Figure 1.
(a) Illustration of a spindle shaped cell adhered to a substrate subjected to cyclic stretch. The stress fibers (SFs) are largely along the long axis of the cell, anchored at focal adhesions (FAs) near the poles. (b) Schematic drawing of focal adhesions in cell-substrate contact based on specific binding between receptors and complementary ligands. Actin filaments anchor into an adhesion plaque that connects substrate via receptor-ligand bond clusters.
Figure 2.
The compliance of the bond-substrate system represented by the effective spring constant K.
The receptors actually bind to specific head groups of certain adhesion molecules, such as fibronectin, coated on the substrate surface.
Figure 3.
The viscoelastic model of a contracting filament.
The structure consisits of a linear spring of stiffness , a dashpot of viscous coefficient
in series, and a parallel module of contraction force
.
Table 1.
Estimated values of the parameters in the model.
Figure 4.
Steady state bond density as a function of substrate rigidity.
Figure 5.
Evolutions of the bond and filament densities.
(a) A relatively stiff substrate of . (b) A relatively soft substrate of
.
Figure 6.
Evolutions of the bond and filament densities corresponding to different cell orientations.
(a) (parallel to stretch direction). (b)
(nearly perpendicular to stretch direction). (c, d) Evolution snapshots of (c) the bond and (d) filament densities, represented by the radial distance from the origin, as a function of cell orientations (
20, 50, 100 and 200, respectively).
Figure 7.
Long-time average filament density as a function of the cell orientation angle
under a 10% stretch at different frequencies.
(a) . (b)
where strain stiffening is not present as the substrate is stretched. (c, d) Effects of (c) strain stiffening and (d) substrate rigidity on
for low frequencies (0.05 Hz and 0.001 Hz, respectively).
Figure 8.
Long-time average filament density as a function of the cell orientation angle
under different values of stretching amplitude (stretch frequency: 1 Hz).
Figure 9.
Reorientation of multiple cells on cyclically stretched substrates.
(a) Alignment of 100 individual cells adhered to a substrate which is subjected to a 10% stretch at 1 Hz. The stretch is applied along the horizontal direction and from left to right, the order parameters corresponding to particular time points are: ,
and
. (b, c) Dynamic evolution of the order parameter
representing instantaneous cell orientation of 100 cells on the cyclically stretched substrate at different values of straining frequency, amplitude and rotational diffusivity. Each error bar reflects the standard deviation (SD) of 10 independent sets of simulation.
Figure 10.
Effects of Poisson's ratio on cell reorientation.
(a) The effective stretching strain acting on each SF as a function of cell orientation angle , influenced by Poisson's ratio
of substrate materials. (b, c, d) Long-time average filament density
as a function of the cell orientation angle
for slow kinetic process (
) and (b)
, (c)
and (d)
without strain stiffening effects, respectively.
Figure 11.
Long-time average filament density
in “Rho-inhibited” cells (
) as a function of the orientation angle
under a 10% stretch at 1 Hz. The results clearly show the difference between the cases with and without strain stiffening effects.