From QSAR models of drugs to complex networks: state-of-art review and introduction of new Markov-spectral moments indices.

Quantitative Structure-Activity/Property Relationships (QSAR/QSPR) models have been largely used for different kind of problems in Medicinal Chemistry and other Biosciences as well. Nevertheless, the applications of QSAR models have been restricted to the study of small molecules in the past. In this context, many authors use molecular graphs, atoms (nodes) connected by chemical bonds (links) to represent and numerically characterize the molecular structure. On the other hand, Complex Networks are useful in solving problems in drug research and industry, developing mathematical representations of different systems. These systems move in a wide range from relatively simple graph representations of drug molecular structures (molecular graphs used in classic QSAR) to large systems. We can cite for instance, drug-target interaction networks, protein structure networks, protein interaction networks (PINs), or drug treatment in large geographical disease spreading networks. In any case, all complex networks have essentially the same components: nodes (atoms, drugs, proteins, microorganisms and/or parasites, geographical areas, drug policy legislations, etc.) and links (chemical bonds, drug-target interactions, drug-parasite treatment, drug use, etc.). Consequently, we can use the same type of numeric parameters called Topological Indices (TIs) to describe the connectivity patterns in all these kinds of Complex Networks irrespective the nature of the object they represent and use these TIs to develop QSAR/QSPR models beyond the classic frontiers of drugs small-sized molecules. The goal of this work, in first instance, is to offer a common background to all the manuscripts presented in this special issue. In so doing, we make a review of the most used software and databases, common types of QSAR/QSPR models, and complex networks involving drugs or their targets. In addition, we review both classic TIs that have been used to describe the molecular structure of drugs and/or larger complex networks. In second instance, we use for the first time a Markov chain model to generalize Spectral moments to higher order analogues coined here as the Stochastic Spectral Moments TIs of order k (πk). Lastly, we report for the first time different QSAR/QSPR models for different classes of networks found in drug research, nature, technology, and social-legal sciences using πk values. This work updates our previous reviews Gonzalez-Diaz et al. Curr Top Med Chem. 2007; 7(10): 1015-29 and Gonzalez-Diaz et al. Curr Top Med Chem. 2008; 8(18):1676-90. It has been prepared in response to the kind invitation of the editor Prof. AB Reitz in commemoration of the 10th anniversary of this journal in 2010.