Letter | Published:

A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity

Nature volume 525, pages 261264 (10 September 2015) | Download Citation

Abstract

Most cancers in humans are large, measuring centimetres in diameter, and composed of many billions of cells1. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division. What is remarkable about cancers is that virtually every neoplastic cell within a large tumour often contains the same core set of genetic alterations, with heterogeneity confined to mutations that emerge late during tumour growth2,3,4,5. How such alterations expand within the spatially constrained three-dimensional architecture of a tumour, and come to dominate a large, pre-existing lesion, has been unclear. Here we describe a model for tumour evolution that shows how short-range dispersal and cell turnover can account for rapid cell mixing inside the tumour. We show that even a small selective advantage of a single cell within a large tumour allows the descendants of that cell to replace the precursor mass in a clinically relevant time frame. We also demonstrate that the same mechanisms can be responsible for the rapid onset of resistance to chemotherapy. Our model not only provides insights into spatial and temporal aspects of tumour growth, but also suggests that targeting short-range cellular migratory activity could have marked effects on tumour growth rates.

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Acknowledgements

Support from The John Templeton Foundation is gratefully acknowledged. B.W. was supported by the Leverhulme Trust Early-Career Fellowship, and the Royal Society of Edinburgh Personal Research Fellowship. I.B. was supported by Foundational Questions in Evolutionary Biology Grant RFP-12-17. M.E.P., R.H.H. and B.V. acknowledge support from The Virginia and D.K. Ludwig Fund for Cancer Research, The Lustgarten Foundation for Pancreatic Cancer Research, The Sol Goldman Center for Pancreatic Cancer Research, and NIH grants CA43460 and CA62924.

Author information

Affiliations

  1. School of Physics and Astronomy, University of Edinburgh, JCMB, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK

    • Bartlomiej Waclaw
  2. Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA

    • Ivana Bozic
    •  & Martin A. Nowak
  3. Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138, USA

    • Ivana Bozic
    •  & Martin A. Nowak
  4. The Sol Goldman Pancreatic Cancer Research Center, Department of Pathology, Johns Hopkins University School of Medicine, 401 North Broadway, Weinberg 2242, Baltimore, Maryland 21231, USA

    • Meredith E. Pittman
    • , Ralph H. Hruban
    •  & Bert Vogelstein
  5. Ludwig Center and Howard Hughes Medical Institute, Johns Hopkins Kimmel Cancer Center, 1650 Orleans Street, Baltimore, Maryland 21287, USA

    • Bert Vogelstein
  6. Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, Massachusetts 02138, USA

    • Martin A. Nowak

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Contributions

B.W., M.A.N., I.B. and B.V. designed the study. B.W. wrote the computer programs and made simulations. B.W., I.B. and M.A.N. made analytic calculations. M.E.P. and R.H.H. carried out experimental work. All authors discussed the results. The manuscript was written primarily by B.W., M.A.N., I.B. and B.V., with contributions from M.E.P. and R.H.H.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Martin A. Nowak.

Extended data

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    This file contains Supplementary Text and Data 1-8.

Videos

  1. 1.

    Simulation of growth and treatment of a small tumor (1e7 cells)

    Treatment begins at T=0. Different colors correspond to cells with different GAs.

  2. 2.

    Simulation of growth of a small tumor (1e7 cells) with no migration and death rate d=0.5.

    Different colors correspond to cells with different GAs.

  3. 3.

    Simulation of growth of a small tumor (1e7 cells) with low migration M=1e-6 and death rate d=0.5.

    Different colors correspond to cells with different GAs.

  4. 4.

    Simulation of growth of a small tumor (1e7 cells) with no migration and selective advantage of driver mutations s=5%.

    Different colors correspond to cells with different driver mutations.

  5. 5.

    Simulation of growth of a small tumor (1e7 cells) with no migration and selective advantage of driver mutations s=1%.

    Only three most-abundant driver mutations have been colored as in Fig. 4

  6. 6.

    Simulation of growth and treatment of a small tumor (1e7 cells) for M=1e-6.

    Cells replicate and die only on the surface. Treatment begins at T=0. Different colors correspond to cells with different GAs.

  7. 7.

    Simulation of growth and treatment of a small tumor (1e7 cells) for no migration (M=0).

    Cells replicate and die only on the surface. Treatment begins at T=0. Different colors correspond to cells with different GAs.

  8. 8.

    Simulation of the off-lattice model, normal tissue with ducts.

    This video shows the simulation of the off-lattice model, normal tissue with ducts.

  9. 9.

    Simulation of the off-lattice model, two balls of cells growing in nearby ducts

    This video shows the simulation of the off-lattice model, two balls of cells growing in nearby ducts. ECM does not break.

  10. 10.

    Simulation of the off-lattice model, two balls of cells growing in nearby ducts

    This video shows the simulation of the off-lattice model, two balls of cells growing in nearby ducts. ECM can replicate.

  11. 11.

    Simulation of the off-lattice model, two balls of cells growing in nearby ducts

    The video shows the simulation of the off-lattice model, two balls of cells growing in nearby ducts. ECM breaks when stretched too much.

  12. 12.

    Simulation of the off-lattice model, two balls of cells growing in a layer of epithelial tissue merge quickly together.

    This video shows the simulation of the off-lattice model, two balls of cells growing in a layer of epithelial tissue merge quickly together.

  13. 13.

    Simulation of the off-lattice model, fast growth in the presence of migration.

    This video shows the simulation of the off-lattice model, fast growth in the presence of migration.

  14. 14.

    Simulation of the off-lattice model, slow growth in the absence of migration.

    This video shows the simulation of the off-lattice model, slow growth in the absence of migration.

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DOI

https://doi.org/10.1038/nature14971

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