Cell-Matrix Elastocapillary Interactions Drive Pressure-Based Wetting of Cell Aggregates

The magnitude of mechanical stresses caused by cell surface tension may be comparable to the bulk elasticity of their matrix on cellular length scales, yet how capillary effects influence tissue shape and motion are unknown. In this work, we induce wetting (spreading and migration) of cell aggregates, as models of active droplets onto adhesive substrates of varying elasticity, and correlate the dynamics of wetting to the balance of interfacial tensions. Upon wetting rigid substrates, cell-substrate tension drives outward expansion of the monolayer. By contrast, upon wetting compliant substrates, cell-substrate tension is attenuated and aggregate capillary forces contribute to internal pressures that drive expansion. Thus, we show by experiments, data-driven modeling, and computational simulations that myosin-driven “active elastocapillary” effects enable adaptation of wetting mechanisms to substrate rigidity and introduce a novel, pressure-based mechanism for guiding collective cell motion.

Popular Summary

Like liquid droplets, living cells and tissues have surface tensions that govern their shape and propensity to wet adhesive substrates. However, unlike droplets, the surface tension of cells and the properties of the cell-substrate interface are not constant but can adapt to the mechanical and chemical properties of their environment. As a result of this adaptation, they exhibit novel modes of contact, adhesion, and wetting. The wetting of tissues involves the collective motion of aggregate cells. Here we show that this motion can switch from a well-known traction-driven migration to a novel pressure-driven motion while retaining comparable wetting rates—demonstrating evidence of cooperation in cell migration between cellular-level and tissue-level forces.

A canonical mode of migration through the extracellular matrix involves the generation of traction forces at the cellular level. However, the magnitude of stresses generated by the surface of cells may be comparable to the stiffness (or modulus) of the matrix. Thus, we observed motion of cells on soft matrices, and we find that, like liquid droplets, the surface tension of cells deforms the matrix in three dimensions. In doing so, a meniscus forms at the contact line, along with an indentation in the center. The curvature of these deformations elevates the internal pressure of the tissue. An increase in internal pressure, combined with a mechanoresponsive decrease in friction at the cell-matrix interface, provides a pressure-based motive force for wetting—or the collective motion of cells from the tissue.

By discovering that motion can be driven by surface tension or pressure accumulated at the tissue level, we can now look for regulators of tissue pressure to influence cancer cell migration or migration during early development. This can point to entirely new targets for influencing motion than those previously identified that control traction at the single-cell level.

Figure 1

Substrate stiffness and aggregate size determine wetting dynamics. (a) Diagram of an aggregate spreading on a fibronectin-coated PAA gel. (b) $z$ profile of F-actin stained aggregate adhered to glass. (c) DIC image of an aggregate spreading on glass. $A_0$ is the projected area of an undeformed aggregate and $A$ is the instantaneous contact area over which the monolayer has spread. (d) Normalized spread area ($A/A_0$) as a function of time and stiffness. (e) Difference in fitting $R^2$ values as a function of stiffness. (f) Spreading rate $(1/A_0)(dA/dt)$ measured between $A=A_0$ and $A=2A_0$ ($N=13$ for 0.7 kPa and $N=10$ for 40 kPa). (g) Spreading rate as a function of aggregate size for 0.7 kPa substrate (red, $N=27$), 40 kPa substrate (blue, $N=18$), and glass (black, $N=8$). Scale bars are $50\mu \mathrm{m}$. $*P<0.05$, $**P<0.01$, $***P<0.001$. ns is nonsignificant. Error bars are mean $\pm$ standard deviation.

Figure 2

Traction stresses are attenuated during wetting to soft substrates. (a) Normalized radial velocity fields $(|{\overrightarrow{v}}_r|/|{\overrightarrow{v}}_{r,\max }|)$ for cumulative displacement of cell motion. F-actin images are used for flow calculation. (b) Left: magnitude of stress vectors $(|\overrightarrow{\sigma }|)$ calculated via TFM of an aggregate spreading on substrates of stiffness 0.7 kPa (top), 2.8 kPa (middle), and 40 kPa (bottom). Right: corresponding kymograph of data in (b) (left). (c) Velocity gradient $(d|\overrightarrow{v}|/dr)$, as a function of substrate stiffness $E$ ($N=12$). (D) Radial stress distribution of a spread aggregate on substrates with stiffness 0.7, 2.8, and 40 kPa ($N=3$). (e) Stress gradient $(d|\overrightarrow{\sigma |}/dr)$ as a function of substrate stiffness $E$ ($N=12$). (F) Normalized radial stresses $(|\overrightarrow{{\sigma }_r}|/|{\overrightarrow{\sigma }}_{r,\max }|)$ for the substrate stiffnesses in (a). Red indicates inward tractions, blue indicates outward tractions. Dashed black line indicates the contact line of aggregates. Yellow dashed lines in (a) and (f) indicate region where the gradients are calculated. ns is nonsignificant. Scale bar is $50\mu \mathrm{m}$. Error bars are mean $\pm$ standard deviation.

Figure 3

Aggregate adhesion induces capillary deformations in the substrate. (a) Top: a reconstructed $z$ slice showing F-actin in a cell aggregate (green) indenting a 0.7 kPa substrate (red). Bottom: a schematic showing relative magnitudes of out-of-plane deformations ($l,z$). (b) $z$ indentation as a function of radial distance from the center of an aggregate. (c) Mean elastocapillary length for all aggregates, as a function of substrate stiffness $E$. The indentation measured at 8.6 kPa corresponds to noise in the measurement of indentation. (d) Meniscus height as a function of aggregate size on $E=0.7\mathrm{kPa}$. (e) Maximum indentation as a function of scaled contact area, $A/A_0$ for untreated (blue) and $10\mu \mathrm{M}$ blebbistatin treated (red) aggregates. (f) Maximum indentation $z_{\max }$ as a function of aggregate radius $R_0$. Pharmacological treatment with blebbistatin vanishes Laplace-like behavior. $0\mu \mathrm{M}$ ($N=75$), $2\mu \mathrm{M}$ ($N=30$), $10\mu \mathrm{M}$ ($N=20$). (g) Diagram of aggregates of different sizes inducing different out-of-plane deformations. Scale bar is $50\mu \mathrm{M}$. $*P<0.05$, $**P<0.01$, $***P<0.001$. ns is nonsignificant. $z_0$ is set to 0 for all measurements.

Figure 4

Capillary forces increase aggregate internal pressure. (a) A schematic describing the decomposition of forces and pressures at $A=A_0$ on deformable substrates. (b) Effective surface tension as a function of substrate stiffness when measured from monolayer stress (red), and active elastocapillary deformations (blue) ($N=10$ samples per data point). Effective elastocapillary length as a function of substrate stiffness calculated from experimental data (solid gray) and under assumption that surface tension stays constant (dashed gray). $l_c$ and $E_c$ are the critical elastocapillary length and critical substrate stiffness, respectively, where the transition between modes of migration occurs. (c) Aggregate spreading rate as a function of the aggregate surface tension on a 0.7 kPa substrate ($N=27$). Surface tension as a function of aggregate size (inset). (d) Pressure on top and bottom section of an aggregate at 0.7 and 8.6 kPa (inset). The dashed black line represents the minimum pressure ($P_{\min }=135.8\pm 4.4\mathrm{Pa}$) required to overcome traction. The dashed blue line is basal pressure ($P_0=109.6\pm 6.2\mathrm{Pa}$) for largest aggregates. Error bars are error propagated from measurements of $l_{\max }$ and $z_{\max }$. (e) Mean pressure on top and bottom sections as a function of substrate stiffness ($N=9$ for 0.7 and 8.6 kPa each). Error bars are mean $\pm$ standard deviation.

Figure 5

Internal pressure drives size-dependent cellular flows on soft substrates. (a) Image of a spreading nuclei-stained aggregate at $z=0\mu \mathrm{m}$, the substrate surface. Red dashed box shows the area underneath the aggregate where (${\rho }_s$) measurements were done. Central circle represents the normal vector of inlet flux ($J_1$) on the plane, arrows showing the outlet flux of cells ($J_2$). (b) ${\rho }_s$ as a function of time for spreading on soft ($E=0.7\mathrm{kPa}$, blue) and stiff ($E=40\mathrm{kPa}$, red) substrates. (c) Significant difference in the rates of change of ${\rho }_s$ on soft ($E=0.7\mathrm{kPa}$, blue) and stiff ($E=40\mathrm{kPa}$, red) substrates. (d) $J_2$ as a function of ${\rho }_0$ on soft substrate ($E=0.7\mathrm{kPa}$). (e) A schematic of the components of the data-driven fluid model to calculate the internal pressure. (f) Normalized internal pressure (within $0<r<40\mu \mathrm{m}$ of aggregate) calculated from the data-driven model ($P_m$) as a function of time for soft ($E=0.7\mathrm{kPa}$, blue) and stiff ($E=25\mathrm{kPa}$, red) substrates. (g) Significant difference in the mean rate of change of internal pressure for aggregates spreading on soft ($E=0.7\mathrm{kPa}$, blue) and stiff ($E=25\mathrm{kPa}$, red) substrates. (h) $J_2$ as a function of $P$. (i) Schematic for pressure-driven and traction-driven flows, which depends upon the stiffness of the substrate $E$. (j) Significant difference in the mean rate of change of traction stresses for aggregates spreading on soft ($E=0.7\mathrm{kPa}$, blue) and stiff ($E=25\mathrm{kPa}$, red) substrates. (k) Mean internal pressure calculated within $0<r<40\mu \mathrm{m}$ of aggregates as a function of aggregates initial radius ($R_0$) in steady state spreading of aggregates on soft ($E=0.7\mathrm{kPa}$, blue) and stiff ($E=25\mathrm{kPa}$, red) substrates.

Figure 6

Friction differentiates pressure-driven from traction-driven motion. Confocal images and alignment vector field showing ordering of F-actin cytoskeleton on glass (a) and 0.7 kPa substrate (b). (c) F-actin and Paxillin stains within an aggregate spreading on 0.7 kPa gel and glass. Scale bars are $25\mu \mathrm{m}$. (d) Focal adhesion size, mean ordering parameter, and effective friction coefficient on soft and stiff substrates ($N=7$ for 0.7 and 40 kPa each). Traction force results from vertex model for stiff (e) $E=30$ and soft (i) $E=10$ substrates. Area outlined by dashed white line indicates the region of cell addition. Scale bar is $20\mu \mathrm{m}$. (e) On rigid substrates ($E=30$), friction is high, and self-propulsion accounts for most of the total traction force that drives motion. (i) On soft substrates ($E=5$), friction is low, and pressure accounts for most of the total traction force that drives motion. (f), (g), and (j) The balance of crawling and growth reproduces exponential and linear behaviors on soft and stiff substrates, respectively. (k) The balance of pressure to self-propelled forces changes as a function of substrate rigidity $E$, with nominal changes to spreading rate ($\epsilon$). a.u. is arbitrary units. (h),(l) Schematic for pressure-driven and traction-driven flows, which depends upon the friction coefficient $\zeta$ (and stiffness $E$) of the substrate. Error bars are mean $\pm$ standard deviation.

Figure 7

Indentation follows a $1/R_0$ decay on substrates of different stiffnesses. (a) Maximum indentation at $R=R_0$ as a function of aggregate size $R_0$ and substrate stiffnesses (0.7 and 2.8 kPa). In both cases we observe that the indentation behavior is well approximated by a $1/R_0$ decay. (b) Maximum indentation scaled by elastocapillary length scale $\gamma /E$ as function of size $R_0$. Collapse of the data to a single regime indicates that indentation is proportional to elastocapillary length. Each point represents a single experiment.

Figure 8

Estimation of aggregate surface tension from 3D deformation data. (a) A schematic showing force balance at the meniscus. The surface tension of the adhered aggregate was estimated by measuring the $z$ indentation, meniscus height, and radial traction forces. $\gamma$ is the tension at the aggregate-media interface, ${\gamma }_{as}$ is the tension at the substrate-media interface, ${\gamma }_s$ is the tension at the substrate-aggregate interface. (b) Traction forces are calculated in the transparent yellow circular region of the TFM maps. Red dashed line shows $r=R_0$. The width of yellow region is $25\mu \mathrm{m}$.

Figure 9

Pressure profiles obtained using continuum fluid model. Pressure profiles of aggregates spreading on soft (a) and stiff (d) substrates, showing a size-independent maximum pressure for aggregates spreading on stiff substrates (b) and size-dependent maximum pressure for aggregates spreading on soft substrates (d). To check that results on internal pressure from the data-driven model were independent the choice of ${\mu }_s$ and ${\mu }_b$, using a set of combinations of the viscosities, qualitatively similar pressure profiles were obtained (e). Mean central pressure as a function of $R_0$ with a different set of viscosities (${\mu }_s=3000\mathrm{Pa}\mathrm{s}$ and ${\mu }_b=1500\mathrm{Pa}\mathrm{s}$) remained uncorrelated for stiff substrates ($E=25\mathrm{kPa}$) (f) and exhibited a significant inverse correlation for soft substrates ($E=0.7\mathrm{kPa}$) (g). Magnitude of traction stresses on soft $E=0.7\mathrm{kPa}$ versus stiff $E=25\mathrm{kPa}$ substrates (h).

Figure 10

Differential growth or traction can capture spreading dynamics. (a)–(f) Results from simulations in which cell crawl speed depends on substrate stiffness and growth rate is constant. (a) Cell crawl speed and (b) growth rate as a function of substrate stiffness ($E$), for different gradients corresponding to (c). (c) Average difference in fitting $R^2$ values, using exponential against linear curves, as a function of substrate stiffness and crawl speed gradient ($n=5$). (d)–(f) Average traction stress ($\sigma$) as a function of distance from the center of the monolayer, $r$ ($n=5$), from soft to stiff substrates (dark to light) when (d) crawl speed decreasing with stiffness, $(\partial v_0/\partial E)=-0.06$, (e) constant crawl speed $(\partial v_0/\partial E)=0$, and (f) crawl speed increasing with stiffness $(\partial v_0/\partial E)=0.06$. (g)–(l) Results from simulations in which growth rate depends on substrate stiffness and cell crawl speed is constant. (g) Cell crawl speed and (h) growth rate as a function of substrate stiffness ($E$), for different gradients corresponding to (i). (i) Average difference in fitting $R^2$ values, using exponential against linear curves, as a function of substrate stiffness and growth gradient ($n=5$). (j)–(l) Average traction stress ($\sigma$) as a function of distance from the center of the monolayer, $r$ ($n=5$), from soft to stiff substrates (dark to light) when (j) growth rate decreasing with stiffness, $(\partial G/\partial E)=-0.033$, (k) constant growth rate $(\partial G/\partial E)=0$, and (l) growth rate increasing with stiffness $(\partial G/\partial E)=0.033$.

Figure 11

Pressure measurement on the bottom surface of the aggregate using JKR Laplace-independent measurement of pressure on the bottom surface of aggregate using JKR approximation agrees qualitatively and quantitatively with Laplace-based measurements.