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Cellular Potts Models for Interacting Cell Populations: Mathematical Foundation, Challenges, and Future Prospects

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Probabilistic Cellular Automata

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 27))

Abstract

Cellular Potts models (CPMs) are extensions of asynchronous probabilistic cellular automata (PCA) developed specifically to model interacting cell populations. They constitute a modeling framework for the field of cell and tissue biology that is particularly useful when the details of intercellular interaction are essentially determined by the shape and the size of the individual cells as well as the length of the contact area between neighboring cells. In this chapter, the mathematical foundation of CPMs and their relation to PCA as well as to standard Markov chains are reviewed. On the basis of their mathematical properties, the challenges of applying CPMs for studying tissue organization from the cell-based approach are explained. In conclusion, future prospects and necessary developments are discussed from the mathematical and the modeling point of view.

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Notes

  1. 1.

    For the Kronecker symbol \(\delta \), it holds that \(\delta (u,v)= 1\) if \(u=v\) and \(\delta (u,v)= 0\) otherwise.

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Acknowledgements

The author thanks Andreas Deutsch for discussions and comments.

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Authors and Affiliations

  1. Hochschule für Technik und Wirtschaft Dresden, University of Applied Sciences, Friedrich-List-Platz 1, 01069, Dresden, Germany

    Anja Voss-Böhme

  2. Zentrum für Informationsdienste und Hochleistungsrechnen, Technische Universität Dresden, 01062, Dresden, Germany

    Anja Voss-Böhme

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  1. Anja Voss-Böhme
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Correspondence to Anja Voss-Böhme .

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Editors and Affiliations

  1. Laboratoire de Mathématiques et Applications UMR 7348, Université de Poitiers, CNRS, Poitiers, France

    Pierre-Yves Louis

  2. University of Technology, Eindhoven, Noord-Brabant, The Netherlands

    Francesca R. Nardi

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Voss-Böhme, A. (2018). Cellular Potts Models for Interacting Cell Populations: Mathematical Foundation, Challenges, and Future Prospects. In: Louis, PY., Nardi, F. (eds) Probabilistic Cellular Automata. Emergence, Complexity and Computation, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-319-65558-1_19

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  • DOI: https://doi.org/10.1007/978-3-319-65558-1_19

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  • Online ISBN: 978-3-319-65558-1

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