Measurement of tissue viscosity to relate force and motion in collective cell migration

TL;DR

The paper addresses how to relate force to motion in collective epithelial migration by decoupling active cellular forces from the tissue’s constitutive response. It treats the cell monolayer as an active viscous fluid with $\sigma^{ve}=\eta \dot{\varepsilon}_s$ and develops two complementary experimental routes to quantify tissue viscosity: (a) a hydrodynamic screening length $\lambda=\sqrt{\eta/\xi}$ inferred from edge protrusion spacing, and (b) a local effective viscosity $\eta^{eff}=\sigma_s/\dot{\varepsilon}_s$ derived from stress and strain-rate maps. The main findings show that tissue viscosity in MDCK epithelial monolayers is on the order of $50$–$250\,\mathrm{Pa\,h}$, that CN03 increases viscosity while cytochalasin D and reduced adhesions decrease it, and that metabolic inhibition reduces activity without changing viscosity in the short term. The study links microstructure (actin stress fibers and E-cadherin adhesions) to macroscopic material properties, providing first experimental measurements of tissue viscosity and a framework to separate active and viscous components of stress, with implications for understanding force–motion relationships in development, wound healing, and cancer invasion.

Abstract

In tissue development, wound healing, and cancer invasion, coordinated cell motion arises from active forces produced by the cells. The relationship between force and motion remains unclear, however, because the forces result from a sum of contributions from activity and the constitutive response of the cell collective. Here, we develop a method to decouple the forces due to activity from those due to constitutive response. As a model of an epithelial tissue, we use a monolayer of epithelial cells in the fluid state, for which the constitutive behavior is that of a viscous fluid. By careful study of the distribution of the ratio between shear stress and strain rate, we show that the order of magnitude of viscosity within the epithelial tissue is 100 Pa-hr and that increasing (decreasing) the actomyosin cytoskeleton and cell-cell adhesions increase (decrease) the magnitude of tissue viscosity. These results establish tissue viscosity as a meaningful way to describe the mechanical behavior of epithelial tissues, and demonstrate a direct relationship between tissue microstructure and material properties. By providing the first experimental measurement of tissue viscosity, our study is a step toward separating the active and constitutive components of stress, in turn clarifying the relationship between force and motion and providing a new means of identifying how active cell forces evolve in space and time.

Figures (14)

• Figure 1: Measurement of hydrodynamic screening length in a cell monolayer. (a) Schematic of distance between protrusions, with the distance indicated by the white bar. (b) Phase contrast images of the leading edge of expanding cell monolayers in control conditions and treated with cytochalasin D or CN03. The protrusions are often led by cells having large lamellipodia. The manually measured distance between protrusions is shown. (c) Summary of manually measured distance between protrusions for treatment with cytochalasin D ($p = 0.001$, two-sample t-test) and CNO3 ($p < 0.001$, two-sample t-test). Each dot represents the average distance between protrusions within a field of view, and black lines indicate means. (d) Quantification of average distance between protrusions. (Left) Representative image of an expanding cell monolayer. (Middle) Linear fit (white) and amplitude, $h$, (blue) of the leading edge. The amplitude is found by taking the orthogonal distance from the linear fit to the leading edge. (Right) Local curvature, $\kappa$, of the leading edge. (e) Average of $\sqrt{h/\kappa}$ after 24 hr of migration for treatments with cytochalasin D ($p < 0.001$, two-sample t-test) and CN03 ($p = 0.004)$, two-sample t-test). Each dot represents an average over an independent field of view, and black lines indicate means.
• Figure 2: Fluorescent labeling of the cytoskeleton, cell-cell, and cell-substrate adhesions. (a) Fluorescent images of actin, vinculin, E-cadherin, nuclei, and merged channels for control (10$\%$ FBS), cytochalasin D, control (2$\%$ FBS), and CN03 treated groups. (b) Relative E-cadherin intensity (ratio of fluorescent intensity at cell-cell junctions to intensity in cytoplasm) for treatment with cytochalasin D compared to its control ($p < 0.001$, two-sample t-test) and CN03 compared to its control ($p = 0.19$, two-sample t-test). (c) Average number of focal adhesions per cell for treatment with cytochalasin D ($p = 0.18$, two-sample t-test) and CN03 ($p = 0.008$, two-sample t-test) compared to their respective controls. Each dot represents the average over a field of view, and black bars indicate means.
• Figure 3: Approach to measure effective viscosity within the monolayer. (a) Phase contrast image of cell monolayer. (b, c) Color map of shear stress, $\sigma_s$ (b) and shear strain rate $\dot{\varepsilon}_s$ (c). (d) Color map of effective viscosity. (e) Histogram of effective viscosity across 6 cell islands over 15 hr. (f) Schematic showing how the distribution of effective viscosity is hypothesized to result from contributions of tissue viscosity and activity. The tissue viscosity $\eta$ is hypothesized to have a small magnitude and positive mean. The active contribution $\zeta$ is hypothesized to have zero mean and a wide distribution, reflecting a wide range of activity in the monolayer. The sum is the effective viscosity $\eta^\mathrm{eff}$, which has a wide distribution and a slightly positive mean.
• Figure 4: Effect of altering actomyosin on effective viscosity. (a) Distribution of effective viscosity for control ($10\%$ FBS) and treatment with cytochalasin D. Inset: Mean of effective viscosity for control ($10\%$ FBS) and treatment with cytochalasin D ($p = 0.002$, two-sample t-test). (b) Distribution of effective viscosity for control ($2\%$ FBS) and treatment with CN03. Inset: mean effective viscosity for control ($2\%$ FBS) and treatment with CN03 ($p = 0.038$, two-sample t-test). In panels (a) and (b), each distribution is across 6 different cell islands per condition over 15 hr; each dot represents the mean over space and time for an independent cell island, and black bars indicate means over the dots. (c) Scatter plot of the standard deviation of effective viscosity against the mean effective viscosity for treatment with cytochalasin D and its control. The slope of the control was 5.52 and the slope with treatment with cytochalasin D was 3.52 ($p < 0.001$, analysis of covariance). (d) Scatter plot of the standard deviation of effective viscosity against the mean of effective viscosity for treatment with CN03 and its control. The slope of the control was 1.49 and the slope with treatment with CN03 was 7.58 ($p < 0.001$, analysis of covariance). In panels c and d, a dot represents the standard deviation and mean over space for one cell island at one point in time.
• Figure 5: The width of the histogram of effective viscosity is controlled by cellular activity. (a) Histograms showing effective viscosity distributions for control (gray) and metabolic inhibition (blue) groups. Data shown is from 6 control and 8 metabolically inhibited cell islands over 1 hr of imaging. Levene's test indicated a statistically significant difference in the variance between control and metabolic inhibition ($p < 0.0001$). Inset: Mean effective viscosity for control and metabolic inhibition groups ($p = 0.343$, two-sample t-test). (b) Histograms showing effective viscosity distributions for control (gray) and blebbistatin (blue) groups. Data shown is from 6 control and 7 blebbistatin-treated cell islands over 2 hr of imaging. Levene's tested indicated a significant difference in the variance between control and blebbistatin groups ($p < 0.0001$). Inset: Mean effective viscosity for control and blebbistain groups ($p = 0.03$, two-sample t-test). In panels a and b, each dot represents a different cell island; black bars indicate means. (c, d) The normalized standard deviation (c) and mean (d) of the distribution of effective viscosity over time before and after treatment with blebbistatin. Data for each cell island were normalized to the values before treatment ($t<0$). The treatment occurred at $t=0$. The dashed lines represent the first 30 min post treatment. Lines represent averages over all 7 blebbistatin-treated cell islands, and bars represent the standard error of the mean. For panel c, the slopes and 95$\%$ confidence intervals were -0.141 [-0.401, 0.118] min$^{-1}$ for time $\in$ (-50, 0) min, -0.722 [-1.27, -0.169] min$^{-1}$ for time $\in$ (0, 30) min, and -0.591 [-0.839, -0.344] min$^{-1}$ for time $\in$ (30, 70) min. For panel d, the slopes and 95$\%$ confidence intervals were -0.0987 [-0.427, 0.23] min$^{-1}$ for time $\in$ (-50, 0) min, -0.361 [-1.27, 0.547] min$^{-1}$ for time $\in$ (0, 30) min, and -0.663 [-0.972, -0.354] min$^{-1}$ for time $\in$ (30, 70) min. In panels c and d, the * symbol represents time periods for which confidence intervals did not span 0, indicating slopes that were statistically different from 0.