Single Cells Spreading on a Protein Lattice Adopt an Energy Minimizing Shape

When spreading onto a protein microlattice living cells spontaneously acquire simple shapes determined by the lattice geometry. This suggests that, on a lattice, living cells’ shapes are in thermodynamic metastable states. Using a model at thermodynamic equilibrium we are able to reproduce the observed shapes. We build a phase diagram based on two adimensional parameters characterizing essential cellular properties involved in spreading: the cell’s compressibility and fluctuations.

Figure 1

Cell shapes on a square lattice of adhesive spots. Top: experimental cell shapes when spreading occurs on 2 (a) 3 (b) 4 (c) or 9 (d) adhesive spots. Focal adhesions are labeled in green and the actin cytoskeleton is labeled in red. The distance between adhesive spots is $10\mu \mathrm{m}$. Bottom: corresponding simulated cells shapes. Color code: white, cell body; red, unoccupied adhesive spot; green: occupied adhesive spot.

Figure 2

Comparison of cell areas in experiments and in simulations. Each point corresponds to one class of shape labeled by the number of adhesive spots. The corresponding shapes are sketched with straight lines. Bars are standard deviations. The dashed line is $y=x$.

Figure 3

Phase diagram of cell shapes as a function of parameters $M$ and $S$. $A_0={10}^4$ is fixed for all simulations. The area of the exact square shape is $A_{\mathrm{sq}}=15376$ square pixels. Dots represent tight cells, triangles represent swollen cells, and squares represent unstable cells. Lines are guides for the eyes, they mark the approximate transition between stable and unstable regions (solid lines) and between swollen and tight cells (dashed line). Images representing 400 averaged shapes illustrate the shapes observed for the corresponding values of the parameters. The colors represent the fraction of occupancy (see inset of Fig. 4). The shape at $M=40$, $S=0.5$ can be unstable, the stable result is represented. The large black circle represents the values for living cells: $M=20$, $S=0.25$ (see text).

Figure 4

Cross sections of cells. $X$ is the distance to the cell center along the horizontal axis. The probability of occupation is defined for each pixel as the fraction of cells which occupy this pixel. Open squares: experiments averaged on 40 thresholded cell profiles (ensemble average). Closed squares and closed circles: simulated cell profiles (time and ensemble average) for a different set of parameters but identical $M=20$ and $S=0.25$ values (filled squares: $J_{\mathrm{cm}}=10$, ${\lambda }_A=2\times {10}^{-4}$, $T=250$, $A_0={10}^4$; closed circle: $J_{\mathrm{cm}}=5$, ${\lambda }_A={10}^{-4}$, $T=125$, $A_0={10}^4$). Insets: corresponding images of the occupation fraction. The color scale has been chosen to enhance low values of intensity [29].