Tetra- and Diarylporphyrins as Photosensitizers
Journal of Medicinal Chemistry, 2006, Vol. 49, No. 11 3303
which does not consider models with a K multivariate correlation
index of the [X] variable block greater than the correlation within
the [X + y] block variables, where X is the molecular descriptors
and y is the response variable.
In the MLR equation of the model, reported in this paper, the
variables are listed in order of relative importance by their
standardized regression coefficients. In fact, since molecular
descriptors do not have equal variance (i.e., they are not autoscaled),
their relative importance in the model is measured better by
standardized regression coefficients (i.e., the coefficients multiplied
by the standard deviation of the corresponding predictor). The errors
of the regression coefficients have also been reported for each
equation.
1-24; structures of the 10 photosensitizers previously synthesized;7
list of the calculated log P values (A log P, M log P, and HYPER-
log P), molecular descriptors, and experimental and predicted log
(1/IC50) (IC50 in nanomolar). This material is available free of charge
References
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Validation. The robustness of the models and their predictivity
were evaluated by both Q2 and bootstrap. In this last procedure
loo
K n-dimensional groups are generated by a randomly repeated
selection of n objects from the original data set. The model obtained
on the first selected objects is used to predict the values for the
excluded sample and then Q2 is calculated for each model. The
bootstrapping was repeated 5000 times for each validated model.
The proposed models are also checked for reliability and
robustness by permutation testing;32 new models are recalculated
for randomly reordered response (Y scrambling) in order to exclude
by chance models.
The actual predictive capability of each model developed on the
training set is verified on an external validation set24 and is
calculated from Q2ext ) 1 - PRESS/SD, where PRESS is the sum
of squared differences between the measured response and the
predicted value for each molecule in the validation set, and SD is
the sum of squared deviations between the measured response for
each molecule in the validation set and the mean measured value
of the training set. A measure to define the accuracy of the proposed
QSARs is also the RMSE (root mean square of errors) that
summarizes the overall error of the model. It is calculated as the
root square of the sum of the squared errors in predictions divided
by their total number (RMSE and RMSEP, calculated separately
for the training and the test/validation sets):
(yi - yˆi)2
∑
i
RMSE )
x
n
Splitting Training/Test for External Validation. To have
compounds for external validation, the original data set of 34
compounds was split into a training set and an external validation
set. The splitting of the data set was realized considering the
distribution of the response value: 2/3 of the studied compounds
(22 objects) were selected as a training set and used for the model
developing, and the remaining 12 molecules were used as a
validation set, to allow the external statistical validation of the
model.
Chemical Domain. QSAR models must always be verified for
their applicability with regard to chemical domain. The presence
of outliers (i.e., compounds with cross-validated standardized
residuals greater than 2.5 standard deviation units) and chemicals
very structurally influential in determining model parameters [i.e.,
compounds with high leVerage value (h)33 greater than 3 p′/n (h*),
where p′ is the number of model variables plus one, and n is the
number of the objects used to calculate the model] was also verified.
The reliability of the predicted data with regard to chemical domain
was verified by the leVerage approach: the predictions for chemicals
of the validation set with a leverage value smaller than h* must be
considered reliable, being into the structural chemical domain of
the training set.
(16) Bonnett, R.; Martinez, G. Photobleaching of compounds of the
5,10,15,20-tetrakis(m-hydroxyphenyl)-porphyrin series (m-THPP, m-
THPC, and m-THPBC). Org. Lett. 2002, 4 (12), 2013-2016.
(17) Henderson, B. W.; Bellnier, D. A.; Greco, W. R.; Sharma, A.; Pandey,
R. K.; Vaughan, L. A.; Weishaupt, K. R.; Dougherty, T. J. An in
vivo quantitative structure-activity relationship for a congeneric
series of pyropheophorbide derivatives as photosensitizers for pho-
todynamic therapy. Cancer Res. 1997, 57, 4000-4007.
(18) Potter, W. R.; Henderson, B. W.; Bellnier, D. A.; Pandey, R. K.;
Vaughan, L. A.; Weishaupt, K. R.; Dougherty, T. J. Parabolic
quantitative structure-activity relationships and photodynamic
therapy: Application of a three-compartment model with clearance
Principal component analysis (PCA) for data exploration was
performed on autoscaled data by the SCAN38 and STATISTICA39
packages.
Supporting Information Available: Spectroscopic data (1H
NMR and UV-vis) and elemental analysis data for compounds