The role of fluctuations and stress on the effective viscosity of cell aggregates

Cell aggregates are a tool for in vitro studies of morphogenesis, cancer invasion, and tissue engineering. They respond to mechanical forces as a complex rather than simple liquid. To change an aggregate''s shape, cells have to overcome energy barriers. If cell shape fluctuations are active enough, the aggregate spontaneously relaxes stresses (“fluctuation-induced flow”). If not, changing the aggregate''s shape requires a sufficiently large applied stress (“stress-induced flow”). To capture this distinction, we develop a mechanical model of aggregates based on their cellular structure. At stress lower than a characteristic stress τ*, the aggregate as a whole flows with an apparent viscosity η*, and at higher stress it is a shear-thinning fluid. An increasing cell–cell tension results in a higher η* (and thus a slower stress relaxation time t_c). Our constitutive equation fits experiments of aggregate shape relaxation after compression or decompression in which irreversibility can be measured; we find t_c of the order of 5 h for F9 cell lines. Predictions also match numerical simulations of cell geometry and fluctuations. We discuss the deviations from liquid behavior, the possible overestimation of surface tension in parallel-plate compression measurements, and the role of measurement duration.