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Thermodynamic measures of cancer: Gibbs free energy and entropy of protein–protein interactions

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Abstract

Thermodynamics is an important driving factor for chemical processes and for life. Earlier work has shown that each cancer has its own molecular signaling network that supports its life cycle and that different cancers have different thermodynamic entropies characterizing their signaling networks. The respective thermodynamic entropies correlate with 5-year survival for each cancer. We now show that by overlaying mRNA transcription data from a specific tumor type onto a human protein–protein interaction network, we can derive the Gibbs free energy for the specific cancer. The Gibbs free energy correlates with 5-year survival (Pearson correlation of –0.7181, p value of 0.0294). Using an expression relating entropy and Gibbs free energy to enthalpy, we derive an empirical relation for cancer network enthalpy. Combining this with previously published results, we now show a complete set of extensive thermodynamic properties and cancer type with 5-year survival.

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References

  1. Rietman, E., Bloemendal, A., Platig, J., Tuszynski, J., Klement, G.L.: Gibbs free energy of protein–protein interactions reflects tumor stage. http://biorxiv.org/content/early/2015/07/13/022491 (2015)

  2. Paliouras, M., Zaman, N., Lumbroso, R., Kapogeorgakis, L., Beitel, L.K., Wang, E., Trifiro, M.: Dynamic rewiring of the androgen receptor protein interaction network correlates with prostate cancer clinical outcomes. Integr. Biol. (Camb.) 3, 1020–1032 (2011). doi:10.1039/c1ib00038a

    Article  Google Scholar 

  3. Freije, W.A., Castro-Vargas, F.E., Fang, Z., Horvath, S., Cloughesy, T., Liau, L.M., Mischel, P.S., Nelson, S.F.: Gene expression profiling of gliomas strongly predicts survival. Cancer Res. 64, 6503–6510 (2004). doi:10.1158/0008-5472.CAN-04-0452

    Article  Google Scholar 

  4. Chung, S.S., Pandini, A., Annibale, A., Coolen, A.C.C., Thomas, N.S.B., Fraternali, F.: Bridging topological and functional information in protein interaction networks by short loops profiling. Sci. Rep. 5, 8540 (2015). doi:10.1038/srep08540

    Article  ADS  Google Scholar 

  5. Hinow, P.R., Rietman, E.A., Omar, S.I., Tuszynski, J.A.: Algebraic and topological indices of molecular pathway networks in human cancers. Math. Biosci. Eng. 12(6), 1289–1302 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Benzekry, S.T., Tuszynski, J.A., Rietman, E.A., Klement, G.L.: Design principles for cancer therapy guided by changes in complexity of protein–protein interaction networks. Biol. Direct 10, 32 (2015). doi:10.1186/s13062-015-0058-5

    Article  Google Scholar 

  7. Breitkreutz, D., Hlatky, L., Rietman, E., Tuszynski, J.A.: Molecular signaling network complexity is correlated with cancer patient survivability. Proc. Natl. Acad. Sci. U.S.A. 109, 9209–9212 (2012). doi:10.1073/pnas.1201416109

    Article  ADS  Google Scholar 

  8. Takemoto, K., Kihara, K.: Modular organization of cancer signaling networks is associated with patient survivability. Biosystems 113, 149–154 (2013). doi:10.1016/j.biosystems.2013.06.003

    Article  Google Scholar 

  9. Gronholm, T., Annila, A.: Natural distribution. Math. Biosci. 210, 659–667 (2007). doi:10.1016/j.mbs.2007.07.004

    Article  MathSciNet  MATH  Google Scholar 

  10. Richmod, P., Solomon, S.: Power laws are disguised Boltzmann laws. Int. J. Mod. Phys. C 12, 333 (2001). doi:10.1142/S0129183101001754

    Article  ADS  Google Scholar 

  11. Rashevsky, N.: Topology and life: in search of general mathematical principles in biology and sociology. Bull. Math. Biophys. 16, 317–348 (1954). doi:10.1007/BF02484495

    Article  MathSciNet  Google Scholar 

  12. Dehmer, M., Mowshowitz, A.: A history of graph entropy measures. Inf. Sci. 181, 57–78 (2011). doi:10.1016/j.ins.2010.08.041

    Article  MathSciNet  MATH  Google Scholar 

  13. Demetrius, L., Manke, T.: Robustness and network evolution - a entropic principle. Physica A 346, 682–696 (2005)

    Article  ADS  Google Scholar 

  14. Manke, T., Demetrius, L., Vingron, M.: An entropic characterization of protein interaction networks and cellular robustness. J. R. Soc. Interface 3, 843–850 (2006). doi:10.1098/rsif.2006.0140

    Article  Google Scholar 

  15. West, J., Bianconi, G., Severini, S., Teschendorff, A.E.: Differential network entorpy reveasl cancer system hallmarks. Sci. Rep. 2, 802 (2012). doi:10.1038/srep00802

    Article  ADS  Google Scholar 

  16. Liu, R., Li, M., Liu, Z.P., Wu, J., Chen, L., Aihara, K.: Identifying critical transitions and their leading biomolecular networks in complex diseases. Sci. Rep. 2, 813 (2012). doi:10.1038/srep00813

    ADS  Google Scholar 

  17. Berretta, R., Moscato, P.: Cancer biomarker discovery: the entropic hallmark. PLoS One 5, e12262 (2010). doi:10.1371/journal.pone.0012262

    Article  ADS  Google Scholar 

  18. Banerji, C.R.S., Miranda-Saavedra, D., Severini, S., Widschwendter, M., Enver, T., Zhou, J.X., Teschendroff, A.E.: Cellular network entropy as the energy potential in Wadddingtons’s differentiation landscape. Sci. Rep. 3, 3039 (2013). doi:10.1038/srep03039

    Article  ADS  Google Scholar 

  19. Greenbaum, D., Colangelo, C., Williams, K., Gerstein, M.: Comparing protein abundance and mRNA expression levels on a genomic scale. Genome Biol. 4, 117 (2003). doi:10.1186/gb-2003-4-9-117

    Article  Google Scholar 

  20. Maier, T., Guell, M., Serrano, L.: Correlation of mRNA and protein in complex biological samples. FEBS Lett. 583, 3966–3973 (2009). doi:10.1016/j.febslet.2009.10.036

    Article  Google Scholar 

  21. Kim, M.S., Pinto, S.M., Getnet, D., Nirujogi, R.S., Manda, S.S., Chaerkady, R., Madugundu, A.K., Kelkar, D.S., Isserlin, R., Jain, S., et al.: A draft map of the human proteome. Nature 509, 575–581 (2014). doi:10.1038/nature13302

    Article  ADS  Google Scholar 

  22. Wilhelm, M., Schlegl, J., Hahne, H., Moghaddas Gholami, A., Lieberenz, M., Savitski, M.M., Ziegler, E., Butzmann, L., Gessulat, S., Marx, H., et al.: Mass-spectrometry-based draft of the human proteome. Nature 509, 582–587 (2014). doi:10.1038/nature13319

    Article  ADS  Google Scholar 

  23. Huang, S., Eichler, G., Bar-Yam, Y., Ingber, D.E.: Cell fates as high-dimensional attractor states of a complex gene regulatory network. Phys. Rev. Lett. 94, 128701 (2005)

    Article  ADS  Google Scholar 

  24. Spindel, S., Sapsford, K.: Evaluation of optical detection platforms for multiplexed detection of proteins and the need for point-of-care biosensors for clinical use. Sensors 14, 22313–22341 (2014)

    Article  Google Scholar 

  25. Breitkreutz, B.J., Stark, C., Tyers, M.: The GRID: the general repository for interaction datasets. Genome Biol. 3, PREPRINT0013 (2002)

    Google Scholar 

  26. Maskill, H.: The Physical Basis of Organic Chemistry. Oxford University Press, New York (1986)

    Google Scholar 

  27. Demetrius, L.: The origin of allometric scaling laws in biology. J. Theor. Biol. 243, 455–467 (2006)

    Article  Google Scholar 

  28. Anderson, J.: An Introduction to Neural Networks. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  29. Demirel, Y., Sandler, S.I.: Thermodynamics and bioenergetics. Biophys. Chem. 97, 87–111 (2002)

    Article  Google Scholar 

  30. Demirel, Y.: Modeling of thermodynamically coupled reaction-transport systems. Chem. Eng. J. 139, 106–117 (2008)

    Article  Google Scholar 

  31. Lucia, U.: Different chemical reaction times between normal and solid cancer cells. Med. Hypotheses 81, 58–61 (2013)

    Article  Google Scholar 

  32. Cancer Genome Atlas Research Network Weinstein, J.N., Collisson, E.A., Mills, G.B., Shaw, K.R., Ozenberger, B.A., Ellrott, K., Shmulevich, I., Sander, C., Stuart, J.M.: The cancer genome atlas pan-cancer analysis project. Nat. Genet. 45, 1113–1120 (2013). doi:10.1038/ng.2764

    Article  Google Scholar 

  33. Cancer Genome Atlas Research, N.: Comprehensive molecular characterization of clear cell renal cell carcinoma. Nature 499, 43–49 (2013). doi:10.1038/nature12222

    Article  ADS  Google Scholar 

  34. Cancer Genome Atlas Research Network: Comprehensive genomic characterization defines human glioblastoma genes and core pathways. Nature 455, 1061–1068 (2008). doi:10.1038/nature07385

    Article  Google Scholar 

  35. Cancer Genome Atlas Research Network: Comprehensive moleclar characterization of human colon and rectal cancer. Nature 487, 330–337 (2012). doi:10.1038/nature11252

    Article  ADS  Google Scholar 

  36. Cancer Genome Atlas, N.: Comprehensive molecular portraits of human breast tumours. Nature 490, 61–70 (2012). doi:10.1038/nature11412

    Article  ADS  Google Scholar 

  37. Cancer Genome Atlas Research Network: Comprehensive genomic characterization of squamous cell lung cancers. Nature 489, 519–525 (2012). doi:10.1038/nature11404

    Article  ADS  Google Scholar 

  38. Cancer Genome Atlas Research Network, Kandoth, C., Schultz, N., Cherniack, A.D., Akbani, R., Liu, Y., Shen, H., Robertson, A.G., Pashtan, I., Shen, R., et al.: Integrated genomic characterization of endometrial carcinoma. Nature 497, 67–73 (2013). doi:10.1038/nature12113

    Article  ADS  Google Scholar 

  39. Breitkreutz, B.J., Stark, C., Reguly, T., Boucher, L., Breitkreutz, A., Livstone, M., Oughtred, R., Lackner, D.H., Bahler, J., Wood, V., et al.: The Biogrid Interaction Database: 2008 update. Nucleic Acids Res. 36, D637–640 (2008). doi:10.1093/nar/gkm1001

    Article  Google Scholar 

  40. Stark, C., Breitkreutz, B.J., Reguly, T., Boucher, L., Breitkreutz, A., Tyers, M.: BioGRID: a general repository for interaction datasets. Nucleic Acids Res. 34, D535–539 (2006). doi:10.1093/nar/gkj109

    Article  Google Scholar 

  41. Shannon, P., Markiel, A., Ozier, O., Baliga, N.S., Wang, J.T., Ramage, D., Amin, N., Schwikowski, B., Ideker, T.: Cytoscape: a software environment for integrated models of biomolecular interaction networks. Genome Res. 13, 2498–2504 (2003). doi:10.1101/gr.1239303

    Article  Google Scholar 

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Acknowledgments

EAR was partly funded by the Newman Lakka Cancer Foundation, and CSTS Healthcare. JAT acknowledges funding from NSERC, Canadian Breast Cancer Foundation and the Allard Foundation. GLK was funded by NIH NIGMS RO1 GM93050, and philanthropic funds from Newman Lakka Cancer Foundation, Campanelli Foundation, Jack in the Beanstalk Foundation, and Binational Science Foundation. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Cancer Institute or the National Institutes of Heath.

Author Contributions

EAR conceived the idea. JAT and EAR collaborated on the thermodynamics. JP contributed key chemical physics concepts. GLK contributed cancer biology concepts. All authors contributed to writing the manuscript.

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Authors and Affiliations

  1. Information and Computer Science Department, University of Massachusetts, Amherst, MA, 01003, USA

    Edward A. Rietman

  2. Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, MA, 02115, USA

    John Platig

  3. Department of Biostatistics, Harvard Chan School of Public Health, Boston, MA, 02115, USA

    John Platig

  4. Department of Oncology, Faculty of Medicine & Dentistry, University of Alberta, Edmonton, Alberta, T6G 1Z2, Canada

    Jack A. Tuszynski

  5. Department of Physics, University of Alberta, Edmonton, Alberta, T6G 2E1, Canada

    Jack A. Tuszynski

  6. Pediatric Hematology Oncology, Floating Hospital for Children at Tufts Medical Center, Boston, MA, USA

    Giannoula Lakka Klement

  7. Sackler School of Graduate Biomedical Sciences, Tufts University, Boston, MA, USA

    Giannoula Lakka Klement

  8. Molecular Oncology Research Institute, Tufts Medical Center, Boston, MA, 02111, USA

    Giannoula Lakka Klement

Authors
  1. Edward A. Rietman
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  2. John Platig
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  4. Giannoula Lakka Klement
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Correspondence to Jack A. Tuszynski.

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Rietman, E.A., Platig, J., Tuszynski, J.A. et al. Thermodynamic measures of cancer: Gibbs free energy and entropy of protein–protein interactions. J Biol Phys 42, 339–350 (2016). https://doi.org/10.1007/s10867-016-9410-y

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  • DOI: https://doi.org/10.1007/s10867-016-9410-y

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