American Institute of Mathematical Sciences

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

Algebraic and topological indices of molecular pathway networks in human cancers

Peter Hinow 1, , Edward A. Rietman 2, , Sara Ibrahim Omar 3, and  Jack A. Tuszyński 4,

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).
Keywords: automorphism groups, Protein-protein interaction networks, cyclomatic number..
Mathematics Subject Classification: Primary: 92C42; Secondary: 94C1.
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
References:
[1]

R. Albert, H.Jeong and A. L. Barabási, Error and attack tolerance of complex networks, Nature, 406 (2000), 378-382. Google Scholar

[2]

W. Alexander, Inhibiting the Akt pathway in cancer treatment, Three leading candidates, Pharmacy and Therapeutics, 36 (2011), 225-227. Google Scholar

[3]

F. Berger, P. Gritzmann S. de Vries, Minimum cycle bases for network graphs, Algorithmica, 40 (2004), 51-62. doi: 10.1007/s00453-004-1098-x.  Google Scholar

[4]

B. Bollobás, Random Graphs, Cambridge University Press, Cambridge, 2001. Google Scholar

[5]

D. Breitkreutz, L. Hlatky, E. Rietman, J. A. Tuszynski, Molecular signaling network complexity is correlated with cancer patient survivability, Proc. Natl. Acad. Sci. USA, 109 (2012), 9209-9212. Google Scholar

[6]

N. Chandra and J. Padiadpu, Network approaches to drug discovery, Expert Opin. Drug Discov., 8 (2013), 7-20. Google Scholar

[7]

P. Csermely, T. Korcsmáros, H. J. M. Kiss, G. London, R. Nussinov, Structure and dynamics of molecular networks: A novel paradigm of drug discovery. A comprehensive review, Pharmacol. Therapeut., 138 (2013), 333-408. Google Scholar

[8]

D. Garlaschelli, F. Ruzzenenti and R. Basosi, Complex networks and symmetry I: A review, Symmetry, 2 (2010), 1683-1709, arXiv:1006.3923. doi: 10.3390/sym2031683.  Google Scholar

[9]

D. Holmes, PI3K pathway inhibitors approach junction, Nat. Rev. Drug Discov., 10 (2011), 563-564. Google Scholar

[10]

D. W. Huang, B. T. Sherman and R. A. Lempicki, Bioinformatics enrichment tools: Paths toward the comprehensive functional analysis of large gene lists, Nucleic Acid Res., 37 (2009), 1-13. Google Scholar

[11]

D. W. Huang, B. T. Sherman and R. A. Lempicki, Systematic and integrative analysis of large gene lists using DAVID bioinformatics resources, Nature Protocols, 4 (2009), 44-57, http://david.abcc.ncifcrf.gov/ Google Scholar

[12]

B. H. Junker, F. Schreiber (editors), Analysis of Biological Networks, John Wiley & Sons, Hoboken, NJ, 2008. Google Scholar

[13]

M. Kanehisa and S. Goto, KEGG: Kyoto Encyclopedia of Genes and Genomes, Nucleic Acid Res., 28 (2000), 23-30, http://www.genome.jp/kegg/. Google Scholar

[14]

M. Kanehisa, S. Goto, S. Kawashima, Y. Okuno and M. Hattori, The KEGG resource for deciphering the genome, Nucleic Acid Res., 32 (2004), D277-D280. Google Scholar

[15]

H. Katebi, K. A. Sakallah and I. L. Markov, Graph symmetry detection and canonical labeling: Differences and synergies, In A Voronkov, editor, The Alan Turing Centenary, pages 181-195. EasyChair, 2012,http://vlsicad.eecs.umich.edu/BK/SAUCY/. Google Scholar

[16]

T. Kavitha, C. Liebchen, K. Mehlhorn, D. Michail, R. Rizzie, T. Ueckerdt and K. A. Zweig, Cycle bases in graphs characterization, algorithms, complexity, and applications, Computer Science Review, 3 (2009), 199-243. Google Scholar

[17]

E. V. Koonin, Y. I. Wolf and G. P. Karev (editors), Power Laws, Scale-Free Networks and Genome Biology, Landes Bioscience, Austin, TX, 2006. Google Scholar

[18]

A. Ma'ayan and B. D. MacArthur (editors), New Frontiers of Network Analysis in Systems Biology, Springer Verlag, Dordrecht, Heidelberg, New York, London, 2012. Google Scholar

[19]

B. D. MacArthur, R. J. Sánchez-García and J. W. Anderson, Symmetry in complex networks, Discr. Appl. Math., 156 (2008), 3525-3531. doi: 10.1016/j.dam.2008.04.008.  Google Scholar

[20]

National Cancer Institute, Surveillance, Epidemiology and End Results (SEER) Program, 2013,, , ().   Google Scholar

[21]

E. A. Rietman, R. L. Karp and J. A. Tuszynski, Review and application of group theory to molecular systems biology, Theor. Biol. Med. Model., 8 (2011), p21. Google Scholar

[22]

P. Shannon, A. Markiel, O. Ozier, N. S. Baliga, J. T. Wang, D. Ramage, N. Amin, B. Schwikowski and T. Ideker, Cytoscape: A software environment for integrated models of biomolecular interaction networks, Genome Res., 13 (2003), 2498-2504. http://cytoscape.org. Google Scholar

[23]

K. Takemoto and K. Kihara, Modular organization of cancer signaling networks is associated with patient survivability, BioSystems, 113 (2013), 149-154. Google Scholar

[24]

The GAP Group, GAP - Groups, Algorithms, and Programming, University of St Andrews, St Andrews, United Kingdom, 2013. http://www.gap-system.org. Google Scholar

[25]

W. Winterbach, P. van Mieghem, M. Reinders, H. Wang and D. de Ridder, Topology of molecular interaction networks, BMC Syst. Biol., 7 (2013), p90. Google Scholar

[26]

Y. Xiao, B. D. MacArthur, H. Wang, M. Xiong and W. Wang, Network quotients: Structural skeletons of complex systems, Phys. Rev. E, 78 (2008), 046102, arXiv:0802.4318. Google Scholar

[27]

J. D. Zhang and S. Wiemann, KEGGgraph: A graph approach to KEGG PATHWAY in R and Bioconductor, Bioinformatics, 25 (2009), 1470-1471, http://bioconductor.org. Google Scholar

show all references

References:
[1]

R. Albert, H.Jeong and A. L. Barabási, Error and attack tolerance of complex networks, Nature, 406 (2000), 378-382. Google Scholar

[2]

W. Alexander, Inhibiting the Akt pathway in cancer treatment, Three leading candidates, Pharmacy and Therapeutics, 36 (2011), 225-227. Google Scholar

[3]

F. Berger, P. Gritzmann S. de Vries, Minimum cycle bases for network graphs, Algorithmica, 40 (2004), 51-62. doi: 10.1007/s00453-004-1098-x.  Google Scholar

[4]

B. Bollobás, Random Graphs, Cambridge University Press, Cambridge, 2001. Google Scholar

[5]

D. Breitkreutz, L. Hlatky, E. Rietman, J. A. Tuszynski, Molecular signaling network complexity is correlated with cancer patient survivability, Proc. Natl. Acad. Sci. USA, 109 (2012), 9209-9212. Google Scholar

[6]

N. Chandra and J. Padiadpu, Network approaches to drug discovery, Expert Opin. Drug Discov., 8 (2013), 7-20. Google Scholar

[7]

P. Csermely, T. Korcsmáros, H. J. M. Kiss, G. London, R. Nussinov, Structure and dynamics of molecular networks: A novel paradigm of drug discovery. A comprehensive review, Pharmacol. Therapeut., 138 (2013), 333-408. Google Scholar

[8]

D. Garlaschelli, F. Ruzzenenti and R. Basosi, Complex networks and symmetry I: A review, Symmetry, 2 (2010), 1683-1709, arXiv:1006.3923. doi: 10.3390/sym2031683.  Google Scholar

[9]

D. Holmes, PI3K pathway inhibitors approach junction, Nat. Rev. Drug Discov., 10 (2011), 563-564. Google Scholar

[10]

D. W. Huang, B. T. Sherman and R. A. Lempicki, Bioinformatics enrichment tools: Paths toward the comprehensive functional analysis of large gene lists, Nucleic Acid Res., 37 (2009), 1-13. Google Scholar

[11]

D. W. Huang, B. T. Sherman and R. A. Lempicki, Systematic and integrative analysis of large gene lists using DAVID bioinformatics resources, Nature Protocols, 4 (2009), 44-57, http://david.abcc.ncifcrf.gov/ Google Scholar

[12]

B. H. Junker, F. Schreiber (editors), Analysis of Biological Networks, John Wiley & Sons, Hoboken, NJ, 2008. Google Scholar

[13]

M. Kanehisa and S. Goto, KEGG: Kyoto Encyclopedia of Genes and Genomes, Nucleic Acid Res., 28 (2000), 23-30, http://www.genome.jp/kegg/. Google Scholar

[14]

M. Kanehisa, S. Goto, S. Kawashima, Y. Okuno and M. Hattori, The KEGG resource for deciphering the genome, Nucleic Acid Res., 32 (2004), D277-D280. Google Scholar

[15]

H. Katebi, K. A. Sakallah and I. L. Markov, Graph symmetry detection and canonical labeling: Differences and synergies, In A Voronkov, editor, The Alan Turing Centenary, pages 181-195. EasyChair, 2012,http://vlsicad.eecs.umich.edu/BK/SAUCY/. Google Scholar

[16]

T. Kavitha, C. Liebchen, K. Mehlhorn, D. Michail, R. Rizzie, T. Ueckerdt and K. A. Zweig, Cycle bases in graphs characterization, algorithms, complexity, and applications, Computer Science Review, 3 (2009), 199-243. Google Scholar

[17]

E. V. Koonin, Y. I. Wolf and G. P. Karev (editors), Power Laws, Scale-Free Networks and Genome Biology, Landes Bioscience, Austin, TX, 2006. Google Scholar

[18]

A. Ma'ayan and B. D. MacArthur (editors), New Frontiers of Network Analysis in Systems Biology, Springer Verlag, Dordrecht, Heidelberg, New York, London, 2012. Google Scholar

[19]

B. D. MacArthur, R. J. Sánchez-García and J. W. Anderson, Symmetry in complex networks, Discr. Appl. Math., 156 (2008), 3525-3531. doi: 10.1016/j.dam.2008.04.008.  Google Scholar

[20]

National Cancer Institute, Surveillance, Epidemiology and End Results (SEER) Program, 2013,, , ().   Google Scholar

[21]

E. A. Rietman, R. L. Karp and J. A. Tuszynski, Review and application of group theory to molecular systems biology, Theor. Biol. Med. Model., 8 (2011), p21. Google Scholar

[22]

P. Shannon, A. Markiel, O. Ozier, N. S. Baliga, J. T. Wang, D. Ramage, N. Amin, B. Schwikowski and T. Ideker, Cytoscape: A software environment for integrated models of biomolecular interaction networks, Genome Res., 13 (2003), 2498-2504. http://cytoscape.org. Google Scholar

[23]

K. Takemoto and K. Kihara, Modular organization of cancer signaling networks is associated with patient survivability, BioSystems, 113 (2013), 149-154. Google Scholar

[24]

The GAP Group, GAP - Groups, Algorithms, and Programming, University of St Andrews, St Andrews, United Kingdom, 2013. http://www.gap-system.org. Google Scholar

[25]

W. Winterbach, P. van Mieghem, M. Reinders, H. Wang and D. de Ridder, Topology of molecular interaction networks, BMC Syst. Biol., 7 (2013), p90. Google Scholar

[26]

Y. Xiao, B. D. MacArthur, H. Wang, M. Xiong and W. Wang, Network quotients: Structural skeletons of complex systems, Phys. Rev. E, 78 (2008), 046102, arXiv:0802.4318. Google Scholar

[27]

J. D. Zhang and S. Wiemann, KEGGgraph: A graph approach to KEGG PATHWAY in R and Bioconductor, Bioinformatics, 25 (2009), 1470-1471, http://bioconductor.org. Google Scholar

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