Topological Indices and Related Descriptors in QSAR and QSPR

There are several different broad approaches to making correlations between chemical structure and some desired property or bioactivity (either of which is here spoken of simply as the “activity”). The relevance of such approaches to quantitative-structure -activity-relationships (QSAR) has now achieved widespread use, perhaps most especially in evaluating bioactivities (e.g., for drug development). One general approach to QSAR seeks to correlate a desired activity with another reference property (e.g., the octanol -water partition coefficient) which is more easily measured; a second general approach seeks to correlate a desired activity to quantum-chemically computed descriptors; and a third general approach seeks to correlate a desired activity with various “topological indices” (which in the mathematical graph-theory literature are usually referred to as “graph invariants”). Especially the first two approaches seem often to have been imagined to associate to a surmised mechanism giving rise to the desired activity, though for bioactivities mechanistic details are in practice often wanting. The present book is dedicated to the third sometimes somewhat controversial but now increasingly successful topological-index approach sindeed the book is focused not only on QSAR but also on quantitative structureproperty relations (QSPR) for other properties. The book consists of 17 chapters by several different leading practitioners in the field. There is a rational plan, with evident coordination between chapters, sometimes engendered by the participation of one of the editors. These chapters might be somewhat approximately divided into four categories: the first consisting of two or three introductory chapters; the second category consisting of six or so chapters presenting a diversity of topological indices; the third consisting of five or so chapters using particular chemical philosophies for the selection of the topological indices to be used; and the fourth consisting of three chapters attending to a few further computational problems and related strategies. The first introductory category includes chapters by Devillers, by Balaban and O. Ivanciuc, and by O. Ivanciuc and Balaban (though the last of these chapters could be included in the next category). Devillers gives some general history of QSAR relating to the other broad approaches not detailed in the present book and makes some related philosophical remarks. Balaban and Ivanciuc present a history focusing on the introductions of various topological indices. The third of these chapters presents a general review of chemical graph-theoretic rudiments, with nice illustrative examples. Multilinear regression analysis is a presumed prerequisite throughout the present book (much as it is also similarly utilized for other broad QSAR approaches outside the scope of the present book). The second set of chapters presenting a great variety of graph invariants includes chapters by O. Ivanciuc, T. Ivanciuc, and Balaban, by O. and T. Ivanciuc, by S. Nikolic ́, N. Trinajstić, and Z. Mihalić, by L. H. Hall and L. B. Kier, and by D. Bonchev (though the last chapter could be placed in the next category instead). Here the graph invariants may often be viewed as obtained in some manner from various graphtheoretic matrices, such as the adjacency, Laplacian, shortest-path distance, Szeged, path, or detour matrices as well as matrices derived therefrom by inverting the elements or “complementing” them or raising them to a power. Particularly in the first chapter of the present set of chapters, attention is directed to the incorporation of heteroatom and bond-weighting aspects of molecular graphs into the design of the topological indices, though such considerations appear in passing in other chapters of this set too, and in the subsequent categories of chapters such considerations are generally explicitly developed or already presumed. The third set of more tightly application-focused chapters are by E. Estrada, by Kier and Hall, by Hall and Kier, by S. C. Basak, by Devillers, and by J. E. Dubois, J. P. Doucet, A. Panaye, and B. T. Fan (though here the first two of these chapters could also be placed in the previous category). Often the topological indices in a chapter here become much restricted in comparison with the possibilities enunciated in the previous set of chapters, but the oft-major point then is that the topological indices are rationally selected within the chemical philosophical approach of the authors. For instance, Kier and Hall focus on their set of “kappa” indices for encoding global shape and flexibility information and their “electrotopological” indices for encoding mean local structural information (including electronegativity characteristics for the various atoms). And Dubois et al . focus on their ordering of substructural features to describe activities which are viewable to be determined by a local region as perturbed by the surrounding environment within the molecule. Basak also describes a method of average neighborhood analysis, using information-theory-related graph invariants. The fourth and final category of chapters concerned with miscellaneous additional problems and related computational strategies are by Basak, B. D. Gute, and G. D. Grunwald, by O. Ivanciuc, and by O. Ivanciuc and Devillers. The chapter by Basak incorporates a variety of extra-graph-theoretic (quantum-chemical or property) information in fitting for an activity. (There are a couple of other earlier chapters which also mention in passing the idea that various pieces of geometric information can be incorporated in indices otherwise resembling standard purely graph-theoretic topological indices.) The chapter by Ivanciuc concerns the use of neural networks to aid in identifying (especially nonlinear) correlations between activity and topological indices. The final chapter is an overview mentioning several available software packages. Overall this∼800-page book provides a reasonably comprehensive and fair presentation of the current field of use of topological indices for QSAR and QSPR. Throughout the book (in virtually every chapter) a variety of illustrative examples are developed, and resultant fits are noted. The book is certainly of value for anyone interested in QSAR and QSPR, regardless of whether the researcher is a practitioner of the topological-index approach or of one of the other oft-used approaches to predict activities. D. J. Klein Texas A&M Uni Versity/Gal Veston