Modelling multi-cellular growth using morphological analysis

Alexandra Fronville; Abdoulaye Sarr; Vincent Rodin

doi:10.3934/dcdsb.2017004

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2017, Volume 22, Issue 1: 83-99. Doi: 10.3934/dcdsb.2017004

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Modelling multi-cellular growth using morphological analysis

1.
European University of Britanny, UBO, LATIM, UMR 1101, Brest, France
2.
European University of Britanny, UBO, Lab-STICC, CNRS, UMR 6285, Brest, France

* Corresponding author: Alexandra Fronville
* Corresponding author: Alexandra Fronville

Received: March 2016

Revised: May 2016

Published: November 2017

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Abstract

The goal of this work is to introduce a mathematical model of multicellular developmental design based on morphological analysis in order to study the robustness of multi-cellular organism development.

In this model each cell is a controlled system and has the same information, an ordered list of cell type. Cells perceive their neighbours during the growth process and decide to divide in a direction given by the reading advancement of the virtual genetic material and depending on the complex interplay between genetic, epigenetic and environment.

Cells can perform distinct functions but in our simulator, two cell types just differ by there color and by permuting the segmentation direction according to the virtual genetic material and the epigenetic control. The switching on and switching off of genes depends on the environment of the cell.The multi-cellular organism has to reach a shape in a given environment to which it has to adapt.

We present in this paper an algorithm based model which is implemented in a virtual 3D-environment. Moreover, the algorithm follows the principle of inertia in that the cells progress through the reading of its virtual genetic material after a punctuated equilibrium or when its viability is at stake.

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Mathematics Subject Classification: Primary:92C17, 92B99;Secondary:93C55.

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Figure 1. Statechart diagram

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Figure 2. French Flag growth

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Figure 3. Gastrulation

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