G. Fracchiolla et al. / Bioorg. Med. Chem. 16 (2008) 9498–9510
9509
value of 0.001 kcal molꢀ1 Åꢀ1. Upon minimization, harmonic con-
Acknowledgment
straints of 2 kcal molꢀ1 Åꢀ2 on the protein backbone atoms of the
complexes were applied. Such an energy-minimization was de-
signed to resolve the clashes between the complex and solvent
molecules gradually. The complex was then subjected to a three
stage equilibration to further relax the protein and the surrounding
solvent. In the first stage, the system was heated from 0 to 300 K
(using the Langevin dynamics method) over 50 ps of simulation
time. In the second stage, the system was equilibrated for 50 ps
using pressure and temperature control to adjust the density of
water to experimental values. In the third stage, a 500 ps of con-
stant volume equilibration at 300 K was carried out. A subsequent
production run was performed, giving a total simulation time of
3 ns. The time step of the simulations was 2.0 fs with a cutoff of
8 Å for the non-bonded interaction, and SHAKE46 was employed
to keep all bonds involving hydrogen atoms rigid.
This work was accomplished thanks to the financial support of
the Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR
2005033023).
Supplementary data
Analytical data for intermediates and final compounds are
given.
Supplementary data associated with this article can be found, in
References and notes
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The method for determining the binding free energy following
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from a MD simulation. The binding free energies (
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D
Gbind) were
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D
Gbind
¼
D
GðcomplexÞ ꢀ ½
D
GðproteinÞ þ GðligandÞꢃ
D
ð1Þ
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where
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G(complex), G(protein), and DG(ligand) are the free ener-
D
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D
D
D
Gbind
¼
D
D
Egas
Eint
GPB
þ
DDGsolv ꢀ T
Eele Evdw
DGnon-polar
D
S
ð2Þ
ð3Þ
ð4Þ
Egas
¼
þ
D
þ
D
Gsolv
¼
D
þ
The sum of molecular mechanical energies,
into contributions from internal energy (
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energy ( Gsolv) is composed of two parts: polar solvation free en-
ergy ( GPB) and non-polar solvation free energy ( Gnon-polar). T
D
Egas, can be divided
D
Eint), electrostatic poten-
D
D
D
D
D
DS
is the entropy contributions of the binding process.
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From the resulting trajectories of the (S)-27/hPPAR
snapshots were extracted every 10 ps to use in calculating
a
complex,
Egas
D
and DDGsolv, giving 300 snapshots for the 3 ns runs. Solvent
water was stripped off of these snapshots before they were used.
The single trajectory approach was applied to estimate the ener-
gies. Estimation of energies in this manner has proven successful
in many studies.47–49 Part of the reason for the success of this
approach is the cancelation of errors that hides the effect of
incomplete sampling. A better approach may be the use of sep-
arate trajectories of protein–ligand complex, free protein, and
free ligand. Unfortunately, due to sampling limitations, the sepa-
rate trajectory approach appeared to be significantly less stable.
D
Egas was obtained using SANDER, and estimation of DGPB was
conducted with the PBSA program in the AMBER suite, which
numerically solves the Poisson–Boltzmann equations to deter-
mine the electrostatic contribution to the solvation free energy.
Dielectric constants of 1 and 80 to represent gas and water
phases, respectively, were applied.
DGnopolar was determined
using the MOLSURF program, which is part of the AMBER suite
of programs.