• Previous Article
    Stochastic volatility with regime switching and uncertain noise: Filtering with sub-linear expectations
  • DCDS-B Home
  • This Issue
  • Next Article
    Property and numerical simulation of the Ait-Sahalia-Rho model with nonlinear growth conditions
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 & 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. Google Scholar

[2]

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

[3]

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

[4]

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

[5]

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

[6]

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

[7]

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

[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. Google Scholar

[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. Google Scholar

[10]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[14]

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

[15]

L. Wolpert, Principles of development, 2006.Google Scholar

show all references

References:
[1]

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

[2]

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

[3]

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

[4]

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

[5]

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

[6]

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

[7]

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

[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. Google Scholar

[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. Google Scholar

[10]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[14]

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

[15]

L. Wolpert, Principles of development, 2006.Google Scholar

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

José Ignacio Tello. Mathematical analysis of a model of morphogenesis. Discrete & Continuous Dynamical Systems - A, 2009, 25 (1) : 343-361. doi: 10.3934/dcds.2009.25.343

[2]

Ana I. Muñoz, José Ignacio Tello. Mathematical analysis and numerical simulation of a model of morphogenesis. Mathematical Biosciences & Engineering, 2011, 8 (4) : 1035-1059. doi: 10.3934/mbe.2011.8.1035

[3]

Danilo T. Pérez-Rivera, Verónica L. Torres-Torres, Abraham E. Torres-Colón, Mayteé Cruz-Aponte. Development of a computational model of glucose toxicity in the progression of diabetes mellitus. Mathematical Biosciences & Engineering, 2016, 13 (5) : 1043-1058. doi: 10.3934/mbe.2016029

[4]

Dominik Wodarz. Computational modeling approaches to studying the dynamics of oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 939-957. doi: 10.3934/mbe.2013.10.939

[5]

Saloni Rathee, Nilam. Quantitative analysis of time delays of glucose - insulin dynamics using artificial pancreas. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3115-3129. doi: 10.3934/dcdsb.2015.20.3115

[6]

Fadoua El Moustaid, Amina Eladdadi, Lafras Uys. Modeling bacterial attachment to surfaces as an early stage of biofilm development. Mathematical Biosciences & Engineering, 2013, 10 (3) : 821-842. doi: 10.3934/mbe.2013.10.821

[7]

Daniela Calvetti, Paul J. Hadwin, Janne M. J. Huttunen, David Isaacson, Jari P. Kaipio, Debra McGivney, Erkki Somersalo, Joseph Volzer. Artificial boundary conditions and domain truncation in electrical impedance tomography. Part I: Theory and preliminary results. Inverse Problems & Imaging, 2015, 9 (3) : 749-766. doi: 10.3934/ipi.2015.9.749

[8]

Hongjing Shi, Wanbiao Ma. An improved model of t cell development in the thymus and its stability analysis. Mathematical Biosciences & Engineering, 2006, 3 (1) : 237-248. doi: 10.3934/mbe.2006.3.237

[9]

James Anderson, Antonis Papachristodoulou. Advances in computational Lyapunov analysis using sum-of-squares programming. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2361-2381. doi: 10.3934/dcdsb.2015.20.2361

[10]

Graciela Canziani, Rosana Ferrati, Claudia Marinelli, Federico Dukatz. Artificial neural networks and remote sensing in the analysis of the highly variable Pampean shallow lakes. Mathematical Biosciences & Engineering, 2008, 5 (4) : 691-711. doi: 10.3934/mbe.2008.5.691

[11]

Graziano Guerra, Michael Herty, Francesca Marcellini. Modeling and analysis of pooled stepped chutes. Networks & Heterogeneous Media, 2011, 6 (4) : 665-679. doi: 10.3934/nhm.2011.6.665

[12]

Shi Jin, Dongsheng Yin. Computational high frequency wave diffraction by a corner via the Liouville equation and geometric theory of diffraction. Kinetic & Related Models, 2011, 4 (1) : 295-316. doi: 10.3934/krm.2011.4.295

[13]

Elena Izquierdo-Kulich, Margarita Amigó de Quesada, Carlos Manuel Pérez-Amor, José Manuel Nieto-Villar. Morphogenesis and aggressiveness of cervix carcinoma. Mathematical Biosciences & Engineering, 2011, 8 (4) : 987-997. doi: 10.3934/mbe.2011.8.987

[14]

Elena Izquierdo-Kulich, José Manuel Nieto-Villar. Morphogenesis of the tumor patterns. Mathematical Biosciences & Engineering, 2008, 5 (2) : 299-313. doi: 10.3934/mbe.2008.5.299

[15]

Thomas Lorenz. Mutational inclusions: Differential inclusions in metric spaces. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 629-654. doi: 10.3934/dcdsb.2010.14.629

[16]

Yanan Wang, Tao Xie, Xiaowen Jie. A mathematical analysis for the forecast research on tourism carrying capacity to promote the effective and sustainable development of tourism. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 837-847. doi: 10.3934/dcdss.2019056

[17]

Marco Campo, José R. Fernández, Maria Grazia Naso. A dynamic problem involving a coupled suspension bridge system: Numerical analysis and computational experiments. Evolution Equations & Control Theory, 2019, 8 (3) : 489-502. doi: 10.3934/eect.2019024

[18]

Mirela Domijan, Markus Kirkilionis. Graph theory and qualitative analysis of reaction networks. Networks & Heterogeneous Media, 2008, 3 (2) : 295-322. doi: 10.3934/nhm.2008.3.295

[19]

Amina Eladdadi, Noura Yousfi, Abdessamad Tridane. Preface: Special issue on cancer modeling, analysis and control. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : i-iii. doi: 10.3934/dcdsb.2013.18.4i

[20]

Andrea Tosin. Multiphase modeling and qualitative analysis of the growth of tumor cords. Networks & Heterogeneous Media, 2008, 3 (1) : 43-83. doi: 10.3934/nhm.2008.3.43

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (8)
  • HTML views (52)
  • Cited by (0)

[Back to Top]