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A key challenge in the embryonic development of complex life forms is the correct specification of cell positions so that organs and limbs grow in the right places. To understand how cells organize themselves in the early stages of development, an interdisciplinary team of MIT applied mathematicians and Princeton University experimenters identified the mathematical principles governing the packaging of interconnected cell bademblies.
In an article entitled "Entropic effects in cell lines", published this month in Nature Physics the team reports direct experimental observations and mathematical modeling of cell packaging in enclosures convex. encountered in many complex organisms, including humans.
In their study, the authors investigated multi-cell packaging in the egg chambers of the Drosophila Drosophila melanogaster, an important model development organism. Each egg chamber contains exactly 16 germ cells that are linked by cytoplasmic bridges, resulting in a series of incomplete cell divisions. The bonds form a branched cell line tree that is surrounded by an approximately spherical shell. At a later stage, one of the 16 cells grows into the fertilizable egg, and the relative positioning of the cells is considered important for the exchange of biochemical signals during the early stages of development.
The group led by Stanislav Y of Princeton Shvartsman, a professor of chemical and biological engineering, and the Lewis-Sigler Institute for Integrative Genomics at Princeton have successfully measured spatial positions and connectivities between individual cells in more than 100 egg rooms. According to Jörn Dunkel, an badociate professor in MIT 's Department of Mathematics, the experimenters, however, had trouble explaining why some tree configurations occurred much more frequently than others
while the' '' ''. Shvartsman's team was able to visualize cellular connections. complex biological systems, Dunkel and postdoc Norbert Stoop, a recent math instructor at MIT, began developing a mathematical framework to describe observed cell packaging statistics.
"This project was an excellent example of an extremely agreeable interdisciplinary collaboration between cell biology and applied mathematics," says Dunkel. The experiments were conducted by Shvartsman's Ph.D. student Jasmin Imran Alsous, who will begin a postdoctoral fellowship at Adam Martin's laboratory at MIT's Department of Biology this fall. They were badyzed in collaboration with the postdoc Paul Villoutreix, who is now at the Weizmann Institute of Sciences in Israel.
Dunkel points out that while human biology is considerably more complex than a fruit fly, the underlying processes share many common aspects.
"Cell trees in the egg chamber store the history of cell divisions, like an ancestry tree in a sense," he says. "What we could do was map the problem of packing the cell tree into an egg chamber on a simple and simple mathematical model that asks: If you take the fundamental convex polyhedra with 16 vertices, how much is there to incorporate 16 cells while keeping all the bridges intact? "
The presence of rigid physical connections between cells adds new interesting constraints that make the problem different from the problems of # 39; most common packaging, like the question of the disposal of oranges. efficiently so that they can be transported in as few containers as possible. The interdisciplinary study of Dunkel and his colleagues, combining modern techniques of biochemical protein labeling, three-dimensional confocal microscopy, computational image badysis and mathematical modeling, shows that the problems of Dunkel et al. 39, tree stacking arise naturally in biological systems. cells in tissues at different stages of development remains a major challenge. According to a variety of biological and physical factors, cells from a single founder cell can develop in very different ways to form muscles, bones and organs such as the brain. Although the development process "involves a large number of degrees of freedom, the end result is very complex but very reproducible and robust," says Dunkel. "This raises the question, often asked by many people, such robust complexity can be understood in terms of a fundamental set of biochemical, physical and mathematical rules," he says. "Our study shows that simple physical constraints, such as cell bridges resulting from incomplete divisions, can significantly affect cell envelopes, what we are trying to do is to identify relatively simple models that make it possible to make predictions Of course, in order to fully understand embryonic development, mathematical simplification must go hand in hand with the experimental discoveries of biology. "
Since incomplete cell divisions have also been observed in amphibians, molluscs, molluscs, birds and mammals, Dunkel hopes that the modeling approach developed in the paper could also apply to these systems
"Physical constraints could play an important role in determining preferences for certain types of animals. Multicellular organizations, and that could t have secondary implications for larger scale tissue. a dynamic that is not yet clear to us: a simple way to think about it is that these cytoplasmic bridges, or other physical connections, can help the body locate the cells in the desired positions. " he says. "It seems like a very robust strategy."
Learn more:
A complete cellular atlas and lineage tree of the immortal
More information:
Jasmin Imran Alsous et al. Entropic effects in cell lines of cell lines, Nature Physics (2018). DOI: 10.1038 / s41567-018-0202-0 Jasmine Imran Alsous et al. Entropic effects in cell lines of cell lines, Nature Physics (2018). DOI: 10.1038 / s41567-018-0202-0
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