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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5865_Библиотеки_им_академика_М_И_Перельмана.pdf
Quantitative Structure-Activity/Property/Toxicity Relationships
( )
( )
Local hardness (η(r)) (Ghosh & Berkowitz, 1985; Yang & Parr, 1985) quantified the unwillingness
of a particular atomic site in a molecule towards chemical attack. However, η(r) cannot be normalized
to η as was done for s(r) to S. η(r) can be expressed as:
2
δ ρ
[ ( )]
r
∫
δρ δρ
F
( ) ( )
r r'
ρ( )
( ')r
r r'=
d (22)
η
1
N
where F[ρ(r)] is the Hohenberg-Kohn universal functional. η(r) can also be expressed as:
δµ
η
( )
r
=
δρ
( )
. (23)
r
( )
r
v
However, due to the dependence of ρ(r) on v(r), the above expression is ambiguous and hence cannot be considered as a basic definition for η(r). Unlike η and S, η(r) and s(r) do not have a reciprocal
relationship. They can be linked as:
η( ) ( )r r∫=s dr 1 (24)
Further, the global hardness can be obtained from η(r) and f(r) as: (Chattaraj et al., 2007)
η η=
( ) ( )r rf dr (25)
∫
Chattaraj et al. (2003) introduced the concept of philicity (ω
α
(r)), which represents the aptitude of a
local atomic site in a molecule towards towards reactivity (electrophilicity or nucleophilicity).
The relation between the local electrophilicity (ω(r)) and the global electrophilicity (ω) can be expressed as:
ω ω=
or,
f dr( )r
∫
ω ω ω= =
f dr dr( ) ( )r r thus, ω ω( ) ( )r r= f . (26)
∫ ∫
Therefore, from the expression it is obvious that ω(r) includes information about both ω and f(r) but
without the knowledge of ω, f(r) alone cannot give any clue about ω(r). One can apply this concept of ω(r) in
α
several types of chemical reaction. Therefore, it will be better to represent philicity as ω
(r) in stead of ω(r).
α has signs of +, – and 0 describing nucleophilic, electrophilic and radical attacks, respectively. Therefore:
α α
ω ω
r r
=
.
f
and f
where ω
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136
k k
α
is the condensed-to-atom local philicity variant for the kth atomic site in a molecule.
k
α α
ω ω
=
, .
(27)
Quantitative Structure-Activity/Property/Toxicity Relationships
The concept of group philicity (ω
α
) (Parthasarathi et al., 2004a) was also put forward in order to
g
describe the reactivity of a group or an atomic assembly. It is generally expressed as a summation of the
α
individual ω
α α
ω ω
=
g k
k
over all the related atoms. Therefore:
k
n
(28)
=∑1
where n describes the number of atoms present in the reacting group and α = +, – and 0 represents
nucleophilic, electrophilic and radical attacks, respectively.
The efficacy of various CDFT based global and local reactivity descriptors in predicting chemical
reactivity are guided by the various electronic structure principles like the principle of maximum hardness
(PMH) (Ayers & Parr, 2000; Chattaraj et al., 1995, 2000; Chattaraj, 1996; Pan et al., 2013; Pan & Chattaraj, 2013; Parr & Chattaraj, 1991; Parr & Zhou, 1993; Pearson, 1987, 1993), minimum electrophilicity
principle (MEP) (Chamorro et al., 2000; Pan et al., 2013; Parthasarathi, 2005), minimum polarizability
principle (MPP) (Chattaraj & Sengupta, 1996, 1997; Chattaraj et al., 1999), minimum magnetizability
principle (MMP) (Tanwar et al., 2006).
With the structural changes and/or substituent effects in a system, the variation of related conceptual
DFT based reactivity descriptors led light into the quantitative correlation between chemical reactivity
and toxicity. They indeed become important tools in building effective regression models for QSAR/
QSPR/QSTR analyses.
4. ELECTROPHILICITY INDEX, NET ELECTROPHILICITY INDEX,
AND THEIR LOCAL VARIANTS IN PREDICTING TOXICITY
Electrophilicity index (ω), net electrophilicity index (Δω±) and the local variants of ω were found to be
very effective tools in predicting toxicity. Some examples are given below.
4.1 Prediction of Toxicity of Various Alkali, AlkalineEarth, Transition-Metal Ions and Arsenic Ions
Roy et al. (2009) attempted to predict the toxicity of arsenic (As3+ and As5+) ions by choosing a
+
training set composed of various alkali and alkaline-earth metal ions (Li
3+
transition metal ions (Cr
(50% Lethal concentration, LC
sets composed of experimental toxicity (50% Lethal dose, LD
, Mn2+, Fe3+, Co2+, Ni2+, Cu2+, Zn2+) along with their experimental toxicity
) in order to get single-parameter regression models. Two training
50
) (Leermakers et al., 2006; Hughes,
50
2002) of two different sets of arsenic derivatives were also considered in order to predict their toxicity by employing several selected parameters. The corresponding atomic number (Z), energy (E),
electrophilicity (ω) and the experimental as well as the calculated toxicity values expressed in terms
of LC
at the B3LYP/6-31+G(d) level are provided in Table 1. The calculated LC50 values in terms
50
of Z and ω were computed as follows:
, Na+, K+, Mg2+, Ca2+) and
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137
Quantitative Structure-Activity/Property/Toxicity Relationships
Table 1. Atomic number (Z), energy (E, au), electrophilicity index (ω, eV), and experimental and calculated LC
values for various selected alkali, alkaline-earth, and transition-metal ions along with arsenic
50
ions at the B3LYP/6-31+G(d) level
Metal Ions Z E ω Expt. LC
Training set
Li
Na
Mg
K
Ca
Cr
Mn
Fe
Co
Ni
Cu
Zn
+ a
+
2+
+ a
2+
3+
2+
3+
2+
2+
2+ b
2+ b
3 −7.28459 22.033 0.215 − 0.283
11 −162.08125 16.607 0.398 0.328 0.287
12 −199.22743 37.645 0.250 0.310 0.272
19 −599.72502 12.909 0.479 − 0.290
20 −676.86695 28.515 0.173 0.165 0.278
24 −1042.22188 495.511 0.019 0.093 −0.053
25 −1149.83984 168.557 0.132 0.075 0.179
26 −1261.27545 413.554 0.0003 0.056 0.005
27 −1381.56785 204.105 0.022 0.038 0.154
28 −1507.03577 331.966 0.069 0.020 0.063
29 −1639.25180 100.906 0.002 0.002 −
30 −1778.15610 65.992 0.007 −0.016 −
Toxicity prediction of arsenic ions
3+
As
5+
As
a
Outliers in the Z model;bOutliers in the ω model.
33 −2231.61591 115.148 − − 0.217
33 −2227.48829 182.990 − − 0.169
(Reprinted with permission from Roy et al., 2009. Copyright © 2009, Springer Science+Business Media B.V.).
50
Calc. LC
50
Z ω
Calc. LC50 = −0.0181×Z+0.5272; (29)
R = 0.923, SD = 0.054, N = 10
Calc. LC
= −7.1×10−04 ×ω +0.2987; (30)
50
R = 0.793, SD = 4.337, N = 10.
In both Z and ω models, two ions were found to be outliers, being Li
2+
and Zn2+ in case of ω- model. However, the Z- model was found to be better in prediction of toxicity
Cu
+
and K+ in case of Z- model and
of ions than that of ω- model but being the same Z value, Z- model could not differentiate the toxicity
3+
of As
(LC
138
and As5+. On the other hand, ω- model can predict the toxicity of As3+ and As5+ correctly, As3+
= 0.217) being more toxic than As5+ (LC50 = 0.169).
50
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Quantitative Structure-Activity/Property/Toxicity Relationships
Further, efficacy of different global descriptors like number of nonhydrogenic atoms (NNH) and ω and
+
different local descriptors like philicity (ω
ing QSTR taking two sets of As-derivatives, whose experimental toxicity were known in terms of LD
) and atomic charges (QAs) at As site were tested in build-
As
50
obtained from two different biological assays (Leermakers et al., 2006; Hughes, 2002).
In both sets, seven As-derivatives were included (Set-I members were Arsenite (As(III)), Arsenobetaine (AsB), Arsenocholine (AsC), Monomethyl arsonic acid (MMA), Dimethyl arsinic acid
(DMA), Trimethyl arsine oxide (TMAO), Tetramethylarsonium ion (TeMA) and Set-II members were
Arsenate [As(V)], Arsenite [As(III)], Arsenobetaine (AsB), Arsenic trioxide (As
), Monomethyl
2O3
arsonic acid (MMA), Dimethyl arsinic acid (DMA), Trimethyl arsine oxide (TMAO)). For each individual descriptor, one-parameter regression analyses were performed. It was found that N
NH
has
reasonably good predictive power towards the toxicity of As-derivatives in both the sets except the
case of TMAO molecule.
+
ω showed better prediction in set-II than in set-I. On the other hand, ω
in set-I than in set-II and Q
could not predict the toxicity of As(III) in both the sets as well as As2O3
As
showed better prediction
As
in set-II. Nevertheless, none of these descriptors could predict the toxicity of all seven molecules in
both the sets. Then possible combinations of these four descriptors were tested towards the prediction of toxicity. Two-parameter regressions were not found that much suitable in predicting toxicity
of all the As-derivatives; however, three-parameter regressions composed of one global (N
+
and two local parameters (ω
and QAs) were capable to represent the toxicity of all the derivatives
As
or ω)
NH
reasonably well (see Figure 1).
The corresponding regression models could be represented as follows:
Set-I:
Calc.LD
= 1.983 × NNH − 5.360 × ω
50
R = 0.866, SD = 2.516, N = 7
Calc.LD
= 1.805 × ω − 16.312 × ω
50
R = 0.898, SD = 2.216, N = 7
Set-II:
Calc.LD
= 0.484 × NNH − 3.232 × ω
50
R = 0.865, SD = 1.254, N = 7
+
−35.926 × QAs + 15.402 (31)
As
+
−85.353 × QAs + 51.415 (32)
As
+
−16.968 × QAs + 10.065 (33)
As
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139
Quantitative Structure-Activity/Property/Toxicity Relationships
Figure 1. Experimental versus calculated toxicity (LD50) values using three-parameter (N
) regression model for the complete set of set-I (1) and II (2) As-derivatives and three-parameter (ω,
Q
As
+
, and QAs) regression model for the complete set of set-I (3) and II (4) As-derivatives
ω
As
(Reprinted with permission from Roy et al., 2009. Copyright © 2009, Springer Science+Business Media B.V.).
NH
, ω
+
As
, and
Calc.LD50= 4.724 × ω − 10.881 × ω
+
−54.889 × QAs + 23.380 (34)
As
R = 0.963, SD = 0.671, N = 7
It was also found that the toxicity prediction power of the combination, ω, ω
+
, ω
that of the combination of N
NH
140
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and QAs.
As
+
and QAs is better than
As
Quantitative Structure-Activity/Property/Toxicity Relationships
4.2 Prediction of the Toxicity (pIGC50) of 252 Aliphatic
Compounds on Tetrahymena Pyriformis
Chattaraj et al. (2007) used global descriptors like the number of carbon atoms (NC), number of nonhy-
+
−
rogenic atoms (N
) in a molecule, ω and local descriptors like ω
NH
max
, ω
311G(d) level in modeling effective QSTR of a large number of aliphatic compounds on T. pyriformis.
Here ω
+
max
charge at the k
that apart from the set of aliphatic amines, the atom number (N
−
and ω
referred to the ω
max
th
site having maximum charge. By studying 252 aliphatic compounds, it was found
α
at an atomic site in which it was maximum. q
k
and NNH) was an important descriptor
C
whereas ω was also turned out as an effective descriptor in most of the cases. The predictability towards
toxicity of two-parameter models based on N
corresponding three-parameter models built by N
max
. Different regression equations adopted in one (NC)- and two (NC, ω)-parameter models are given
q
k
Table 2. N
-based single parameter model could predict toxicity fairly in most of the cases. In few cases
C
and ω was also found almost same with respect to the
C
, ω and any one descriptor from NNH, ω
C
like carboxylic acids, halogenated acids, amino alcohols and amines, it did not work. However, except
amines the predictability towards toxicity of the model was found to improve significantly in coupling N
and ω
–
were also found to be important in describing toxicity. With
max
was termed as the crude alternative
C
versus calculated pIGC50 values are displayed in Figure 2.
50
2
values implied the effectiveness
adj
with ω. In cases of amines, q
max
k
the observation that in many cases, similar results were obtained, N
of log P. The plots of experimental pIGC
2
2
, R
Quite large R
and variance adjusted to degrees of freedom, R
cv
of these models in building QSTR.
max
max
, q
computed at the HF/6-
k
max
implied atomic
k
+
−
, ω
max
max
,
C
4.3 Prediction of Toxicity of Several Polyaromatic Hydrocarbons (PAH)
The global and local electrophilicities computed at the B3LYP/6-31G(d) level were used to predict the
toxicity of several polyaromatic hydrocarbons (PAH) (Roy et al., 2006c). The toxicity was represented in
terms of pIC
50% of radio-labeled tetrachlorodibenzo-p-dioxin (TCDD) from the arylhydrocarbon (Ah) receptor. As
a training set, dependent and independent variables were considered as the experimental pIC
of the electron acceptor toxin like polychlorinated dibenzofurans (PCDF) and ω, respectively. Further,
this model was also employed on another set of polychlorinated biphenyls (PCB). General structures of
PCDFs, and PCBs are provided in Tables 3 and 4, respectively, along with the atom numbering, identitity
number and substitution pattern. The fractional number of electrons (ΔN) shifted from the PCDFs, PCBs
and amines (A) to the nucleic acid bases/DNA base pairs (B) was also used as a descriptor to describe
toxicity. The positive values of ΔN for PCDFs and PCBs implied their electron accepting nature whereas
the negative values for amines recognized them as electron donors. Reasonably good correlation was
found to exist between ΔN (in between toxin and guanine) and ω having R = 0.991. The correlation
between ΔN and exp. pIC
on ΔN and ω and exp. pIC
PCDFs and GCWC (Guanine-Cystosine Watson-Crick) base-pairs, good correlations were observed.
The calculated parameters (ω and ω
training set of PCDFs and PCBs are given in Table 5. In case of PCDFs, ω values gave a correlation R
value of 0.891 whereas in case of PCBs, it was 0.834 (see Figure 4). The toxicity of aliphatic amines
expressed by the 50% inhibitory growth concentration (IGC
, which could be defined as the molar concentration of these chemicals required to displace
50
values
50
was 0.881 whereas that obtained from the two-parameter regression based
50
was 0.892 (see Figure 3). Similarly, in cases of interactions in between
50
+
) along with the experimental and predicted pIC50 values of the
max
) towards ciliate fresh-water protozoa Tet-
50
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141
Quantitative Structure-Activity/Property/Toxicity Relationships
Table 2. Regression models for different groups of aliphatic compounds for estimating their toxicity
towards Tetrahymena pyriformis
Molecules Regression Equations R SD
Aliphatic electron acceptors
Diols (N = 10) pIGC
Halogenated alcohols (N = 11) pIGC
Saturated alcohols (N = 32) pIGC
Carboxylic acids (N = 28) pIGC
Halogenated acids (N = 11) pIGC
Mono esters (N = 31) pIGC
Diesters (N = 20) pIGC
Aldehydes (N = 13) pIGC
Ketones (N = 15) pIGC
= 0⋅4497 × NC – 4⋅0855 0⋅9683 0⋅2781
50
= 0⋅8059 × log P – 1⋅4688 0⋅9892 0⋅1617
pIGC
50
= –12⋅4224 × ω + 0⋅3554 × NC + 7⋅6094 0⋅9826 0⋅2070
pIGC
50
= 10⋅0678 × ω + 0⋅9625 × log P – 10⋅5043 0⋅9934 0⋅1270
pIGC
50
= 0⋅3271 × NC – 2⋅0248 0⋅8923 0⋅3852
50
= 0⋅7783 × log P – 1⋅3735 0⋅9486 0⋅2561
pIGC
50
= – 6⋅2863 × ω + 0⋅1982 × NC + 4⋅5793 0⋅9424 0⋅2855
pIGC
50
= –4⋅0784 × ω + 0⋅5772 × log P + 2⋅7468 0⋅9646 0⋅2169
pIGC
50
= 0⋅4144 × NC – 3⋅0801 0⋅9634 0⋅3456
50
= 0⋅7745 × log P – 2⋅0034 0⋅9903 0⋅1777
pIGC
50
= 0⋅8927 × ω + 0⋅4261 × NC – 3⋅9484 0⋅9636 0⋅3451
pIGC
50
= 1⋅6835 × ω + 0⋅8138 × log P – 3⋅5796 0⋅9907 0⋅1739
pIGC
50
= 0⋅1116 × NC – 0⋅9678 0⋅6676 0⋅2917
50
= 0⋅2857 × log P – 0⋅7006 0⋅9586 0⋅1070
pIGC
50
= – 5⋅4426 × ω + 0⋅0338 × NC + 4⋅8562 0⋅8801 0⋅1860
pIGC
50
= –0⋅3944 × ω + 0⋅2715 × log P – 0⋅2924 0⋅9589 0⋅1066
pIGC
50
= 0⋅2257 × NC – 1⋅3481 0⋅6564 0⋅3632
50
= 0⋅4620 × log P – 0⋅8744 0⋅8107 0⋅2285
pIGC
50
= 1⋅8930 × ω + 0⋅0976 × NC – 2⋅2827 0⋅9186 0⋅1903
pIGC
50
= 1⋅6012 × ω + 0⋅2001 × log P – 1⋅8388 0⋅9169 0⋅1762
pIGC
50
= 0⋅3645 × NC – 2⋅7969 0⋅9189 0⋅3710
50
= 0⋅7599 × log P – 2⋅0274 0⋅9645 0⋅2396
pIGC
50
= –10⋅9131 × ω + 0⋅2554 × NC + 8⋅1384 0⋅9352 0⋅3330
pIGC
50
= –3⋅0902 × ω + 0⋅6960 × log P + 1⋅0027 0⋅9655 0⋅2365
pIGC
50
= 0⋅2861 × NC – 2⋅884 0⋅9299 0⋅3382
50
= 0⋅6338 × log P – 1⋅3322 0⋅9539 0⋅2632
pIGC
50
= –4⋅8166 × ω + 0⋅1999 × NC + 1⋅1227 0⋅9636 0⋅2460
pIGC
50
= –4⋅2407 × ω + 0⋅4687 × log P + 1⋅7763 0⋅9790 0⋅1834
pIGC
50
= 0⋅2230 × NC – 1⋅4027 0⋅8980 0⋅2459
50
= 0⋅4628 × log P – 0⋅8864 0⋅9227 0⋅1988
pIGC
50
= –2⋅5248 × ω + 0⋅1228 × NC + 1⋅3002 0⋅9332 0⋅2008
pIGC
50
= –2⋅1731 × ω + 0⋅2904 × log P + 1⋅2280 0⋅9496 0⋅1664
pIGC
50
= 0⋅4147 × NC – 3⋅4470 0⋅9850 0⋅2249
50
= 0⋅7720 × log P – 2⋅0314 0⋅9872 0⋅2048
pIGC
50
= –3⋅2176 × ω + 0⋅38989 × NC – 0⋅6459 0⋅9855 0⋅2211
pIGC5
0
= –1⋅4487 × ω + 0⋅7511 × log P – 0⋅8080 0⋅9873 0⋅2041
pIGC
50
continued on following page
142
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Quantitative Structure-Activity/Property/Toxicity Relationships
Table 2. Continued
Molecules Regression Equations R SD
Aliphatic electron donors
Amino alcohols (N = 18) pIGC
Acetylenic alcohols (N = 13) pIGC
Unsaturated alcohols (N = 25) pIGC
Amines (N = 25) pIGC
Copyright © 2007, Indian Academy of Sciences).
= 0⋅2255 × NC – 2⋅3296 0⋅4711 0⋅4596
50
= 0⋅3533 × log P – 1⋅0529 0⋅5829 0⋅2468
pIGC
50
= 8⋅9875 × ω + 0⋅1464 × NC – 7⋅4431 0⋅9152 0⋅2100
pIGC
50
= 8⋅5520 × ω + 0⋅2282 × log P – 6⋅3481 0⋅9377 0⋅1697
pIGC
50
= 0⋅3332 × NC – 2⋅2125 0⋅8942 0⋅4218
50
= 0⋅5506 × log P – 0⋅8071 0⋅8842 0⋅3891
pIGC
50
= 3⋅7452 × ω + 0⋅3707 × NC – 5⋅0494 0⋅9080 0⋅3947
pIGC
50
= 0⋅2523 × ω + 0⋅5538 × log P – 0⋅9858 0⋅8843 0⋅3890
pIGC
50
= 0⋅4093 × NC – 3⋅3473 0⋅8580 0⋅3311
50
= 0⋅7587 × log P – 1⋅6861 0⋅9315 0⋅2185
pIGC
50
= –2⋅2250 × ω + 0⋅3641 × NC – 1⋅7327 0⋅9136 0⋅2622
pIGC
50
= –0⋅0271 × ω + 0⋅7568 × log P – 1⋅6679 0⋅9315 0⋅2185
pIGC
50
= 0⋅1136 × NC – 1⋅3456 0⋅2711 0⋅3965
50
= 0⋅4609 × log P – 1⋅1380 0⋅8534 0⋅1833
pIGC
50
= –0⋅1700 × ω + 0⋅1116 × NC – 1⋅2295 0⋅2723 0⋅3964
pIGC
50
= 0⋅9307 × ω + 0⋅4792 × log P – 1⋅7367 0⋅8641 0⋅1792
pIGC
pIGC
1⋅8782
pIGC
1⋅4885
50
= 0⋅1162 × q
50
= 0⋅0681 × q
50
max
+ 2⋅1524 × ω
k
max
+ 1⋅3490× ω
k
–
max
–
max
(Reprinted with permission from Chattaraj et al., 2007.
+ 0⋅0669 × NC –
+ 0⋅2802 × log P –
0⋅8692 0⋅2037
0⋅9429 0⋅1293
rahymena pyriformis was also assessed. Due to the lack of global nucleophilicity, local nucleophilicity
+
) was applied as a descriptor for this set. This model was then further employed for the test set of
(ω
max
amino alcohols. It was found that despite the occurrence of a very good correlation, there was some cross
validation problem. Additionally, the use of the amines and amino alcohols together as both training and
test sets provided fair correlation.
4.4 Structure-Toxicity Analysis on Chloroanilines
Padmanabhan et al. (2006a) further developed QSTR for aquatic toxicity (log(IGC
chloroanilines (CA) against T. pyriformis at the B3LYP/6-311++G(d,p) level as given in Table 6. The
-1
experimental and calculated log(IGC
-1
experimental log(IGC
) value (Schultz, 1999) as a dependent variable and ω as an independent vari-
50
) are also given in Table 6. The regression equation considering
50
able was as follows:
log(IGC
N = 9, r
-1
) = −4.414 + 56.035 ω (35)
50
2
= 0.968, SD = 0.144.
-1
)) of a set of nine
50
143
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Quantitative Structure-Activity/Property/Toxicity Relationships
Figure 2. Observed versus calculated pIGC
values using two-parameter (ω, NC) regression models for
50
the (a) Complete set of aliphatic electron acceptors and (b) complete set of aliphatic electron donors
(Reprinted with permission from Chattaraj et al., 2007. Copyright © 2007, Indian Academy of Sciences).
The plot between exp. and calc. log(IGC
-1
) (see Figure 5) showed that ω could describe the aquatic
50
toxicity of these CA systems superbly having a correlation coefficient (r) of 0.984.
4.5 Prediction of Toxicity of Phenol, Nitrobenzene, and Benzonitrile-Derivatives
ω and its local variants, local electrophilicity index (ω
employed in order to describe the toxicity of a large number (174) of aromatic compounds towards
T. pyriformis, mainly belonging to the family of phenols, nitrobenzenes and benzonitriles (Roy et al.,
2006b). At first, depending on their electron donating/accepting nature measured by comparing their
χ values with those of the nuclei acid bases (adenine, thymine, guanine, cytosine and uracil) and DNA
base pairs (GCWC and ATH), they were divided into two classes viz., 97 phenol derivatives having
electron donating group and 77 nitrobenzenes and benzonitriles having electron accepting group. The
regression models were used for the complete set of aromatic donors as
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α
) computed at the HF/6-31G(d) level were also
k
Quantitative Structure-Activity/Property/Toxicity Relationships
Table 3. Polychlorinated dibenzofurans with identity number (ID) representing the substitution pattern
ID X
1
X
2
X
3
X
4
X
6
X
7
X
8
1 H Cl H H H H H H
2 H H H Cl H H H H
3 H Cl H H Cl H H H
4 H Cl H H H H Cl H
5 Cl H Cl H Cl H H H
6 Cl H Cl H H H Cl H
7 H Cl Cl Cl H H H H
8 H Cl Cl H H H Cl H
9 H Cl H H Cl Cl H H
10 H Cl Cl Cl Cl H H H
11 H Cl Cl Cl H H Cl H
12 H Cl Cl H H Cl Cl H
13 Cl Cl H Cl Cl Cl H H
14 Cl Cl Cl Cl H H Cl H
15 Cl Cl Cl H H Cl Cl H
16 H Cl Cl Cl H Cl Cl H
17 Cl Cl Cl Cl H Cl Cl H
18 H Cl Cl Cl Cl Cl Cl H
19 H Cl Cl H Cl H Cl H
20 Cl Cl Cl H Cl H H H
21 Cl Cl Cl H H Cl H H
22 Cl H Cl Cl H Cl Cl H
23 H Cl Cl Cl H Cl H Cl
24 Cl Cl Cl H H Cl H Cl
25 Cl Cl Cl H H Cl H H
26 Cl H Cl Cl H Cl Cl H
27 H Cl Cl Cl H Cl H Cl
(Reprinted with permission from Roy et al., 2006c. Copyright © 2006, Springer Science+Business Media, Inc.).
X
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