Figure 3.

The metastatic MDA-MB-231 spheroid exhibits an unjammed fluid-like phase and undergoes drastically different patterns of invasion depending on collagen concentration

(A and B) Representative equatorial cross-sections of multiphoton images show MDA-MB-231 macro-spheroids exhibiting distinct invasion patterns when embedded in low density (2 mg/mL) versus high density (4 mg/mL) collagen for 48 h. DAPI-stained cell nuclei are shown in red and collagen fibers from SHG are shown in green. In low density collagen (A), these metastatic cells scatter from the spheroid core as individual, gas-like particles. Conversely, in high density collagen (B), single-cell dominant scattering is subdued and invasion is in the form of collective, fluid-like protrusions. We note that the center of MDA-MB-231 spheroids is devoid of cells, as confirmed by staining of histological cross-sections (Figure S6), and thus result in a hollow shell of highly motile cells rather than a nearly solid spherical structure. Only cells that remain part of the collective are included in the structural analyses (STAR Methods, Figure S2), hence the absence of data for the first 200 μm of the associated radial distributions.

(C) Average Voronoi volumes suggest that MDA-MB-231 cells have larger volumes with respect to their MCF-10A counterparts (cf. Figure 2C). In 2 mg/mL collagen, cell volumes remain roughly independent of radial position. In 4 mg/mL collagen, instead, cell volumes show a decreasing radial gradient. This decrease in cell volume from the spheroid core to the invasive protrusion suggests elevated stress in invading cells from confinement by the collagen matrix.

(D and E) The corresponding cell shapes are shown as 2D cross-sections, color-coded according to their respective 3D Shape Index (SI). Regardless of collagen concentration, cells from MDA-MB-231 spheroids display higher SI with respect to MCF-10A spheroids (cf. Figures 2D and 2E).

(F) Radial distribution of average SI values is consistent with an unjammed fluid-like phase (horizontal dashed line indicates solid-fluid transition point at SI = 5.4 (Merkel and Manning, 2018)). In high density collagen, a radially decreasing gradient in SI suggests that cells jam while invading collectively under matrix confinement.

(G and H) Representative DIC images are shown for MDA-MB-231 macro-spheroids cultured in 2 and 4 mg/mL collagen, with cell migratory trajectories (from optical flow, STAR Methods) superimposed in red. The spheroid boundaries are outlined in black. The entire DIC time-lapse video capturing the dynamics of invasion over 48 h is shown in Video S1. Cell dynamics mirrors structural signatures of cell jamming/unjamming.

(I) Radial distributions of RMS speed quantified for the last 8-h observation window (40–48 h) show that cells in MDA-MB-231 macro-spheroids have homogeneously higher speeds with respect to MCF-10A spheroids (cf. Figure 2I) and are thus more fluid-like. In low density collagen, cell speed increases further as soon as cells detach from the spheroid and invade as single, gas-like particles (inset, where the radial position of the spheroid boundary is marked by a dashed vertical line). This observation supports the proposed analogy of fluid-to-gas transition. In high density collagen, RMS speed decrease radially with collective invasion, and is supportive of a fluid-to-solid transition due to confinement-induced jamming (Haeger et al., 2014). Data for radial distributions are presented as mean ± STD (n = 3 for both 2 and 4 mg/mL spheroids).