Gradients in solid surface tension drive Marangoni-like motions in cell aggregates

The surface tension of living cells and tissues originates from the generation of nonequilibrium active stresses within the cell cytoskeleton. Here, using laser ablation, we generate gradients in the surface tension of cellular aggregates as models of simple tissues. These gradients of active surface stress drive large-scale and rapid toroidal motion. Subsequently, the motions spontaneously reverse as stresses reaccumulate and cells return to their original positions. Both forward and reverse motions resemble Marangoni flows in viscous fluids. However, the motions are faster than the timescales of viscoelastic relaxation and the surface tension gradient is proportional to mechanical strain at the surface. Further, due to active stress, both the surface tension gradient and surface strain are dependent upon the volume of the aggregate. These results indicate that surface tension can induce rapid and highly correlated elastic deformations in the maintenance of tissue shape and configuration.

Figure 1

Cell ablation at the aggregate surface induces rapid, internal toroidal motions. (a) Left: DIC image of a cell aggregate immediately prior to ablation. The location of the ablation is at the red asterisk. Time is time after ablation ($t=0$ sec). Right: Kymographs depicting material displacement around the cell surface. The yellow dashed line indicates the path over which kymographs are calculated. The white dotted line indicates the region over which PIV is applied. (b) PIV of cellular motion ($\vec{\mathrm{v}}$) analyzed from DIC images, taken at two different time points. The time between frames is 1 sec. (c) Mean speed and net material transport over time. The timescales of relaxation and reversal are denoted by ${\tau }_1$, ${\tau }_2$, and ${\tau }_3$. (d) Left: Image of a cell aggregate. Right: Corresponding kymographs with 50 $\mu \mathrm{M}$ Blebbistatin. (e) PIV of cellular displacements with 50 $\mu \mathrm{M}$ Blebbistatin. (f) Mean speed and net material transport for Blebbistatin treated aggregate. Scale bars are $30\mu \mathrm{m}$.

Figure 2

The mechanical relaxation is slow compared to the timescales of motion. (a) Bright-field image of an aggregate in the micropipette. (b) A step in pressure ($\mathrm{\Delta }P$) is applied to a cell aggregate of radius $R_0$ that brings the aggregate into the pipette, a length $L$ and induces a strain, ${\varepsilon }_a$, as a function of time. The solid black line represents ${\tau }_v$. (c) Modified Maxwell model applied to the evolution of ${\varepsilon }_a$ with time. In the model, $E_1$ and $E_2$ are elastic modulus, and ${\eta }_1$ and ${\eta }_2$ are dashpots representing dissipative elements. $f$ represents the stress applied to the system, in analogy to the applied pressure by the micropipette. (d) The effective elastic modulus $E_{\mathrm{eff}}$ and viscosity $\left(\eta \right)$ obtained from fitting experimental data. (e) Viscoelastic relaxation time ${\tau }_v$ of aggregates for an applied pressure of 1 kPa, in comparison with motion timescales ${\tau }_1$, ${\tau }_2$, and ${\tau }_3$ as defined in Fig. 1 ($n=10$). Scale bar is 30 $\mu \mathrm{m}$. *** $p<0.001$, ** $p<0.01$.

Figure 3

Motions are driven by solidlike surface stresses. (a) Cell displacement $\vec{u}$ (black vectors), areal strain field ($\varepsilon =\mathbf{\nabla }·\vec{u}$) due to displacement (color map), and surface stresses (red vectors) associated with deformation at $t$ = 5 sec (during ${\tau }_1$) and $t$ = 115 sec (during ${\tau }_3$). (b) Change in surface tension in forward and (c) reverse motion, as a function of angular position $\theta$, as measured from constitutive models. Asterisks indicate the region of ablation. The black arrow in (b) and (c) denotes the maximum change in surface tension at a given instant. Scale bar is 30 $\mu \mathrm{m}$.

Figure 4

Surface tensions are size dependent and solidlike. (a) Distribution of nuclear shapes inside an aggregate color coded by their strain defined as ${\varepsilon }_N=\mathrm{AR}-1$. Scale bar is 30 $\mu \mathrm{m}$. (b) Average nuclear strain ($n=36$) varies with the size of the aggregate $R_0$. (c) Surface tension gradient $\mathrm{\Delta }\gamma$ ($n=10$) varies with the size of the aggregate $R_0$. (d) Surface tension gradient vs nuclear strain. The red dot indicates nuclear strain in the presence of 50 $\mu \mathrm{M}$ Blebbistatin. The slope of the curve represents the apparent surface modulus. ** $p<0.01$ ns is not significant.