A mathematical view on cell packing


This illustration reveals the embedding of a cell lineage tree on a convex equilateral polygon with 16 vertices. Cell connections are displayed in red. Credit: NorbertStoop

A crucial difficulty in the embryonic advancement of intricate life types is the appropriate requirements of cell positions so that organs and limbs grow in the ideal locations. To comprehend how cells organize themselves at the earliest phases of advancement, an interdisciplinary group of used mathematicians at MIT and experimentalists at Princeton University determined mathematical concepts governing the packagings of interconnected cell assemblies.

In a paper entitled “Entropic effects in cell lineage tree packings,” released this month in NaturePhysics, the group reports direct speculative observations and mathematical modeling of cell packagings in convex enclosures, a biological packing issue experienced in lots of intricate organisms, consisting of human beings.

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In their research study, the authors examined multi-cellular packagings in the egg chambers of the fruit fly Drosophila melanogaster, an essential developmental design organism. Each egg chamber includes precisely 16 germline cells that are connected by cytoplasmic bridges, arising from a series of insufficient cell departments. The linkages form a branched cell- lineage tree which is confined by a roughly round hull. At some later phase, among the 16 cells becomes the fertilizable egg, and the relative positioning of the cells is believed to be very important for the biochemical signal exchange throughout the early phases of advancement.

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The group run by Princeton’s Stanislav Y. Shvartsman, a teacher of chemical and biological engineering, and the Lewis-SiglerInstitute for Integrative Genomics at Princeton was successful in determining the spatial positions and connections in between specific cells in more than 100 egg chambers. The experimentalists discovered it hard to describe, nevertheless, why particular tree setups took place far more often than others, states Jörn Dunkel, an associate teacher in the MIT Department of Mathematics.

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So while Shvartsman’s group had the ability to imagine the cell connections in intricate biological systems, Dunkel and postdoc Norbert Stoop, a current MIT mathematics trainer, started to establish a mathematical structure to explain the stats of the observed cell packagings.

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“This project has been a prime example of an extremely enjoyable interdisciplinary collaboration between cell biology and applied mathematics,”Dunkel states. The experiments were carried out by Shvartsman’sPh D. trainee Jasmin Imran Alsous, who will start a postdoctoral position at Adam Martin’s laboratory in the MIT Department of Biology this fall. They were examined in cooperation with postdoc Paul Villoutreix, who is now at the Weizmann Institute of Science in Israel.

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Dunkel mentions that while human biology is substantially more intricate than a fruit fly’s, the underlying tissue company procedures share lots of typical elements.

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“The cell trees in the egg chamber store the history of the cell divisions, like an ancestry tree in a sense,” he states. “What we were able to do was to map the problem of packing the cell tree into an egg chamber onto a nice and simple mathematical model that basically asks: If you take the fundamental convex polyhedrons with 16 vertices, how many different ways are there to embed 16 cells on them while keeping all the bridges intact?”

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The existence of stiff physical connections in between cells includes intriguing brand-new restraints that make the issue various from the most typically thought about packing issues, such as the concern of the best ways to set up oranges effectively so that they can be transferred in as couple of containers as possible. The interdisciplinary research study of Dunkel and his associates, which integrated contemporary biochemical protein labelling strategies, 3-D confocal microscopy, computational image analysis, and mathematical modeling, reveals that constrained tree packing issues occur naturally in biological systems.

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Understanding the packing concepts of cells in tissues at the numerous phases of advancement stays a significant difficulty. Depending on a range of biological and physical elements, cells stemming from a single creator cell can establish in significantly various methods to form muscles, bones, and organs such as the brain. While the developmental procedure “involves a huge number of degrees of freedom, the end result in many cases is highly complex yet also very reproducible and robust,” Dunkel states.

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“This raises the question, which many people asked before, whether such robust complexity can be understood in terms of a basic set of biochemical, physical, and mathematical rules,” he states. “Our study shows that simple physical constraints, like cell-cell bridges arising from incomplete divisions, can significantly affect cell packings. In essence, what we are trying to do is to identify relatively simple tractable models that allow us to make predictions about these complex systems. Of course, to fully understand embryonic development, mathematical simplification must go hand-in-hand with experimental insight from biology.”

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Since insufficient cell- departments have actually likewise been seen in amphibians, mollusks, birds, and mammals, Dunkel hopes the modeling technique established in the paper may be relevant to those systems also.

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“Physical constraints could play a significant role in determining the preferences for certain types of multicellular organizations, and that may have secondary implications for larger-scale tissue dynamics which are not yet clear to us. A simple way you can think about it is that these cytoplasmic bridges, or other physical connections, can help the organism to localize cells into desired positions,” he states.”This would appear to be a very robust strategy.”


Explore even more:
A total cell atlas and lineage tree of the never-ceasing flatworm.

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More info:
JasminImran Alsous et al. Entropic results in cell lineage tree packagings, NaturePhysics(2018). DOI: 10.1038/ s41567-018-0202 -0 Jasmin Imran Alsous et al. Entropic results in cell lineage tree packagings, NaturePhysics(2018). DOI: 10.1038/ s41567-018-0202 -0.

Journal referral:
NaturePhysics.

Provided by:
MassachusettsInstitute ofTechnology

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