Multicellular density fluctuations in epithelial monolayers

Changes in cell size often accompany multicellular motion in tissue, and cell number density is known to strongly influence collective migration in monolayers. Density fluctuations in other forms of active matter have been explored extensively, but not the potential role of density fluctuations in collective cell migration. Here we investigate collective motion in cell monolayers, focusing on the divergent component of the migration velocity field to probe density fluctuations. We find spatial patterns of diverging and converging cell groups throughout the monolayers, which oscillate in time with a period of approximately 3–4 h. Simultaneous fluorescence measurements of a cytosol dye within the cells show that fluid passes between groups of cells, facilitating these oscillations in cell density. Our findings reveal that cell-cell interactions in monolayers may be mediated by intercellular fluid flow.

Figure 1

(a) Phase contrast microscopy of a confluent MDCK monolayer exhibits a patchy, heterogeneous cell number density distribution; $\mathrm{scale}\mathrm{bar}=150\mu \mathrm{m}$. (b) To study fluid flow between regions of cells, the layer is dyed with membrane-impermeable dye that concentrates and dilutes with changes in cell volume; $\mathrm{scale}\mathrm{bar}=100\mu \mathrm{m}$. (c) Velocity fields of cell motion superimposed on top of divergence fields show coherent patterns of spreading (positive) and contracting (negative) regions spanning hundreds of microns.

Figure 2

(a) The dynamic structure factor $S\left(q,\omega \right)/S\left(q\right)$ is computed and fitted with Rayleigh (blue) and Brillouin (red) peaks to determine dispersion relations for divergent cell motion and intercellular fluid flow. (b) The divergence dispersion relation shows a standing wave mode at wavelengths longer than 250 μm with a characteristic period of $\sim 3\mathrm{h}$.) (c) The fluorescence intensity dispersion relation shows a propagating mode that scales like $q$ with a group velocity of $25\mu \mathrm{m}/\mathrm{h}$. (d) The ratio of temporal Fourier transforms of intensity and divergence, $S_i\left(\omega \right)/S_d\left(\omega \right)$, scales as ${\omega }^2$, showing that fluorescence intensity is proportional to the first time derivative of divergence.

Figure 3

The average space-time divergence autocorrelation function (a) reveals standing wave dynamics in the velocity field, exhibiting oscillations along $R$ at $\tau =0$ (b) and along $\tau$ at $R=0$ (c). By contrast, the fluorescence intensity autocorrelation function (d) exhibits only a diagonal band of correlation and no significant oscillations, which arises from propagative motion. The slope of this feature is close to the single-cell migration speed (red dashed line) at short times but increases at long times and distances (e). We fitted lines to the contour of this correlation separately at short times and long times, finding speeds of $14.86\pm 0.02\mu \mathrm{m}/\mathrm{h}$ and $22.5\pm 0.3\mu \mathrm{m}/\mathrm{h}$ (blue lines are fits; ± ranges are 95% confidence intervals of fitted slopes).

Figure 4

The divergence autocorrelation function of cells treated with $100\mu \mathrm{M}$ CBX (a) shows distinct anticorrelation peaks at $R=100\mu \mathrm{m}$ and $\tau =2\mathrm{h}$ (b),(c). (d) The fluorescence intensity autocorrelation function of CBX-treated cells exhibits a diagonal band of intensity that is much broader along the $R$ direction than observed for undrugged cells. (e) A contour constructed from intensity-moment analysis has a slope of $6.7\pm 0.01\mu \mathrm{m}/\mathrm{h}$, which suggests that the correlation function may reflect single-cell motion and potentially a dramatically reduced propagation of fluid between cells. (f) Confocal $X-Z$ slices of an undrugged monolayer show a flat surface; $\mathrm{scale}\mathrm{bar}=10\mu \mathrm{m}$, while (g) X-Z slices of cells treated with CBX show a rough surfaces; $\mathrm{scale}\mathrm{bar}=10\mu \mathrm{m}$.

Figure 5

A pixel-by-pixel pressure difference map estimated from velocity divergence. Positive values are associated with regions of contracting cells expelling fluid. Negative values are associated with regions of expanding cells. At any time these pressure fluctuations occur between $+100$ and $-100\mathrm{Pa}$ about zero.

Figure 6

MDCK monolayer dyed with calcein fluorescent dye (a) before ($\mathrm{scale}\mathrm{bar}=150\mu \mathrm{m}$), (b) during, and (c) after indentation. The radius of the contact area, $R_i$, is denoted by the yellow dotted line. By comparing (a) and (c) it can be seen that cell shape recovers with little or no damage to the monolayer. (d) Change in integrated dye intensity inside the contact area $(R<R_i)$ and outside the contract area $(R>R_i)$ during indentation show transport of fluid and regions of varying size show systematic changes in transported dye with distance from the pressure source.

Figure 7

(a) The divergence theorem relates the total divergence of a velocity vector field v within area $S$ to the line integral of the components of the velocity vectors normal to the area boundary $l$. (b) Schematic of a converging vector field with area $S$ centered about point $(x,y)$. (c) Schematic of boundary line $l$ defined by normal vectors $\mathbf{n}$. (d) The divergence of the velocity field is computed by taking the sum of the product of $v_x$ and $n_x$ and the product of $v_y$ and $n_y$ for all $N$ discrete positions, $\mathrm{\Delta }l$, around the boundary line. (e) Visual representation of equation in (d) for the converging velocity field. Red represents positive vectors and blue represents negative vectors in a right-handed coordinate system and green represents a value of zero. (f) The average divergence at a point $(x,y)$ is approximated as the divergence divided by the area in $S$. This process is performed at each vector position to determine the divergence map of the whole cell motion velocity field.