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

Abstract

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.

Tissue cohesion and the mechanics of cell rearrangement

“…2G). This effect leads to Newtonian tissue flow at sufficiently low stress and, together with the energy barrier, it determines viscosity (Marmottant et al, 2009) (Box 2). We calculated tensions at cell contacts β* as described above, and contact areas from cell sizes and the sizes of interstitial gaps (Box 2, Table 1; supplementary material Fig.…”

“…Viscosity as a function of tissue surface tension Marmottant et al (2009) modelled tissue flow by starting from the plastic flow of foams. In a foam, the liquid walls surrounding the air-filled cells minimise their surface due to liquid-air interfacial tension.…”

“…This feature is essential for many morphogenetic processes, and is extensively studied at the subcellular level during epithelial cell rearrangement. It also underlies the liquidlike behaviour of tissues (Gordon et al, 1972;Forgacs et al, 1998;Marmottant et al, 2009), which invites the analysis of cell rearrangement at a more generalised, mechanical level.…”

“…While cohesion ensures tissue integrity, it also confers resistance to largescale movement. This resistance is measured as tissue viscosity (Gordon et al, 1972;Marmottant et al, 2009;Rieu and Sawada, 2002;Mombach et al, 2005). To understand the basic mechanics of cell rearrangements in liquid-like tissues, the relationship between tissue cohesion and viscosity needs to be clarified.…”

“…We then determine a number of additional cellular parameters, in part derived from an analysis of cell adhesion, and use these to show that a recent model of tissue viscosity (Marmottant et al, 2009) predicts and explains the linear relationship between tissue surface tension and viscosity. These findings have far-reaching implications for the mechanics of cell rearrangement.…”