Biological Signaling Pathways and Potential Mathematical Network Representations: Biologic

Establishing the role of different genes in the development of cancer can be a daunting task starting with the detection of genes that are important in the illness from high throughput biological experiments. These experiments belong to the –omics denomination, as in genomics, proteomics, metabolomics and the like. Furthermore, it is safe to say that even with a list of potentially important genes; it is highly unlikely that these show changes in expression in isolation. A biological signaling path is a more plausible underlying mechanism. This research focuses on identifying a signaling pathway of potential biomarkers based on the correlations between these genes of interest. The key challenge here is to consolidate information from multiple microarray experiments with inconsistent units and multiple performance measures. This work attempts the analysis of a microarray experiment to build a mathematical network problem through methods such as the Traveling Salesman Problem (TSP) and Minimum Spanning Tree (MST); both methods are well known combinatorial optimization problems. Preliminary results are presented from a pre-selected group of 12 potential lung cancer biomarkers identified through multiple criteria optimization framework previously published by our research group. Through the utilization of both the TSP and MST optimum solutions are obtained from a total of 12! and 12¹⁰ possible solutions respectively.  This represents the significance of this work, the fact of being able to obtain an optimal from thousands of possible solutions. Identifying cancer biomarkers is an important step in diagnoses, prognosis, and prevention of this disease; but just as important is how these biomarkers are related or interact is just as important. For this reason it is important to discover a signaling pathway among these biomarkers. Both the TSP and MST are able to obtain optimal solutions which could potentially represent signaling pathways once further validation is carried out. Uncovering signaling pathways of potential biomarkers could possible further the understanding of the origins and evolution of cancer, if validation succeeds.