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

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.

💡 Research Summary

Collective cell migration underlies essential biological processes such as tissue development, wound healing, and cancer invasion. Although traction force microscopy and monolayer stress microscopy can quantify the total forces generated by a cell sheet, these forces are a superposition of active stresses produced by the cells and passive, constitutive stresses arising from the tissue’s material response. Disentangling these two contributions is critical for establishing a clear force‑motion relationship, yet experimental methods to directly measure the passive component—tissue viscosity—have been lacking.

In this study the authors treat an epithelial monolayer (MDCK cells) in its fluid‑like state as a viscous fluid, justified by rapid turnover of actin (≈ 14 s) and E‑cadherin (≈ 4 min) relative to the migration time scale (≈ 3 h). They develop two independent, complementary approaches to estimate the tissue viscosity η.

Approach 1 – Hydrodynamic screening length (λ).
Theory predicts λ = p η/ξ, where p ≈ 2π and ξ is the cell‑substrate friction coefficient. λ represents the distance over which viscous stresses propagate and, experimentally, it can be identified with the spacing between protrusions at the leading edge of an expanding cell sheet. The authors cultured MDCK cells against a barrier, removed the barrier, and allowed the monolayer to expand for 24 h. Using phase‑contrast imaging they manually measured the distance between neighboring protrusions and also implemented an automated edge‑detection plus sine‑curve fitting to compute λ ≈ ph/κ (h = amplitude of edge perturbation, κ = curvature).

Pharmacological perturbations revealed that cytochalasin D (actin polymerization inhibitor) reduced λ, whereas CN03 (RhoA activator) increased λ. Assuming ξ remains constant, these changes imply a decrease and increase of η, respectively. Fluorescent staining confirmed that cytochalasin D reduced stress fibers and E‑cadherin intensity without affecting focal adhesion number, supporting a viscosity drop with unchanged friction. Conversely, CN03 increased both stress fibers and focal adhesions; the latter would raise ξ, yet λ still grew, indicating that the increase in η outweighed any friction change.

Approach 2 – Distribution of effective viscosity (η_eff).
The second method directly computes η_eff = σ_s/˙ε_s at each spatial location, where σ_s is the measured shear stress and ˙ε_s the local shear strain rate obtained from velocity fields (PIV). Although the active shear stress σ_a is unknown, the authors argue that the spatial average of η_eff approximates the true tissue viscosity η. Across control monolayers η_eff averaged ≈ 100 Pa·hr (≈ 3.6 × 10⁴ Pa·s). CN03 treatment raised the mean η_eff by ~50 %, while cytochalasin D and blebbistatin (myosin II inhibitor) lowered it dramatically. A metabolic inhibitor that suppresses cellular activity without altering the cytoskeleton had no significant effect on η_eff, reinforcing that structural changes—not mere activity level—drive viscosity modulation.

Key Findings and Implications

1. Quantitative Viscosity: The study provides the first experimental estimate of epithelial tissue viscosity, on the order of 100 Pa·hr.
2. Structure‑Viscosity Link: Increases in actomyosin stress fibers raise η, whereas reductions in filamentous actin or myosin activity lower η. Cell‑cell adhesion (E‑cadherin) also contributes positively, while focal adhesion density primarily influences friction ξ.
3. Methodological Advance: By using both λ (protrusion spacing) and η_eff (stress/strain‑rate ratio), the authors demonstrate two convergent, non‑invasive ways to infer η in living, self‑propelling tissues.
4. Modeling Impact: With η measured, the total stress can be decomposed into σ = σ_a + η ˙ε, enabling predictive continuum models of collective migration that separate active force generation from passive material response.
5. Biological Relevance: The ability to map spatial and temporal variations in η offers a new avenue to study how drugs, genetic perturbations, or disease states (e.g., tumor stiffening) alter tissue mechanics and, consequently, migration patterns.

Overall, this work bridges a critical gap between mechanical measurements and theoretical descriptions of collective cell behavior, establishing tissue viscosity as a meaningful, experimentally accessible material parameter that directly reflects underlying cytoskeletal and adhesive architecture.