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Phase Transitions in Spatial Networks as a Model of Cellular Symbiosis

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Complex Networks and Their Applications VII (COMPLEX NETWORKS 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 813))

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Abstract

Random Geometric or Spatial Graphs, are well studied models of networks where spatial embedding is an important consideration. However, the dynamic evolution of such spatial graphs is less well studied, at least analytically. Indeed when distance preference is included the principal studies have largely been simulations. An important class of spatial networks has application in the modeling of cell symbiosis in certain tumors, and, when modeled as a graph naturally introduces a distance preference characteristic of the range of cell to cell interaction. In this paper we present theoretical analysis, and, experimental simulations of such graphs, demonstrating that distance functions that model the mixing of the cells, can create phase transitions in connectivity, and thus cellular interactions. This is an important result that could provide analytical tools to model the transition of tumors from benign to malignant states, as well as a novel class of spatial network evolution.

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References

  1. Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74 (2002)

    Google Scholar 

  2. G. B. a. L. Barabási., : Competition and multiscaling in evolving networks. Europhys. Lett. 54, 13 (2000)

    Google Scholar 

  3. Barthélemy, M.: Crossover from scale-free to spatial networks. Europhys. Lett. 63(6), 915–921 (2003)

    Article  Google Scholar 

  4. Barthélemy, M.: Spatial networks. Phys. Rep. 499(1–3), 1–101 (2011)

    Article  MathSciNet  Google Scholar 

  5. Bianconi, G.: Rare events and discontinuous percolation transitions. 022314, 1–11 (2017)

    Google Scholar 

  6. Bianconi, G., Barabási, A.-L.: Bose-Einstein Condensation in Complex Networks. Phys. Rev. Lett. 86(24), 5632–5635 (2001)

    Article  Google Scholar 

  7. Broido, A.D., Clauset, A.: Scale-free networks are rare. 26–28 (2018)

    Google Scholar 

  8. Calbo, J., van Montfort, E., Proost, N., van Drunen, E., Beverloo, H.B., Meuwissen, R., Berns, A.: A functional role for tumor cell heterogeneity in a mouse model of small cell lung cancer. Cancer Cell 19(2), 244–256 (2011)

    Article  Google Scholar 

  9. Cleary, A.S., Leonard, T.L., Gestl, S.A., Gunther, E.J.: Tumour cell heterogeneity maintained by cooperating subclones in Wnt-driven mammary cancers. Nature 508(1), 113–117 (2014)

    Article  Google Scholar 

  10. Dall, J., Christensen, M.: Random geometric graphs. 1–9 (2002)

    Google Scholar 

  11. Dettmann, C.P., Georgiou, O.: Random geometric graphs with general connection functions. Phys. Rev. E 93(3), 1–16 (2016)

    Article  MathSciNet  Google Scholar 

  12. Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F.: Critical phenomena in complex networks. 80 (2007)

    Google Scholar 

  13. Dorogovtsev, S.N., Mendes, J.F.F., Samukhin, A.N.: Structure of growing networks with preferential linking. Phys. Rev. Lett. 85(21), 4633–4636 (2000)

    Article  Google Scholar 

  14. Georgiou, O., Dettmann, C., Coon, J.: K-connectivity for confined random networks. 103:1–6 (2013). arXiv preprint arXiv:1304.1329

  15. Good, B.H., McDonald, M.J., Barrick, J.E., Lenski, R.E., Desai, M.M.: The dynamics of molecular evolution over 60,000 generations. Nature 551(7678), 45–50 (2017)

    Article  Google Scholar 

  16. Greaves, M., Maley, C.C.: Clonal evolution in cancer. Nature 481(7381), 306–313 (2012)

    Article  Google Scholar 

  17. Hanahan, D., Weinberg, R.A.: Cell - Hallmarks of cancer: the next generation. Cell, Volume 144, Issue 5, 646-674, 4 March 2011 144(5), 646–674 (2011)

    Google Scholar 

  18. Heppner, G.H.: Tumor heterogeneity. Cancer Res. 44(6), 2259–2265 (1984)

    Google Scholar 

  19. Lim, J.S., et al.: Intratumoural heterogeneity generated by Notch signalling promotes small-cell lung cancer. Nature 545(7654), 360–364 (2017)

    Google Scholar 

  20. Manna, S.S., Sen, P.: Modulated scale-free network in Euclidean space. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 66(6), 4 (2002)

    Google Scholar 

  21. Ostilli, M., Bianconi, G.: Statistical mechanics of random geometric graphs: geometry-induced first-order phase transition. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 91(4), 1–14 (2015)

    Article  MathSciNet  Google Scholar 

  22. Park, J., Newman, M.E.J.: Statistical mechanics of networks. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 70(6 2):1–13 (2004)

    Google Scholar 

  23. Reeves, M.Q., Kandyba, E., Harris, S., Del Rosario, R., Balmain, A.: Multicolour lineage tracing reveals clonal dynamics of squamous carcinoma evolution from initiation to metastasis. Nat. Cell Biol. 20(6), 699–709 (2018)

    Article  Google Scholar 

  24. Rozenfeld, A.F., Cohen, R., Ben-Avraham, D., Havlin, S.: Scale-free networks on lattices. Phys. Rev. Lett. 89(21), 2–5 (2002)

    Article  Google Scholar 

  25. Schrödinger, E.: Statistical thermodynamics. Courier Corporation (1989)

    Google Scholar 

  26. Sen, P., Banerjee, K., Biswas, T.: Phase transitions in a network with a range-dependent connection probability. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 66(3), 1–4 (2002)

    Google Scholar 

  27. Tabata, T.: Morphogens, their identification and regulation. Development 131(4), 703–712 (2004)

    Article  Google Scholar 

  28. Tammela, T., et al.: A Wnt-producing niche drives proliferative potential and progression in lung adenocarcinoma. Nature 545(7654), 355–359 (2017)

    Article  Google Scholar 

  29. Tee, P., Wakeman, I., Parisis, G., Dawes, J., Kiss, I.: Constraints and entropy in a model of network evolution. Eur. Phys. J. B 90(11) (2017)

    Google Scholar 

  30. Wright, S.: The shifting balance theory and macroevolution. Ann. Rev. Genet. 16(1), 1–20 (1982)

    Article  Google Scholar 

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Acknowledgement

The authors would like to thank Prof. Istvan Z. Kiss for many helpful comments whilst preparing the manuscript, in particular discussion of the network model.

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Authors and Affiliations

  1. Philip Tee University of Sussex, Brighton, BN1 9RH, UK

    Philip Tee

  2. Beyond Center, Arizona State University, Tempe, Arizona, 85287, USA

    Philip Tee

  3. Allan Balmain UCSF Helen Diller Family Comprehensive Cancer Center, 1450 3rd Street, San Francisco, California, 94143, USA

    Allan Balmain

Authors
  1. Philip Tee
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  2. Allan Balmain
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Corresponding author

Correspondence to Philip Tee .

Editor information

Editors and Affiliations

  1. Nokia Bell Labs, Cambridge, UK

    Luca Maria Aiello

  2. IUT Lumière, University of Lyon, Bron Cedex, France

    Chantal Cherifi

  3. LE2I UMR CNRS 6306 9, University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  4. Mathematical Institute, University of Oxford, Oxford, UK

    Renaud Lambiotte

  5. Department of Computer Science and Technology, The Computer Laboratory, University of Cambridge, Cambridge, UK

    Pietro Lió

  6. Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA

    Luis M. Rocha

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Tee, P., Balmain, A. (2019). Phase Transitions in Spatial Networks as a Model of Cellular Symbiosis. In: Aiello, L., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L. (eds) Complex Networks and Their Applications VII. COMPLEX NETWORKS 2018. Studies in Computational Intelligence, vol 813. Springer, Cham. https://doi.org/10.1007/978-3-030-05414-4_47

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