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From Chemical Graphs in Computer-Aided Drug Design to General Markov-Galvez Indices of Drug-Target, Proteome, Drug-Parasitic Disease, Technological, and Social-Legal Networks

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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 to large systems. We can cite for instance, drug-target protein interaction networks, drug policy legislation networks, or drug treatment in large geographical disease spreading networks. In any case, all these networks have essentially the same components: nodes (atoms, drugs, proteins, microorganisms and/or parasites, geographical areas, drug policy legislations, etc.) and edges (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 despite the nature of the object they represent. The main reason for this success of TIs is the high flexibility of this theory to solve in a fast but rigorous way many apparently unrelated problems in all these disciplines. Another important reason for the success of TIs is that using these parameters as inputs we can find Quantitative Structure-Property Relationships (QSPR) models for different kind of problems in Computer-Aided Drug Design (CADD). Taking into account all the above-mentioned aspects, the present work is aimed at offering a common background to all the manuscripts presented in this special issue. In so doing, we make a review of the most common types of 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. Next, we use for the first time a Markov chain model to generalize Galvez TIs to higher order analogues coined here as the Markov-Galvez TIs of order k (MGk). Lastly, we illustrate the calculation of MGk values for different classes of networks found in drug research, nature, technology, and social-legal sciences.

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Keywords: Complex networks; Markov chains; QSAR; biosystems; diseasome; drug-disease networks; drug-target networks; food webs; host-parasite networks; social-legal networks; topological indices

Document Type: Research Article

Publication date: December 1, 2011

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  • Current Computer-Aided Drug Design aims to publish all the latest developments in drug design based on computational techniques. The field of computer-aided drug design has had extensive impact in the area of drug design. Current Computer-Aided Drug Design is an essential journal for all medicinal chemists who wish to be kept informed and up-to-date with all the latest and important developments in computer-aided methodologies and their applications in drug discovery. Each issue contains a series of timely, in-depth reviews written by leaders in the field, covering a range of computational techniques for drug design, screening, ADME studies, etc., providing excellent rationales for drug development.
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