Accumulation of driver and passenger mutations during tumor progression
Ivana Bozic a,b, Tibor Antal a,c, Hisashi Ohtsuki d, Hannah Carter e, Dewey Kim e, Sining Chen f, Rachel Karchin e, Kenneth W. Kinzler g, Bert Vogelstein g,1, and Martin A. Nowak a,b,h,1
-Author Affiliations
aProgram for Evolutionary Dynamics, andbDepartment of Mathematics, Harvard University, Cambridge, MA 02138;cSchool of Mathematics, University of Edinburgh, Edinburgh EH9-3JZ, United Kingdom;dDepartment of Value and Decision Science, Tokyo Institute of Technology, Tokyo 152-8552, Japan;eDepartment of Biomedical Engineering, Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD 21218;fDepartment of Biostatistics, School of Public Health, University of Medicine and Dentistry of New Jersey, Piscataway, NJ 08854;gLudwig Center for Cancer Genetics and Therapeutics, and Howard Hudges Medical Institute at Johns Hopkins Kimmel Cancer Center, Baltimore, MD 21231; andhDepartment of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138
Contributed by Bert Vogelstein, August 11, 2010 (sent for review May 26, 2010)
Abstract
Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the current study, we provide a mathematical model that begins to address this challenge. We model tumors as a discrete time branching process that starts with a single driver mutation and proceeds as each new driver mutation leads to a slightly increased rate of clonal expansion. Using the model, we observe tremendous variation in the rate of tumor development—providing an understanding of the heterogeneity in tumor sizes and development times that have been observed by epidemiologists and clinicians. Furthermore, the model provides a simple formula for the number of driver mutations as a function of the total number of mutations in the tumor. Finally, when applied to recent experimental data, the model allows us to calculate the actual selective advantage provided by typical somatic mutations in human tumors in situ. This selective advantage is surprisingly small—0.004 ± 0.0004—and has major implications for experimental cancer research.
genetics, mathematical biology
Footnotes
1To whom correspondence may be addressed. E-mail: bertvog@gmail.com or martin_nowak@harvard.edu.
Author contributions: I.B., T.A., R.K., B.V., and M.A.N. designed research; I.B., T.A., H.O., H.C., D.K., and S.C. performed research; I.B., T.A., H.O., H.C., D.K., S.C., R.K., and M.A.N. contributed new reagents/analytic tools; I.B., T.A., R.K., K.W.K., B.V., and M.A.N. analyzed data; and I.B., T.A., R.K., K.W.K., B.V., and M.A.N. wrote the paper.
The authors declare no conflict of interest.
This article contains supporting information online at
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PDF gratuito deste artigo aqui.
Ivana Bozic a,b, Tibor Antal a,c, Hisashi Ohtsuki d, Hannah Carter e, Dewey Kim e, Sining Chen f, Rachel Karchin e, Kenneth W. Kinzler g, Bert Vogelstein g,1, and Martin A. Nowak a,b,h,1
-Author Affiliations
aProgram for Evolutionary Dynamics, and
bDepartment of Mathematics, Harvard University, Cambridge, MA 02138;
cSchool of Mathematics, University of Edinburgh, Edinburgh EH9-3JZ, United Kingdom;
dDepartment of Value and Decision Science, Tokyo Institute of Technology, Tokyo 152-8552, Japan;
eDepartment of Biomedical Engineering, Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD 21218;
fDepartment of Biostatistics, School of Public Health, University of Medicine and Dentistry of New Jersey, Piscataway, NJ 08854;
gLudwig Center for Cancer Genetics and Therapeutics, and Howard Hudges Medical Institute at Johns Hopkins Kimmel Cancer Center, Baltimore, MD 21231; and
hDepartment of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138
Contributed by Bert Vogelstein, August 11, 2010 (sent for review May 26, 2010)
Abstract
Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the current study, we provide a mathematical model that begins to address this challenge. We model tumors as a discrete time branching process that starts with a single driver mutation and proceeds as each new driver mutation leads to a slightly increased rate of clonal expansion. Using the model, we observe tremendous variation in the rate of tumor development—providing an understanding of the heterogeneity in tumor sizes and development times that have been observed by epidemiologists and clinicians. Furthermore, the model provides a simple formula for the number of driver mutations as a function of the total number of mutations in the tumor. Finally, when applied to recent experimental data, the model allows us to calculate the actual selective advantage provided by typical somatic mutations in human tumors in situ. This selective advantage is surprisingly small—0.004 ± 0.0004—and has major implications for experimental cancer research.
genetics, mathematical biology
Footnotes
1To whom correspondence may be addressed. E-mail: bertvog@gmail.com or martin_nowak@harvard.edu.
Author contributions: I.B., T.A., R.K., B.V., and M.A.N. designed research; I.B., T.A., H.O., H.C., D.K., and S.C. performed research; I.B., T.A., H.O., H.C., D.K., S.C., R.K., and M.A.N. contributed new reagents/analytic tools; I.B., T.A., R.K., K.W.K., B.V., and M.A.N. analyzed data; and I.B., T.A., R.K., K.W.K., B.V., and M.A.N. wrote the paper.
The authors declare no conflict of interest.
This article contains supporting information online at
+++++
PDF gratuito deste artigo aqui.
