Topological solution for cell proliferation in intestinal crypt

 

1-crypt

2-crypt

3-crypt

4-crypt

5-crypt

6-crypt

7-crypt

8-crypt

9-crypt

10-crypt

11-crypt

12-crypt

NOTE:
As the title of this paper indicates, the paper does not include the consideration of the cell death. In this paper, the division waves are initiated by the cell division between pentagons in the bottom. But I also found that a division wave can be initiated by the death of a pentagon in the crypt bottom. This second mechanism of initiation does not depend on the positions of the pentagons, and therefore the crypt is functioning indefinitely.
I did not publish this second mechanism separately, but the opportunity to use it came when I asked S. Fedorov to try building a 3-D computer model of the crypt. He indeed created a wonderful 3-D computer simulation program that was published in 2005 on the Internet (http://www.cell-division-program.com/). And still later, this computer program was used in the paper comparing the topology of the crypt with the topology of the carbon nanotubes (https://arxiv.org/abs/1106.5705).
Generally, the phenomenon of local onset of cell proliferation following cell death can be a direct consequence of the topological situation arising in a tissue after cell death. The phenomenon of tissue regeneration as well as finding of the regularly occuring cell death at the crypt bottom where cell divisions are initiated could be the examples.

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