Glass-like dynamics of collective cell migration

Abstract

Collective cell migration in tissues occurs throughout embryonic development, during wound healing, and in cancerous tumor invasion, yet most detailed knowledge of cell migration comes from single-cell studies. As single cells migrate, the shape of the cell body fluctuates dramatically through cyclic processes of extension, adhesion, and retraction, accompanied by erratic changes in migration direction. Within confluent cell layers, such subcellular motions must be coupled between neighbors, yet the influence of these subcellular motions on collective migration is not known. Here we study motion within a confluent epithelial cell sheet, simultaneously measuring collective migration and subcellular motions, covering a broad range of length scales, time scales, and cell densities. At large length scales and time scales collective migration slows as cell density rises, yet the fastest cells move in large, multicell groups whose scale grows with increasing cell density. This behavior has an intriguing analogy to dynamic heterogeneities found in particulate systems as they become more crowded and approach a glass transition. In addition we find a diminishing self-diffusivity of short-wavelength motions within the cell layer, and growing peaks in the vibrational density of states associated with cooperative cell-shape fluctuations. Both of these observations are also intriguingly reminiscent of a glass transition. Thus, these results provide a broad and suggestive analogy between cell motion within a confluent layer and the dynamics of supercooled colloidal and molecular fluids approaching a glass transition.

Fig. 1.

MDCK cells within a confluent monolayer migrate in a spatially heterogeneous manner (A, B). The average area of contiguous regions of the fastest velocity vectors defines ξ_h, the area of dynamic heterogeneities (B, white regions). As cell density rises, ξ_h grows from an area of about 10 cell bodies to 30 cell bodies (C, inset: ξ_h in μm²). The average migration speed of cells within the entire field of view, v, decreases with increasing cell density (D). (Scale bar, 100μm.).

Fig. 2.

The dynamic structure factor S(q,ω) of the migrating cell monolayer is calculated to quantify cooperative and self motions over a broad range of length scales and time scales (A). An example slice through S(q,ω) at q = 0.8 rad μm^-1 shows that the spectral line shape is well described by the DHO model, consisting of a diffusive Rayleigh peak (red line) and a Brillouin peak (blue line) (B). The spectrum of diffusing particles is dramatically different than the DHO spectrum, as seen on a log - log plot (C, diffusing particle data: empty black square, red line: Rayleigh peak fit, cell data: filled black circle, blue line: DHO fit).

Fig. 3.

The width of the Rayleigh peak, Γ₀(q), is the q-dependent inverse relaxation time, and is equal to D₀ q² (A, empty black square: σ = 1,479 mm^-2, empty red circle: σ = 2,088 mm^-2, empty green triangle: σ = 2,214 mm^-2, empty inverted blue triangle: σ = 2,634 mm^-2). The average of Γ₀(q)/q² over high q yields a well defined self-diffusivity, D₀ (A, inset). Migration distances over 200 min. durations, by diffusion and migration, are calculated from v and D₀, showing that collective migration decreases to levels of self-diffusive motion with increasing cell density. At the highest density, insufficient dynamic range in S(q,ω) prevented the extraction of a diffusivity. (B). An Arrhenius plot of as a function of cell density illustrates the analogy between motion within the cell monolayer and particulate supercooled fluids approaching a glass transition (C, blue line: AM equation fit, red line: VFT equation fit).

Fig. 4.

Analysis of the Brillouin peaks in S(q,ω) yield dispersion relations of cell motion, Ω(q), at each cell density (A). The DOS of cell motion, extracted from Ω(q), exhibits two sets of peaks, analogous to boson peaks in supercooled fluids (B). The peaks at lower frequencies and wave vectors correspond to the time scale and length scale of cell shape oscillations; the peaks at higher frequencies and wave vectors correspond to the time scale and length scale of cell divisions (C, D). (σ₂ = 1,550 mm^-2, σ₄ = 1,480 mm^-2, σ₁₁ = 1,880 mm^-2, σ₁₂ = 2,090 mm^-2, σ₁₄ = 2,210 mm^-2, σ₁₅ = 2,550 mm^-2, and σ₁₆ = 2,630 mm^-2)