Force localization modes in dynamic epithelial colonies

Abstract

Collective cell behaviors, including tissue remodeling, morphogenesis, and cancer metastasis, rely on dynamics among cells, their neighbors, and the extracellular matrix. The lack of quantitative models precludes understanding of how cell-cell and cell-matrix interactions regulate tissue-scale force transmission to guide morphogenic processes. We integrate biophysical measurements on model epithelial tissues and computational modeling to explore how cell-level dynamics alter mechanical stress organization at multicellular scales. We show that traction stress distribution in epithelial colonies can vary widely for identical geometries. For colonies with peripheral localization of traction stresses, we recapitulate previously described mechanical behavior of cohesive tissues with a continuum model. By contrast, highly motile cells within colonies produce traction stresses that fluctuate in space and time. To predict the traction force dynamics, we introduce an active adherent vertex model (AAVM) for epithelial monolayers. AAVM predicts that increased cellular motility and reduced intercellular mechanical coupling localize traction stresses in the colony interior, in agreement with our experimental data. Furthermore, the model captures a wide spectrum of localized stress production modes that arise from individual cell activities including cell division, rotation, and polarized migration. This approach provides a robust quantitative framework to study how cell-scale dynamics influence force transmission in epithelial tissues.

FIGURE 1:

The traction stress distribution in epithelial colonies can vary widely for the same geometry. (A) A colony with traction stresses localized at the colony periphery. Left, the shapes of cells and the overall pattern shape visualized with the membrane marker Stargazin-GFP, scale bar = 25 µm. Middle, traction stress heatmap for the colony at left—the colony shape is outlined in white. Right, strain energy density as a function of Δ, the distance from the colony border, normalized to the value at Δ = 0. The peak at or near Δ = 0 is the defining feature of colonies with peripheral stress localization. Right, inset, schematic of the procedure used to generate strain energy density profiles. (B) A colony with a higher proportion of internal traction stresses. Left–right: cell and colony shapes visualized with Stargazin-GFP, traction heatmap showing stresses localized to hot spots distributed throughout the colony interior, strain energy density profile that increases with Δ.

FIGURE 2:

For colonies with peripheral localization of traction stress, a continuum mechanical model quantitatively captures traction stress distribution. (A) Schematic of the continuum mechanical model. (B–D) Peripheral localization of traction stresses in ZO-1/2 dKD MDCK colonies is quantitatively captured by a homogeneous continuum model for cohesive cell colonies. (B) Phase contrast images of ZO-1/2 dKD MDCK cells in stadium-shaped micropatterns of constant area and varying radii of curvature. (C) Traction stress heatmaps for constant area colonies, averaged over n = 4–9 different colonies. (D) Continuum model results for given colony geometries with model parameters: , and . (E) Colony strain energy is independent of colony shape. Each data point represents the average over n = 4–9 colonies. (F) Strain energy does not depend on the number density of cells within a colony. (G) Traction stress organization in unconstrained MDCK colonies can also be described by the continuum model. Left to right, phase contrast, experimental traction map, and continuum model traction map images for an adherent colony on an unpatterned substrate. Model parameters are the same as in D. All scale bars = 25 μm.

FIGURE 3:

Active adherent vertex model for epithelial cell colonies can be benchmarked to experiments to capture spatial variations in traction stress. (A) Simulation image for a cell colony on a micropattern (top) and a zoomed-in region illustrating the mechanical forces acting on adherent cells (bottom). (B) Time-averaged traction stress maps for varying curvature radii of the micropattern: r = 22 µm (top), r = 34 µm (middle), and r = 46 µm (bottom). (C) Strain energy as a function of radius of curvature for a fixed area of the pattern. (D) Strain energy as a function of cell density for fixed pattern shape.

FIGURE 4:

Increased cell motility promotes strain energy localization throughout the cell colony. (A) Time-averaged traction stress maps, (B) averaged strain energy density normalized by the boundary value, and (C) cell trajectory plots for low motility cells, , (top), medium motility cells, , (middle), and high motility cells, , (bottom). Δ is the distance from the boundary and is defined as negative outside of the cell colony and positive inside the cell colony. Scale bar represents 50 µm. (D) Traction stress decay length λ and (E) rate of cell neighbor exchanges (intercalations) for varying cell motility speed and cell shape index. The decay length λ is measured by fitting to the relevant strain energy density profiles.

FIGURE 5:

Colonies with interior traction stresses exhibit high degree of individual cell motility. (A, B) Colonies with peripheral localization of traction stresses have cells that appear jammed and do not reorganize traction stresses rapidly. By contrast, colonies with interior traction stresses have highly motile cells and exhibit dynamic peaks in traction stresses. From left to right: Phase contrast images and nuclear tracks over 3.5 h for two colonies of ZO-1/2 dKD MDCK cells, representative traction maps from each colony, and the strain energy density profiles corresponding to the traction maps. Scale bar = 25 μm. (A) A colony with low motility (mean cell speed = 0.079 µm/min) and traction stresses localized to the colony periphery. (B) A colony with higher motility (mean cell speed = 0.236 µm/min) and a higher proportion of internal stresses. (C) Colonies with higher motility have a longer decay length for strain energy as a function of distance from border. This relationship holds in experiments (left) and is predicted by the vertex model (right) to be robust over a wide range of motilities, using each simulation used in Figure 4D. The red line in the left panel of C shows the linear fit of the data shown with slope = 69.53 min and y-intercept = 5.313 μm. The radii of curvature for the colonies shown in A and B are 65 and 70 µm, respectively.

FIGURE 6:

Traction stress localization during cell rounding and division. (A) Stargazin-GFP images showing a cell (outlined in white) contracting and dividing. (B) Traction maps corresponding to A. As the cell contracts, traction stresses are exerted just exterior to the mitotic cell, directed inward toward the plane of division. Once the cell finishes dividing, the stresses begin to dissipate. (C) Cell shapes during a simulated mitotic event in the vertex model for a low-motility cell colony, , . The dividing cell is highlighted in red. Full details of the cell division implementation are given in the Supplemental Material. (D) Traction maps corresponding to C. All scale bars = 10 µm.

FIGURE 7:

Internal traction stresses form during colony rotation. (A) Stargazin-GFP images of a colony on a circular pattern (radius of curvature = 47.5 µm) rotating counterclockwise about the pattern center. Curved arrow indicates direction of motion. (B) Traction maps corresponding to A. (C) Cell shapes during rotation simulated by the vertex model, for high motility, , . Blue arrows show the direction of cell motion. Cell polarities align with cell velocity with time scale min and turn away from the micropattern boundary with time scale min. Full details can be found in the Supplemental Material. (D) Traction maps corresponding to C. All scale bars = 25 µm.