Triangles bridge the scales: Quantifying cellular contributions to tissue deformation.

Matthias Merkel (1, 2) , Raphael Etournay (3, 4) , Marko Popović (1) , Guillaume Salbreux (5, 1) , Suzanne Eaton (4) , Frank Jülicher (1)

1 MPI-PKS - Max Planck Institute for the Physics of Complex Systems
2 Syracuse University
3 Génétique et Physiologie de l'Audition
4 MPI-CBG - Max Planck Institute of Molecular Cell Biology and Genetics
5 The Francis Crick Institute [London]

In this article, we propose a general framework to study the dynamics and topology of cellular networks that capture the geometry of cell packings in two-dimensional tissues. Such epithelia undergo large-scale deformation during morphogenesis of a multicellular organism. Large-scale deformations emerge from many individual cellular events such as cell shape changes, cell rearrangements, cell divisions, and cell extrusions. Using a triangle-based representation of cellular network geometry, we obtain an exact decomposition of large-scale material deformation. Interestingly, our approach reveals contributions of correlations between cellular rotations and elongation as well as cellular growth and elongation to tissue deformation. Using this triangle method, we discuss tissue remodeling in the developing pupal wing of the fly Drosophila melanogaster.

Keywords: Biomechanics; Elastic deformation; Morphogenesis; Plastic deformation; Plasticity; Shear deformation; Strain; Viscoelasticity; Viscoplasticity

Domains: Life Sciences [q-bio]; Cellular Biology; Physics [physics]; Condensed Matter [cond-mat]; Soft Condensed Matter [cond-mat.soft]; Physics [physics]; Mechanics [physics]; Fluid mechanics [physics.class-ph]

Matthias Merkel, Raphael Etournay, Marko Popović, Guillaume Salbreux, Suzanne Eaton, et al.. Triangles bridge the scales: Quantifying cellular contributions to tissue deformation.. Physical Review E , 2017, 95 (3), pp.032401. ⟨10.1103/PhysRevE.95.032401⟩. ⟨pasteur-01545825⟩