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Modeling Cellular Systems pp 67–79Cite as

Sampling from T Cell Receptor Repertoires

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Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 11))

Abstract

Modern single-cell sequencing techniques allow the unique T cell receptor (TCR) signature of each of a sample of hundreds of T cells to be read. The mathematical challenge is to extrapolate from the properties of a sample to those of the whole repertoire of an individual, made up of many millions of T cells. We consider the distribution of the number of repeats of any TCR in a sample, the mean number of cells needed to find a repeat with probability one half, and the relationship between the true distribution of clonal sizes and that experimentally observed in a sample. In the simplest hypothesis for the structure of the repertoire, the same number of cells make up each clonotype. We also consider the case where the distribution of clonal sizes is geometric, and examples where a small fraction of clones in the repertoire are expanded.

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Acknowledgements

The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007–2013) through the Marie-Curie Action “Quantitative T cell Immunology” Initial Training Network, with reference number FP7-PEOPLE-2012-ITN 317040-QuanTI.

   We have benefitted from discussions with Pedro Gonçalves and Benedita Rocha, and from the helpful comments of an anonymous referee.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    Marco Ferrarini, Carmen Molina-París & Grant Lythe

Authors
  1. Marco Ferrarini
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  2. Carmen Molina-París
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  3. Grant Lythe
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Corresponding authors

Correspondence to Marco Ferrarini , Carmen Molina-París or Grant Lythe .

Editor information

Editors and Affiliations

  1. Heidelberg University, Heidelberg, Germany

    Frederik Graw

  2. Heidelberg University, Heidelberg, Germany

    Franziska Matthäus

  3. Heidelberg University, Heidelberg, Germany

    Jürgen Pahle

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Ferrarini, M., Molina-París, C., Lythe, G. (2017). Sampling from T Cell Receptor Repertoires. In: Graw, F., Matthäus, F., Pahle, J. (eds) Modeling Cellular Systems. Contributions in Mathematical and Computational Sciences, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-45833-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-45833-5_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45831-1

  • Online ISBN: 978-3-319-45833-5

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