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January  2017, 22(1): 83-99. doi: 10.3934/dcdsb.2017004

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

Received  March 2016 Revised  May 2016 Published  December 2016

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.

Citation: Alexandra Fronville, Abdoulaye Sarr, Vincent Rodin. Modelling multi-cellular growth using morphological analysis. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 83-99. doi: 10.3934/dcdsb.2017004
References:
[1]

J. -P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, 1990.

[2]

J. -P. Aubin, Viability Theory, Birkhauser, 1991.

[3]

J. -P. Aubin, Mutational and Morphological Analysis: Tools for Shape Regulation and Morphogenesis, Birkhauser, 2000. doi: 10.1007/978-1-4612-1576-9.

[4]

J. -P. Aubin, A. Bayen and P. Saint-Pierre, Viability Theory: New Directions, Springer, 2011. doi: 10.1007/978-3-642-16684-6.

[5]

G. Beurier, F. Michel and J. Ferber, A morphogenesis model for multiagent embryogeny, in: Artificiel Life (ALife X), 2006.

[6]

J. Ferber, Multi-Agent System: An Introduction to Distributed Artificial Intelligence, 1999.

[7]

A. FronvilleF. HarrouetA. Desilles and P. Deloor, Simulation tool for morphological analysis, ESM, 2010 (2010), 127-132. 

[8]

A. Fronville, A. Sarr, P. Ballet and V. Rodin, Mutational analysis-inspired algorithms for cells self-organization towards a dynamic under viability constraints, Self-Adaptive and Self-Organizing Systems (SASO), IEEE Sixth International Conference on, 2012 (2012). doi: 10.1109/SASO.2012.15.

[9]

A. Gorre, Evolutions of tubes under operability constraints, Journal of Mathematical Analysis and Applications, 216 (1997), 1-22.  doi: 10.1006/jmaa.1997.5476.

[10]

G. M. P. Hoare, N Jennings Foundations of Distributed Artificial Intelligence, 1996.

[11]

A. Lesne, Robustness: Confronting lessons from physics and biology, Biological Reviews, 83 (2008), 509-532.  doi: 10.1111/j.1469-185X.2008.00052.x.

[12]

T. Lorenz, Mutational Analysis A Joint Framework for Cauchy Problems In and Beyond Vector Spaces, Springer, 2010. doi: 10.1007/978-3-642-12471-6.

[13]

N. OlivierM. A. Luengo-OrozL. DuloquinE. FaureT. SavyI. VeilleuxX. SolinasD. DébarreP. BourgineA. SantosN. Peyriéras and E. Beaurepaire, Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy, Science, 329 (2010), 967-971.  doi: 10.1126/science.1189428.

[14]

J. Tisseau, Virtual reality --in virtuo autonomy --, Ph. D. thesis, University of Rennes I, 2001.

[15]

L. Wolpert, Principles of development, 2006.

show all references

References:
[1]

J. -P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, 1990.

[2]

J. -P. Aubin, Viability Theory, Birkhauser, 1991.

[3]

J. -P. Aubin, Mutational and Morphological Analysis: Tools for Shape Regulation and Morphogenesis, Birkhauser, 2000. doi: 10.1007/978-1-4612-1576-9.

[4]

J. -P. Aubin, A. Bayen and P. Saint-Pierre, Viability Theory: New Directions, Springer, 2011. doi: 10.1007/978-3-642-16684-6.

[5]

G. Beurier, F. Michel and J. Ferber, A morphogenesis model for multiagent embryogeny, in: Artificiel Life (ALife X), 2006.

[6]

J. Ferber, Multi-Agent System: An Introduction to Distributed Artificial Intelligence, 1999.

[7]

A. FronvilleF. HarrouetA. Desilles and P. Deloor, Simulation tool for morphological analysis, ESM, 2010 (2010), 127-132. 

[8]

A. Fronville, A. Sarr, P. Ballet and V. Rodin, Mutational analysis-inspired algorithms for cells self-organization towards a dynamic under viability constraints, Self-Adaptive and Self-Organizing Systems (SASO), IEEE Sixth International Conference on, 2012 (2012). doi: 10.1109/SASO.2012.15.

[9]

A. Gorre, Evolutions of tubes under operability constraints, Journal of Mathematical Analysis and Applications, 216 (1997), 1-22.  doi: 10.1006/jmaa.1997.5476.

[10]

G. M. P. Hoare, N Jennings Foundations of Distributed Artificial Intelligence, 1996.

[11]

A. Lesne, Robustness: Confronting lessons from physics and biology, Biological Reviews, 83 (2008), 509-532.  doi: 10.1111/j.1469-185X.2008.00052.x.

[12]

T. Lorenz, Mutational Analysis A Joint Framework for Cauchy Problems In and Beyond Vector Spaces, Springer, 2010. doi: 10.1007/978-3-642-12471-6.

[13]

N. OlivierM. A. Luengo-OrozL. DuloquinE. FaureT. SavyI. VeilleuxX. SolinasD. DébarreP. BourgineA. SantosN. Peyriéras and E. Beaurepaire, Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy, Science, 329 (2010), 967-971.  doi: 10.1126/science.1189428.

[14]

J. Tisseau, Virtual reality --in virtuo autonomy --, Ph. D. thesis, University of Rennes I, 2001.

[15]

L. Wolpert, Principles of development, 2006.

Figure 1.  Statechart diagram
Figure 2.  French Flag growth
Figure 3.  Gastrulation
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