Testing the differential adhesion hypothesis across the epithelial-mesenchymal transition

We analyze the mechanical properties of three epithelial/mesenchymal cell lines (MCF-10A, MDA-MB-231, MDA-MB-436) that exhibit a shift in E-, N- and P-cadherin levels characteristic of an epithelial−mesenchymal transition associated with processes such as metastasis, to quantify the role of cell cohesion in cell sorting and compartmentalization. We develop a unique set of methods to measure cell–cell adhesiveness, cell stiffness and cell shapes, and compare the results to predictions from cell sorting in mixtures of cell populations. We find that the final sorted state is extremely robust among all three cell lines independent of epithelial or mesenchymal state, suggesting that cell sorting may play an important role in organization and boundary formation in tumours. We find that surface densities of adhesive molecules do not correlate with measured cell–cell adhesion, but do correlate with cell shapes, cell stiffness and the rate at which cells sort, in accordance with an extended version of the differential adhesion hypothesis (DAH). Surprisingly, the DAH does not correctly predict the final sorted state. This suggests that these tissues are not behaving as immiscible fluids, and that dynamical effects such as directional motility, friction and jamming may play an important role in tissue compartmentalization across the epithelial−mesenchymal transition.

Approach 2: The radius of the contact area can be estimated by using conclusions from the Hertz theory for two elastic spheres in contact [S1]. When such two spheres touch and deform each other, the radius r of the circular contact area = can be calculated from the indentation depth d and the radii R1, R2 of both spheres: The indentation depth can be easily extracted from the recorded AFM force-distance curves. However, two adherent cells are far from being ideal spheres. Hence, it is necessary to assign "effective" radii calculated from the projected surface areas A1, A2: ~ eff, = with = 1,2 (S.3) In order to detect possible correlations for either of the two approaches, the estimated contact area A can be plotted versus the (unnormalized) maximum adhesion force for all cells measured. In supplementary figure S.2, such plots are shown for the MCF-10A cell line as an example.
Since the plotted data points do not show any significant correlation, the suggested approaches cannot be considered a solution to our problem.
Approach 3: With a side-view onto the two contacting cells, the contact area A could be calculated from the contact length (diameter of the contact area). We slightly modified our setup by gluing a small 45° tilted mirror next to the cantilever, permitting a lateral view by looking from the bottom into the mirror. A gooseneck lamp was used to provide the necessary illumination from the side, see supplementary figure S.3. With low magnifying objectives, the image resolution is simply not sufficient to extract meaningful distances. Using higher magnifying objectives, the aberrations due to the crude optics become too severe. Plots of the estimated contact area versus the (unnormalized) adhesion force. In (a), the contact area A was approximated by the smaller projected surface area of the two cells in contact (approach 1). In (b), A was calculated from the indentation depth and the effective radii of both cells in contact (approach 2). In both cases, no significant correlation is visible. In comparison to the unnormalized values, the difference between MDA-MB-231 and MCF-10A is significantly reduced, while the difference between MCF-10A and MDA-MB-436 has not changed very much, but it is slightly increased. However, these normalized values still show the same order as the unnormalized ones.

S.2. Measurement of the viscoelastic cell properties and cell size
Method: An automated microfluidic Optical Stretcher (OS) was used to measure viscoelastic properties and the size of individual suspended cells. The OS method is described in detail in [S2, S3]. In brief, the central part of an OS is a microfluidic chip with a flow channel and perpendicular to it two opposing optical fibres emitting counter-propagating divergent laser beams, see supplementary figure S.4. The cells to be measured are in suspension within the flow channel. Individual cells can be trapped between the two laser beams and then deformed along the laser axis by increasing the laser power. The surface forces that a cell experiences result from a photon momentum transfer of the laser light, arising from the refractive index difference at the boundary between surrounding medium and a dielectric particle, i.e. the cell. The pattern of the laser power was chosen to be comparable to a classical step-stress, i.e. creep, experiment that measures the compliance. In particular, a laser power of 0.1 W was applied for 1 s for trapping a cell, 1.2 W for 2 s for deformation and 0.1 W for 2 s for trapping

S.3. Predicting the tissue surface tension from the cell shape
It might be relevant to explore whether the small-scale structure of individual cells driven by local energy minimization is consistent with macroscopic cell sorting behaviour. In figures 5 and 6, images bisecting the roughly circular aggregates of a single cell type have been analyzed. Instead of focusing on tissue-level surface tension, interfacial tensions between individual cells will be studied in the following. Observations confirm that near the surface, cell-cell contacts are oriented radially, and simple force balance then relates the tension along cell-cell contacts > CC and the tension > CM along cell-medium interfaces to the geometry of the cell: where θ is the angle between the cell-medium interface and a vector tangent to the surface of the aggregate [S4, S5], see figure 6 (a). Note that this ignores contributions from fluid incompressibility, bulk elasticity, etc., but in previous cases this approach has proven to be sufficient. In addition, the macroscopic tissue surface tension is related to these single cell interfacial tensions. GRANER et al. ignore changes to cell shapes and find the macroscopic tissue surface tension C TM with respect to the cell culture medium is simply related to the interfacial cell tensions [S6]: A more complicated theory that correctly accounts for changes to cell shapes predicts two regimes: one where GRANER's formula is approximately correct and one where it breaks down completely [S4]. The first regime occurs when the adhesion and corresponding downregulation of cortical tension is weak, and then, the cells at the edge maintain an aspect ratio close to unity. The latter regime is characterized by large adhesion, weak cortical tension along contacting interfaces, and spreading of cells on the surface. Let us assume the cells stay close to aspect ratio unity. This seems to be true for the MDA-MB-231 and the MDA-MB-436 cells, but for the MCF-10A it is hard to tell as the second layer of cells is barely visible in the fluorescence images. If the MCF-10A surface cells do spread out, then it suggests that they have about the same surface tension as if they had a flat interface (B = 0°). Combining equations (S.6) and (S.7), the macroscopic tissue surface tension is then given by: C TM = > CM (1 − sin B) (S.8) Using the measured contact angles from figure 6 (b), the following predictions for tissue surface tensions can be made: MDA

S.4. Theory for cell segregation rates as a function of TST
SIGGIA developed a theoretical description of the growth of pseudo periods at long times due to droplet coalescence, demonstrating N O ∝ P [S7]. BEYSENS et al. analyzed the dynamics of sorting of chick embryonic cells and found a region where the pseudo period increased linearly with time [S8]. In general, one does not expect that the linear scaling should persist at all timescales. At early times, the total volume of an aggregate of mixed cell types compacts as the cells form strong adhesive contacts and voids between cells disappear, and during this timeframe cell motion is not dominated by droplet coalescence. At later times, the linear regime must end when the droplet size approaches the final aggregate size [S7]. A straight line is fitted to the linear regime of Lm to determine its slope m corresponding to a coalescence rate. The highest slope is found for the MDA-MB-231 / MCF-10A mixtures, meaning their domains coalesce fastest, while MDA-MB-231 / MDA-MB-436 mixtures show the smallest slope. If the phases of the two cell populations (labelled with index 1 and 2) behave as Newtonian fluids, the slope of this line is Q 12 = R(∆C 12 )/T UVW , where ∆C 12 is the interfacial tension between the two populations and T UVW ≔ max (T , T ) is the larger viscosity of the two populations [S9]. NIKOLAYEV et al. have found that R~0.03 for arbitrary self-similar drop shapes [S10]. Finally, Young's equation at the onset of complete wetting states ∆C 12~| C 1M − C 2M |, where C 1M and C 2M correspond to the surface tension between the cell culture medium and the cell population which is enveloped.
The images of the final steady states of segregation experiments already make specific predictions about the surface tensions of the cell populations. Namely, if tissue population 1 is enveloped by population type 2, then C 1M > C 2M . Therefore, the final states for our cell lines suggest C TM (436) > C TM (10A) > C TM (231). In order to compare this to the results for the pseudo period, we must make an additional assumption about the viscosities of the populations. Namely, we assume that populations with higher surface tensions have higher viscosities. This is reasonable, as both viscosity and surface tension should be generated by adhesive interactions between cells (and regulation of the cortical network via those adhesive molecules.) In addition, tissue surface tensiometer measurements of developmental tissues consistently find that tissues with higher surface tension also possess higher viscosities [S11].
If we order tissues by their surface tensions, C 1M > C 2M > C 3M , and additionally assume T 1 > T 2 > T 3 , then this leads to a testable prediction for the pseudo period data: