Dissecting Collective Cell Behavior in Polarization and Alignment on Micropatterned Substrates

Abstract

Pattern-dependent collective behaviors of cells have recently raised intensive attention. However, the underlying mechanisms that regulate these behaviors are largely elusive. Here, we report a quantitative study, combining experiment and modeling, on cell polarization and arrangement on a micropatterned substrate. We show that cells exhibit position-dependent collective behaviors that can be regulated by geometry and stiffness of the patterned substrate. We find that the driving force for these collective behaviors is the in-plane maximum shear stress in the cell layer that directs the arrangement of cells. The larger the shear stress, the more the cells preferentially align and polarize along the direction of the maximum principal stress. We also find that the aspect ratio of cell polarization shape and the degree to which cells preferentially align along the direction of maximum principal stress exhibit a biphasic dependence on substrate rigidity, corresponding to our quantitative predictions that the magnitude of the maximum shear stress is biphasically dependent on the stiffness of the substrate. As such, the driving force of these cell collective behaviors can be quantified using the maximum shear stress.

Figure 1

Cell polarization and alignment on ring patterns of different substrate stiffnesses. (A) Phase-contrast images of cell morphology and alignment, and associated fluorescence images of actin on ring patterns of three different stiffnesses, i.e., 60 kPa gel, 40 kPa gel, and 10 kPa gel. Scale bars,200 μm. (B) Schematic diagram of cell morphology and alignment corresponding to the phase-contrast images in (A), where the ring pattern is divided into three regions, the inner, middle, and outside regions. (C) Histograms of the statistics of cell population for three different angle ranges in the three different regions of the ring pattern on the stiffest matrix. (D) Histograms of statistics of the cell aspect ratio for different angle ranges in the different regions of the ring pattern on the stiffest matrix. (E) The mean aspect ratio of cells versus their distance from the center of the ring pattern at different stiffnesses. (F) The mean cell orientation angle as a function of the distance for three different stiffnesses. (G) The mean cell area as a function of the distance. (H) The alignment of actin as a function of the distance. Note that the asterisks indicate that the differences between the results on 40 kPa gel and those on both 60 kPa and 10 kPa gel are statistically significant (p < 0.05). To see this figure in color, go online.

Figure 2

Cell polarization and alignment on ring patterns with different inner radii. (A) Phase-contrast images of cell morphology and alignment in the cell layer on ring patterns with five different inner radii. (B and C) The mean cell aspect ratio (B) and mean cell angle (C) as functions of cell distance from the ring center for rings of different inner radius. (D) The mean cell area shows an independence of distance and inner radius. Scale bars, 200 μm. To see this figure in color, go online.

Figure 3

Predictions of the in-plane principal stresses and maximum shear stress in the cell layer. (A) Side view of the mechanical model of the cell layer adhering to the patterned substrate via adhesion molecules. (B) Top view of the model. The cell monolayer is considered as a homogeneous membrane of a ring shape, with the inner and outer radii denoted by R₀ and R₁, respectively. (C) Predictions of the distribution of the in-plane minimum and maximum principal stresses, ${\sigma }_{\text{r}}$ and ${\sigma }_{\theta }$, as well as the in-plane maximum shear stress, ${\overline{\tau }}_{\max }$, for three different substrate stiffnesses. (D) Predictions of the distribution of the principal stresses and shear stress, ${\sigma }_{\text{r}}$, ${\sigma }_{\theta }$, and ${\overline{\tau }}_{\max }$, for rings of different inner radius. (E) Color maps of the maximum and minimum principal stresses and the maximum shear stress in the cell layer on the ring pattern for three different stiffnesses, corresponding to the results in (C). (F) Color maps of the maximum and minimum principal stress and the maximum shear stress in the cell layer on ring patterns with three different inner radii, corresponding to the results in (D). To see this figure in color, go online.

Figure 4

Measurements of cell alignment and polarization on various geometrical patterns compared with model predictions. (A–D) Phase-contrast images of cells on a square pattern with a circular hole (A), an indented-square pattern (B), a rectangular pattern (C), and an elliptical pattern (D). The colored boxes indicate typical regions of different magnitudes of maximum shear stress. (E–H) Histograms of the mean aspect ratios of cells at different regions in accordance with the colored boxes labeled in (A)–(D), respectively. (E–H insets) Color maps showing model predictions of the maximum shear stress of the corresponding pattern geometries. (I–L) Histograms of the mean cell angle in different regions are in accordance with the colored boxes labeled in (A)–(D), respectively. Scale bars, 200 μm. To see this figure in color, go online.

Figure 5

Measurement of the traction force and in-plane stresses in the cell layer. (A) Phase-contrast images of cells on ring patterns on 10 kPa and 30 kPa gels. The vectorial representation of the maximum principal stress is given to show the orientation of cells relative to the stress tensor. (B) Color maps and vectorial representation of traction on ring patterns of two different stiffnesses, showing that the traction is generally in the radial direction. (C) Vectorial representation of the in-plane maximum principal stress on ring patterns of two different stiffnesses, calculated based on the measurement of the traction force. (D) Vectorial representation of the in-plane minimum principal stress. (E) Color maps of the in-plane maximum shear stress. (F) Color maps of the displacement fields of the ring substrates for the 10 kPa gel and the 30 kPa gel. (G) Radial component of traction as a function of the cell distance from the center of the ring pattern for the two different substrate stiffnesses, where the solid lines represent model predictions, and the dots represent experimental measurements. (H) In-plane maximum principal stress as a function of the cell distance from the center of the ring pattern, where the solid lines represent model predictions and the dots represent calculations based on experimental measurements of traction. (I) The in-plane minimum principal stress; (J) the in-plane maximum shear stress. To see this figure in color, go online.

Figure 6

Polarization and alignment of cells depend on cell contractility, cell-cell adhesion, and cell-matrix adhesion. (A) Phase-contrast images of the cell layer on the ring pattern for the cases of control, treatment by cytochalasin-D, treatment by anti-N-cadherin, and treatment by anti-integrin. (B) Cytochalasin-D treatment dramatically reduced the aspect ratio of cells and increased the cell angle, particularly at the ring edge. (C) Anti-N-cadherin treatment also reduced the aspect ratio and increased the cell angle, with a slightly reduced effect compared to treatment by cytochalasin-D. (D) Anti-integrin treatment decreased the aspect ratio more dramatically than treatment by either cytochalasin-D or anti-N-cadherin, but it increased the cell angle only slightly. To see this figure in color, go online.