Foreword

To the edifice of Mathematical Chemistry, a new brick is being added by the present book, edited by S. C. Basak, G. Restrepo and J. L. Villaveces. During the last three decades, Dr. Subhash C. Basak’s (the “apostle to USA and India”) persistent efforts have led to the organization of eleven international symposia centered on Mathematical Chemistry and held either at the University of Minnesota Duluth- Natural Resources Research Institute, or at various locations in India. The second editor, Dr. Guillermo Restrepo, is the “apostle to Latin America”, who, in collaboration with Drs. Basak and Villaveces, organized two recent mathematical chemistry symposia in Colombia; he co-authored two chapters in this book: one in Vol. 2 deals with similarity in molecular structure reflected in similarity of chemical reactions and then in similarity of reaction networks; the other chapter in the present Vol. 1 presents a comparison between statistical methods for analyzing physical and chemical features determining how chemical elements combine into substances.

An important feature is the fact that from the 27 chapters of the two volumes, seven have been written by the scientists who initiated the research in the respective field. Thus, Professors A. Kerber and C. Rücker with several collaborators describe their latest version of the computer program MOLGEN 5.0 for molecular structure generation. Dr. A. Nandy reviews the beginnings and present status of graphical representations for DNA, RNA, and protein sequences – the very essence of life on our planet. Professor D. Bonchev’s overall topological representation of molecular structure is the topic of an interesting chapter; the newly developed Bourgas indices, which are real numbers, offer a promise as discriminating molecular descriptors for measuring graph complexity and centrality. Molecular topology is also the topic of a chapter by J. Galvez and his collaborators, which provides a pedagogical approach to the development and use of topological indices for drug design. N. Trinajstić with two coworkers present for acyclic graphs the matrices and derived topological indices that result from summing or multiplying local graph invariants (vertices or edges). P. Willett and two coworkers review similarity-based virtual screening of molecules for bioactivity based on weighted two-dimensional fingerprint fragments. Last but not least, S. C. Basak’s chapters discuss (1) the factors that have led to the rapid development of discrete mathematical applications in chemistry during the last few decades; one of these factors has been the development of hardware and software allowing the exploration of large chemical databases for understanding the structural basis of physical and biochemical properties, enabling computer-aided drug design to become an indispensable tool of the pharmaceutical industry; and (2) the molecular descriptors (especially topological indices) as tools for hierarchical QSAR modeling (topostructural, topochemical, geometrical/chiral, and 3Ddescrriptors); in turn, quantum chemical computational methods – semiempirical followed by abinitio – have their hierarchy, first ignoring and then taking into account the solvent.

Among topics dealing with biomedical applications, mention should be made of chapters describing: (i) computational methods (molecular docking and dynamics) for the molecular design of substances that inhibit sensing systems; (ii) pharmacophore models for repellants and biocides against insects or protozoa; (iii) factors influencing protein folding and how to control them; (iv) for the more restricted class of proteins that are metalloenzymes, critical evaluations of quantumchemical methods for explaining the catalytic activity; (v) computer-aided drug design for antitubercular compounds based on structural descriptors; (vi) for an analogous purpose, various QSAR models exemplified by five toxicological studies using the program CAESAR; (vii) QSAR modeling of toxicity for marine algae; (viii) drug-likeness evaluated by comparison with known drug databases and databases for bioactive molecules that are not drugs.

Finally, the reader will also find interesting chapters on (i) topological ranking of fullerene stability; (ii) molecular descriptors with high discriminating ability, i. e. low degeneracy; (iii) the periodicity of di-, tri-, and tetra-atomic molecules; (iv) molecular taxonomy, extended to various types of elementary particles, not only atoms; (v) statistical methodology to be employed in QSAR/QSPR when the number of properties exceeds the number of structures;(vi) so-called comparability graphs for analyzing molecular graphs and network data; (vii) using point set topology for chemical and biochemical; applications; (viii) employing conceptual density functional theory for a deeper understanding of chemical reactivity.

One should congratulate the editors for having persuaded 68 scientists from 15 countries (Austria, China, Colombia, Croatia, Denmark, Germany, India, Iran, Italy, Malaysia, Slovenia, Spain, Turkey, United Kingdom, USA) to write the 27 chapters of these two volumes, and to coordinate their contributions.

Students, professors, and anyone interested in chemical or biomedical research based on discrete applied mathematics will profit from reading this book.