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On the Probability of Random Genetic Mutations for Various Types of Tumor Growth

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Abstract

In this work, we consider the problem of estimating the probability for a specific random genetic mutation to be present in a tumor of a given size. Previous mathematical models have been based on stochastic methods where the tumor was assumed to be homogeneous and, on average, growing exponentially. In contrast, we are able to obtain analytical results for cases where the exponential growth of cancer has been replaced by other, arguably more realistic types of growth of a heterogeneous tumor cell population. Our main result is that the probability that a given random mutation will be present by the time a tumor reaches a certain size, is independent of the type of curve assumed for the average growth of the tumor, at least for a general class of growth curves. The same is true for the related estimate of the expected number of mutants present in a tumor of a given size, if mutants are indeed present.

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Acknowledgements

The author wishes to thank Professor Dmitry Dolgopyat for his helpful discussions and the reviewers for their valuable comments. The work of CT was supported in part by the National Institute of Health under Grant T32 CA009337, by the joint National Science Foundation/National Institute of General Medical Sciences program under Grant DMS-0758374 and by the National Cancer Institute under Grant R01CA130817.

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Authors and Affiliations

  1. Department of Biostatistics, Harvard University and Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, CLS11007, 450 Brookline Ave, Boston, MA, 02215, USA

    Cristian Tomasetti

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  1. Cristian Tomasetti
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Correspondence to Cristian Tomasetti.

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Tomasetti, C. On the Probability of Random Genetic Mutations for Various Types of Tumor Growth. Bull Math Biol 74, 1379–1395 (2012). https://doi.org/10.1007/s11538-012-9717-1

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