# American Institute of Mathematical Sciences

2015, 12(6): 1289-1302. doi: 10.3934/mbe.2015.12.1289

## Algebraic and topological indices of molecular pathway networks in human cancers

 1 Department of Mathematical Sciences, University of Wisconsin – Milwaukee, P.O. Box 413, Milwaukee, WI 53201-0413 2 Newman-Lakka Institute, Tufts University School of Medicine, Boston, MA 02111, United States 3 Cross Cancer Institute, University of Alberta, Edmonton, T6G 2E1, Canada 4 Cross Cancer Institute and Department of Physics, University of Alberta, Edmonton, T6G 2E1, Canada

Received  October 2014 Revised  February 2015 Published  August 2015

Protein-protein interaction networks associated with diseases have gained prominence as an area of research. We investigate algebraic and topological indices for protein-protein interaction networks of 11 human cancers derived from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. We find a strong correlation between relative automorphism group sizes and topological network complexities on the one hand and five year survival probabilities on the other hand. Moreover, we identify several protein families (e.g. PIK, ITG, AKT families) that are repeated motifs in many of the cancer pathways. Interestingly, these sources of symmetry are often central rather than peripheral. Our results can aide in identification of promising targets for anti-cancer drugs. Beyond that, we provide a unifying framework to study protein-protein interaction networks of families of related diseases (e.g. neurodegenerative diseases, viral diseases, substance abuse disorders).
Citation: Peter Hinow, Edward A. Rietman, Sara Ibrahim Omar, Jack A. Tuszyński. Algebraic and topological indices of molecular pathway networks in human cancers. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1289-1302. doi: 10.3934/mbe.2015.12.1289
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