A rheological mechanism sufficient to explain the kinetics of cell sorting

When two different vertebrate embryonic tissues are dissociated into individual cells, which are then recombined into mixed aggregates, the differing cells sort out within the aggregates to form a characteristic structure. The kinetics of cell sorting closely resembles the kinetics of breaking of an unstable emulsion of two immiscible liquids. We investigate the consequences of the postulate that cell rearrangement in such a system is driven by the tension at the interfaces between the two cell populations and resisted by “tissue viscosities”, the latter being a newly recognized parameter of cell sorting. Using preliminary experimental data on cell population interfacial tensions and on the time for fusion of two identical spherical aggregates, the viscous liquid model leads to estimates for tissue viscosities in the range of 0.4 × 106 to 0.7 × 108 poise. Also, using two other independent sets of data, one on the time for breaking of a roughly cylindrical cell aggregate into a few clusters, and the other on the time for the rounding-up of an approximately ellipsoidal tissue mass into a roughly spherical mass, tissue viscosities are again estimated to be in the range of 106 to 1.5 × 108 poise. In attempting to find a possible basis for such high effective viscosities, we propose that: (i) tissue viscosities would most likely result from sliding friction between the cell membranes; (ii) the cell membranes would have to possess protrusions of molecular or macromolecular dimensions; and (iii) the ratio of the surface tension to the logarithm of viscosity should, if this model is correct, be approximately constant, independent of the tissue.