A R T I C L E S
Guimar a˜ es et al.
9
The preparation of the enzymatic system was much facilitated
∆G
p
(AfB) values and 0.9 × 10 configurations per ∆G
g
(AfB)
2
4
+
by use of the Chop delegate program. Charge neutrality for
the protein was imposed by assigning normal protonation states
at physiological pH to basic and acidic residues near the active
site and making the adjustments for neutrality to the most distant
residues. As for the protonation and tautomeric states for
histidine residues, the defaults in the Chop software were
employed. The entire system was solvated with a 22 Å radius
water cap consisting of 852 molecules. A half-harmonic potential
value. Since no cutoffs were used for the GTPH fGTP
6
transformation, 5 × 10 configurations of full equilibration and
6
10 × 10 configurations of data collection were applied for each
window in water or protein to reduce the computational cost
for these simulations. This is possible because only the partial
charges (the hydrogen atom connected to the N(7) atom has no
Lennard-Jones parameters) are perturbed in this transformation,
providing a very fast convergence for the free energy values
obtained. The independent FEP simulations for each pair of
ligands were all performed in the same direction, according to
the convention shown in Figure 2b. The energy-minimized
2
with a force constant of 1.5 kcal/mol ·Å was applied to water
molecules at distances greater than 22 Å from the center of the
2
5
system to discourage evaporation. As discussed previously,
7
the use of a spherical cap of water rather than periodic boundary
conditions affects the calculated free energies of hydration in
simple systems. Therefore, to cancel any potential errors, a 22
Å cap with 1474 water molecules was also used for the AfB
crystal structure for the complex between eIF4E and m GTP
provided the initial configuration for the FEP simulations in all
complex environments. The other five starting configurations
per transformation were randomly selected from the equilibration
phase of each respective first FEP run at a λ value of 0.05. A
similar scheme was applied to the simulations in the gas phase
and water.
w
unbound perturbations, yielding ∆G (AfB).
MC Simulations. The AfB transformations in all environ-
ments were performed using the single topology approach by
melding the force field parameters for bond lengths, bond angles,
3
0
MCPRO 2.0 was used to perform all MC calculations.
1
9
torsions, and nonbonded interactions. In order to keep the
number of atoms constant, dummy (DM) atoms were introduced
for hydrogens that exist in one state and have no counterpart in
the other. Bond lengths for perturbations requiring an atom
mutation or an annihilation or creation of a hydrogen were not
sampled and were treated as geometrical parameters. Bonds
containing a DM atom have an equilibrium value of 0.5 Å.
Shrinking the bond length for DM atoms is a common practice
Established procedures including Metropolis and preferential
sampling were employed, and statistical uncertainties were
obtained from the batch means procedure with batch sizes of 1
× 10 configurations. Attempted moves of the cap analogs in
water occurred every 10 configurations, while, in the complex,
attempted moves of the protein and cap analogs occurred every
10 and 80 configurations, respectively. The TIP4P model was
used for water, and the complexes were represented with the
OPLS-AA force field, with the exception of the CM1A atomic
6
17
31
1
9,26-29
32
to improve convergence in FEP simulations.
The bond
angles involving dummy atoms have the same parameters as
their counterparts in the other state. Associated unphysical
contributions to the free-energy differences cancel in a ther-
charges for the ligands.
Experimental Details
7
2
6,28
In Vitro IC50 Determination of eIF4E m GTP Binding.
modynamic cycle.
The MC/FEP calculations for the AfB
Human eIF4E protein (NP_001959) was produced as an N terminal
FLAG-HIS fusion protein in BL21 bacterial cells and purified by
transformations were executed at 25 °C using double-wide
1
9
sampling. Residue-based cutoffs of 10 Å were employed in
7
m GTP-Sepharose affinity chromatography (GE Healthcare).
+
all transformations except the one from GTPH to GTP. As
7
Protein was eluted with 100 µM m GDP and dialyzed extensively
this transformation involves a charge mutation from -2 to -3
e, no cutoffs were applied. In this manner, since the water-
phase and solvated eIF4E models have equal radii and the same
dielectric constant outside the spherical system, the missing
long-range electrostatic interactions between the solvent mol-
ecules not included in the finite models and the ligands with
into storage buffer. For binding analysis, eIF4E protein (50nM final)
was biotinylated and bound to streptaviden-coated scintillation
3
proximity assay beads (GE Healthcare) in the presence of H-
7
m GTP (1mCi/mL, Moravek Biochemicals) in binding buffer (20
mM HEPES, pH 7.4, 50 mM KCL, 1 mM DTT and 0.5 mM
EDTA). To determine competitive inhibition of eIF4E binding,
compounds were added in an 11-point, 3-fold dilution dose
series, and loss of radioactive signal was monitored by scintil-
lation counting. IC50 values were calculated by nonlinear
regression curve fitting using GraphPad Prism analysis software
different molecular charges would cancel out when computing
+
∆
∆Gbind for the GTPH fGTP transformation.
The initial and final states were coupled using 10 windows
with values for the coupling parameter (λ) evenly distributed
(
GraphPad Software).
Chemical Synthesis. Synthetic route and procedure for the
between 0 and 1 (0.05, 0.15, ..., 0.85, 0.95). Initial relaxation
6
of the solvent was performed for 5 × 10 configurations,
preparation of compounds 1 and 2 are provided in the Supporting
Information.
6
followed by 20 × 10 configurations of full equilibration and
6
3
0 × 10 configurations of data collection for each window in
Results and Discussion
water or protein, whereas for the gas-phase simulations, 5 ×
6
6
Long MC/FEP simulations were performed generating smooth
free-energy curves for the AfB transformations in all environ-
ments (Figure 3). As noted above (eqs 1-3), the binding process
may be decomposed into dehydration and transfer from the gas
1
0 configurations of equilibration and 10 × 10 configurations
of data collection were employed. The ∆G values obtained for
each window are averages of six independent MC runs, giving
9
a total of 3.3 × 10 configurations per ∆G
w
(AfB) and
phase to the protein. The relative free energies, ∆∆Gtransf
∆Ghyd, and ∆∆Gbind, between all cap analogs are reported in
Table 1.
,
∆
(
(
(
(
24) Tirado-Rives, J. Chop; Yale University: New Haven, CT, 2002.
25) Essex, J.; Jorgensen, W. L. J. Comput. Chem. 1995, 16, 9510–972.
26) Boresch, S.; Karplus, M. J. Phys. Chem. A 1999, 103, 103–118.
27) Pearlman, D. A.; Kollman, P. A. J. Chem. Phys. 1991, 94, 4532–
(30) Jorgensen, W. L. MCPRO, Version 2.0; Yale University: New Haven,
CT, 2005.
4
545.
(
(
28) Price, D. J.; Jorgensen, W. L. J. Comput-Aided Mol. Design 2001,
(31) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, W.; Klein,
M. L. J. Chem. Phys. 1983, 79, 926–935.
1
5, 681–695.
29) Guimar a˜ es, C. R. W.; Boger, D. L.; Jorgensen, W. L. J. Am. Chem.
Soc. 2005, 127, 17377–17384.
(32) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc.
1996, 118, 11225–11236.
1
8142 J. AM. CHEM. SOC. 9 VOL. 131, NO. 50, 2009