Indian Journal of Chemistry Vol. 42A, June 2003, pp. 1405-1413

Application of selected traditional structural descriptors to QSRR and QSAR analysis of barbiturates

Alina Pyka'*, Elzbieta KI(pCzyflska2 & Jacek Bojarski2

ISilesian Academy of Medicine, Faculty of Pharmacy, Department of Analytical Chemistry, 4 Jagiellonska Street, 41-200 Sosnowiec, Poland

2Medical College of JagieUonian University, Department of Organic Chemistry, 9 Medyczna Street, 3~8 Krakow, Poland

Received 24 January, 2003

Thirteen barbiturates have been separated by reversed-phase thin layer chromatography with thirteen mobile phases. The RM values of barbiturates investigated have been correlated with the selected traditional structural descriptors, with the partition coefficients of the compounds, and with the dipole moments (~) or with the pennittivities (E",p.) of the mobile phases applied. The most accurate prediction of the RM values of the barbiturates in all the mobile phases investigated, have been achieved by use of two-parametric equation employing the dipole moments (or the pennittivities) of the mobile phases, and one topological indices from among the topological indices oX, lX, °xv

, lXV, R, W, A, 18 and three parametric equations employing the dipole moments (or the pennittivities) of the mobile phases, and two topological indices (Ia and IX as weIl as fa and IXV), or one electrotopological descriptor (SdssC or SssssC) or Gutman index (M or MV), and selected partition coefficient. However, Randic indices of O-order (X and °XV) are the most universal for QSAR analysis of barbiturates investigated.

Introduction Graph theory is a branch of mathematics that deals

with the way objects are connected l. The connectivity

in a system is an essential quality of graph theory. Graph theory has been used in chemistry2-11 and biolog/,",12. Topological indices have generally been used for evaluation of the chemical structures of organic compounds, both homologous series and specified isomers5

,11 ,13 , Especially interesting from a physicochemical and biological points of view are correlations between topological indices and specified physical constants, biological activity as well as chromatographic retention5,11 ,14. The fundamental basis of these investigations is that the structure of a molecule determines its properties. This can be expressed by the mathematical dependence5,1':

P = j{S) ... (I)

where P is any physical, chemical, parmacological or toxicological property of a molecule, and S is any descriptor of structural aspects of the molecule.

The most important topological indices were discussed in reviews2,5,11,13.18. From all of them, the R d· , (0 I 2 0 v I v 2 V) G (M) W' an IC X, X, X, X , X, X, utman , lener (W), and Balaban (lB) indices are the best, in terms of their applications, such as: Quantitative Structure-

Activity Relationships (QSAR), Quantitative Structure-Property Relationships (QSPR), and Quantitative Structure-Retention Relationships (QSRR) for organic compounds5,11,13,14,16,19.

We have previously proposed equations enabling prediction of TLC RM values from the dipole moments of mobile phases, topological indices, and the net electron charge of selected hydrocarbons and their quinones, which were analyzed by adsorption TLCo. The dipole moment (or the permittivity) of mobile phases and numerical values of structural descriptors have been used to predict the RM values of higher unsaturated fatty acids21 , tocopherols22

, methyl esters of higher fatty acids23

, higher fatty acids, hydroxy fatty acids and their esters24 and some terpenes25 .

The aim of this work was to estimate of usefulness of selected traditional topological indices to calculate partition coefficients, RMo values of lipophilicity, biological activity and calculate and predict RM values of selected 5,5-disubstituted derivatives of barbituric acid when separated by reversed-phases thin-layer chromatography (RPTLC).

Materials and Methods 5,5-Disubstituted barbituric acid derivatives

investigated (Table 1) were commercial samples obtained from different drug manufacturers.

1406 iNDIAN 1 CHEM, SEC A, JUNE 2003

Table I-Structure and names of the investigated 5,5-disubstituted barbituric acid derivatives

H

~riYO R 5 3N....,. 4 H

R2 0

Compound C5 substituents of Drug name No. barbituric acid

I 5,5-diethyl Barbital 2 5-ethyl-5-( I-methylbutyl) Pentobarbital 3 5-ethyl-5-n-pentyl 4 5-ethyl -5-n-octyl 5 5-ethyl-5-sec-butyl Butabarbital 6 5-ethyl-5-isopentyl Amobarbital 7 5-ethy 1-5-( 4,4-d i methy Ihex y I) 8 5-ethy 1-5-(3-meth y Icyclohex y I) 9 5-ethyl-5-phenyl Phenobarbi tal 10 5-allyl-5-isopropyl Aprobarbital II 5-allyl-5-isobutyl Butalbital 12 5-allyl-5-sec-butyl Talbutal 13 5-ally 1-5-(2-cyclopenten y I) Cyclopal

Topological indices and electrotopological states The selected topological indices based on

connectIvIty: Randic eX, lX, 2X, °xv, lXV,

2XV),5.11.13.17.26.27 Gutman (M, MV)1 5.28, Pyka (X0I2,

X:;12)29.30,on distance matrix: Rouvray (R) 13, Wiener

(W) 13,31, Balaban (Is) 32, and Pyka (A, °B, IB, C, o )29.30 indices were calculated for the barbituric acid derivatives. The Rouvray, Wiener, Balaban, and Pyka indices were calculated by building the distance matrix and determining its elements by means of values given by Barysz et al. 33. The sums of electrotopological states SdO, SdssC, SsCH3, SssNH, and SssssC in the molecules of barbituric acid derivatives investigated were obtained from internet data34 .

The methods of calculation of the topological indices and electrotopological states were presented in numerous reviews2,11 ,13,15,19,)5,

Reversed phase thin layer chromatography Thin-layer chromatography was performed on TLC

aluminium sheets 20 x 20 cm RP-18 F254s (Merck, Darmstadt, No. 10559). The mixtures of methanol­water were used as the mobile phases. Methanol content was varied by 5% volume from 40 to 100%.

The ethanol solutions (1 % w/v) of the investigated compounds were applied on the start line of plates with Hamilton syringe (10 Ill) . The plates were developed at room temperature in a classical flat

bottom chamber (Camag, Switzerland) previously saturated for 30 min. The chromatograms were developed on 12 cm distance at 21±1°C. After development and drying the spots were visualized with the UV light (254 nm). The chromatograms were run in duplicates. The RF values were the mean values from duplicated runs and were used for calculation of RM parameters according to the expression:

RM = log(l /RF-l) ... (2)

The dipole moments (Ilmph) and pennittivities (Cmph) of the mobile phases used were calculated from36:

Ji:p" = L N i Jii2 ... (3)

i=1

£= ~ v£ L.J I I ... (4)

i=1

where Ni and Ili are the mass fraction and dipole moment, and Vi and Ci are the volume fraction and permittivity, respectively, of the ith component of mobile phase.

Partition coefficients The partition coefficients (lAlogP, c1ogP, 10gPKowin)

were calculated using different theoretical procedures for investigated barbituric acid derivatives34.37-41. The IAlogP predictor was developed by interactive analysis, using default set of 238 MolconnZ molecular indices generated from 13,000 organic structures with accurately measured 10gP values and using neutral networks technology to drive a set of 10 fold cross-validated networks34. The c10gP is the "constructionistic" fragmental system from Hansch and Le037.39,41. The 10gPKowin procedure is based on atom/fragmental contributions34,37. These partition coefficients were obtained from internet data34. Moreover, the partition coefficients were calculated from fragmental constants, according to the method of Rekker41-43, using Eqs 5 and 6.

II

log PRek(WithOUI e M ) = L a iIi i=1

II II

logPRek = La;!i + L kiCM i=1 i=1

.. . (5)

.. . (6)

with f denoting the hydrophobic fragmental constant, the lipophilicity contribution of a constituent part of a

PYKA el al.: QSRR & QSAR ANALYSIS OF BARB/TURA TES 1407

structure to the total lipophilicity, and a is a numerical factor indicating the incidence of a given fragment in the structure. CM denotes the magic constant (=0.289) and ki gives the frequency of this constant in the structure under consideration.

CorreLation anaLysis Correlation analysis by the least squares method

was performed using the computer programs Statistica PL 6.0 and Statgraphics Plus v.2.1. The multiple equations were obtained using stepwise variable selection.

Results and Discussion Tables 2 and 3 show numerical values only of those

structural descriptors which were useful in QSRR and QSAR analysis for the calculation of the partition coefficients, RMO, biological activities and RM values of 5,5-disubstituted barbituric acid derivatives. The

numerical values of the topological indices based on

h d · . (M 0 I M V 0 v I v d tea Jacency matnx , X, X, Xo12, , X, X, an

X~12) are listed in Table 2 for the compounds

investigated. The numerical values of topological indices based on distance matrix (R, W, IB, A, 'B, and D) for the compounds investigated, and the sum of electrotopological states of selected groups of the barbiturates are listed in Table 3.

The RM values obtained by the use of thirteen methanol+water mobile phases of the 5,5-disubstituted derivatives of barbituric acid investigated are listed in Table 4. Table 4 also contains respective values of dipole moments and permittivities of the mobile phases used.

The numerical values of partition coefficients calculated by use of different procedures for the compounds investigated are li sted in Table 5, which also contains the RMO values. The RMO values were obtained by extrapolating the RM values to zero

Table 2-Numerical values of topological indices based on the adjacency matrix for investigated barbiturates

Compound M Ox IX Xol 2 MV °Xv IXV X~12

No.

1 94 8.9497 5.0963 5.7184 214 7.6389 4.2338 4.6086

2 108 11.2342 6.5170 7.3054 228 9.9234 5.6545 6.2022

3 106 11.0710 6.5963 7.2431 226 9.7602 5.7338 6.1370

4 118 13.1924 8.0963 8.7462 238 11.8816 7.2338 7.6411

5 104 10.5271 6.0170 6.7912 224 9.2162 5. 1545 5.6869

6 108 11.2342 6.4521 7.4388 228 9.9234 5.5896 6.3451

7 124 13.5710 7.8034 9. 1008 244 12.2602 6.9409 8.0122

8 124 12.2257 7.2459 8.3637 244 10.9149 6.3834 7.2771

9 150 10.6294 6. 1963 6.8759 270 9.3186 5.3338 5.7687

10 112 10.1044 5.5883 6.5293 232 8.7936 4.7268 5.4321

11 116 10.8116 6.0614 7.1095 236 9.5008 5. 1999 6.0174

12 116 10.8116 6.1263 6.9572 236 9.5008 5.2648 5.8541

13 136 10.6734 6.4167 7.1721 256 9.3626 5.5552 6.0764

Table 3-Numerical values of topological indices based on the distance matrix and E-states for investigated barbiturates.

Topological indices based on distance matrix E-states Compound R W Is A IB D SdssC SssNH SssssC

No. 1 376.59 188.81 15.924 106.53 0.4966 23.905 -1.7176 4.1853 -1.0616 2 716.19 358.61 19.472 183.56 0.3994 39.049 -1 .6554 4.3621 -1.0933 3 782. 19 391.61 18.686 201.65 0.3644 40.2 17 -1.6303 4.3373 -1 .0525 4 1475.79 738.41 20.914 349.63 0.2688 61.911 - 1.6003 4.4059 -1.0569 5 573.66 287.35 18.478 151 .28 0.4374 33.354 - 1.6819 4.3139 -1.0946 6 756.19 378.61 18.956 193.85 0.3756 41.758 -1.6552 4.3309 -1.0712 7 1331.79 666.41 21.893 312.01 0.2961 63.467 -1.6351 4.4067 -0.8709 8 983.26 492.15 15.641 236.02 0.3781 52.174 -1.5347 4.5191 -1.0618 9 746.81 373.92 15.569 183.83 0.4422 38.002 -1.9029 4.2804 -1.3103 10 563.66 282.35 18.621 148.29 0.4429 32.997 -1 .8587 4.2183 -1.2126 11 709.19 355.11 19.546 181.22 0.4007 39.574 -1.8165 4.2664 -1.1906 12 687. 19 344.11 19.844 175.42 0.4147 37.151 - 1.8157 4.2861 -1.2040 13 793.72 397.38 15. 132 195.83 0.4187 41.402 -1 .0446 4.3278 -1.2717

1408 [NDlAN J CHEM, SEC A, JUNE 2003

Table 4--1be ~ values of the investigated compounds for different methanol content in methanol :water mobile phase and the dipole moments (J.l) and permittivities (£) values of the meth3llol+water mobile phases

M~I __ ~ __ ~~ __ ~ ____ ~ ____ ~~~~v~ru=u~~f~~ro=~~~oo~n=o~. ~~ __ ~~ __ ~ __ ~~ __ content 2 3 4 5 6 7 8 9 10 11 12 13

Description of mobile phases

(%) I! [D) E

100 ~.803 ~.613 ~.654 ~.949 ~.893 -0.764 ~.720 --(J.723 1.6998 32.62

95 ~.689 ~.542 ~.559 ~.402 ~.675 ~.616 ~.484 ~516 ~.767 -0.722 ~.657 ~.635 ~.597 1.7099 34.91

90 ~.667 ~.325 ~.387 ~. 124 -0.459 -0.476 ~.246 ~.314 ~.61O -{)6()2 ~.464 -0.431 --(J.399 1.7197 37.20

85 ~.608 ~.220 -0.251 0.040 ~.359 ~.319 ~.085 ~.177 ~.498 ~.436 -0.353 -0.310 ~.282 1.7291 39.48

80 ~..524 ~.094 ~.096 0.232 ~.316 ~. 197 0.092 ~.061 ~.339 ~.335 -0.246 ~. 192 --(J.150 1.7383 41.77

75 ~.485 ~.035 0.022 0.446 ~. 1I2 ~.028 0.314 0.084 ~.296 ~.296 ~. 146 ~.095 ~.083 1.7472 44.06

70 ~.294 0.117 0.143 0.589 ~.039 0.070 0.597 0.236 ~.162 -0.154 ~.042 0.022 0.01 4 1.7558 46.35

65 ~.I94 0.233 0.284 0.882 0.077 0.254 0.730 0.397 ~.085 ~.084 0.072 0.140 0.149 1.7642 48.64

60 ~.082 0.394 0.409 1.070 0.157 0.339 1.064 0.594 0.010 0.000 0.163 0.223 0.240 1.7723 50.92

55

50

45

40

~.078 0.459 0.493

0.056 0.704

0.147 0.855

0.356 0.533

0.460 0.692

0.570 0.839

0.792 0.198 0.208 0.366 0.413

0.979 0.406 0.348 0.514 0.504

0.462 0.458 0.656 0.650

0.833

0.405 1.7803 53.21

0.547 1.7880 5550

0.692 1.7954 57.79

1.8027 60.08

Table 5-LogP values calculated using different theoretical procedures and experimental RMO values.

Compound AlogPS WogP c10gP logPKowlN logPRek logPRek(wilhoul e m) RMO

No.

1 2 3 4

5 6

7 8 9 10

11 U 13

0.74

2.17

2. 12

3.57

1.59

1.84 3.19

2.33

1.41

Ll9 1.34

1.81

1.63

0.57

1.92

2.09

3.66 1.38

2.06

3.31

2.23

1.89

Ll5 1.71

1.50

1.27

0.65

2.11

2.24

3.83

1.58

2.11

357

2.68

1.37

LlO 1.63

1.63

1.36

methanol concentration in methanol-water mobile phase.

Use of selected structural descriptors and partition coefficients to QSRR analysis of barbiturates investigated

The two-parametric and three-parametric correlation equations obtained which enable calculation of RM values of the 5,5-disubstituted barbituric acid derivatives for chromatography with the thirteen mobile phases with different methanol contents are listed in Table 6. Table 6 lists only those two-parametric equations, which have determination coefficients R~ 93 and three-parametric equations which have R 2 greater than two-parametric equations.

0.60

2.00

2.08

3.55

1.51

2.00

3.44

2.80

1.33

1.38

1.87

1.87

2.16

0.78

2.34

2.34

3.90

1.82

2.34

3.90

3.41

1.66 1.41

1.93

1.93

1.63

0.78

2.34

2.34

3.90

1.82

2.34

3.90

2.97

1.66

1.41

1.93

1.93

1.63

0.920

1.957

1.984

3.514

1.661

2.118

3.566

2537

1.564 1.476 1.783

1.739

1.764

The dipole moments (or the permittivities) characterize and differentiate between each mobile phase. To correlate equations it is necessary to introduce a property differentiating the 5,5-disubstituted barbituric acid derivatives investigated. Such properties can be the topological indices, electrotopological states of selected groups, or partition coefficients. Correlation equations (7)-(18) characterize the mobile phases by dipole moments. The valence Randic indices °xv and IX" give similar regressions to Eqs (7), (8) and (13), respectively. Also, topological Gutman MY index gives similar regression to Eq. (18). Analogously, the correlation equations taking into account the permittivities of the mobile phases, instead of the dipole moments of the

PYKA et al.: QSRR & QSAR ANALYSIS OF BARBITURATES 1409

mobile phases, have also statistical significance. For example:

RM=-4.535 (±O.lO8) + 0.0560 (±O.OOI2)x Emph

+ 0.181 (±O.OO8)xOX .. . (19) n=l44; R2=94.82; F=1292; s=O.I04; p<O.OOOI; DW=l.44

RM=-4.274(±O.0994) + 0.0563 (±O.OOI1)x Cmph

+0.0183(±O.0045)xIB

+0.251 (±O.012)x IX ... (20) n=I44; R2=95.65; F=1025; s=O.099; p<O.OOOl; DW=1.69

For the correlation equations given by Eqs (7)-(20) there was no correlation between any pairs of the terms used in the equations.

All the correlation equations listed in Table 6 are statistically significant. For all correlation equations the P-value is less than 0.0001. Since the p-value in the Anova table is less than 0.01, there is a statistically significant relationship between the variables at the 99% confidence level. For all correlation equations obtained the Durbin-Watson (OW) statistic value is greater than 1.4. The high value of determination coefficients (R2), value of the Fisher test (F) and small values of standard error of the estimate (s), and significance levels (p) of the equations presented in Table 6 and Eqs (19) and (20) are indicative of the special physicochemical importance of the topological indices, electrotopological states as well as partition coefficients.

The correlation Eqs (7)-(20) can be used to calculate RM values of investigated barbiturates using the different volume composition [%] of methanol in methanol-water mobile phases. For example, the relationship between RM values measured experimentally and the values calculated by use of Eq. (19) is shown in Fig. 1. Ten points in Eq. 19 has the studentized residual greater than 2.00. The studentized residual between 2 and 3 is obtained for 5,5-diethyl barbituric acid (100%, 95%), 5-ethyl-5-n­octyl barbituric acid (95%, 65%), 5-ethyl-5-( 4,4-dimethylhexyl) barbituric acid (90%, 80%,60%), and 5-ethyl-5-phenyl barbituric acid (60%). Moreover the studentized residual is equal to -3.61 for 5-ethyl-5-(4,4-dimethylhexyl) barbituric acid (95%), and for 5-ethyl-5-n-octyl barbituric acid (60%), it is 3.61. These points are particularly distant from straight line.

Equations (7)-(20) can also be used to predict the RM values of the 5,5-disubstituted barbituric acid, the measurement points of which have not been taken into consideration in the equation. A test was performed on Eqs (14) and (20) to determine how well they predict values of points not included in the training set. Nine values were removed from the training sets (Eqs 14 and 20): 5-ethyl-5-n-pentyl barbituric acid (separated in methanol: water, 95 :5, v/v), butalbital (separated in methanol:water, 80:20, and 50:50, v/v), talbutal (separated in methanol:water, 75:25, v/v), aprobarbital (separated in methanol:water, 70:30, v/v), barbital (separated in methanol: water, 65:35, and 60:40, v/v), cyclopal (separated in methanol:water, 65:35, v/v), and amobarbital (separated in methanol :water, 60:40, v/v) and the sub­set of two-parametric or three-parametric equations were recalculated as:

Table 6---The characteristics of the multiple correlation equations that enable calculation of the RM values of the compounds investigated

Eq. Equation No. 7 RM =-27.787 (to.567) + 14.752 (to.316)xllmph + 0.178 (to.008)x"X

8 RM =-27 .625(tO.55I ) + 14.810 (to.309)xllmph + 0.266(tO.0 12)x1X

9 RM =-26.484(tO.62I) + 14.812(tO.353)xllmph + O.OOO72(tO.OOOO4)xR

10 RM=-26.485(tO.621) + 14.8 I 2(tO.353)xllmph + 0.00143 (to.OOOO8)xW

11 RM =-26.598 (to.605) + 14.824 (to.344)xllmph + 0.00333 (to.00017)xA

12 RM =-24.487 (to.553) + 14.814 (to.316)xllmph - 3.60I(tO.167)x IB

13 RM =-27.864 (to.526) + 14.827 (to.293)Xllmph + 0.0184 (±O.0046)x Is +0.246 (to.012)x IX

14 RM =-26.120(±0.503) + 14.810 (to.284 )Xllmph +0.184 (±O.038)x(SdssC)+ O.235(tO.0 I O)xIOgPRCk(wilhoul em)

15 RM =-25.915 (to.574) + 14.8 I 2(tO.325)xllmph +O.277(tO.044)x(SdssC)+ 0.246 (to.OI 2)xIAlogP

16 RM =-26.134 (to. 50 I) + 14.841 (to.283)xllmph +0.174 (to.038)x(SdssC)+ 0.236(tO.0 10)xc\ogP

17 RM =-26.113 (to.509) + 14.799 (to.285)xllmph +O.257(tO.086)x(SssssC)+ 0.253 (to.O 12)x logPKowin

18 RM =-26. I 92(tO.498) + 14.785(tO.282)xllmph - 0.00206 (to.00058)xM+ 0.281 (to.O II)x logPKowin

a)for all equations p< 0.000 I; DW> 1.4; and n= 144

Statistical data') R2 F s

94.69 1258 0.109

94.96 1329 0.106

93.40 997 0.1 2 1

93.40 997 0.121

93 .76 1058 0.118

94.70 1260 0.109

95.49 988 0.100

95.75 1052 0.098

94.46 795 0.111

95.79 1063 0.097

95.72 1045 0.098

95.83 1072 0.097

1410 INDIAN J CHEM, SEC A, JUNE 2003

1.6

I 2 . . . . . . --- - --- -- - - - -- ---------r------------- - - - -----T- - - --- -- ---- - ---------r--- - -----------------"]"- - ------------------ - -r----~--~-----------

i :: .........III •••••••••• ioo······· :e-~~ ....... . i 0.0 ----------·-----------r----------------------r--------_______________ -!- ______ o 0 ~ l~--- ------ --- ---- -t---------------------

-0.4 -----------------------;- --- ------ --------------f·-- ---------b ---- ------------------j-----------------------+----------------------i i 0 . 0 . .

08 ~iO oor+rl -1.2 I • •

-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0

calculated R M

Fig. I- Relat ionships between the experimental RM values of the compounds in vestigated and the RM val ues calculated by use of Eq.(19) Relationships between the experi mental RM values of the barbiturates investigated and the RM values calculated using of ego: RM =-26. I 92(±0.498) + 14.785(±0.282)x~l"'ph - 0.00206 (to.00058)xM+ 0.281 (to.O II )x 10gPKowin n=I44; R2=95.83 ; F=I072; s=0.097; p<O.OOOI; DW=1.50 where: J.lmph denotes the dipole moments of mobile phases applied, M denotes Gutman index, and ]ogPKowin denotes theoretical partition coefficient based on atom/fragmental contributions.

Table 7-RM values of compounds omitted from Eqs. (2 1), and (22), and predicted by these equations

RM Omitted point Experimental Predicted 11'1 RM I Predicted /1'1 RM / (% content of methanol in methanal-water mobile phase)")

5-ethyl-5-n-pentyl barbituric acid (95 %) butalbital (80%) talbutal (75%) aprobarbital (70%) barbital (65 %) cyclopal (65 %) barbital (60%) amobarbital (60%) butalbital (50%)

' Explanations in section, Results and Discussion"

RM =-26.142 (±0_526) + 14.8333(±0.298)xJ..lmph +0_191 (±0.041 )x(SdssC) +0.232(±0.011)xlogPRek(withoutCm) ___ (21)

n =135; R2=95 _69; F=971; s=0_100; p<O_OOOl ; DW=L55

RM =-4A84(±0_1 09) + 0_0563 (±O.OO 12)x Cmph + 0_0183(±0.0047)xln +0.250 (±O_013)x IX

n =135; R2=95_54; F=934; DW=L72

_. _ (22) s=0_102; p<O_OOOl;

The RM values for 5,5-disubstituted barbituric acid derivatives, omitted during the derivation of Eqs (21)

by Eg.(2 1) by Eq _(22)

-0.559 -0.548 0.011 -0.525 0_034

-0.246 -0.258 0.012 -0.257 0_011

-0.095 -0.126 0.031 -0.106 0_011

-0. !54 -0_128 0.026 -0_134 0_020

-0.194 -0. 125 0.069 -0_178 0_016

0.149 0. 198 0_049 0_138 0_011

-0.082 -0.005 0.077 -0_050 0_032

0.339 0.372 0.033 0.345 0_006 0.514 0.478 0.034 0.516 0_002

and (22) and subsequently predicted USIng these equations, are listed in Table 7_

These equations are statistically significant and can be used for reasonably good prediction of the RM values of the barbituric acid derivatives investigated_ There is high compatibility between experimental and predicted RM values for barbiturates omitted in correlation equations_

Use of seLected structuraL descriptors to QSAR analysis of barbiturates investigated

We correlated the RMO values, the partition coefficients, and biological activity of barbituric acid derivatives investigated_ The RMO values, similar to the

PYKA et al.: QSRR & QSAR ANALYSIS OF BARBITURATES 1411

Table 8-Coefficients (r) for linear dependencies between RMO' log I/C and the best structural descriptors.

Structural RMO Partition coefficients log lie) logl/Cb)

descriptor IAlogP c10gP IOgPKowlN 10gPRek 10gPRek(without COl) Coml2ound no. 1-3 ,6,9-11 1,2,6,9-11

°xv 0.9862 0.9581 0.9743 0.9729 0.9840 0.9894 0.9345 0.9756

IXV 0.9720 0.9560 0.9725 0.9758 0.97 17 0.9747 0.9238 0.9164

X:12 0.9758 0.9308 0.9575 0.9784 0.9804 0.9752 0.9359 0.9805

Ox 0.9862 0.9582 0.9744 0.9729 0.9841 0.9894 0.9345 0.9756

IX 0.9720 0.9561 0.9725 0.9757 0.9717 0.9742 0.9237 0.9161

Xo I2 0.9767 0.9327 0.9590 0.9788 0.9811 0.9763 0.9368 0.9795

R 0.9737 0.9587 0.9481 0.9583 0.9347 0.9494 0.8217 0.8855

W 0.9737 0.9587 0.9481 0.9583 0.9347 0.9494 0.82 17 0.8855

A 0.9756 0.9648 0.9556 0.9604 0.9372 0.9542 0.8610 0.9166 IS -0.9647 -0.9628 -0.97 12 -0.9525 -0.9381 -0.9652 -0.9488 -0.9762

D 0.9822 0.9442 0.9515 0.9784 0.9625 0.9650 0.8693 0.9468

SssNH 0.8195 0.7923 0.8548 0.8483 0.8277 0.8191 0.9461 0.8678

a C is concentration causing 50% inhibition of divi sion of Arbacia Egg cells at pH 8 (data taken from44) ; b data for barbiturate inhibition of rat brain oxygen consumption (data taken from44

)

partition coefficients, describe the lipophilicity of barbiturates. It was stated, that linear dependences exist between RMO values, partition coefficients, biological activities and some topological indices. The correlation coefficients (r) of linear relationships in QSAR analysi s of barbiturates investigated are listed in Table 8. The correlation coefficients with best topological indices only were presented in Table 8.

The RMO values were best correlated with topological indices based on adjacency matrix oX, lX,

° v I v d v II d' . R XoI2, X , X , an XOl2 as we as Istance matnx ,

W, A, IB, and D (r>0.96). For example:

RMO = -3 .94 1 (±O.30S) + 0.608(±0.031)x OXV ... (23) n=13; r= 0.9862; s=O.131; F=391; p<O.OOOI

We affirmed, that oX, lX, °xv, and IXV indices are the

best for calculation of particular partition coefficients (r>O.9S). For example:

IAlogP= -S.370(±O.6S9)+0.6S2(±0.OS9)xOX ... (24) n=13; r=O.9S82; F=123.2; s=0.2SI; p<O.OOOl

clogP= -6.1S4(±O.S70)+0.730(±0.OSI )XOX ... (2S) n=13; r=O.9744; F=206.3 ; s=0.217; p<O.OOOl

logPKowin= -4.394(±O.409)+0.878(±0.OSS)XXO I2' " (26) n=13; r=O.9788; F=2SI.0; s=O.l77; p<O.OOOl

IOgPRek= -6. 1 67(±O.46l)+0.7SS(±0.04l)xOx ... (27) n=13 ; r=0.9841; F=337.4; s=0.176; p<O.OOOl

IOgPRek(wilhoul Cm)= -S.91S(±0.361) +0.730(±0.032)xOX .. . (28)

n=13 ; r=0.9894; F=SI3.0; s=0.138; p<O.OOOl

Also, we received satisfactory correlations between partition coefficients and some topological indices based on distance matrix: R, W, A I B and D (r>0.93).

Biological actIVIties of some barbiturates investigated were obtained from literature44

. The barbiturate concentrations (log lie') causing SO% inhibition of division of Arbacia Egg cells at pH 8 (for barbital, pentobarbital, amobarbital, phenobarbital, aprobarbital, butalbital, and S-ethyl-S­n-pentyl barbituric acid) are the best correlated with topological index IB and electrotopo}ogical state SssNH:

log IICa) = 6.984(±0.693) - 11 .088(±1.6S2)x IB

... (29) n=7; r= - 0.9488; s=0.186; F=4S; p<O.OOS

loglle') =-31.0S1 (±S.1 IS) + 7.800 (±1.194)xSssNH

n=7 ; r= 0 .9461; s=0.191; F=42; p<O.OOS ... (30)

Also, we received satisfactory correlations between log lie' and some topological indices based on

adjacency matrix: oX, °x v, XOl2 and X ~12 (r>0.93).

Data for barbiturate inhibition (logllCb) of rat brain

oxygen consumption (for barbital, pentobarbital, amobarbital, phenobarbital , aprobarbital, and

1412 £NOlAN J CHEM, SEC A, JUNE 2003

butalbital) are the best correlated with topological indices based on adjacency matrix oX, °xv, Xol2 and

X~12 and topological index 18. For example:

10gIlCb)= -3.356 (±0.592) + 1.024(±O.103)x X~12

... (31) n=6; 1- 0.9805; s=0.146; F=99; p<O.OOl

It was stated, that the topological indices M, MV, 2X,

2XV, °B, C, and electrotopological states SdO, SdssC, SsCH3, and SssssC for QSAR analysis of investigated barbiturates were not useful. However, Randie indices of O-order (OX and °XV) are most universal for QSAR analysis of barbiturates investigated.

Conclusions It was stated, that the selected traditional

topological indices could be used to QSAR and QSRR analysis of barbituric acid derivatives. The RM values of barbiturates investigated have been correlated with the selected structural descriptors, with the partition coefficients of the compounds, and with the dipole moments (!lmph) or with the permittivities (Emph) of the mobile phases applied. The most accurate prediction of the RM values of the barbiturates in all the mobile phases investigated, were achieved by use of two-parametric equations employing the dipole moments (or the permittivities) of the mobile phases, and one topological index from among the topological indices oX, lX, °xv, lXV, R, W, A, IB and three parametric equations employing the dipole moments (or the permittivities) of the mobile phases, and two topological indices (lB and IX as well as IB and IXV), or one electrotopological descriptor (SdssC or SssssC) or Gutman index (M or MV

), and selected partition coefficient. The high determination coefficients and significance levels of the equations presented herein are indicative of the special physicochemical significance of the topological indices, which were mentioned above. The practical value of the presented models is in calculating and in predicting RM values of yet unknown 5,5-disubstituted barbituric acid derivatives. Yet, the Randie indices of O-order eX and °XV) are most universal for QSAR analysis of barbiturates investigated.

Moreover, the methods presented are very simple and may be recommended for the purpose of the quantitative structure-retention relationship and the quantitative structure-activity relationship analysis of barbi turates.

Theoretical determination of the partitIOn coefficients, biological activities, RMO, and RM values of organic compounds has special significance if standards are not available. The methods presented for determination of partition coefficients, biological activities, RMO, and RM values might also be useful in the design of drugs.

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