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A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development

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Abstract

Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a “progression” of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma–carcinoma progression, from regulatory processes to cell–cell signaling pathways.

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Authors and Affiliations

  1. Department of Mathematics “F. Enriques”, University of Milan, Via Saldini 50, 20133, Milan, Italy

    Giovanni De Matteis

  2. Department of Informatics, Systems and Communication, University of Milan Bicocca, Viale Sarca 336, 20126, Milan, Italy

    Alex Graudenzi & Marco Antoniotti

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  1. Giovanni De Matteis
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Correspondence to Alex Graudenzi.

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This work has been supported by Regione Lombardia under the research project Retro Net through the grant 12-4-5148000-40; U.A 053.

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De Matteis, G., Graudenzi, A. & Antoniotti, M. A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development. J. Math. Biol. 66, 1409–1462 (2013). https://doi.org/10.1007/s00285-012-0539-4

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