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tinuum solvent surface generalized Born model[37] based on ꢅqv-
ist’s model.[26b] A Liaison simulation combined a MM calculation
with experimental data to build a model scoring function used to
correlate or to predict ligand–protein binding free energies. The as-
sumption used was that the binding energy could be approximat-
ed by comparing the energy of the bound complex (Ub) with the
energy of the free ligand–receptor system (Uf). The binding affinity
between the receptor and ligand was expressed in the LIE-SGB
model [Eq. (3)]:
analysis. The following empirical docking, MM LIE, and QM DFT de-
scriptors were tested to design predictive models: GScore(Glide),
ECoul(Glide), Evdw(Glide), GScore(Liaison), Gbind(LIE), Uvdw(LIE), Uelec(LIE),
Ucav(LIE), EHOMO(DFT), and ELUMO(DFT). The empirical descriptors from
docking and LIE calculations were described in detail in Docking
and LIE method with Liaison Sections. The QM descriptors and
HOMO and LUMO energies of the inhibitors were calculated with
the DFT method (M06-2X/LACVP**+)[33] by using the Jaguar pro-
gram[35] of the Schrçdinger package. We used leave-group-out
(LGO) cross-validation tests to evaluate the predictive power of
a generated regression model. In LGO, the original set of samples
was divided into n subsets. Then, n regressions were generated,
each time a different subset was omitted. Each of the n regressions
was then used to predict the expected dependent value for the
compounds in the omitted subset.
b
f
DGbindðLIEÞ ¼ að< Uvdw > ꢁ < Uvdw >Þþ
ð3Þ
b
f
b
f
bð< Uelec > ꢁ < Uele >Þ þ gð< Ucav > ꢁ < Ucav >Þ
The net electrostatic interaction energy in continuum solvent is
given by Equation (4):
Acknowledgements
Uelec ¼ Ucoul þ 2Urxn
ð4Þ
This study was supported by the Hungarian Scientific Research
Fund (NKTH-OTKA CK-77712), and TꢃMOP 4.2.1/B-09/1/KONV-
2010-0007 and TꢃMOP-4.2.2./B-10/1-2010-0024 projects co-fi-
nanced by the European Union and the European Social Fund, as
well as Jꢀnos Bolyai Research Scholarships (to L.J. and T.D.) of
the Hungarian Academy of Sciences. J.K. and I.T. acknowledge fi-
nancial support from the Scientific Grant Agency of the Ministry
of Education of Slovak Republic and Slovak Academy of Sciences
(the projects VEGA-02/0159/12 and VEGA-02/0101/11), and the
Research & Development Operational Programme funded by the
ERDF (Centre of Excellence on Green Chemistry Methods and Pro-
cesses, CEGreenI, Contract No. 26240120001, and Amplification of
the Centre of Excellence on Green Chemistry Methods and Pro-
cesses, CEGreenII, Contract No. 26240120025).
This gave a total of four possible LIE interaction energy compo-
nents, namely, van der Waals energy (Uvdw) and Coulomb energy
(Ucoul) between the ligand and enzyme, and the reaction field
energy (Urxn) and cavity energy (Ucav) between the ligand and con-
tinuum solvent. The parameters a, b, and g were calculated by fit-
ting LIE terms against experimental Ki values of inhibitors from the
training set. For the LIE-SGB calculations, QM partial charges for li-
gands were used from the DFT calculations (see the Docking Sec-
tion). An energy minimization sampling protocol with a truncated
Newton algorithm was used to obtain LIE energy terms from the
lowest energy point reached by the minimization. A size of flexible
protein region around the inhibitor for the geometry optimizations
was set to 4/7 ꢅ (start of restrained shell/start of frozen shell). The
OPLS2005 force field[32] with a residue-based cutoff distance of
15 ꢅ was used.
GScore(Liaison) was the Glide docking score (see Docking Section),
which was re-scored based on geometry relaxation of the enzyme
site and docked ligand during LIE sampling. Thus, GScore(Liaison)
was the modified GScore(Glide). It should not be interpreted mislead-
ingly as DGbind(LIE), which was calculated from the fitting LIE proce-
dure.
Keywords: density functional calculations
inhibitors · structure–activity relationships · substituent effects
·
enzymes
·
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Statistical analysis and QSAR descriptors
To generate SAR hypotheses, statistics, and validate the accuracy
of the predictive models, we used the statistical package Strike[38]
of the Schrçdinger package. The predicted binding free energies
of inhibitors (DGbind) calculated from the linear equation of energy
terms of selected descriptors were fitted against experimental ones
(DGexptl) by using the MLR method. DGexptl was calculated from ex-
perimentally measured inhibition constants (Ki) at a temperature of
T=310.15 K by using Equation (5):
DGexptl ¼ ꢁRTlnð1=KiÞ
ð5Þ
To maximize the predictive ability of a model, it was necessary to
reduce the dimensionality of the data by identifying the most rele-
vant descriptors. First, we used principal component analysis (PCA)
to identify a number of important factors with an eigenvalue of
more than one. Then, MLR methods were used to select descriptor
variables that made the largest contributions to the regression
˝
gedos, J. Marton, B. Kꢁnya, L. Virꢀg, L. Somsꢀk, P. Gergely, P. Bai, PLOS
[7] a) I. R. Kelsall, S. Munro, I. Hallyburton, J. L. Treadway, P. T. W. Cohen,
ꢃ 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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