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

Proceedings of the National Academy of Sciences of the United States of America (2009-10-07)
Philippe Marmottant, Abbas Mgharbel, Jos Käfer, Benjamin Audren, Jean-Paul Rieu, Jean-Claude Vial, Boudewijn van der Sanden, Athanasius F M Marée, François Graner, Hélène Delanoë-Ayari
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 tau*, the aggregate as a whole flows with an apparent viscosity eta*, and at higher stress it is a shear-thinning fluid. An increasing cell-cell tension results in a higher eta* (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.

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Pluronic® F-127, powder, BioReagent, suitable for cell culture