The Differential Interfacial Tension Hypothesis (DITH): A Comprehensive Theory for the Self-Rearrangement of Embryonic Cells and Tissues

[+] Author and Article Information
G. Wayne Brodland

Department of Civil Engineering, University of Waterloo, Waterloo ON N2L 3G1, Canada

J Biomech Eng 124(2), 188-197 (Mar 29, 2002) (10 pages) doi:10.1115/1.1449491 History: Received June 07, 2001; Revised December 05, 2001; Online March 29, 2002
Copyright © 2002 by ASME
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Phenomena that occur in aggregates of embryonic cells. Expanded from Armstong 12.
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The cell model. (a) Structural components important to cells include microfilaments, microtubules, the cell membrane, cell adhesion molecules (CAMs), the cell cytoplasm and networks of intermediate filaments (IFs). (b) The mechanical effects of these components are approximated by an equivalent interfacial tension γLD and an effective cytoplasmic viscosity μ, and represented, respectively, by rod-like and triangular elements in the finite element model. After Brodland and Chen 26, although in the present context, a cross-section rather than a plan view is intended.
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The forces acting at a generic triple junction
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A summary of the conditions for cell sorting, mixing, and checkerboard-pattern formation. The arrows along the top of the figure indicate where the simulations shown in Fig. 5 fall along the γLD continuum.
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Some of the phenomena that can occur in a heterotypic planar aggregate. (a) Initial configuration with γLL=12 and γDD=20.(b) Total mixing and partial checkerboard (γLD=3).(c) Partial mixing (γLD=14).(d) Partial sorting (γLD=22).(e) Strong sorting, but edges do not release from the boundaries for the reasons described in the text (γLD=40).(f) Fluid behavior starting from configuration (e), as characterized by no tensions along the homotypic interfaces (γLLDD=0 and γLD=40).
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Triple junctions involving two cells and a medium. Part (b) of the figure can be interpreted as two individual cells of types L and D or as two homotypic cell masses of types L and D.
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A summary of the conditions for engulfment and separation of tissues. The arrow marked A corresponds to the simulation shown in Fig. 8, while that marked B corresponds to one in which separation occurs (unpublished) and for which γLMDM=20 and γLD=150.
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Total engulfment of one type of tissue (L) by another (D)(γLLDD=5,γLD=25,γLM=150,γDM=70)
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An aggregate consisting of three cell types. (a) Initial configuration of dark (D), intermediate (I) and light (L) cells (γDD=25,γIILLIMLM=20,γDIDL=50,γIL=10,γDM=100).(b) Final configuration showing total engulfing of the dark cells by the intermediate and light cells (with one exception), active mixing of the light and intermediate cells with each other, and sorting of the dark cells from the other two types, all as predicted by the theory. The dark cell masses do not totally round up due to mechanical interactions with the surrounding cells.
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Sorting in three-dimensions versus two-dimensions. Cells that appear to be isolated islands in a cross-sectional plane or two-dimensional simulation may be connected together by bridges that exist if the third dimension were included. Contraction along the surfaces of such bridges would cause them to shorten and would draw islands such as A and B together, while in other locations taking cells out of the plane, as implied at C.




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