Biological signaling pathways and potential mathematical network representations: biological discovery through optimization

Establishing the role that different genes play in the development of cancer is a daunting task. A step toward this end is the detection of genes that are important in the illness from high‐throughput biological experiments. Furthermore, it is safe to say that it is highly unlikely that these show expression changes independently, even with a list of potentially important genes. A biological signaling pathway is a more plausible underlying mechanism as favored in the literature. This work attempts to build a mathematical network problem through the analysis of microarray experiments. A preselection of genes is carried out with a multiple criteria optimization framework previously published by our research group 1. Afterward, application of the Traveling Salesperson Problem and Minimum Spanning Tree network optimization models are proposed to identify potential signaling pathways via the most correlated path among the genes of interest. Biological evidencing is provided to assess the effectiveness of the proposed methods. The capability of our analysis strategy is also demonstrated through the undertaking of meta‐analysis studies. Three important aspects are novel in this work: (1) our joint analyses of different groups of lung cancer states reveal new correlations, biologically evidenced, and previously undocumented; (2) computation of the correlation coefficients from expression differences leads to an effective use of network optimization methods; and (3) the methods yield mathematically optimal correlation structures: no other configuration is better correlated using the available information.