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Simulation of cellular compaction and internalization in mammalian embryo development—II. Models for spherical embryos

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Abstract

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.

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Author notes

  1. Harold W. Lewis III

    Present address: IBM Corporation, 1701 North St., T58/25-2, 13760, Endicott, NY, USA

  2. Richard L. Thompson

    Present address: La Jolla Institute, P.O. Box 1434, 92038, La Jolla, CA, USA

Authors and Affiliations

  1. Department of Systems Science, State University of New York, 13901, Binghamton, NY, USA

    Harold W. Lewis III, Narendra S. Goel & Richard L. Thompson

Authors
  1. Harold W. Lewis III
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  2. Narendra S. Goel
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  3. Richard L. Thompson
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Lewis, H.W., Goel, N.S. & Thompson, R.L. Simulation of cellular compaction and internalization in mammalian embryo development—II. Models for spherical embryos. Bltn Mathcal Biology 50, 121–142 (1988). https://doi.org/10.1007/BF02459949

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  • DOI: https://doi.org/10.1007/BF02459949

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