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
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