift in the D166 OH bond stretching frequency, its hydrogen
bond interaction with the now phosphorylated substrate oxygen
decreases significantly as compared to the transition state. It is,
however, stronger than that in the reactant state. As a result of
protonation, the interaction between the carboxylate oxygen of
the D166 and the conserved water molecule is substantially
weakened (2.84 Å). Our calculations show an 11% shift in the
OH stretching frequency in water as compared to 20% in the
reactant state (see Figure 3). The interaction between the D166
and T201, which coordinates the unprotonated side of the
carboxylate group, remains strong at 2.67 Å.
The transferred γ-phosphoryl group continues to interact with
K168 in the product state. The distance to the oxygen on the
γ-phosphoryl group is 2.6 Å, which is similar to the values
observed in the reactant and transition states. The hydrogen bond
Valiev et al.
angle is 154°. The strength of this hydrogen bond increases
significantly in the product state. We calculated the shift in the
NH bond stretching frequency shift of 25% in the product state
(compare to 14 and 17% in the reactant and transition states,
respectively). The increased strength of the interaction between
K168 and the γ-phosphoryl group was also evident in our prior
first principles molecular dynamics simulations that showed a
rapid proton exchange between the two groups.
The secondary Mg2 ion continues its approach to the β-γ
bridging oxygen of the ATP with a final distance of 1.99 Å in
the product state. It continues to be 5-fold coordinated due to
its loss of interaction with the N171 residue (see Figure 2c).
Conclusion
The rapid transfer of the γ-phosphoryl group of ATP to serine,
threonine, or tyrosine residues of a target protein carried out
by the kinase family of enzymes is arguably the most important
post-translational protein modification carried out in eukaryote
cells. This process has been the subject of intensive experimental
investigations,1-16 which has significantly advanced the understanding of the structural and functional properties of kinase
enzymes. Further progress in this area can greatly benefit from
more direct and detailed molecular level information that can
be obtained from computational modeling. Several key requirements have to be met before such computational studies can
serve as reliable source information about the catalytic process
in kinase enzymes. Bond breaking and formation, inherent to
any enzymatic reaction, should be described by an adequate
level of quantum mechanical theory. In our prior work,19 we
have demonstrated that in the case of the phosphorylation
reaction in cAPK, such a quantum mechanical description should
be at least at the level of density functional theory. The protein
environment and its finite temperature fluctuations should be
properly reflected in the calculation, because they can have an
important implication for the reaction mechanism and its overall
energetics. The many degrees of freedom brought in by the
presence the protein environment significantly complicate the
computational analysis. For example, the total energy description
of the reaction process is no longer adequate and has to be
replaced by free energy simulations providing a statistical
average over many protein conformations. Standard algorithms
for transition states and reaction pathways developed for small
systems have to be modified to account for the complex potential
energy surface of the large protein system. All of these issues
are important for a reliable and accurate theoretical description
of the phosphorylation process in kinase proteins and have not
yet been addressed in prior computational studies6,10,32 of these
systems.
In this work, the phosphorylation reaction in cAPK was
studied using a combination of quantum mechanical and
molecular mechanics methodologies. A large active site region
around the phosphoryl transfer region process was treated at
the DFT/B3LYP level of theory, while the rest of the system
was described using classical molecular mechanics. This strategy
provided an accurate description of electronic structure effects
during the reaction process and retains the constraints imposed
by the surrounding protein matrix. The structural optimizations
of stable reactant and product complexes were combined with
dynamical simulations to ensure complete relaxation of the
protein environment. Unlike prior QM/MM investigations,20 no
assumptions were made regarding the reaction coordinate;
instead, the full reaction pathway was determined selfconsistently using novel implementation of the NEB QM/MM
approach. Such reaction pathway calculations have not yet been
Phosphorylation Reaction in cAPK Protein
performed for a kinase-mediated phosphorylation process in the
native protein environment and offer unique insight into the
reaction mechanism. Improving upon prior computational studies,6,10,32 our calculations also took into account dynamical
fluctuations of the protein environment at finite temperature by
means of double perturbation free energy approach. The free
energy analysis offers a more realistic description of the reaction
process and provides a reliable estimate of activation free energy
that can be compared to experimental kinetic data.
In agreement with prior experimental observations, we found
the reactant state complex of cAPK to be largely preformed for
efficient transfer of the phosphoryl group. The tight network
of interactions (see Table 1 and Figure 2a) in the active site
ensures near-attack conformations of the residues important to
the reaction process. The calculated free energy profile provides
a unique identification of the predominantly dissociative transition state complex with a planar metaphosphate group located
midway between the ADP and the substrate. The structure of
the transition state complex and the corresponding activation
free energy of 15 kcal/mol are all in agreement X-ray17 data
and kinetic measurements.1,37 In contrast to prior QM/MM
calculations,20 we found the overall exothermic reaction process
with the product state located 3 kcal/mol below the reactant
state (see Figure 4), which is for the first time in good agreement
with experimental data.37 The analysis of the reaction pathway
showed a complex sequence of structural rearrangements, clearly
indicating the inadequacy of a simple reaction coordinate
assumed in prior QM/MM simulations.20 The major structural
changes occurring during the reaction process state involve
positions of the γ-phosphoryl group of the ATP, the secondary
Mg2 ion, and the side chain angle (χ2) of D166. The abstraction
of the substrate proton toward the D166 is initiated9,64 only as
the system crosses the transition state, which is consistent with
experimental pH data.9
Our calculations identify the importance of the secondary
Mg2 ion as an active site element contributing to the evolution
and stabilization of the transition state. This metal ion is
undercoordinated in the reactant state, facilitating its Lewis acid
attack on the β-γ-bridging oxygen. This activates the cleavage
of the bond connecting the β- and γ- phosphoryl groups and
stabilizes the leaving ADP group. Although this finding may
appear surprising, given “inhibitory” label attributed to this metal
ion, from a chemical point of view, the benefit from metal ion
stabilization of the negative charge accumulation on the β-γbridging oxygen during the phosphorylation seems very plausible.27 In addition, the evidence from the kinetic rate measurements is that the occupation of the secondary metal site has a
major effect on the ADP release (the rate-limiting step) but not
on the actual chemical transfer step.37
The role of the D166 in the catalytic mechanism of cAPK
received considerable attention in both experimental and
computational studies. The results obtained in the present study
correlate well with our prior gas-phase calculations.19 In the
reactant complex, the near attack orientation of the D166 with
respect to the substrate hydroxyl group is facilitated by
interactions with T201, N171, and a conserved water molecule.
The latter interaction is particularly strong and can be seen in
the X-ray structures of cAPK11,15,17,48,49 and other kinase
proteins.65 The same water molecule is also directly coordinated
to the essential Mg1 ion, providing a good structural anchor
between the D166 and the ATP-Mg complex. D166 forms a
hydrogen bond to the substrate hydroxyl group; however, the
strength of this interaction in the reactant complex does not
warrant an early abstraction of the substrate proton but may
J. Phys. Chem. B, Vol. 111, No. 47, 2007 13463
play a role in maintaining a favorable orientation of the substrate
with respect to the ATP. The strength of the D166-substrate
interaction increases significantly in the transition state with the
resulting low-barrier hydrogen bond, contributing to the stabilization of this state and initiating the abstraction of the substrate
proton. These observations are consistent with a concerted
catalytic base assignment for D166.63
Acknowledgment. This research was performed using the
MSCF in EMSL, a national scientific user facility sponsored
by the U.S. DOE, OBER and located at PNNL. We acknowledge support to M.V. from the Advanced Scientific Computing
Research program of the U.S. Department of Energy, Office of
Science (DE-AC06-76RLO 1830), to J.A.A. from NSF (111068)
and NIH (GM 67969), and to S.S.T. from NIH-GM19301. Many
helpful discussions with Jack Kyte are gratefully acknowledged.
References and Notes
(1) Adams, J. A. Chem. ReV. 2001, 101, 2271.
(2) Johnson, D. A.; Akamine, P.; Radzio-Andzelm, E.; Madhusudan;
Taylor, S. S. Chem. ReV. 2001, 101, 2243.
(3) Mildvan, A. S. Proteins: Struct. Funct. Genet. 1997, 29, 401.
(4) Adams, J. A. Biochemistry 2003, 42, 601.
(5) Hubbard, S. R. EMBO J. 1997, 16, 5572.
(6) Iyer, G. H.; Garrod, S.; Woods, V. L.; Taylor, S. S. J. Mol. Biol.
2005, 351, 1110.
(7) Iyer, G. H.; Moore, M. J.; Garrod, S.; Taylor, S. S. FASEB J. 2005,
19, A295.
(8) Iyer, G. H.; Moore, M. J.; Taylor, S. S. J. Biol. Chem. 2005, 280,
8800.
(9) Kim, K.; Cole, P. A. J. Am. Chem. Soc. 1997, 119, 11096.
(10) Lee, S. R.; Kwon, K. S.; Kim, S. R.; Rhee, S. G. J. Biol. Chem.
1998, 273, 15366.
(11) Zheng, J. H.; Knighton, D. R.; Ten Eyck, L. F.; Karlsson, R.;
Xuong, N. H.; Taylor, S. S.; Sowadski, J. M. Biochemistry 1993, 32, 2154.
(12) Shaltiel, S.; Cox, S.; Taylor, S. S. Proc. Natl. Acad. Sci. U.S.A.
1998, 95, 484.
(13) Wu, J.; Yang, J.; Kannan, N.; Madhusudan; Xuong, N. H.; Ten
Eyck, L. F.; Taylor, S. S. Protein Sci. 2005, 14, 2871.
(14) Yang, J.; Canaves, J.; Juliano, C.; Xuong, N. H.; Ten Eyck, L.;
Taylor, S. S. FASEB J. 2003, 17, A574.
(15) Yang, J.; Ten Eyck, L. F.; Xuong, N. H.; Taylor, S. S. J. Mol.
Biol. 2004, 336, 473.
(16) Zhou, J.; Adams, J. A. Biochemistry 1997, 36, 15733.
(17) Madhusudan; Akamine, P.; Xuong, N. H.; Taylor, S. S. Nat. Struct.
Biol. 2002, 9, 273.
(18) Akamine, P.; Madhusudan; Wu, J.; Xuong, N. H.; Ten Eyck, L.
F.; Taylor, S. S. J. Mol. Biol. 2003, 327, 159.
(19) Valiev, M.; Kawai, R.; Adams, J. A.; Weare, J. H. J. Am. Chem.
Soc. 2003, 125, 9926.
(20) Cheng, Y. H.; Zhang, Y. K.; McCammon, J. A. J. Am. Chem. Soc.
2005, 127, 1553.
(21) Diaz, N.; Field, M. J. J. Am. Chem. Soc. 2004, 126, 529.
(22) Henkelman, G.; LaBute, M. X.; Tung, C. S.; Fenimore, P. W.;
McMahon, B. H. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 15347.
(23) Hart, J. C.; Sheppard, D. W.; Hillier, I. H.; Burton, N. A. Chem.
Commun. 1999, 79.
(24) Hutter, M. C.; Helms, V. Protein Sci. 1999, 8, 2728.
(25) Garcia-Viloca, M.; Gao, J.; Karplus, M.; Truhlar, D. G. Science
2004, 303, 186.
(26) Admiraal, S. J.; Herschlag, D. J. Am. Chem. Soc. 1999, 121, 5837.
(27) Admiraal, S. J.; Herschlag, D. Chem. Biol. 1995, 2, 729.
(28) Admiraal, S.; Herschlag, D. FASEB J. 1995, 9, A1432.
(29) Zhang, X. Y.; Houk, K. N. Acc. Chem. Res. 2005, 38, 379.
(30) Poulsen, T. D.; Garcia-Viloca, M.; Gao, J. L.; Truhlar, D. G. J.
Phys. Chem. B 2003, 107, 9567.
(31) Bruice, T. C. Acc. Chem. Res. 2002, 35, 139.
(32) Friesner, R. A.; Guallar, V. Annu. ReV. Phys. Chem. 2005, 56, 389.
(33) Gao, J. L.; Truhlar, D. G. Annu. ReV. Phys. Chem. 2002, 53, 467.
(34) Warshel, A. Annu. ReV. Biophys. Biomol. Struct. 2003, 32, 425.
(35) Valiev, M. J. Comput. Chem., to be submitted.
(36) Bylaska, E. J.; Jong, W. A. D.; Kowalski, K.; Straatsma, T. P.;
Valiev, M.; Wang, D.; Aprà, E.; Windus, T. L.; Hirata, S.; Hackler, M. T.;
Zhao, Y.; Fan, P.-D.; Harrison, R. J.; Dupuis, M.; Smith, D. M. A.;
Nieplocha, J.; Tipparaju, V.; Krishnan, M.; Auer, M. N.; Brown, E.;
Cisneros, G.; Fann, G. I.; Früchtl, H.; Garza, J.; Hirao, K.; Kendall, R.;
Nichols, J. A.; Tsemekhman, K.; Wolinski, K.; Anchell, J.; Bernholdt, D.;
Borowski, P.; Clark, D. C.; Dachsel, H.; Deegan, M.; Dyall, K.; Elwood,
13464 J. Phys. Chem. B, Vol. 111, No. 47, 2007
D.; Glendening, E.; Gutowski, M.; Hess, A.; Jaffe, J.; Johnson, B.; Ju, J.;
Kobayashi, R.; Kutteh, Z. L.; Littlefield, R.; Long, X.; Meng, B.; Nakajima,
T.; Niu, S.; Pollack, L.; Rosing, M.; Sandrone, G.; Stave, M.; Taylor, H.;
Thomas, G.; Lenthe, J. v.; Wong, A.; Zhang, Z.. A Computational Chemistry
Package for Parallel Computers, 5.0th ed.; NWChem, 2006.
(37) Adams, J. A.; Taylor, S. S. Protein Sci. 1993, 2, 2177.
(38) Schafer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992, 97,
2571.
(39) Straatsma, T. P.; Philippopoulos, M.; McCammon, J. A. Comput.
Phys. Commun. 2000, 128, 377.
(40) Zhang, Y. K.; Liu, H. Y.; Yang, W. T. J. Chem. Phys. 2000, 112,
3483.
(41) Henkelman, G.; Jonsson, H. J. Chem. Phys. 2000, 113, 9978.
(42) Henkelman, G.; Uberuaga, B. P.; Jonsson, H. J. Chem. Phys. 2000,
113, 9901.
(43) Valiev, M.; Garrett, B. C.; Tsai, M.-K.; Kowalski, K.; Kathmann,
S. M.; Schenter, G. K.; Dupuis, M. J. Chem. Phys. 2007, 127,
51102.
(44) Dupuis, M.; Schenter, G. K.; Garrett, B. G.; Arcia, E. E. J. Mol.
Struct.-Theochem 2003, 632, 173.
(45) Armstrong, R. N.; Kondo, H.; Kaiser, E. T. Proc. Natl. Acad. Sci.
U.S.A. 1979, 76, 722.
(46) Bossemeyer, D.; Engh, R. A.; Kinzel, V.; Ponstingl, H.; Huber, R.
EMBO J. 1993, 12, 849.
(47) Granot, J.; Mildvan, A. S.; Kaiser, E. T. Arch. Biochem. Biophys.
1980, 205, 1.
(48) Madhusudan; Trafny, E. A.; Xuong, N. H.; Adams, J. A.; Ten Eyck,
L. F.; Taylor, S. S.; Sowadski, J. M. Protein Sci. 1994, 3, 176.
Valiev et al.
(49) Zheng, J. H.; Trafny, E. A.; Knighton, D. R.; Xuong, N. H.; Taylor,
S. S.; Ten Eyck, L. F.; Sowadski, J. M. Acta Crystallogr., Sect. D: Biol.
Crystallogr. 1993, 49, 362.
(50) Pauling, L. The Nature of the Chemical Bond; Cornell University
Press: Ithaca, NY, 1960.
(51) Cannon, J. F. J. Comput. Chem. 1993, 14, 995.
(52) Akola, J.; Jones, R. O. J. Phys. Chem. B 2006, 110, 8110.
(53) Gibbs, C. S.; Zoller, M. J. J. Biol. Chem. 1991, 266, 8923.
(54) Skamnaki, V. T.; Owen, D. J.; Noble, M. E. M.; Lowe, E. D.; Lowe,
G.; Oikonomakos, N. G.; Johnson, L. N. Biochemistry 1999, 38, 14718.
(55) Cleland, W. W.; Frey, P. A.; Gerlt, J. A. J. Biol. Chem. 1998, 273,
25529.
(56) Bhatnagar, D.; Roskoski, R.; Rosendahl, M. S.; Leonard, N. J.
Biochemistry 1983, 22, 6310.
(57) Armstrong, R. N.; Kondo, H.; Granot, J.; Kaiser, E. T.; Mildvan,
A. S. Biochemistry 1979, 18, 1230.
(58) Bright Wilson, E. J.; Decius, J. C.; Cross, P. C. Molecular
Vibrations; Dover: New York, 1955.
(59) The bond orders were calculated using Pauling’s formula. For PO,
the reference bond length was 1.73 Å and OH 1.99 Å.
(60) Schiott, B.; Iversen, B. B.; Madsen, G. K. H.; Larsen, F. K.; Bruice,
T. C. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 12799.
(61) Cleland, W. W.; Kreevoy, M. M. Science 1994, 264, 1887.
(62) Frey, P. A.; Whitt, S. A.; Tobin, J. B. Science 1994, 264, 1927.
(63) Kyte, J. personal communication.
(64) Kim, K.; Cole, P. A. J. Am. Chem. Soc. 1998, 120, 6851.
(65) Lowe, E. D.; Noble, M. E. M.; Skamnaki, V. T.; Oikonomakos,
N. G.; Owen, D. J.; Johnson, L. N. EMBO J. 1997, 16, 6646.