(1988). "Simulation of cellular compaction and internalization in mammalian embryo development—II. Models for spherical embryos." <i>Bulletin of Mathematical Biology</i> 50(2), 121-142.
(1988). "Simulation of cellular compaction and internalization in mammalian embryo development—II. Models for spherical embryos." Bulletin of Mathematical Biology 50(2), 121-142.
Lewis III, Harold W., Narendra S. Goel, and Richard L. Thompson. "Simulation of cellular compaction and internalization in mammalian embryo development—II. Models for spherical embryos." Bulletin of Mathematical Biology 50, no. 2 (1988): 121-142.
A model based upon minimization of surface energy as an explanation for the phenomena of compaction and internalization of cells during mammalian embryo development is generalized for three-dimensional cells. It is shown that, for a spherical embryo, if cells are assumed to be polygonal cones in shape, the simulation of these phenomena for three-dimensional cells is equivalent to simulations of deformations of two-dimensional cells on the surface of a sphere. This equivalence is used to show that in the optimal compacted structure, with no internal cells, the cross-sections of cells in general are not regular polyhedra. Further, the internalization occurs when the number of cells exceeds a critical value which seems to depend on the relative sizes and biophysical properties of cells.
Thompson's professional affiliation listed at:
Department of Systems Science, State University of New York
Binghamton, NY 13901
Permanent address:
La Jolla Institute, P. O. Box 1432, La Jolla, CA 92038., U.S.A.