How does extracellular matrix rigidity affect the fluidity of an embedded spheroid?

The extracellular matrix (ECM) that surrounds a tissue, such as a cancer spheroid, is known to regulate spheroid behavior, with stiffer ECM promoting invasion. Using a computational model, we explore how a simple mechanical interaction between a spheroid and its ECM promotes changes in the spheroid’s rigidity, morphology and the shapes of its constituent cells, as well as the ECM’s rigidity and structure. We model the spheroid using a vertex model and the ECM using a spring network model, with an additional term describing the interfacial tension between the spheroid and ECM. Both vertex and spring network models transition between rigid and floppy phases, depending on their respective tuning parameters (cell shape and spring rest length) and imposed strain. Therefore, we expect, and find, that by mechanically coupling the two systems, changes to the phase of one system can drive changes to the phase of the other. We identify two regimes of interest—one in which compression of the spheroid dominates and one in which stretching dominate. We find that isotropic compression promotes fluidity of tissue and preserves the relationship between cell shape and tissue phase, while stretching by the ECM results in rather different behavior.