Correlating Tissue-level Elasticity and Surface Tension with Cellular-level Properties and Shape Statistics

Cellular aggregates are well known for their liquid-like, viscoelastic behavior. Upon mechanical compression and relaxation, cells within an aggregate rearrange themselves to minimize system energy. However, quantitative correlations between the aggregate-level properties and the cellular-level properties are largely unclear. In this work, we simulate 2D cellular rearrangement inside an initially circular aggregate upon plate compression using Surface Evolver. Two tissue energy models from previous literatures are implemented. By attributing the volume-associated energy to bulk elasticity and the surface-associated energy to surface tension, we quantitatively correlate the mechanical properties of aggregate with cellular-level properties as well as cell shapes and statistics for each model. The results suggest that under certain conditions, cells on aggregate surface can maintain a much higher energy state than those in the interior, which corroborates our previous experimental work (Yu et al., BpJ 114, 2703-16).