American Institute of Mathematical Sciences

Advanced
2010, 7(2): 259-275. doi: 10.3934/mbe.2010.7.259

Surface tension and modeling of cellular intercalation during zebrafish gastrulation

Colette Calmelet 1, and  Diane Sepich 2,

1. 

Department of Mathematics and Statistics, California State University, Holt Hall 181, Chico, CA 95929, United States
2. 

Department of Biological Sciences, Vanderbilt University, MRBIII Suite 4260A, Nashville, TN 37203, United States

Received  July 2009 Revised  November 2009 Published  April 2010

In this paper we discuss a model of zebrafish embryo notochord development based on the effect of surface tension of cells at the boundaries. We study the process of interaction of mesodermal cells at the boundaries due to adhesion and cortical tension, resulting in cellular intercalation. From in vivo experiments, we obtain cell outlines of time-lapse images of cell movements during zebrafish embryo development. Using Cellular Potts Model, we calculate the total surface energy of the system of cells at different time intervals at cell contacts. We analyze the variations of total energy depending on nature of cell contacts. We demonstrate that our model can be viable by calculating the total surface energy value for experimentally observed configurations of cells and showing that in our model these configurations correspond to a decrease in total energy values in both two and three dimensions.
Keywords: cortical tension, anisotropic adhesion, Cellular Potts Model, mophogenetic movements, zebrafish, total energy, modeling, stability., Cellular intercalation, surface tension.
Mathematics Subject Classification: Primary: 92-08, 92-C15; Secondary: 65C05, 68U9.
Citation: Colette Calmelet, Diane Sepich. Surface tension and modeling of cellular intercalation during zebrafish gastrulation. Mathematical Biosciences & Engineering, 2010, 7 (2) : 259-275. doi: 10.3934/mbe.2010.7.259
[1]

Marco Scianna, Luigi Preziosi, Katarina Wolf. A Cellular Potts model simulating cell migration on and in matrix environments. Mathematical Biosciences & Engineering, 2013, 10 (1) : 235-261. doi: 10.3934/mbe.2013.10.235
[2]

Mostafa Adimy, Fabien Crauste, Laurent Pujo-Menjouet. On the stability of a nonlinear maturity structured model of cellular proliferation. Discrete & Continuous Dynamical Systems, 2005, 12 (3) : 501-522. doi: 10.3934/dcds.2005.12.501
[3]

Grigor Nika, Bogdan Vernescu. Rate of convergence for a multi-scale model of dilute emulsions with non-uniform surface tension. Discrete & Continuous Dynamical Systems - S, 2016, 9 (5) : 1553-1564. doi: 10.3934/dcdss.2016062
[4]

Chengchun Hao. Cauchy problem for viscous shallow water equations with surface tension. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 593-608. doi: 10.3934/dcdsb.2010.13.593
[5]

Min Chen, Nghiem V. Nguyen, Shu-Ming Sun. Solitary-wave solutions to Boussinesq systems with large surface tension. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1153-1184. doi: 10.3934/dcds.2010.26.1153
[6]

Samuel Walsh. Steady stratified periodic gravity waves with surface tension II: Global bifurcation. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 3287-3315. doi: 10.3934/dcds.2014.34.3287
[7]

Hyung Ju Hwang, Youngmin Oh, Marco Antonio Fontelos. The vanishing surface tension limit for the Hele-Shaw problem. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3479-3514. doi: 10.3934/dcdsb.2016108
[8]

Calin Iulian Martin. Dispersion relations for periodic water waves with surface tension and discontinuous vorticity. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 3109-3123. doi: 10.3934/dcds.2014.34.3109
[9]

Roman M. Taranets, Jeffrey T. Wong. Existence of weak solutions for particle-laden flow with surface tension. Discrete & Continuous Dynamical Systems, 2018, 38 (10) : 4979-4996. doi: 10.3934/dcds.2018217
[10]

Nataliya Vasylyeva, Vitalii Overko. The Hele-Shaw problem with surface tension in the case of subdiffusion. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1941-1974. doi: 10.3934/cpaa.2016023
[11]

Samuel Walsh. Steady stratified periodic gravity waves with surface tension I: Local bifurcation. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 3241-3285. doi: 10.3934/dcds.2014.34.3241
[12]

Eduardo Ibarguen-Mondragon, Lourdes Esteva, Leslie Chávez-Galán. A mathematical model for cellular immunology of tuberculosis. Mathematical Biosciences & Engineering, 2011, 8 (4) : 973-986. doi: 10.3934/mbe.2011.8.973
[13]

Ying Sue Huang, Chai Wah Wu. Stability of cellular neural network with small delays. Conference Publications, 2005, 2005 (Special) : 420-426. doi: 10.3934/proc.2005.2005.420
[14]

Sergei A. Avdonin, Boris P. Belinskiy. Controllability of a string under tension. Conference Publications, 2003, 2003 (Special) : 57-67. doi: 10.3934/proc.2003.2003.57
[15]

Jie Wang, Xiaoqiang Wang. New asymptotic analysis method for phase field models in moving boundary problem with surface tension. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3185-3213. doi: 10.3934/dcdsb.2015.20.3185
[16]

Shengfu Deng. Generalized pitchfork bifurcation on a two-dimensional gaseous star with self-gravity and surface tension. Discrete & Continuous Dynamical Systems, 2014, 34 (9) : 3419-3435. doi: 10.3934/dcds.2014.34.3419
[17]

Marcelo M. Disconzi, Igor Kukavica. A priori estimates for the 3D compressible free-boundary Euler equations with surface tension in the case of a liquid. Evolution Equations & Control Theory, 2019, 8 (3) : 503-542. doi: 10.3934/eect.2019025
[18]

Claude-Michel Brauner, Michael L. Frankel, Josephus Hulshof, Alessandra Lunardi, G. Sivashinsky. On the κ - θ model of cellular flames: Existence in the large and asymptotics. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 27-39. doi: 10.3934/dcdss.2008.1.27
[19]

Michael Frankel, Victor Roytburd, Gregory I. Sivashinsky. Dissipativity for a semi-linearized system modeling cellular flames. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 83-99. doi: 10.3934/dcdss.2011.4.83
[20]

Alexis B. Cook, Daniel R. Ziazadeh, Jianfeng Lu, Trachette L. Jackson. An integrated cellular and sub-cellular model of cancer chemotherapy and therapies that target cell survival. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1219-1235. doi: 10.3934/mbe.2015.12.1219

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (21)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy