The effect of one additional driver mutation on tumor progression

Authors

  • Johannes G. Reiter,

    1. IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria
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    • These authors contributed equally to this work.
  • Ivana Bozic,

    Corresponding author
    1. Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
    2. Department of Mathematics, Harvard University, Cambridge, MA, USA
    • IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria
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    • These authors contributed equally to this work.
  • Benjamin Allen,

    1. IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria
    2. Department of Mathematics, Emmanuel College, Boston, MA, USA
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  • Krishnendu Chatterjee,

    1. IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria
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  • Martin A. Nowak

    1. Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
    2. Department of Mathematics, Harvard University, Cambridge, MA, USA
    3. Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA
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Correspondence Martin A. Nowak, Program for Evolutionary Dynamics, 1 Brattle Square Ste. 6, Cambridge, MA 02138-3758, USA. Tel.: +1 617 496 4737; Fax: +1 617 496 4629; e-mail: martin_nowak@harvard.edu

Abstract

Tumor growth is caused by the acquisition of driver mutations, which enhance the net reproductive rate of cells. Driver mutations may increase cell division, reduce cell death, or allow cells to overcome density-limiting effects. We study the dynamics of tumor growth as one additional driver mutation is acquired. Our models are based on two-type branching processes that terminate in either tumor disappearance or tumor detection. In our first model, both cell types grow exponentially, with a faster rate for cells carrying the additional driver. We find that the additional driver mutation does not affect the survival probability of the lesion, but can substantially reduce the time to reach the detectable size if the lesion is slow growing. In our second model, cells lacking the additional driver cannot exceed a fixed carrying capacity, due to density limitations. In this case, the time to detection depends strongly on this carrying capacity. Our model provides a quantitative framework for studying tumor dynamics during different stages of progression. We observe that early, small lesions need additional drivers, while late stage metastases are only marginally affected by them. These results help to explain why additional driver mutations are typically not detected in fast-growing metastases.

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