Abstract
Cancer dynamics is sometimes associated to well-defined transitions between qualitative properties of neoplasms, or even to the shift from presence to regression. Cancer is largely understood as a Darwinian evolution experiment within organisms, characterized by a break of cooperation between cells. Some patterns of sudden change have been identified as phase transitions, similar to those known from the physics of phase changes. Two of them are analyzed here: (a) the shift from cancer to cancer-free tissues under the interaction with the immune system, and (b) the predicted existence of a threshold of instability associated to unstable tumorigenesis. The nature, evidence and implications of these transitions are discussed.
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Notes
- 1.
Specifically, if we have a chain of length L involving a sequence with only one zero, and assuming that μ b is the probability of mutation per unit and replication round, the probability of recovering the master is given by P(N → M) = μb(1 — b)L−1. If μb is very small, we can approximate (1 — μb)L−1 ≈ exp(—L + 1) ≈ exp(—L). Since L is typically large, the exponential term makes the probability of back mutation extremely small.
- 2.
This is in contrast with standard, so called equilibrium transitions, were we move from one phase to another by increasing the temperature, but the previous phase can be recovered by decreasing the temperature again, which cannot occur in our example by lowering mutation rates.
References
Adam, J.A., Bellomo, N.: A survey of models for tumor-immune system dynamics. Birkhauser, Boston (1996)
Cahill, D.P., Kinzler, K.W., Vogelstein, B., Lengauer C.: Genetic instability and darwinian selection in tumors. Trends Genet. 15, M57-M61 (1999)
Cole, W.H.: Spontaneous regression of cancer and the importance of finding its cause. Natl. Cancer Inst. Monogr. 44, 5–9 (1976)
Cui, Z., Willingham, M.C., Hicks, A.M., Alexander-Miller, M.A., Howard, T.D., Hawkins, G.A., Miller, M.S., Weir, H.M., Du, W., DeLong, C.J.: Spontaneous regression of advanced cancer: Identification of a unique genetically determined, age-dependent trait in mice. Proc. Natl. Acad. Sci. USA 100, 6682–6687 (2003)
Deisboeck, T.S., Couzin, I.D.: Collective behavior in cancer cell populations. Bioessays 31, 190-197(2009)
Domingo, E., Holland, J.J.: Mutation rates and rapid evolution of RNA viruses. In: Morse, S. (ed.) The evolutionary biology of RNA viruses, pp. 161–183, Raven Press, New York (1994)
Eigen, M.: Self-organization of matter and the evolution of biological macromolecules. Naturwiss. 58, 465-523(1971)
Eigen, M., McCaskill, Schuster, P.: (1987) The molecular quasispecies. Adv. Chem. Phys. 75, 149-263(1987)
Fox, J.F., Loeb, L.A.: Lethal mutagenesis: targeting the mutator phenotype in cancer. Seminars Cancer Biol. 20, 353–359 (2010)
Garay, R.P., Lefever, R.: A kinetic approach to the immunology of cancer: stationary state properties of effector-target cell reactions. J. Theor. Biol. 73, 417–438 (1978)
Gatenby, R.A.: Application of competition theory to tumour growth: implications for tumour biology and treatment. Europ. J. Cancer 32A, 722–726 (1996)
Gatenby, R.A., Frieden, B.R.: Application of information theory and extreme physical information to carcinogenesis. Cancer Res. 62, 3675–3684 (2002)
Greaves, M., Maley, C.C.: Clonal evolution in cancer. Nature 481, 306–313 (2012)
Lengauer, C., Kinzler, K.W., Vogelstein, B.: Genetic instabilities in human cancers. Nature 396, 643–649 (1998)
Loeb, L.A.: Mutator phenotype may be required for multistage carcinogenesis. Cancer Res. 51, 3075-3079(1991)
Loeb, L.A., Essigmann, J.M., Kazazi, F., Zhang, J., Rose, K.D., Mullins, J.I.: Lethal mutage- nesis of HIV with mutagenic nucleoside analogs. Proc. Natl. Acad. Sci. USA 96, 1492–1497 (1999)
Mallet, D.G., de Pillis, L.G.: A cellular automata model of tumor-immune system interactions. J. Theor. Biol. 239, 334–350 (2006)
Merlo, L.M.F., Pepper, J.W., Reid, B.J., Maley, C.C.: Canceras an evolutionary and ecological process. Nature Rev. Cancer 6, 924–935 (2006)
Nowell, P.C. : The clonal evolution of tumor cell populations. Science 194, 23–32 (1976)
Rosenberg, S.A.: Progress in human tumor immunology and immunotherapy. Nature 411, 380-384(2001)
Schuster, P.: How do RNA molecules and viruses explore their worlds? In: Cowan, G.A., Pines, D., Meltzer, D. (eds.) Complexity: metaphors, models and reality, pp. 383–418. Addison- Wesley, Reading, MA (1994)
Solé, R.V.: Phase transitions in unstable cancer cell populations. Eur. Phys. J. B 35, 117–124 (2003)
Solé, R.V.: Phase transitions. Princeton University Press, Princeton (2011)
Solé, R.V., Deisboeck, T.S.: An error catastrophe in cancer? J. Theor. Biol. 228, 47–54 (2004)
Solé, R.V., Goodwin B.: Signs of Life: How complexity pervades biology. Basic Books, New York (2001)
Solé, R.V., Rodriguez-Caso, C., Deisboeck, T.S., Saldanya, J.: Cancer stem cells as the engine of unstable tumor progression. Journal of Theoretical Biology 253, 629–637 (2008)
Spencer, S., Gerety, R., Pienta, K., Forrest, S.: Modeling somatic evolution in tumorigenesis. PLoS Comput. Biol. 2, e108 (2006)
Weaver, B.A.A., Silk, A.D., Montagna, C., Verdier-Pinard, P., Cleveland, D.W.: Aneuploidy acts both oncogenically and as a tumor supressor. Cancer cell 11, 25–36 (2007)
Weinberg, R.A.: The Biology of Cancer. Garland, New York (2007)
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Solé, R.V. (2012). Phase Transitions in Cancer. In: d’Onofrio, A., Cerrai, P., Gandolfi, A. (eds) New Challenges for Cancer Systems Biomedicine. SIMAI Springer Series. Springer, Milano. https://doi.org/10.1007/978-88-470-2571-4_3
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DOI: https://doi.org/10.1007/978-88-470-2571-4_3
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