Cell reorientation under cyclic stretching

Abstract

Mechanical cues from the extracellular microenvironment play a central role in regulating the structure, function and fate of living cells. Nevertheless, the precise nature of the mechanisms and processes underlying this crucial cellular mechanosensitivity remains a fundamental open problem. Here we provide a novel framework for addressing cellular sensitivity and response to external forces by experimentally and theoretically studying one of its most striking manifestations--cell reorientation to a uniform angle in response to cyclic stretching of the underlying substrate. We first show that existing approaches are incompatible with our extensive measurements of cell reorientation. We then propose a fundamentally new theory that shows that dissipative relaxation of the cell's passively-stored, two-dimensional, elastic energy to its minimum actively drives the reorientation process. Our theory is in excellent quantitative agreement with the complete temporal reorientation dynamics of individual cells measured over a wide range of experimental conditions, thus elucidating a basic aspect of mechanosensitivity.

Figures

Figure 1. Cyclic stretching reorients cells and SFs along two mirror-image angles

a-b, Phase-contrast images of REF-52 fibroblast cells on a fibronectin-coated PDMS substrate, before (a) and after (b) 6 hours of cyclic stretching (10% strain at 1.2Hz), show reorientation from random cell alignments to two, well defined, mirror-image angles. The largest principal strain (stretch) was applied in the horizontal direction as shown by double sided arrow. Bar = 100μm. c-c’, Closeup of reoriented cells (c) shows SF alignment (c′) at a similar angle to the cell body. SFs were imaged after being stained with fluorescently labeled phalloidin. Bar = 40μm. d, The mean SF orientation of individual, polarized, cells (< θSF >) matches the cell body orientation (θcell body). Data from different experiments (red squares correspond to cells from (b)) yield a linear relation of slope ~1 between the two angles (black line is the best fit: θcell body ≈ 1.02·θSF). The final orientation angle varies due to the cyclic stretching conditions (see Fig. 2 for more details). Inset shows how θcell body was determined in phase-contrast images as the long axis angle of the dark, actin-rich, cell core. Error bars represent 95% confidence intervals. Bar = 40μm. e, Analysis of individual SF orientations, θSF, at the end of the cyclic stretching (~1000 SFs from (b) and its vicinity) reveals an angular distribution with two sharp peaks, as contrasted with initial random configuration (dashed red line).

Figure 2. The final orientation angle is determined by the strains in the underlying substrate and differs from previous theoretical models

a, Cartoon of a single cell (light blue ellipse) on a deformable 2D substrate (magenta), that is stretched with principal strains: εxx & εyy (in our experiments εxx is extensional and εyy compressive). ρ marks the direction of cell body, SF (red) and FA (yellow) polarization which is at angle, θ, relative to the direction of the principal strain εxx. b, Schematic presentation of different loading and clamping conditions (left) and phase-contrast images of typical cell orientations at the end of the stretch cycles (right). The 2cm × 2cm PDMS substrate depicted in magenta, is stretched (red arrows) via clamps (black solid lines) attached at its boundaries. By adjusting the clamps’ location and size we could tune the strains transferred to the ~1 mm2 region of interest (inner dashed box), at the substrate’s center. In this manner we could control the final cell orientation (dashed yellow lines are guides to the eye). Bar = 100μm. c, The measured final orientation angle, θ‒, as a function of the biaxiality ratio, r. Each point (blue circles = SF orientations, red squares = cell body orientations) was extracted from a different experiment (1.2Hz, 4-24% strain) and represents the mean angle for the relevant cell population (n>30) in the region of interest. The green and black lines are respectively the zero strain (Eq. 1) and zero stress (Eq. 2) theoretical predictions. The dashed black line is the minimal stress prediction which extends the zero stress prediction to regions where the latter has no solution. Error bars represent 95% confidence intervals. Inset shows the SF angular distribution of a single experiment. Note that the zero strain prediction (dashed red line) is an outlier in the measured distribution, and cannot account for the discrepancy observed.

Figure 3. Final orientation angle is correctly captured by the proposed theory

As predicted by the theory (Eq. 7), a linear relation between cos2(θ‒) and (r+1)−1 is clearly observed, where θ‒ is the measured final orientation angle (blue circles are data from Fig. 2c). This excellent agreement (solid black line is the best fit to Eq. 7) depends on a single parameter, b, where both the slope and the intercept are uniquely determined by it (b =1.13 ± 0.04 extracted from fit). In comparison, the zero strain prediction (Eq. 1) is depicted by the dashed black line. Additional measurements - performed on a much softer substrate (~20 kPa compared to ~1MPa) (red squares) as well as data extracted from the literature for a different cell line (green diamonds) – fall on the same line. This suggests that the elastic properties, associated with the b parameter in our theory, do not depend on substrate stiffness and are possibly cell line independent. Inset shows the same data, best fit and zero strain prediction, as above, with θ‒ plotted directly vs. r. Error bars represent 95% confidence intervals.

Figure 4. Reorientation dynamics are quantitatively explained by the proposed theory

a, Phase contrast snapshots tracking a single cell reorientation dynamics under cyclic stretching (r=0.38, ε˘xx =0.11 at 1.2Hz). The elapsed time from the beginning of cyclic stretching is marked on each image. b, Cell body orientations, θ, of six cells, originally polarized in different directions, were recorded from the onset of cyclic stretching, t=0 (r=0.36, ε˘xx =0.11 at 1.2Hz). Reorientation takes place by a smooth rotation towards the closer of the two mirror-image final alignment angles (here: ± 64°). The individual dynamics leading up to these set points strongly depends on the initial orientation. The reorientation duration is not a simple function of the total rotation angle. Comparing the recorded reorientations to the theory’s predictions (Eq. 6) we find that individual best fits (solid curves) are not only in excellent agreement with measurements, but also all yield the same τ=6.6 ± 0.4s value (b=1.13, independently extracted from Fig. 3, and c=1, as explained in the Supplementary Note 1, were used in the analysis). c, Cells initially oriented at a similar initial angle rotate towards different final orientations according to the applied biaxiality ratio (triangles: r = 0.25, diamonds: r = 0.48, circles: r = 0.69; ε˘xx ≈ 0.10 at 1.2Hz for all three). The theory accurately describes the reorientation dynamics and predicts the same τ ~6.6s value for different cells under a wide range of experimental conditions (solid curves are single parameter fits to Eq. 6). Therefore, analysis of the smooth reorientation of a single cell towards the final orientation predicts the rotational dynamics of all other cells, even when stretched under widely different experimental conditions. d, Phase contrast snapshots tracking a single cell initially co-aligned with the stretching direction. The cell loses polarity shortly after the onset of cyclic stretching (t=400s). This is quickly followed (t=1000s) by a de-novo polarization at an angle close to the final orientation from which the cell smoothly rotates to θ‒ (stretch parameters as in (a)). In a & d, the largest principal strain (stretch) was applied in the horizontal direction and bar = 50μm.