oa Editorial [Hot Topic: Applications of Graph Theory, Network Theory, and Chemotopology to Structure-Activity Relationships and Characterization of Metabolic Processes (Guest Editors: Subhash C. Basak and Guillermo Restrepo)]

Understanding how drugs cause the desired effect on the organism is of utmost importance for drug design. This is not only a scientific motto, but also an economic issue which pharmaceutical companies have comprehended quite well. Understanding the relationship between the structure of a substance and its biological activity is critical for drug discovery. A wealth of knowledge has been generated to grasp such relationships mainly from quantum chemical and mathematical description of molecules. Due to the large number of chemical substances with potential biological activity, which are normally collected in real or virtual libraries, the first step in the search for new drugs is to screen the chemical libraries which may lead to new drugs with less side effects and desirable therapeutic activity. Screening large libraries with quantum chemical tools normally can be very demanding on computer resources. In contrast, the use of mathematical characterization of molecules allows screening within a reasonable time and with low computational costs. This kind of relationship between mathematics and chemistry is one of the interests of the field of theoretical chemistry currently known as Mathematical Chemistry. Due to its interaction with other disciplines like biochemistry, the omics sciences, drug design, predictive toxicology, and development of new materials, mathematical chemistry has become an interesting area of research, with scientific meetings spread all over the world. This issue of Current Computer-Aided Drug Design (CCADD) gathers several of the manuscripts presented at the First Mathematical Chemistry Workshop of the Americas (1MCWA), held in Bogota (Colombia) at the campus of the Universidad de los Andes (August 21-22, 2009). The meeting was sponsored by the Universidad de los Andes (Colombia), the Universidad de Pamplona (Colombia), the Natural Resources Research Institute of the University of Minnesota Duluth (USA),) and the International Society of Mathematical Chemistry. Guillermo Restrepo (Universidad de Pamplona), Jose L. Villaveces (Universidad de los Andes) and Subhash C. Basak (University of Minnesota) were the chairpersons of the event. The 1MCWA was the first international workshop on Mathematical Chemistry organized in Latin America and its aim was to spread the scope of events on Mathematical Chemistry organized by Subhash C. Basak and collaborators using two Indo-US forums i.e. Indo-US Workshop on Mathematical Chemistry (http://gisdata.nrri.umn.edu/pers/pm/indous6/general.htm) and Indo-US Lecture Series on Discrete Mathematical Chemistry (http://www.nrri.umn.edu/indouslecture). The 1MCWA was also the continuation of a series of courses/events on Mathematical Chemistry organized by Guillermo Restrepo: 7th North-eastern Symposium of Mathematics (Colombia, 2009); 9th WSEAS International Conference on Computers (Greece, 2005); Quantum Similarity (Colombia, 2005); Mathematical Chemistry: Periodicity (Colombia, 2004); and Mathematical Chemistry (Colombia, 2001). The six papers collected in the CCADD issue cover different themes of current interest for the mathematical chemistry community as well as for the field of drug design. In the first paper, “On Molecular Graph Comparison”, Jenny A. Melo and Edgar Daza review some distance and similarity coefficients developed to quantify similarity between molecular structures characterized by molecular graphs. This manuscript can be, therefore, linked to the previous CCADD issue on “Chemo-Bioinformatics Based Mathematical Descriptors and their Applications in Computational Drug Design”, Volume 6, Number 4, December 2010, where seven papers cover applications of graph theoretical characterization of molecules to predicting molecular stability, screening of large chemical libraries, computational drug design, predicting anti-HIV activity of substances and characterization of drug-DNA interactions. The second paper, “Chemotopology: Beyond Neighbourhoods”, by Guillermo Restrepo and Heber Mesa reviews the chemotopological method, a procedure which combines classification results with topology to study chemical sets. The authors describe the mathematical basis of the method and illustrate its applications by using examples of chemical sets like amino acids, benzimidazoles and steroids, among others. “Quantitative Structure-Activity Relationships for Anticancer Activity of 2-Phenylindoles Using Mathematical Molecular Descriptors” is the title of the third paper, where Subhash C. Basak, Qianhong Zhu and Denise Mills developed reliable models for predicting activity of 89 phenylindole derivatives against breast cancer. This paper is an instance of how easily computed mathematical descriptors from the chemical graph theory are a good option for estimating biological activities of potential drugs. In the fourth manuscript, “Comparison of QSARs and Characterization of Structural Basis of Bioactivity Using Partial Order Theory and Formal Concept Analysis: A Case Study with Mutagenicity”, Guillermo Restrepo, Subhash C. Basak and Denise Mills use elements of order theory to assess the performance of different QSAR models developed to predict mutagenicity of 95 aromatic and heteroaromatic amines. In so doing, they moot order theory as a versatile tool to compare QSAR methodologies, in general, on the basis of their particular statistics. The manuscript also introduces a novel data analysis technique, Formal Concept Analysis, which can be considered as an approach to relate molecular frameworks with biological activity for the treated property: mutagenicity. Andres Bernal and Edgar Daza turn more biological when treating mathematically chemical networks in the fifth paper of this issue: “Metabolic Networks: Beyond the Graph”. They describe the metabolic network as a complex network of chemical reactions and point out how wrong conclusions may arise from a naive graph interpretation of such networks. As a constructive critique, the authors discuss how the use of other kinds of mathematical structures i.e. hypergraphs, is more suitable to deal with metabolic networks.....