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Modelling development with cell complexes in one, two, and three dimensions

Banff International Research Station for Mathematical Innovation and Discovery

A wide variety of modeling problems can be approached by dividing the problem into a spatial arrangement of discrete components which communicate with one another. Modeling multicellular development fits this framework well; a tissue is composed of discrete cells which communicate by methods such as hormonal signaling or mechanosensing. One of the chief challenges in modeling development is that the number and arrangement of components changes, as cells grow and divide. By choosing the right underlying structural representation, however, the task of the modeler can be made easier. Representing a growing tissue with the mathematical formalism of the cell complex lets the modeler consider interactions locally and assign properties to entities of the right dimension. I describe a framework for developmental plant modeling based on cell complexes, and demonstrate models of development in one, two, and three dimensions.

Mathematics; Biology and other natural sciences; Mathematical biology

video/mp4

Author affiliation: Max Planck Institute for Plant Breeding Research

2018-07-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/66421

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/