Biomedical Engineering Reference
In-Depth Information
that molecular interaction i elds for a series of compounds contain information that can be used for
the understanding and prediction of the biological activity of the compounds.
3.7.2 D
EVELOPMENT
OF
A
3D-QSAR M
ODEL
FOR
S
UBSTITUTED
F
LAVONES
The starting point for the development of a 3D-QSAR model is a series of molecules and their bio-
logical activities at a given receptor. To illustrate the methodology, we will use a series of substituted
l avones also used in the pharmacophore modeling section earlier.
A crucial i rst step in a 3D-QSAR analysis is the alignment of the molecules. This is equivalent
to the development of a pharmacophore model (see Figure 3.1). For the l avones the alignment has
been discussed earlier. Thirty-four substituted l avones were used as a training set for developing
the 3D-QSAR model. For each molecule located in a gridbox and aligned according to the pharma-
cophore model, the interaction energies with two probes, a methyl probe and a water probe, were
calculated by GRID. To i nd a correlation between the biological activity and the calculated molecu-
lar interaction i elds, the method of partial least squares projections to latent structures (PLS) in
GOLPE is used (for more details see Further Readings). In essence, PLS contracts the original
description of each molecule (i.e., the molecular interaction i elds) into a few descriptive dimen-
sions/variables that are used for the correlation.
It is essential to validate the 3D-QSAR model. This should optimally be done internally as well
as externally. For internal validation, also called cross validation, a portion of the training set com-
pounds are left out and a new model of this reduced training set is built. This model is then used
to predict the activities of compounds left out. This procedure is repeated a number of times. The
results of the predictions of left out compounds are summarized in terms of a predictive correlation
coefi cient
q
2
, which should be larger than 0.5 for a high-quality 3D-QSAR model. External valida-
tion is performed by predicting the activities of compounds (the test set), which have not been used
to build the 3D-QSAR model. The results of this validation may be given as a standard error of
prediction (SDEP).
Figure 3.14 displays the results for the series of 34 substituted l avones used as a training set and
seven substituted l avones as a test (validation) set. The conventional correlation coefi cient
r
2
is
10
9
8
7
6
5
4
4
5
6
7
8
9
10
Experimental (p
K
i
)
FIGURE 3.14
Experimental and predicted afi nities. The training set is shown as uni lled squares and the
test set as i lled triangles.
