Cell sorting is analogous to phase ordering in fluids

Abstract

Morphogenetic processes, like sorting or spreading of tissues, characterize early embryonic development. An analogy between viscoelastic fluids and certain properties of embryonic tissues helps interpret these phenomena. The values of tissue-specific surface tensions are consistent with the equilibrium configurations that the Differential Adhesion Hypothesis predicts such tissues reach after sorting and spreading. Here we extend the fluid analogy to cellular kinetics. The same formalism applies to recent experiments on the kinetics of phase ordering in two-phase fluids. Our results provide biologically relevant information on the strength of binding between cell adhesion molecules under near-physiological conditions.

Figure 1

Schematic representation of the compression plate apparatus used to measure tissue surface tension and viscoelastic properties.

Figure 2

Typical force relaxation in a chicken heart cell aggregate after compression.

Figure 3

(Upper) Gas and liquid phase ordering in SF₆ under reduced gravity, after a thermal quench of 0.7 mK below the critical point (45.564°C). The container diameter is 12 mm. Gas and liquid eventually order with the liquid phase wetting the container wall and surrounding the gas phase, corresponding to σ_wl<σ_wg, where σ_wl and σ_wg are the wall-liquid and the wall-gas interfacial tensions, respectively. a, b, and c correspond to 120 s, 275 s and 3,960 s after quench, respectively. (Lower) Sorting out of chicken embryonic pigmented epithelial cells (dark) from chicken embryonic neural retinal cells (light). The average aggregate size is 200 μm. At the end of sorting, neural retinal cells preferentially wet the external tissue culture medium surrounding the aggregates. σ_tn(= 1.6 dyne/cm)<σ_tp(= 12.6 dyne/cm)³, where σ_tn and σ_tp are the tissue culture medium-neural retina and the tissue culture medium-pigmented epithelium interfacial tensions, respectively. a, b, and c correspond to 17 h, 42 h, and 73 h after initiation of sorting, respectively.

Figure 4

Time evolution of the pseudoperiod during sorting. Squares, upright and inverted triangles, and diamonds denote four different runs. The fit with a straight line has goodness R² = 0.98.