Compression Induced Fluidization in Vertex Models of Epithelial Tissues

Vertex models are useful for simulating mechanics and collective behavior in confluent tissues. A notable feature of vertex models is a rigidity transition that occurs at zero cell motility. The transition can occur when the preferred perimeter of cells in the model drops below a threshold value, causing a large increase in junctional tensions and endowing the tissue with a finite yield stress. As a result, the rigidity transition is often described as occurring at a critical ratio of the preferred cell perimeter to the square root of the preferred area. In apparent contradiction to this conventional wisdom, a recent paper¹ reported the striking finding that cell aggregates in the vertex model can fluidize under compression and used a mean field model to rationalize this observation. Here, we show that compression-induced fluidization is in fact an exact consequence of the most common vertex model free energy. We further explore numerically whether this phenomenon is robust to variations in the form of the free energy and comment on its implications for analysis of experimental data.

References Cited

1. Parker, A., Marchetti, M. C., Manning, M. L., and Schwarz, J. M. (2020) How does the extracellular matrix affect the rigidity of an embedded spheroid? arXiv.2006.16203v1[q-bio.CB]