Indian Journal of Chemistry

Sect. A: Inorganic, Bio-inorganic, Physical, Theoretical & Analytical

 

 

VOLUME 42A

NUMBER 6

JUNE 2003

 

 

CONTENTS

Part 1 : Theory
Review

 

1207

 

Chemical graph theory – facts and fiction

 

 

 

 

Milan Randić

 

 

 

Graph Theory (GT) and its applications in chemistry, known as Chemical Graph Theory (CGT), appear to be two of the most misunderstood areas of theoretical chemistry. Possible causes for misunderstanding are briefly  outlined and remedies  suggested, including a test on the knowledge of GT and CGT.

Papers

 

1219

 

On the structural interpretation of topological indices

 

 

 

Anton Perdih* & Branislav Perdih

 

 

 

To perform the structural interpretation of topological indices and physicochemical properties, the approach using structural features like the size of the molecule, the number and  position of branches, separation between them, the type of branches, and the type of the branched structure is generally applicable.

 

1227

 

Applications of information theory in chemical graph theory

 

 

Elena V  Konstantinova*, Vladimir A Skorobogatov & Maxim V Vidyuk

 

 

 

The application of information theory to the problem of characterizing molecular structures is presented. The information indices based on the distance in a graph are considered with respect to their correlating ability and discriminating power.

 

1241

 

Relations between topological indices of large chemical trees

 

 

 

 

 

 

Ivan Gutman*, Dusica Vidovic, Boris Furtula, & Aleksander Vesel

 

 

 

Several approximate relations have been established between eigenvalue sum and Hosoya index, greatest graph eigenvalue and connectivity index, Wiener index and smallest positive Laplacian eigenvalue, greatest Laplacian and greatest ordinary graph eigenvalue, Zenkevich and Wiener index, and hyper-Wiener and Wiener index and these hold good for alkanes with n=10 or fewer carbon atoms. Applying an algorithm for generating trees uniformly by random, these regularities have been tested for very large chemical trees (n=50).

 

1246

 

Towards branching indices

 

 

 

 

 

 

Anton Perdih

 

 

 

Topological indices Vj(-1/2,-1/2), Vj(-1/2,-1), Vij(-1/4,-1), Vij(-1/4,-1/3), Lj(-1/3,-1/4), Lij(-1/4,-1/2), lnMij(1/3,1/4), as well as lnMij(‑4,1) are promising candidates for branching indices. Using a logarithm of the index or the geometric mean of the value of the nondiagonal elements of the matrix among the multiplication-derived indices, improves the situation greatly. These indices can be a good source to derive branching indices of the BIA group.

 

1258

 

A new chemical index inspired by biological plastic evolution

 

 

 

 

 

 

 

 

Francisco Torrens

 

 

 

This paper presents an application of plastic evolution to a new index (coordination index, Ic) for molecular characterization. Ic is applied to series of phenyl alcohols and 4‑alkylanilines, and compared to charge indices for dipole moment. The parameters needed to calculate Ic are the standard enthalpy of formation, molecular surface area and molecular weight. The correlations between these indices and the number of C atoms in alkyl chain indicate a homogeneous molecular structure of the phenyl alcohols and 4‑alkylanilines.

 

1264

 

Partition of Wiener-type indices, especially for trees

 

 

 

 

 

 

Douglas J Klein

 

 

 

Different ways are noted to partition the Wiener index of a molecular graph G into contributions associated to different substructures of G, particularly, for the case where G is a tree and the substructures are sites or bonds.  Representative related partitionings for some related graph invariants are also established.  Paralleling the definition of Wiener (or Hosoya) polynomials, the partitioning results are used to motivate Szeged polynomials.

 

1270

 

On the Wiener index decomposition for catacondensed benzenoid graphs

 

 

 

 

 

 

Andrey A Dobrynin

 

 

 

Some properties based on the decomposition of the Wiener index for catacondensed benzenoid graphs are presented. It is shown that  if and only if , where  denotes the sum of distances between vertices of degree 2 in a benzenoid graph .

 

1272

 

Chemical applications of the Laplacian spectrum. VII. Studies of the Wiener and Kirchhoff indices

 

 

 

 

Ivan Gutman*, Dusica Vidovic &
Boris Furtula

 

 

 

Some chemical applications of the Laplacian spectra are reported. By means of Kel'mans theorem a previously known formula for the Wiener and Kirchhoff index is deduced. It is shown that the Wiener index is correlated with the algebraic connectivity. Lower and upper bounds for the Kirchhoff index are obtained.

 

1279

 

On variable Wiener index

 

 

 

Bono Lucic, Ante Milicevic, Sonja Nikolic & Nenad Trinajstic*

 

 

 

A variable Wiener index vW, applicable only to acyclic structures, is defined as S [n1(e) n2 (e)]l.  As a test case, the structure-boiling point modeling of isomeric octanes is used.

 

1283

 

Layer matrices and distance property descriptors

 

 

 

 

Mircea V Diudea* & Oleg Ursu

 

 

 

The TOPOCLUJ software package is designed to calculate topological descriptors from topological matrices and/or polynomials. Several weighting schemes including group electronegativity, group mass and partial charges are proposed.

 

1295

 

A novel topological index for coding of alternant systems

 

 

 

 

 

 

 

 

 

 

Lemi Turker

 

 

 

Starting with the concept of T(A) graphs for alternant hydrocarbons, a novel topological index is defined which  differentiates isomeric as well as isospectral molecules very well.

 

 

1298

 

Fully angular hexagonal chains extremal with regard to the largest eigenvalue

 

 

 

Wai Chee Shiu*, Peter Che Bor Lam &
Lian-zhu Zhang

 

 

 

The hexagonal chain (unbranched catacondensed benzenoid molecule) with minimum leading eigenvalue among fully angular hexagonal chains having a given number of hexagons is reported.

 

1304

 

Approximating the total pi-electron energy of phenylenes in terms of spectral moments

 

 

 

 

 

 

 

 

Svetlana Markovic

 

 

 

The total p-electron energy of phenylenes is approximated by means of a linear combination of spectral moments of both molecular and line graphs.

 

 

1309

 

Graph energy - a useful molecular structure-descriptor

 

 

 

Ivan Gutman*, Dusica Vidovic, Natasa Cmiljanovic, Svetlana Milosavljevic &
Slavko Radenkovic

 

 

The energy of a graph  is a molecular structure-descriptor applicable in QSPR and QSAR studies of both unsaturated and saturated organic compounds.

Part 2: Applications

Reviews

 

1315

 

From molecular graphs to drugs. A review on the use of topological indices in drug design and discovery

 

 

 

 

Ernesto Estrada*, Grace Paltewicz &
Eugenio Uriarte

 

 

 

           ®       

 

      Graphs                    Tis                  Drugs

 

1330

 

Applications of topological indices to structure-activity relationship modelling and selection of mineral collectors

 

 

 

 

Ramanathan Natarajan*, Palanichamy Kamalakanan & Inderjit Nirdosh

 

 

 

Papers

1347

Introducing the complete graphs for the inner-core electrons

 

 

 

Lionello Pogliani

 

 

 

 

 

1354

 

Maximum topological distances based indices as molecular descriptors for QSPR. V - Modeling the free energy of hydrocarbons

 

 

Pablo Duchowicz, Romulo G. Sinani,
Eduardo A Castro* & Andrey A Toropov

 

 

 

The Gibbs free energy for a set of 60 hydrocarbons is calculated on the basis of  topological indices defined from the distance and detour matrices within the   realm of the QSPR theory. Topological indices calculated from detour matrix yield rather satisfactory predictions of Gibbs free energy for hydrocarbons.

 

1360

 

Selected structural descriptors and R_M values for calculation and prediction of molar volume of homologous series of saturated fatty acids

 

 

Alina Pyka* & Katarzyna Bober

 

 

 

The linear relationship between experimental molar volume values and Gutman index M for homologous series of saturated fatty acids, from ethanoic to octadecanoic is

Vm = 4.321(±0.008)M – 32.014(±0.487),

where n=17   R2 =99.99   F=260096   s=0.68   p<0.001.

 

1368

 

QSAR modeling of polychlorinated aromatic compounds

 

 

 

 

 

 

 

Mihaela Caprioara* & Mircea V Diudea

 

 

 

Polychlorinated dibenzofurans, dibenzo-p-dioxins and biphenyls have been characterized on the basis of topological descriptors. A QSAR study is performed to emphasize the  relation between some topochemical and electronic parameters and their binding affinity to the aryl hydrocarbon receptor. The main feature influencing the binding activity of these compounds is a partial charge-based descriptor, a measure of the molecular electronic properties derived  using the correlation weights of these local invariants.

 

1379

 

Topological investigations of binary and ternary mixtures containing cyclic ether: Excess isoentropic compressibilities

 

 

 

 

 

Vinod K Sharma*, Romi & Satish Kumar

 

 

 

Speed of sound, of 1,3-dioxolane + toluene or + o- or + p-xylene binary and 1,3-dioxolane + toluene + o- or + p-xylene ternary mixtures have been measured over the whole mole fraction range at 298.15 K. Excess isentropic compressibility, KSE values have been calculated employing density values of the binary and ternary mixtures and graph theory. KSE values predicted by graph theoretical approach compare reasonably well with the KSE values determined from experimental data.

 

1385

 

Use of topological indices in predicting aryl hydrocarbon receptor binding potency of dibenzofurans: A hierarchical QSAR approach

 

 

 

 

 

 

 

Subhash C. Basak*, Denise Mills,
Moiz Mumtaz & Krishnan Balasubramanian

 

 

 

 

1392

 

True prediction by consensus for small sets of cyclooxigenase-2 inhibitors

 

 

 

 

 

 

 

 

Jesus Vicente de Julian-Ortiz, Emili Besalu* & Ramon Garcia-Domenech

 

 

 

A set of 21 previously published COX-2 inhibitors has been analyzed in order to obtain a new paradigm capable of obtaining true predictions of the activity.

 

 

1405

 

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

 

 

 

 

 

 

Alina Pyka*, Elzbieta Kepczynska &
Jacek Bojarski

 

 

 

Relationships between the experimental RM values of the barbiturates investigated and the RM values have been calculated using the relation

 

RM =-26.192(±0.498) + 14.785(±0.282) ´ mmph - 0.00206

(±0.00058) ´ M + 0.281 (±0.011) ´ logPKowin

 

[n=144; R2=95.83; F=1072; s=0.097; p<0.0001; DW=1.50],

where  mmph denotes the dipole moments of mobile phases applied,   M denotes Gutman index, and logPKowin  denotes theoretical partition coefficient based on atom/fragmental contributions.

 

1414

 

Novel topochemical descriptors for predicting anti-HIV activity

 

 

 

 

Sunil Gupta, Manjeet Singh &
Anil Kumar Madan*

 

 

 

The discriminating power of three novel adjacency-cum-distance based chemical topological descriptors termed as eccentric-adjacency topochemical indices have been investigated to estimate anti-HIV activity of 107 derivatives of 6-(phenylthio)thymines. The high discriminating power of eccentric-adjacency topochemical indices along with other mathematical tools can be exploited for drug design.

 

1426

 

Use of distance-based topological indices in modeling antihypertensive activity: Case of 2-aryl-imino-imidazolidines

 

 

Vijay K. Agrawal*, Sneha Karmarkar, Padmakar V. Khadikar, Shachi Shrivastava &
Istvan Lukovits

 

 

 

Topological modeling of antihypertensive activity of 2-aryl-imino-imidazolidines is reported . An excellent model is obtained in multi-parametric regression containing c and logRB along with  two indicator parameters.

 

1436

 

Equlizied electronegativity and topological indices: Application for modeling toxicity of nitrobenzene derivatives

 

 

Padmakar V Khadikar*, Istvan Lukovits,
Vijay K. Agrawal, Shachi Shrivastava,
Mona Jaiswal, Ivan Gutman,
Sneha Karmarkar & Anjali Shrivastava

 

 

 

Use of equalized electronegativity (ceq) in modeling toxicity of nitrobenzene is discussed. Results show that more reliable models can be obtained when ceq is combined with topological indices. The results are discussed by using multiple regression and cross-validation procedures.

 

1442

 

Hosoya indices and a new approach to molecular similarity

 

 

 

 

 

 

 

 

 

Lemi Turker

 

 

 

 

Authors for correspondence are indicated by (*)

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1207-1218

 

 

Chemical graph theory—Facts and fiction

Milan Randić

National Institute of Chemistry, Hajdrihova 19, Ljubljana, Slovenia

 

Received 31 January 2003

 

 

Graph Theory (GT) and its applications in chemistry, the so-called Chemical Graph Theory (CGT), appear to be two of the most misunderstood areas of theoretical chemistry. We outline briefly possible causes for misunderstanding and suggest remedies, including a test on the knowledge of GT and CGT.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1219-1226

 

 

On the structural interpretation of topological indices

Anton Perdih* & Branislav Perdih

Mala vas 12, SI-1000 Ljubljana, Slovenia

 

Received 18 November 2002

 

 

The atom contribution approach, the bond contribution approach, the contribution of terminal or interior atoms or bonds approaches to their values do not seem to be viable approaches to perform the structural interpretation of topological indices and physicochemical properties. On the other hand, the approach of structural interpretation using the structural features like the size of the molecule, the number of branches, the position of branches, the separation between them, the type of branches, and the type of the branched structure is generally applicable.

 

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1227-1240

 

 

Applications of information theory in chemical graph theory

Elena V Konstantinova*, Vladimir A Skorobogatov, Maxim V Vidyuk

Sobolev Institute of Mathematics, Russian Academy of Sciences,

Novosibirsk, 630090, Russia, e_konsta@math.nsc.ru, skrbg@maltar.org.il

Budker Institute of Nuclear Physics, Russian Academy of Sciences, Novosibirsk, 630090, Russia, vidyuk@inp.nsk.su

 

Received 30 December 2002

 

 

Information theory has been used in various branches of science. During recent years it is applied extensively in chemical graph theory for describing chemical structures and for providing good correlations between physico-chemical and structural properties. The application of information theory to the problem of characterizing molecular structures is presented in the paper. The information indices based on the distance in a graph are considered with respect to their correlating ability and discriminating power.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1241-1245

 

 

Relations between topological indices of large chemical trees

Ivan Gutman*, Dušica Vidović& Boris Furtula

Faculty of Science, University of Kragujevac, P.O.Box 60, YU-34000 Kragujevac, Yugoslavia

and

Aleksander Vesel

Department of Mathematics, PEF, University of Maribor, Koroska cesta 160, SI-2000 Maribor, Slovenia

 

Received 16 October 2002

 

 

Several approximate relations have recently been established between molecular-graph-based structure descriptors of alkanes, in particular between (a) eigenvalue sum and Hosoya index, (b) greatest graph eigenvalue and connectivity index, (c) Wiener index and smallest positive Laplacian eigenvalue, (d) greatest Laplacian and greatest ordinary graph eigenvalue, (e) Zenkevich and Wiener index, and (f) hyper-Wiener and Wiener index. These all have been found to hold for alkanes with n=10 or fewer carbon atoms, and verified on samples consisting of all alkane isomers. Applying an algorithm for generating trees uniformly by random we have now tested these regularities for very large chemical trees (n=50). It has been found that regularities (c) and (f) hold equally well in the case of very large chemical trees, whereas regularities (a), (d) and (e) are applicable, but with significantly attenuated accuracy. Regularity (b) vanishes at large values of n.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1246-1257

 

 

Towards branching indices

Anton Perdih

Mala vas 12, SI-1000 Ljubljana, Slovenia

 

Received 2 December 2002

 

 

Topological indices Vj(-1/2,-1/2), Vj(-1/2,-1), Vij(-1/4,-1), Vij(-1/4,-1/3), Lj(-1/3,-1/4), Lij(-1/4,-1/2), lnMij(1/3,1/4), as well as lnMij( 4,1) are promising candidates for branching indices. The indices Vij(-1/4,-1.09) and lnMij(1.29,1), as well as lnMij( 3.59 : 1) have the best characteristics. Modification of summation-derived indices using a root or a logarithm of the index values improves their characteristics only marginally. Using a logarithm of the index or the geometric mean of the value of the nondiagonal elements of the matrix among the multiplication-derived indices, improves the situation greatly, up to the level observed among summation-derived indices. The values of indices Vj(-1/2,-1/2), Vij( 1/4,-1), Vij( 1/4, 1/3), Lj(-1/3,-1/4), and Lij(-1/4,-1/2) increase with the size of the molecule as well as with branching. These indices belong to the branching indices of the BIM group.The value of the index lnMij(1/3,1/4) increases with the size of the molecule and decreases with branching, whereas the reverse is true for the index lnMij(-1/3,1/4). These indices can be a good source to derive branching indices of the BIA group.

 

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1258-1263

 

 

A new chemical index inspired by biological plastic evolution

Francisco Torrens

Institut Universitari de Ciència Molecular, Universitat de València, Dr. Moliner 50, E-46100 Burjassot (València), Spain

 

Received 10 January 2003

 

 

This paper presents an application of plastic evolution to design a new chemical index (the coordination index, Ic) that permits molecular characterization. Ic is applied to homologous series of phenyl alcohols and 4-alkylanilines, and compared to charge indices for dipole moment. The parameters needed to calculate Ic are minus the standard enthalpy of formation T, molecular surface area S and molecular weight W. The correlations between Ic, T, S, W and the number of C atoms in the alkyl chain indicate a homogeneous molecular structure of the phenyl alcohols and 4 alkylanilines.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1264-1269

 

 

Partitioning of Wiener-type indices, especially for trees

Douglas J Klein

Texas A & M University at Galveston, Galveston, Texas 77553-1675, USA

 

Received 1 February 2003

 

 

Different possible ways are noted to partition the so-called Wiener index of a molecular graph G into contributions associated to different substructures of G, particularly, for the case where G is a tree and the substructures are sites or bonds. Representative related partitionings for some related graph invariants are also established. Paralleling the definition of Wiener (or Hosoya) polynomials, the partitioning results are used to motivate Szeged polynomials.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1270-1271

 

 

On the Wiener index decomposition for
catacondensed benzenoid graphs

Andrey A. Dobrynin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia

 

Received 24 January 2003

 

 

The Wiener index ( ) is a structural descriptor of organic molecules. It is defined as the sum of distances between all vertices of a molecular graph. Some properties based on the decomposition of the Wiener index for catacondensed benzenoid graphs are presented. In particular, it is shown that if and only if , where denotes the sum of distances between vertices of degree 2 in a benzenoid graph .

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1272-1278

 

 

Chemical applications of the Laplacian spectrum.
VII. Studies of the Wiener and Kirchhoff indices

Ivan Gutman*, Dušica Vidović & Boris Furtula

Faculty of Science, University of Kragujevac, P.O.Box 60, YU-34000 Kragujevac, Yugoslavia

 

Received 10 September 2002

 

 

Some further chemical applications of the Laplacian spectra are reported. The Kel'mans theorem for the calculation of the coefficients of the Laplacian characteristic polynomial is stated and exemplified. By means of this theorem a (previously known) formula for the Wiener and Kirchhoff index is deduced. It is shown that the Wiener index is correlated with the “algebraic connectivity”, namely, the smallest positive Laplacian eigenvalue. Lower and upper bounds for the Kirchhoff index are obtained.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1279-1282

 

 

On variable Wiener index

Bono Lučić, Ante Miličević, Sonja Nikolić & Nenad Trinajstić*

The Rugjer Bošković Institute, P.O. Box 180, HR-10002 Zagreb, Croatia

 

Received 16 January 2003

 

 

A variable Wiener index vW, applicable only to acyclic structures, is defined as  [n1(e) n2(e)] For the optimal exponentthat value of  should be selected which gives the smallest standard error of estimate, s, in the structure-property modeling. As a test case, the structure-boiling point modeling of isomeric octanes is used. It is found that the optimal exponent is =1/3 which gives a two-parameter model with the lowest value of s (0.72C) of all tested models. Close to this model is a two-parameter model based on the variable Wiener index with exponent =-1/3 (s=0.83C). Among the published models, only four- and five-parameter models, based on the overall connectivity indices, produce lower values of s (0.71C, 0.55C).

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1283-1294

 

 

Layer matrices and distance property descriptors

Mircea V Diudea*

Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, 3400 Cluj, Romania

and

Oleg Ursu

Department of Chemistry, Cleveland State University 2121 Euclid Avenue, Cleveland, Ohio 44115, USA

 

Received 19 November 2002

 

 

Several topological indices–numerical descriptors encoding topological attributes of a molecular graph have been used both in graph discriminating analysis and correlating studies for modeling of a variety physico-chemical properties and biological activities. However, only few software packages, viz., CODESSA, MOLCONN Z, Dragon, TOSS MODE and POLLY, are available for calculating topological indices. These incorporate correlating analysis statistics, as well. The TOPOCLUJ software package is designed to calculate topological descriptors from topological matrices and/or polynomials. Several weighting schemes including group electronegativity, group mass and partial charges are proposed. Topological indices derived from the matrices like adjacency, connectivity, distance, detour, distance-path, detour-path, Cluj, their reciprocal matrices, walk-matrices, walk-operated matrices, layer- and shell-matrices have been successfully used in correlating studies and graph discriminating analysis during the last decade. Several novel topological matrices, like distance-path, Cluj (with its variants), layer-matrices, walk matrix, walk (triple matrix) operator, characteristic and "property" polynomials, and the corresponding topological descriptors may be calculated by the TOPOCLUJ software package.

 

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1295-1297

 

 

A novel topological index for coding of alternant systems

Lemi Türker

Middle east Technical University, Department of Chemistry, 06531, Ankara, Turkey

 

Received 17 September 2002

 

 

Starting with the concept of T(A) graphs for alternant hydrocarbons, a novel topological index is defined. The index differentiates isomeric as well as isospectral molecules very well. The index is applicable to saturated or unsaturated systems and can be extended to heteroatom containing structures.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1298-1303

 

 

Fully angular hexagonal chains extremal with regard to the largest eigenvalue1

Wai Chee Shiu1, Peter Che Bor Lam1 & Lian-zhu Zhang2

1Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong.

2Department of Mathematics, Zhangzhou Teachers College, Zhangzhou, Fujian 363000, China

 

Received 25 November 2002

 

 

Let G be a molecular graph with characteristic polynomial . The leading eigenvalue of G is the largest root of the equation . In this paper, the hexagonal chain (unbranched catacondensed benzenoid molecule) with minimum leading eigenvalue among fully angular hexagonal chains having a given number of hexagons is determined

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1304-1308

 

 

Approximating total pi-electron energy of phenylenes in terms of spectral moments

Svetlana Marković

Faculty of Science, University of Kragujevac, P.O.B. 60, YU-34000 Kragujevac, Yugoslavia

 

Received 24 January 2003

 

 

The total pi-electron energy of phenylenes is approximated by means of a linear combination of the first few spectral moments of both molecular and line graphs. The two sets of moments produce very similar results, with very high accuracy. It is found that over 99.8% of the HMO total pi-electron energy of phenylenes is determined by the number of carbon atoms. Number of bay regions plays a significant role in the dependence of E on molecular topology of phenylenes

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1309-1311

 

 

Graph energy —A useful molecular structure-descriptor

Ivan Gutman, Dušica Vidović, Nataša Cmiljanović, Svetlana Milosavljević & Slavko Radenković

Faculty of Science, University of Kragujevac, P.O.Box 60, YU-34000 Kragujevac, Serbia & Montenegro

 

Received 27 January 2003

 

 

The energy E(G) of a graph G is, by definition, equal to the sum of absolute values of the eigenvalues of G. The motivation for such a definition comes from molecular orbital theory, where E(G) pertains to the total -electron energy of the conjugated hydrocarbon whose molecular graph is G. However, E(G) is a well-defined quantity for all graphs. It has been shown that E(G) serves as a structure-descriptor in the case of saturated, -electron, systems. The correlations of various physico-chemical properties of alkanes with E(G) are found to be of similar quality as the correlations with other traditionally employed molecular structure-descriptors (Wiener and connectivity indices).

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1315-1329

 

 

From molecular graphs to drugs. A review on the use of topological indices in drug design and discovery

Ernesto Estrada1,*, Grace Patlewicz & Eugenio Uriarte2

1Safety and Environmental Assurance Centre (SEAC), Unilever R&D, Colworth House, Sharnbrook,

Bedford MK44 1LQ, UK

2Faculty of Pharmacy, Department of Organic Chemistry, University of Santiago de Compostela,

15706 Santiago de Compostela, Spain

 

Received 28 January 2003

 

 

A review on the use of topological indices (TIs) in the process of drug design and development is presented on the basis of the most recent advances in this field. The first part of this work is focussed on introducing the definitions of terms used in drug design and discovery, graph-theoretical chemistry as well as topological indices. The second part of the review discusses the use of topological indices in the lead discovery and optimization processes, including similarity/dissimilarity studies, rational combinatorial library design, QSAR, the issue of 2D versus 3D QSAR, as well as the use of novel chemometric techniques, such as artificial neural networks, genetic algorithms and partial least squares in combination with TIs. Recent advances on the definition of TIs accounting for three dimensional molecular features (topographic indices) and molecular chirality are also presented.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1330-1346

 

 

Applications of topological indices to structure-activity relationship modelling and selection of mineral collectors

Ramanathan Natarajan*, Palanichamy Kamalakanan & Inderjit Nirdosh

Department of Chemical Engineering, Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1

 

Received 8 January 2003

 

 

Topological indices (TI) are extensively used as molecular descriptors in building Quantitative Structure-Activity Relationships (QSAR), Quantitative Structure-Property Relationships (QSPR) and Quantitative Structure-Toxicity Relationships (QSTR). We have applied the QSAR approach for the first time to froth flotation and modelled the separation efficiencies (Es) of four series of collectors namely, cupferrons, o-aminothiophenols, mercaptobenzothiozoles and arylhydroxamic acids used for the beneficiation of uranium, lead, zinc and copper ores, respectively. Principal components extracted from topological indices are found to form linear regression equations that can predict the separation efficiencies of the first three classes of collectors. Inclusion of substituent constant or quantum mechanical parameters did not improve the fit and this may be due to the absence of large variation in electronic effects among the molecules in each class. A quadratic fit has been obtained instead of linear regression in the case of arylhydroxamic acids. The separation efficiencies of the members have been predicted within experimental error (5%) by the best regression equations in each series. From the statistical models built, it may be generalized that Es = f(TI). To extend the applications of TI in the field of mineral processing, a similarity space of 587 arylhydroxamic acids has been constructed using principal components extracted from Tis. Ten compounds have been selected for synthesis and testing. The approach appears to provide an efficient scientific tool for the selection of collectors from a virtual database and may lead to an inexpensive and quick method for the identification of new collectors.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1347-1353

 

 

Introducing the complete graphs for the inner-core electrons

Lionello Pogliani

Dipartimento di Chimica, Università della Calabria, 87030 Rende (CS), Italy.

 

Received 23 January 2003

 

 

Odd complete graphs have been used to encode the inner-core electrons of atoms with principal quantum number n  2. An algorithm based on this conjecture has been used to derive a set of connectivity basis indices that have been used to model the molecular polarizabilities of a set of fifty four organic compounds, and the rates of hydrogen abstraction of a set of twenty two phenethylamines. The model of the first property is very good, and the model of the second property is satisfactory. The basis indices used for modeling allow an interesting interpretation of the obtained results.

 

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1354-1359

 

 

Maximum topological distances based indices as molecular descriptors for QSPR. V–Modeling the free energy of hydrocarbons

Pablo Duchowicz1, Rómulo G. Siñani2, Eduardo A Castro1* & Andrey A Toropov3

1CEQUINOR, Departamento de Química, Facultad de Ciencias Exactas, Universidad, Nacional de La Plata, Calles 47 y 115, C.C. 962, La Plata 1900, Argentina

2Vostok Innovation Company, Azimstreet 4, Tashkent 700047, Uzbekistan

3Departamento de Química, Universidad Mayor de San Andrés, Campus Universitario, Calle 27 Cota-Cota, La Paz, Bolivia

 

Received 29 August 2002

 

 

The Gibbs free energy for a set of 60 hydrocarbons is calculated on the basis of topological indices defined from the distance and detour matrices within the realm of the QSPR theory. Linear and non-linear polynomials fittings are performed and the results demonstrate the need to resort to higher-order regression functions in order to obtain better agreements between theoretical results and experimental thermodynamics data. Topological indices calculated from detour matrix yield rather satisfactory predictions of Gibbs free energy for hydrocarbons.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1360-1367

 

 

Selected structural descriptors and RM values for calculation and prediction of molar volume of homologous series of saturated fatty acids

Alina Pyka* & Katarzyna Bober

Silesian Academy of Medicine, Faculty of Pharmacy, Department of Analytical Chemistry,

4 Jagiellonska Street, 41-200 Sosnowiec, Poland

 

Received 24 January, 2003

 

 

Homologous series of saturated fatty acids, from ethanoic to octadecanoic, have been characterized by selected structural descriptors based on distance matrix, adjacency matrix, information theory as well as electrotopological states. Fatty acids, from pentanoic to octadecanoic have been separated by means of RP-HPTLC, on plates RP-18 with and without concentrating zone, using mobile phases methanol-water, ethanol-water and n-propanol-water in volume ratio 100:0, 95:5 as well as 90:10. The relationships existing between molar volume (Vm) and structural descriptors or RM values (obtained by means of RP-HPTLC) of saturated fatty acids have been investigated. Comparison and estimation of usefulness of structural descriptors selected and RM values for calculating and predicting of molar volume of saturated fatty acids, from ethanoic to octanoic, is presented. It is stated that both structural descriptors and RM values can serve for calculating and predicting the molar volume of fatty acids investigated, but the selected traditional structural descriptors better described the molar volume than the RM values.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1368-1378

 

 

QSAR modeling of polychlorinated aromatic compounds

Mihaela Căprioară* & Mircea V Diudea

Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, 3400 Cluj, Romania

 

Received 19 November 2002

 

 

Polychlorinated aromatic compounds viz., dibenzofurans (PCDFs), dibenzo-p-dioxins (PCDDs) and biphenyls (PCBs) have been characterized on the basis of topological descriptors. A quantitative structure-activity relationship (QSAR) study is performed in order to emphasize the relation between some topochemical and electronic parameters and their binding affinity to the aryl hydrocarbon receptor (AhR). The models reveal that the main feature influencing the binding activity of these compounds is a partial charge-based descriptor, a measure of the molecular electronic properties derived using the correlation weights of these local invariants. The linear regression equations enables to predict correctly the binding affinity of the polychlorinated derivatives. The present model shows good agreement with literature data.

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1379-1384

 

 

Topological investigations of binary and ternary mixtures containing
cyclic ether: Excess isentropic compressibilities

Vinod K Sharma*, Romi & Satish Kumar

Department of Chemistry, Maharshi Dayanand University Rohtak 124 001, India

 

Received 31 January 2003

 

 

Speed of sound U, of 1,3-dioxolane (i) + toluene (j) or + o- or + p-xylene (j) binary and 1,3-dioxolane (i) + toluene (j) + o- or + p-xylene(k) ternary mixtures have been measured over the whole mole fraction range at 298.15 K. Excess isentropic compressibility, KSE values have been calculated employing density, ij and ijk speed of sound values of the binary and ternary mixtures. The KSE values for the binary and ternary mixtures have also been evaluated by employing graph theory. It has been observed that KSE values predicted by graph theoretical approach compare reasonably well with the KSE values determined from experimental data.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1385-1391

 

 

Use of topological indices in predicting aryl hydrocarbon receptor binding potency of dibenzofurans: A hierarchical QSAR approach

Subhash C Basaka*, Denise Millsa, Moiz Mumtazb & Krishnan Balasubramanianc

a Natural Resources Research Institute, University of Minnesota Duluth, 5013 Miller Trunk Highway, Duluth, MN 55811, USA

b Computational Toxicology Laboratory, Division of Toxicology, Agency for Toxic Substances and Disease Registry (ATSDR), Executive Park Building 4, 1600 Clifton Road, E-29, Atlanta, GA 30333, USA

c Department of Applied Sciences, University of California Davis, Hertz Hall, L-794 Livermore, CA 94550, Chemistry &

Material Science Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94550 and

Glenn T. Seaborg Center, Lawrence Berkeley National Laboratory, Berkeley CA 94720

 

Received 1 February 2003

 

 

Topostructural (TS) and topochemical (TC) indices, geometrical descriptors, and ab initio (STO-3G) quantum chemical indices have been employed either alone or hierarchically in the development of quantitative structure-activity relationship (QSAR) models of the aryl hydrocarbon (Ah) receptor binding potency of a set of 34 dibenzofurans. Results show that, for the full set, the TS and TC indices explain most of the variance in the data. The addition of 3-D and quantum chemical indices make only slight improvement in the predictive capability of QSAR models.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1392-1404

 

 

True prediction by consensus for small sets of cyclooxigenase-2 inhibitors

Jesus Vicente de Julián-Ortiz1, Emili Besalú*1,2, Ramón García-Domenech3

1Institut de Química Computacional. Universitat de Girona. Spain

2Departament de Química. Universitat de Girona. Spain

3Unidad de Investigación de Diseño de Fármacos y Conectividad Molecular. Universitat de València. Spain.

 

Received 11 February 2003

 

 

A set of 21 previously published COX-2 inhibitors has been analyzed in order to obtain a new paradigm capable of obtaining true predictions of the activity. Overfitting in the models has effectively been prevented even for small training sets. The most significant variables for the prediction of the property have been selected, and outliers have also been easily identified with this approach. Topological indices have been used as descriptors.

 

 

 

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 Pyka1*, Elzbieta Kępczyńska2 & Jacek Bojarski2

1Silesian Academy of Medicine, Faculty of Pharmacy, Department of Analytical Chemistry,

4 Jagiellońska Street, 41-200 Sosnowiec, Poland

2Medical College of Jagiellonian University, Department of Organic Chemistry, 9 Medyczna Street, 30-688 Kraków, 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 (mph) or with the permittivities (mph) 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 permittivities) of the mobile phases, and one topological indices from among the topological indices o, 1, o, 1, R, W, A, 1B and three parametric equations employing the dipole moments (or the permittivities) of the mobile phases, and two topological indices (IB and 1 as well as IB and 1), or one electrotopological descriptor (SdssC or SssssC) or Gutman index (M or M), and selected partition coefficient. However, Randić indices of 0-order (o and o) are the most universal for QSAR analysis of barbiturates investigated.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1414-1425

 

 

Novel topochemical descriptors for predicting anti-HIV activity

Sunil Gupta1, Manjeet Singh1 & Anil Kumar Madan*2

1 Department of Pharmaceutical Sciences and Drug Research, Punjabi University, Patiala 147 002, India

2 Faculty of Pharmaceutical Sciences, M.D. University, Rohtak 124 001, India

 

 

Received 29 December 2002

 

 

The discriminating power of three novel adjacency-cum-distance based chemical topological descriptors termed as eccentric-adjacency topochemical indices have been investigated to estimate anti-HIV activity of 107 derivatives of 6-(phenylthio)thymines. The values of eccentric-adjacency topochemical indices of each derivative in the dataset have been computed and suitable models developed after identification of the active ranges. Subsequently, each derivative has been assigned a biological activity which was then compared with the reported anti-HIV activity. The use of models based upon these topochemical indices result in prediction of anti-HIV activity with an accuracy of 81-89 %. An excellent relationship between eccentric-adjacency topochemical indices and anti-HIV activity of 6-(phenylthio) thymine derivatives can be attributed to sensitivity of the proposed topochemical indices towards nature, number and relative position of heteroatoms. The high discriminating power of eccentric-adjacency topochemical indices along with other mathematical tools can be exploited for drug design.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1426-1435

 

 

Use of distance-based topological indices in modeling antihypertensive activity: Case of 2-aryl-imino-imidazolidines

Vijay K Agrawala*, Sneha Karmarkar b, Padmakar V Khadikar b & Shachi Shrivastavaa

a QSAR and Computer Chemical Laboratories, APS University, Rewa 486 003, India,

e-mail: vijay-agrawal@lycos.com

bResearch Division, Laxmi Fumigation and Pest Control Pvt. Ltd., 3 Khatipura, Indore 452 007, India.

and

Istavan Lukovits

Chemical Research Center,Hungarian Academy of Sciences, H-1525 Budapest P.O.B. 17, Hungary

e-mail:lukovits@chemres.hu

 

Received 31 October 2002

 

 

This paper describes topological modeling of antihypertensive activity of 2-aryl-imino-imidazolidines. A large pool of distance-based topological indices consisting of W, B, , J, Sz, and log RB is initially used for this purpose. An excellent model is obtained in multi-parametric regression containing  and logRB along with two indicator parameters

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1436-1441

 

 

Equalized electronegativity and topological indices: Application for modeling toxicity of nitrobenzene derivatives

Padmakar V.Khadikar1,*, Istvan Lukovits2, Vijay K.Agrawal3, Shachi Shrivastava3’, Mona Jaiswal4,

Ivan Gutman5 , Sneha Karmarkar1 & Anjali Shrivastava4

1Research Division, Laxmi Fumigation & Pest Control (P), 3,Khatipura, Indore 452 007, India

*E-mail: pvkhadikar@rediffmail.com

2Chemical Research Center, Hungarian Academy of Sciences, H-1525 Budapest, P. O. Box 17, Hungary

3QSAR & Computer Chemical Laboratories, A.P.S. University, Rewa 486 003, India

4Department of Chemistry, Govt. Model and Autonomous Holkar College, Indore 452 001, India

5Faculty of Science, University of Kragujevac, P. O. Box 60, YU-34000 Kragujevac, Serbia & Montenegro

 

Received 6 January 2003

 

 

Use of equalized electronegativity (eq) in modeling toxicity of nitrobenzene is discussed. Results show that more reliable models can be obtained when eq is combined with topological indices. The results are discussed by using multiple regression and cross-validation procedures.

 

 

 

Indian Journal of Chemistry

Vol. 42A, June 2003, pp. 1442-1445

 

 

Hosoya indices and a new approach to molecular similarity

Lemi Türker

Middle East Technical University, Department of Chemistry, 06531, Ankara, Turkey

 

Recieved 9 September 2002

 

 

A vector model based on the truncated Hosoya indices has been introduced. Two novel indices (cos and T) are proposed and used for a series of compounds that had been tested previously on Galleria mellonella L. females as sex-attractants. The model also enables to visualize better the relationship between the property/activity and structure (the Hosoya indices).