Entropic effects in cell lineage tree packings
Author(s)
Imran Alsous, Jasmin; Villoutreix, Paul; Stoop, Norbert; Shvartsman, Stanislav Y.; Dunkel, Joern
DownloadAccepted version (837.7Kb)
Terms of use
Metadata
Show full item recordAbstract
Optimal packings [1, 2] of unconnected objects have been studied for centuries [3–6], but the packing principles of linked objects, such as topologically complex polymers [7, 8] or cell lineages [9, 10], are yet to be fully explored. Here, we identify and investigate a generic class of geometrically frustrated tree packing problems, arising during the initial stages of animal development when interconnected cells assemble within a convex enclosure [10]. Using a combination of 3D imaging, computational image analysis, and mathematical modelling, we study the tree packing problem in Drosophila egg chambers, where 16 germline cells are linked by cytoplasmic bridges to form a branched tree. Our imaging data reveal non-uniformly distributed tree packings, in agreement with predictions from energy-based computations. This departure from uniformity is entropic and affects cell organization during the first stages of the animal’s development. Considering mathematical models of increasing complexity, we investigate spherically confined tree packing problems on convex polyhedrons [11] that generalize Platonic and Archimedean solids. Our experimental and theoretical results provide a basis for understanding the principles that govern positional ordering in linked multicellular structures, with implications for tissue organization and dynamics [12, 13].
Date issued
2018-08-08Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Nature Physics
Publisher
Springer Science+Business Media
Citation
Imran Alsous, J. et al. "Entropic effects in cell lineage tree packings." Nature Physics 14, 10 (October 2018): 1016–1021 © 2018 The Author(s)
Version: Author's final manuscript
ISSN
1745-2473
1745-2481
Keywords
General Physics and Astronomy