Biomedical Engineering Reference
In-Depth Information
0.90 and
q
2
is 0.77. The SDEP for the seven test set molecular is 0.51. Thus, the 3D-QSAR model
developed is of high quality with high internal as well as external predictivity and may reliably be
used for the prediction of the afi nities of new compounds.
The results of a 3D-QSAR analysis are usually analyzed by contour maps of the PLS coefi -
cients. Each grid point is associated with two coefi cients from the PLS analysis, one coefi cient (
c
k
)
is related to interactions with the methyl probe, the other one (
c
l
) to interactions with the water probe
(Equation 3.2). These coefi cients and the corresponding
E
tot
values describe the relative importance
of each grid point for explaining the variation in biological activity. The total p
K
i
is a summation
over all gridpoints.
p
K
=-
log
K
=
c E
(methyl probe)
+
c E
(water probe)
(3.2)
i
i
k
tot
l
tot
A more positive value of p
K
i
means a higher afi nity. Thus, a more positive value of
E
tot
(methyl
probe) together with a positive value of
c
k
gives a positive contribution to p
K
i
(a higher afi nity).
A negative sign of
c
k
and a positive value of
E
tot
(methyl probe) give a negative contribution to p
K
i
(a lower afi nity). Figure 3.15 displays contour maps of regions of negative and positive PLS coef-
i cients. Such maps may be used as guidelines for the design of new compounds. It should i rst be
noted that there is the absence of contours around the carbonyl group. QSAR relates variation in
molecular properties to variation in biological activity and since the carbonyl group is present in
all test set molecules there is no (or very small) contributions to the variation in afi nity from this
group.
In Figure 3.13a the cyan regions correspond to negative PLS coefi cients. Substituents that have
repulsive vdW interactions with the methyl probe in these regions, i.e., positive
E
tot
values, give a
negative contribution to the afi nity (a lower afi nity). Thus, even small substituents in the 6-, 4
′
-,
and 5
-position are predicted to result in an afi nity
decrease. Compounds
3.8
and
3.9
in Figure 3.3 are two examples of the effects of substitution in the
4
′
- positions and also very large substituent in the 3
′
-positions. Furthermore, it has been reported that the 6-isopropyl compound has a 10-fold
lower afi nity than the 6-bromo compound
3.2
in Figure 3.2.
The yellow regions in Figure 3.15a correspond to positive PLS coefi cients. Thus, substituents
that have repulsive interactions with the methyl probe in these regions (i.e., signii cantly positive
E
tot
values) are predicted to give an increase of the afi nity. Small substituents in the 6-position and
small as well as large substituents in the 3
′
- and 5
′
′
-position are thus predicted to be favorable for the afi nity
5'
4'
6'
6
3'
(a)
(b)
FIGURE 3.15
Contour maps of the PLS coefi cients for (a) the methyl probe, negative coefi cients (−0.002
level) are shown in cyan and positive coefi cients (+0.003 level) in yellow (b) the water probe, negative coef-
i cients (−0.006 level) are shown in cyan and positive coefi cients (+0.004 level) in yellow. Compound
3.13
is
shown to illustrate the size of the regions.
