J. Chem. In5 Comput. Sci. 1993, 33, 590-594
590
Study on Structure-Activity Relationships of Organic Compounds: Three New Topological Indices and Their Applications Yu-Yuan Yao, Lu Xu,' Yi-Qiu Yang, and Xiu-Shun Yuan Changchun Institute of Applied Chemistry, Academia Sinica, Changchun 130022, Jilin, People's Republic of China Received October 7, 1992 In this paper, three new topological indices, Ax,,A,, and Ax,, have been developed for use in multivariate analysis in structure-property relationship (SPR) and structure-activity relationship (SAR) studies. Good results have been obtained by using them to predict the physical and chemical properties and biological activities of some organic compounds. Quantitative structureactivity relationships (QSAR) have been shown to be a powerful research tool and are being used in many fields. There are two basic kinds of molecular predictors used in QSAR. One of them involves parameters that bear relation to free energy and usually represent some important physicochemical properties of mokcules, e.g., hydrophobic, electronic, and steric parameters. The another category of molecular descriptor is the topological index which is produced directly from molecular structure, e.g., the Wiener index W,1-3 Randic index x," Hosoya index 2,sand Balaban index J.6 In recent years, the latter type of predictor has gained substantial attention in explaining biological activities and physical and chemical properties of organic compounds. However, there are only a few topological indices which can be used to describethe molecular structures containingmultiple bonds and heteroatoms. At present, one of the most popular indices is the molecular connectivity descriptor suggested by Kier and Hall.' The index GAI advanced by Xu et al.*g9has also been successfully used in QSPR studies of neutral phosphorus extractants and in discrimination of &/trans isomers. In this study, three topological indices have been devised to describe the molecular structures not only of alkanes but also molecules containing heteroatoms, multiple bonds, and rings. METHOD
The three topological indices are generated from path matrices A. B. and C,- respectively. These three matrices are defined as follows: A = (uij), uij =
if there is a path of length 1 between vertices i and j otherwise if there is a path of length 2 between vertices i and j otherwise
c = (Cij)'
cij =
(1
if there is a path of length 3
between vertices i and j otherwise
Table I. VDW Radii of Common Atoms B 0.98 F 1.35 C 1.80 Si 1.38 P 1.90 N 1S O 0
S
1.40
Br I
1.95 2.15
1.85
For instance, the hydrogen-suppressed graph and corresponding matrices A, Byand C of 2-methylbutane are
2 0
1
I - [0; 1
0
0
0
p i] 0
0
B=[:
0
3
0
0
2
2
0
2
4 0
2
0
i i i] 0
C=[! 0
0
0
i 0
0
3
0
0
3
j] 0
Augmented path matrices G I X 3 are obtained by adding two columns into matrices A, B, and C, respectively, so as to reflect the structural traits of the heteroatoms and multiple bonds involved. We also take 2-methylbutane as an example; its augmented path matrices G143 are 1 0 1 0 1
0
1.34 1.34 1.34 1.34 1.34
0 1 0 0 0
1 1.73 1.41 1
1.34 1.34 1.34 1.34 1.34
0 0 2 0 2 0 2 0 2
0 0 2 0
0 2 0 0 0 2 0 0 0 2 0 01
1.34 1.34 1.34 1.34 1.34
0 0 0 3 0
0 0 0 0 0
0 0 0 0 0
11 1 1.73 G, = 1.41 1 1
0 1 0 1 0
0 0 1 0 0
1 1.73 G , = 1.41 1 1
3 0 0 0 3
1 0 0 0
1
0 0 0 3 0
The elements in the first column of matrices C1-G3 are square roots of vertex degrees, and the elements in the second column represent the square roots ofthevander Waals (VDW)
0095-233819311633-0590304.00/0 0 1993 Amcrican Chemical Society
J. Chem. Inf. Comput. Sci., Vol. 33, No. 4, 1993 591
STRUCTURE-ACTIVITY RELATIONSHIPS OF ORGANIC COMPOUNDS Table 11. Ax,-Ad and Boiling Points of Alkanes compound 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
AX,
3.3000 5.6669 7.8392 7.9885 9.8972 10.0455 10.2827 11.8958 12.0115 12.0525 12.2646 12.1542 13.8625 13.9503 13.9874 14.0322 14.1606 14.1070 14.0409 14.2271 14.2967 15.8107 15.8774 15.9131 15.9184 15.9544 16.0469 16.0106 15.9829 15.9436 16.1146 16.0448 16.0504 16.5383 16.2004 16.1183 16.2287 16.1050 16.37 15
ethane propane n-butane 2-methylpropane n-pentane 2-methylbutane 2,2-dimethylpropane n-hexane 2-methylpentane 3methylpentane 2,2-dimethylbutane 2,3-dimethylbutane n-hexane 2-methylhexane 3-methylhexane 3-ethylpentane 2,2-dimethylpentane 2,3-dimethylpentane 2,4-dimethylpentane 3,3-dimethylpentane 2,2,3-trimethylbutane n-octane 2-methylheptane 3-methylheptane 4methylheptane 3-ethylhexane 2,2-dimethylhexane 2,3-dimethylhexane 2,4-dimethylhexane 2,5-dimethylhexane 3,3-dimethylhexane 3,4-dimethylhexane 2-methyl-3-ethylpentane 3-methyl-3-ethylpentane 2,2,3-trimethylpentane 2,2,4-trimethylpentane 2,3,3-trimethylpentane 2,3,4-trimethylpentane
2,2,3,3-tetramethylbutane
radii of atoms. From matrices GI-G~,we can obtain matrices Z1-Z3:
AX,
AX,
2.8000 6.0459 8.5529 13.0764 11.6612 14.5963 24.2755 14.3288 17.5400 16.6500 25.3260 18.1478 16.8855 19.3758 19.7022 19.1897 27.6607 20.7716 22.6454 26.6298 27.0273 19.2375 21.4680 21.4806 22.17 10 21.8962 28.7682 23.1371 24.2984 22.8713 29.0337 23.2529 23.6453 28.2243 29.4635 31.5374 28.7363 25.2149 31.6124
2.8000 4.6669 9.2097 6.4885 12.2496 14.8237 8.2827 14.8403 16.9178 21.8185 20.6586 24.8448 18.8597 18.8066 23.5319 28.6999 22.3396 30.7744 20.2652 3 1.9429 35.1277 22.1497 23.8259 26.1465 25.7617 30.0869 23.7612 31.9671 25.6591 21.7795 33.1820 35.7401 37.0947 58.9443 40.4990 24.7994 45.3279 38.4623 49.8827
descriptor AX,
2.80 3.80 4.53
3.53
Ax,, Ax, Ax,, Ax, Ax,, Ax, Ax,, Ax,, Ax,
2.80 4.53 3.21 3.80 2.80 3.80 3.53 4.21 2.80 3.80 11.80 3.53 3.21 2.80 3.53 4.80 4.25 3.53
11.80 3.53
2.80 3.53 3.21 20.80 2.80 11.80 3.53 3.21 2.80 11.80 10.80 3.53 7.21 8.80 4.25
3.53 2.80 6.80
3.53 3.21 3.53 7.21
280 6.80 3.53 3.53
6.80 280 2.80
10.80
where, G1'43'are the tranpose matrices of GI+. new topological indices are defined as where Xmaxl-h,, Z3. The A,,-A,,
1 1
bP (calc) -76.14 -38.63 -3.24 -9.71 28.79 25.55 10.18 60.61 56.20 58.78 45.00 57.62 92.06 88.60 88.63 90.5 1 75.58 88.67 83.61 78.93 79.42 123.59 120.27 120.9 1 119.60 120.83 108.50 119.34 116.45 118.63 109.22 119.74 119.04 118.78 109.94 104.17 111.96 116.85 108.74
Table III. Results of Correlation Analysis between Various Combinations of Ax,-Ax, and Boiling Points of Alkanes Ax,
3.80 3.53 4.21 3.53 7.80 4.25
bP (expt) -88.63 -42.07 -0.50 -1 1.73 36.07 27.85 9.50 68.74 60.27 63.28 49.74 57.99 98.43 90.05 91.85 93.48 79.20 89.78 80.50 86.06 80.88 125.67 117.65 118.93 117.71 118.53 106.84 115.61 109.43 109.10 111.97 117.72 115.65 118.26 109.23 99.23 114.76 113.46 106.47
r
S
0.9846 0.7537 0.7421 0.9959 0.9855 0.7979 0.9959
8.7251 32.7660 33.4201 4.5841 8.5664 30.4698 4.6490
F
n
2170.30 608.49 31.53 1406.74
39 39 39 39 39 39 39
Used to facilitate the computation of the three indices, the van der Waals radii of the common atoms are shown in Table I. APPLICATIONS OF TOPOLOGICAL INDICES &,-Ax,
The three
are the largest eigenvalues of matrices Z1values of 2-methylbutane are
A,, = 10.0455, Ax2= 14.8963, A,, = 14.8237
1. Alkanes. It is of interest to test methods on data for alkanes because good data are generally available for complete isomer sets. In this paper A,,-A,, values of 39 alkanes containing 2-8 carbon atoms were calculated and are listed in Table 11. Table I11 shows a summary of the correlation coefficients, r, standard deviations, s, and F-test values by various combinations of A,,-A,,. It can be seen from Table I11 that the best individual descriptor is A,, with r = 0.9846 and s = 8.7251. Better results have been achieved by using the combination of A,,
592 J. Chem. In& Comput. Sci., Vol. 33, No. 4, 1993
YAO
ET AL.
Table V. Results of Correlation Analysis betweea Various Combinations of A,,-A,, and Boiling Points of Alcohols descriptor
4 AX2 '4x3
= .9
Ax,, Ax, Ax,, Ax, Ax2,Ax3 Ax,, Ax29 Ax,
0
40-
P
00
P
i -401
0
r
S
0.9052 0.4418 0.5723 0.9743 0.9332 0.5724 0.9780
14.8387 31.3306 28.6396 7.9806 12.7377 28.6398 7.4988
F
n
318.12 114.85 8.28 242.04
37 37 37 37 37 37 37
O0
O-
0
0 220
-
0 0
-80
-40
0 40 calculated bp( 'c)
80
120
Figure 1. Plot of observed boiling points vs calculated boiling points of alkanes.
Table IV. A,,-Ax3 and Boiling Points of Alcohol Compounds
1
2 3 4 5
6 7
8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
compound methanol ethanol 1-propanol 2-propanol 1-butanol 2-butanol 2-methyl-1-propanol 2-methyl-2-propanol 1-pentanol 2-pentanol 3-pentanol 2-methyl- 1-butanol 3-methyl-1-butanol 2-methyl-2-butanol 3-methyl-2-butanol 2,2-dimethyl-1propanol 1-hexanol 2-hexanol 3-hexanol 2-methyl- 1-pentan01 3-methyl-1-pentan01 4-methyl- 1-pentan01 2-methyl-2-pentanol 3-methyl-2-pentanol 4-methyl-2-pentanol 2-methyl-3-pentanol 3-methyl-3-pentanol 2-ethyl-1-butanol 2,Zdimethyl- 1-butanol 2,3-dimethyl-l-butanol 3,3-dimethyl-1-butanol 2,3-dimethyl-2-butanol 3,3-dimethy1-2-butanol 1-heptanol 1-octanol 1-nonanol 1-decanol
A,,
A,,
3.0976 5.4746 7.6573 7.8007 9.7202 9.8628 9.8714 10.0976 11.7211 11.8314 11.8720 11.8804 11.8396 12.0821 11.9766 12.0961
2.5976 5.8284 8.3661 128538 11.4583 14.3690 14.4825 24.0559 14.1407 17.3099 16.4279 16.5067 17.3667 25.0985 17.9546 25.2581
13.6BO 13.7717 13.8120 13.8193 13.8203 13.7788 13.9792 13.9309 13.8644 13.9297 14.0459 13.8610 14.0590 13.9376 13.9930 14.1176 14.1238 15.6377 17.5745 19.5034 21.4266
16.7056 19.1464 19.2870 19.3742 19.3374 19.2329 27.4254 20.5661 22.4374 20.5904
26.3955 19.0234 26.5469 20.6108 27.5317 26.7931 26.9196 19.0644 21.3351 23.5232 25.6519
bP A, (expt) 2.5976 64.7 4.4752 78.3 a.9686 97.2 6.3016 82.3 12.0534 117.7 1 4 . 5 ~ 3 99.6 14.5899 107.9 8.0986 82.4 14.6582 137.8 16.6930 119.0 21.5494 115.3 21.6088 128.7 16.7766 131.2 20.4278 102.0 24.6156 111.5 20.4315 113.1
d bc )
157.0 139.9 135.4 148.0 152.4 151.8 121.4 134.2 131.7 126.5 122.4 146.5 136.8 149.0 143.0 118.6 120.0 176.3 195.2 213.1 230.2
153.4 147.8 145.2 145.0 145.1 147.7 125.6 138.7 139.1 138.6 123.4 143.3 123.1 138.6 125.4 121.3 121.0 172.4 191.7 211.1 230.8
18.6384 18.5853 23.1430 23.1899 23.3000 18.6568 22.1120 30.5531 20.0744 30.5076 31.5904 28.5027 31.7318 30.5913 22.2290 34.9025 34.9036 21.9498 24.8307 27.8040 30.5163
52.5 76.1 97.2 88.4 115.9 108.3 108.0 88.7 135.1 126.6 126.6 126.5 126.5 106.2 122.0 105.9
60
Not only would useful topological indices be easy to derive, but also they would possess high structure selectivity, i.e. indices will differ in value whenever they characterize two graphs that are not isomorphic. A comparative study of several topological indices by Razinger et a1.I0 confirmed that the discriminating power of Balaban's J index is remarkable and reaches its initial degenerate value with alkane isomers containing 1 1 carbon atoms. In the present work, it has been found that both A, and Ax, are able to distinguish all the isomers of alkanes up to 1 1 carbon atoms, and among 159 undecanes there is one duplicate value of index A,,. 2. Alcohols. Because the most interesting structures possessing activity are rather complex molecules with multiple bonds and/or heteroatoms, it is quite important that topological indices are able to characterize these kinds of molecules. Alcohol contains one heteroatom, oxygen, whose VDW radius is 1.40 (Table I). The significant correlation between boiling point and the topological indices A,,-A,, and high structure selectivities of these three indices has been found for alcohols. The supporting data are presented in Table IV. The results of the correlation analysis are listed in Table V. It is clear that the best result can be obtained with the combination of all three indices. The regression equation, correlation coefficient, F-test value, and standard deviation are bp O C = 17.4838
+ 18.6511AxI- 2.0450AX1
+ 14.1708AXl- 2.7805AX1- 0.6229Ax, (2)
(1)
r = 0.9959, F = 217.3047, s = 4.5841, n = 39
The boiling points calculated by eq 1 are also listed in Table 11. Figure 1 shows the relationship between the observed boiling points of alkanes and boiling points calculated by eq 1.
220
Figure 2. Plot of observed boiling points vs calculated boiling points of alcohols.
and AXl. Statistical analysis yields the following result. bp O C = -131.9603
100 140 180 calculated b p ( C )
r = 0.9780, F = 242.0399, s = 7.4988, n = 37 The plot of the observed boiling points versus boiling points calculated by eq 2 is shown in Figure 2. 3. Barbiturates. Barbiturates were thought to be nonspecific narcotic agents principally because log P (P= partition coefficient in octanol-water) correlates very well with their
J. Chem. In$ Comput. Sci., Vol. 33, No. 4, 1993 593
STRUCTURE-ACTIVITY RELATIONSHIPS OF ORGANIC COMPOUNDS Table VI. log P and Topological Indices Ax,-Axl for Barbiturates with Structure I
log P 1 2 3 4 5 6 7 8 9 10 11
RI
Rz
AX,
'4x2
Ax,
exptl
calc
methyl ethyl propyl allyl methyl ethyl propyl butyl isobutyl amyl isoamyl
1-methyl, l-propenyl 1-methyl, l-propenyl l-methyl, l-propenyl l-methyl, l-propenyl 1-methylvinyl 1-methylvinyl 1-methylvinyl 1-methylvinyl 1-methylvinyl 1-methylvinyl 1-methylvinyl
3 1.9219 33.8157 35.6742 37.5330 31.0761 32.9670 34.8206 36.6749 36.6896 38.5335 38.5381
51.8177 54.3626 56.2542 57.7404 50.8345 53.3982 55.8622 56.7721 58.5235 58.1687 60.0193
97.0396 107.4888 108.7299 111.1818 95.221 1 105.9361 107.0816 109.5384 119.6529 1 11.2351 121.5974
0.65 1.15 1.65 2.15 0.15 0.65 1.15 1.65 1.45 2.15 1.95
0.55 0.96 1S O 2.02 0.32 0.72 1.27 1.64 1.64 2.33 2.17
Table Vn. log P and Topological Indices Ax,-Ax,for Barbiturates with Structure I1 log P 12 13 14 15 16 17 18 19 20 21 22 23 24 25
RI
R2
Ro
AX,
AX2
AX3
exptl
calc
methyl ethyl propyl isopropyl methyl ethyl propyl isopropyl methyl ethyl methyl methyl propyl ethyl
ethyl ethyl ethyl ethyl methyl methyl methyl methyl propyl propyl isopropyl butyl butyl ethyl
methyl methyl methyl methyl ethyl ethyl ethyl ethyl methyl methyl methyl methyl methyl propyl
33.9096 35.7997 37.6555 37.6737 33.9286 35.8177 37.6724 37.6908 35.7597 37.6523 35.7572 37.6131 39.5086 39.5344
53.4735 56.0127 57.9238 59.2067 53.9510 56.4716 58.3897 59.6247 54.8940 57.4307 55.5639 56.2789 58.8 191 59.7796
99.0809 109.6860 110.9629 120.9469 100.2572 110.4755 111.8534 121.3889 100.9102 111.4127 101.2083 101.9917 112.4071 114.8177
1.15 1.65 2.15 1.95 1.15 1.65 2.15 1.95 1.65 2.15 1.45 2.15 2.65 2.65
1.12 1.53 2.07 1.92 1.11 1.52 2.06 1.91 1.65 2.06 1.65 2.20 2.61 2.59
Table WI. Results of the Correlation Analysis between Ax,-Ax, and log P of Barbiturates dcscriptor Ax, AX2 AX, Ax,, Ax2 Ax,, Ax,
Axp Ax, Ax,, A,, Ax,
r
S
0.9700 0.8780 0.6224 0.9786 0.9790 0.9599 0.9791
0.1530 0.301 1 0.4923 0.1324 0.1311 0.1803 0.1339
F
n
248.50 253.73 128.91 162.07
25 25 25 25 25 25 25
2.
jl
Q
2.0.
9
-j1 . 5 -
!
0 Q
1.0-
biological potency.ll Other studied2 show a dependence of the action of barbiturates upon chemical structure. Therefore, it was of interest to carry out a correlation analysis of log P and topological parameters. Correlations between the topological indices A,,-A,, and log P for barbiturates have been revealed by this investigation. The topological indices Ax,-A,, and log Pof 25 barbiturate acid derivatives with structure I and structure I1 are listed in Table VI and Table VII, respectively.
0
ll o o 0
0. 5
1
0. 5
1. 0
1. 5
2. 0
2. 5
obpcrved logp
Figure 3. Plot of calculated log P values vs observed log P values of barbitures.
coefficient, F-test value, and standard deviation are log P = -7.5991
HNKNH 0 HNKNH 0 Table VI11 shows the results of the correlation analysis between various combinations of Ax,-A,, and log P values of these compounds. It is clear from Table VI1 that the combination of A,, and AX3gives the best result. The regression equation, correlation
+ 0.3042/1,, - 0.0161AX3
(3)
r = 0.9790, s = 0.1311, F = 253.73, n = 25
The plot of the observed log P versus the calculated log P based on eq 3 is shown in Figure 3. 4. Nitrogen-Containing Aromatic Molecules. The 18 nitrogen-containing aromatic molecules given in Table IX have activities of inhibition to the population growth of tetrahymena that are applied in this paper. The molecular
594 J. Chem. If. Comput. Sci., Vol. 33, No. 4, 1993
1 .
YA0
ET AL.
Table IX. Nitrogen-Containing Molecules and Their Activities 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
pyridine 3-picoline 4-picoline 3,4-lutidine quinoline 4-phenylpyridine acridine aniline 3-toluidine etoluidine 3,4-xylidine 1-naphthylamine 4-aminobiphenyl nitrobenzene 3-nitrotoluene 4-nitrotoluene 4-nitro-+xylene 4-nitrobiphenyl
16.2462 18.2208 18.2212 20.1810 27.3730 32.0861 38.1744 18.2630 20.2034 20.2008 22.1347 29.2913 33.9767 22.7907 24.6856 24.6829 26.5796 33.7190
22.2459 27.0819 27.0499 30.8706 41.8459 45.3290 57.1935 27.0741 3 1.9202 30.81 19 35.0 104 45.5792 48.1754 33.4581 37.4021 36.9886 40.5718 5 1.1373
18.7464 26.7527 26.8258 38.8383 52.8343 5 7.8735 8 1.2076 26.7617 33.9390 33.0246 44.2257 62.7174 64.4747 42.0925 46.5200 50.7205 58.3159 72.9092
1.1853 1.0175 0.8921 0.505 1 -0.0132 -0.6576 -1.3979 0.2201 0.4133 0.1271 0.2878 -0.2218 -0,8239 0.0645 -0.3098 -0.2366 -0.6383 -1 .oooo
1.2
-
0.8
-
0. 4
-
h
vi 0
:: 0.0-
c 3
-0.4
-
-0.8
-
-1.2
10
Table X. Results of Correlation Analysis between Ax,-Ax, and the Activities of Nitrogen-Containing Compounds dcscriotor ~
r
S
n
-0.9320 -0.9336 -0.9363
0.2638 0.2606 0.2542
18 18 18
5U Ad
70
90
Figure 4. Plot of activities of nitrogen-containing compounds vs topological index Ax,.
of the results obtained in this paper demonstrate convincingly that the A,,-A,, proposed here are useful topological indices.
~
Ax, Ax2 Ax,
30
REFERENCES AND NOTES structures of these compounds are more complex than the molecules mentioned above. In this study the correlations between the topological indices A,,-A,, and acute toxicities (the concentration which inhibits 50% growth IGCSO) are observed for the 18 selected compounds. Table X shows that satisfactory results can be obtained by using only a single index, so no combination of A,,-A,, was used. The best regression analysis is log (IGCSO) = 1.7292 - 0.0378Ax,
(4)
r = -0.9363, s = 0.2542, n = 18
A plot of the log (IGCSO) values versus A,, shows a direct linear correlation (Figure 4). These results based on indices A,,-A,, are quite similar to that obtained by Schultz et al.13 using a hydrophobic parameter. CONCLUSION The A,,-A,, indices, suggested in this paper, correlate significantly with a number of physicochemical properties and biological activities. The study also indicates that the three topological indices have high structural selectivity. All
Wiener, H. Structural Determination of Paraffin Boiling Points. J. Am. Chem. Soc. 1947,69, 17-20. Wiener, H. Vapor Pressure-Temperature Relationships among the Branched Paraffin Hydrocarbons. J. Phys. Colloid Chem.1948, 52, 425-43 1. Wiener, H. Relation of the Physical Properties of the Isomeric Alkanes to Molecular Structure. J. Phys. Colloid Chem. 1948,52,1082-1089. Randic, M. On CharactcrizationofMolecular Branching. J. Am. Chem. Soc. 1975, 97,66094615. Hosoya, H. Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated Hydrocarbons. Bull. Chem. Soc. Jpn. 1971,44, 2332-2339. Balaban, A. T. Topological Indica B a d on Topological Distances in Molecular Graphs. Pure Appl. Chem. 1983,55, 199-206. Kier, I. B.; Hall, L. H. Molecular Connectivity in Chemistry and Drug Research; Academic: New York, 1976. Xu,L.; Wang, H. Y.;Su,Q. A Newly Roped Molecular Topological Index for the Discrimination of Cis/Trane Isomers and for the Studies of QSARJQSPR. Comput. Chem. 1992,16,187-194. (9) Xu, L.; Wang, H. Y.; Su, Q. Correlation Analysis in Structure and Chromatographic Data of Organophosphorus Compounds by GAL Comput. Chem. 1992,16, 195-199. Razinger, M.; Chretien, J. R.; Dubois, J. E. Structural Selectivity of Topological Indexes in Alkane Series. J. Chem. Inf Comput. Sci. 1985, 25. 23-21. --, -- -
(1 1) Hansch,C.;Anderson,S.M.Structure-Activity RelationinBarbiturates and Its Similarityto That in Other Narcotics. J. Med. Chem. 1967.10, 745-753. (12) Basak, S.C.; Monsrud, L. J.; Rosen, M. E.; Franc, C. M.; Macnuson, V. R. A Comparative Study of Lipophilicity and Topological Indexes in Biological Correlation. Acta Pharm. Jugosl. 1986, 36, 81-95. (13) Kaiser, K. L. E., Ed. QSAR in Environmental Toxicology, Hamilton, Ontario, Canda, 1983; Reidel: Dordrecht, The Netherlands, 1984; pp 337-357.
