Cooperativity between Cell Contractility and Adhesion

In living cells, the cytoskeleton connects to the extracellular environment through focal adhesions, multimolecular structures that can sense applied force. A model is presented that for the first time explains why the focal adhesions tend to high-curvature regions at the cell periphery. It is based on experimental evidence for positive feedback between adhesion formation and assembly of actomyosin bundles (stress fibers). The model predicts that the focal adhesions propagate by treadmilling with a velocity proportional to the integrin diffusion coefficient.

Figure 1

Schematic representation of adhesion-stress fiber interaction (top view of a thin cell lying on a flat 2D substratum). Tension generated along the stress fibers causes focal adhesions to stabilize and grow. Unbound integrins freely diffuse in the 2D cell membrane. New stress fibers, are nucleated at focal adhesions.

Figure 2

(a) Steady-state phase diagram in 1D (${\alpha }_0=0$). At $\beta <1/8$, there are two stable states: active (A) and inactive (I); otherwise, only the inactive state exists. (b) Patterns of steady-state adhesion distribution: discontinuous distribution with large adhesions at the end points in the active state (left), and continuous low-density distribution in the inactive state (right).

Figure 3

(a)–(c) Propagation of adhesions to the ends of a 1D fragment. Numerical solution of 1D Eqs. (2) with ${\alpha }_0=0.01$, $\alpha =100$, $\beta =0.025$, $\tilde{D}=0.01$. Densities of bound (blue line) and free (red line) integrins are plotted along the $y$ axis. Initially, there are no stress fibers, and adhesions are concentrated in the center of the fragment. (d) Adhesion doublet formed from an isolated cluster of bound integrins: fluorescent adhesion protein and stress fibers are shown in red and blue, respectively. Arrows indicate the direction of the doublet expansion. $\mathrm{B}\mathrm{a}\mathrm{r}\approx 2\mu \mathrm{m}$ (adapted from [23]).

Figure 4

Experiment and simulation of the pattern of cell adhesion on a square substrate. (a) Cell landscape imaged with the atomic force microscope. Diagonal lines originating at the corners are stress fibers. (b) Fluorescent focal adhesion protein, vinculin (green) [12]. (c) Adhesion density as a function of position on a square cell membrane. Numerical solution of Eqs. (2) on a square at time $\tau =10$, with ${\alpha }_0=0.001$, $\alpha =100$, $\beta =0.1$, $\tilde{D}=\infty$. Initially, there were no stress fibers, and adhesions were concentrated in the center of the square.

Figure 5

(a) Steady-state distribution of adhesions along the boundary of an ellipsoidal cell with the eccentricity $e=0.42$. Adhesion density is plotted in arbitrary units (${\alpha }_0=0$). (b) Adhesion density $c$ as a function of curvature $k$. (Note, that this dependence becomes significantly nonlinear at the points with sufficiently low curvature.)