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Optimal pathways control fixation of multiple mutations during cancer initiation

      Abstract

      Cancer starts after initially healthy tissue cells accumulate several specific mutations or other genetic alterations. The dynamics of tumor formation is a very complex phenomenon due to multiple involved biochemical and biophysical processes. It leads to a very large number of possible pathways on the road to final fixation of all mutations that marks the beginning of the cancer, complicating the understanding of microscopic mechanisms of tumor formation. We present a new theoretical framework of analyzing the cancer initiation dynamics by exploring the properties of effective free-energy landscape of the process. It is argued that although there are many possible pathways for the fixation of all mutations in the system, there are only a few dominating pathways on the road to tumor formation. The theoretical approach is explicitly tested in the system with only two mutations using analytical calculations and Monte Carlo computer simulations. Excellent agreement with theoretical predictions is found for a large range of parameters, supporting our hypothesis and allowing us to better understand the mechanisms of cancer initiation. Our theoretical approach clarifies some important aspects of microscopic processes that lead to tumor formation.
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      References

        • Weinberg R.A.
        The Biology of Cancer.
        Garland Science, 2013
        • Lodish H.
        • Berk A.
        • Matsudaira P.
        • et al.
        Molecular Cell Biology.
        Macmillan, 2008
        • Nowak M.A.
        Evolutionary Dynamics: Exploring the Equations of Life.
        Harvard University Press, 2006
        • Hanahan D.
        • Weinberg R.A.
        The hallmarks of cancer.
        Cell. 2000; 100: 57-70https://doi.org/10.1016/s0092-8674(00)81683-9
        • Tomasetti C.
        • Vogelstein B.
        Cancer etiology. Variation in cancer risk among tissues can be explained by the number of stem cell divisions.
        Science. 2015; 347: 78-81https://doi.org/10.1126/science.1260825
        • Tomasetti C.
        • Li L.
        • Vogelstein B.
        Stem cell divisions, somatic mutations, cancer etiology, and cancer prevention.
        Science. 2017; 355: 1330-1334https://doi.org/10.1126/science.aaf9011
        • Hanahan D.
        • Weinberg R.A.
        Hallmarks of cancer: the next generation.
        Cell. 2011; 144: 646-674https://doi.org/10.1016/j.cell.2011.02.013
        • Dominik W.
        • Natalia K.
        Dynamics of Cancer: Mathematical Foundations of Oncology.
        World Scientific, 2014
        • Lahouel K.
        • Younes L.
        • Tomasetti C.
        • et al.
        Revisiting the tumorigenesis timeline with a data-driven generative model.
        Proc. Natl. Acad. Sci. U S A. 2020; 117: 857-864https://doi.org/10.1073/pnas.1914589117
        • Komarova N.L.
        • Sengupta A.
        • Nowak M.A.
        Mutation–selection networks of cancer initiation: tumor suppressor genes and chromosomal instability.
        J. Theor. Biol. 2003; 223: 433-450https://doi.org/10.1016/s0022-5193(03)00120-6
        • Iwasa Y.
        • Michor F.
        • Nowak M.A.
        Stochastic tunnels in evolutionary dynamics.
        Genetics. 2004; 166: 1571-1579https://doi.org/10.1534/genetics.166.3.1571
        • Foo J.
        • Leder K.
        • Michor F.
        Stochastic dynamics of cancer initiation.
        Phys. Biol. 2011; 8: 015002https://doi.org/10.1088/1478-3975/8/1/015002
        • Paterson C.
        • Clevers H.
        • Bozic I.
        Mathematical model of colorectal cancer initiation.
        Proc. Natl. Acad. Sci. U S A. 2020; 117: 20681-20688https://doi.org/10.1073/pnas.2003771117
        • Teimouri H.
        • Kochugaeva M.P.
        • Kolomeisky A.B.
        Elucidating the correlations between cancer initiation times and lifetime cancer risks.
        Sci. Rep. 2019; 9: 18940-18948https://doi.org/10.1038/s41598-019-55300-w
        • Teimouri H.
        • Kolomeisky A.B.
        Temporal order of mutations influences cancer initiation dynamics.
        Phys. Biol. 2021; 18https://doi.org/10.1088/1478-3975/ac0b7e
        • Haeno H.
        • Maruvka Y.E.
        • Michor F.
        • et al.
        Stochastic tunneling of two mutations in a population of cancer cells.
        PLoS One. 2013; 8: e65724https://doi.org/10.1371/journal.pone.0065724
        • Ashcroft P.
        • Michor F.
        • Galla T.
        Stochastic tunneling and metastable states during the somatic evolution of cancer.
        Genetics. 2015; 199: 1213-1228https://doi.org/10.1534/genetics.114.171553
        • Proulx S.R.
        The rate of multi-step evolution in Moran and Wright–Fisher populations.
        Theor. Popul. Biol. 2011; 80: 197-207https://doi.org/10.1016/j.tpb.2011.07.003
        • Weinreich D.M.
        • Chao L.
        Rapid evolutionary escape by large populations from local fitness peaks is likely in nature.
        Evolution. 2005; 59: 1175-1182
        • Weissman D.B.
        • Desai M.M.
        • Feldman M.W.
        • et al.
        The rate at which asexual populations cross fitness valleys.
        Theor. Popul. Biol. 2009; 75: 286-300https://doi.org/10.1016/j.tpb.2009.02.006
        • Guo Y.
        • Vucelja M.
        • Amir A.
        Stochastic tunneling across fitness valleys can give rise to a logarithmic long-term fitness trajectory.
        Sci. Adv. 2019; 5: eaav3842https://doi.org/10.1126/sciadv.aav3842
        • Tang E.
        • Agudo-Canalejo J.
        • Golestanian R.
        Topology protects chiral edge currents in stochastic systems.
        Phys. Rev. X. 2021; 11: 031015
        • Sherr C.J.
        Principles of tumor suppression.
        Cell. 2004; 116: 235-246https://doi.org/10.1016/s0092-8674(03)01075-4
        • Kolomeisky A.B.
        Motor Proteins and Molecular Motors.
        CRC Press, 2015
        • Phillips R.
        • Kondev J.
        • Orme N.
        • et al.
        Physical Biology of the Cell.
        Garland Science, 2012
        • Knudson A.G.
        Mutation and cancer: statistical study of retinoblastoma.
        Proc. Natl. Acad. Sci. U S A. 1971; 68: 820-823https://doi.org/10.1073/pnas.68.4.820
        • Knudson A.G.
        Two genetic hits (more or less) to cancer.
        Nat. Rev. Cancer. 2001; 1: 157-162https://doi.org/10.1038/35101031
        • Nowak M.A.
        • Komarova N.L.
        • Lengauer C.
        • et al.
        The role of chromosomal instability in tumor initiation.
        Proc. Natl. Acad. Sci. U S A. 2002; 99: 16226-16231https://doi.org/10.1073/pnas.202617399
        • Lynch M.
        Rate, molecular spectrum, and consequences of human mutation.
        Proc. Natl. Acad. Sci. U S A. 2010; 107: 961-968https://doi.org/10.1073/pnas.0912629107
        • Orr H.A.
        The genetic theory of adaptation: a brief history.
        Nat. Rev. Genet. 2005; 6: 119-127https://doi.org/10.1038/nrg1523
        • Gillespie J.H.
        Molecular evolution over the mutational landscape.
        Evolution. 1984; 38: 1116-1129https://doi.org/10.1111/j.1558-5646.1984.tb00380.x
        • Lieberman E.
        • Hauert C.
        • Nowak M.A.
        Evolutionary dynamics on graphs.
        Nature. 2005; 433: 312-316https://doi.org/10.1038/nature03204
        • Sinha S.
        • Malmi-Kakkada A.N.
        • Thirumalai D.
        • et al.
        Spatially heterogeneous dynamics of cells in a growing tumor spheroid: comparison between theory and experiments.
        Soft Matter. 2020; 16: 5294-5304https://doi.org/10.1039/c9sm02277e