Simulations of Cell Behavior on Substrates of Variegated Stiffness and Architecture - Computer Models in Biomechanics - page 33

Fig. 3.2 ( a ) Cell total focal adhesion fraction F T and ( b ) total force F T exerted by a cell adhered
to a flat gel substrate in steady state, where Young's modulus E of the gel is varied from 2 to
200 kPa
We note that the total force F T applied by the cell to the gel is also an indicator
of the degree of stress fiber development. Although we do not plot the results, we
can confirm that in our simulations, cells on stiffer gels have higher average concen-
trations of stress fibers compared to cells on more compliant gels. Consistent with
the trends in Figs. 3.1 and 3.2 , the average concentration of stress fibers in a cell
reaches an asymptote at a gel modulus of approximately 50 kPa.
3.4 Models of Cell Behavior on Micro-Posts
The distribution of traction forces exerted by a cell on its adhered substrate has been
measured by seeding cells on a bed of micro-posts and determining the independent
deflections of the posts (Tan et al., 2003 ; Saez et al., 2005 ). The isolated islands
of cell-substrate interaction on post tops allow discrete measurement of tractions
forces, and the size and shape of focal adhesions. In the experiments of Saez et al.
( 2005 ), the stiffness of the posts is varied and the average force per post F avg exerted
by the cell is recorded. This quantitative study demonstrates that the average force
per post increases as the post stiffness is increased regardless of post-bed geometry
or cell area. We use these measurements to test our model, and, as noted above, to
calibrate it.
On top of the posts, the cell forms adhesions; the studies by Tan et al. ( 2003 ) and
Chen et al. ( 2003 ) find that (a) focal adhesions, measured by vinculin staining, on
top of posts near the edge of the cell are the largest, (b) posts interior to the cell have
negligible focal adhesions, and (c) the focal adhesion distribution forms a horseshoe
shape around the top perimeter of the posts. In addition, Tan et al. ( 2003 ) found that
F avg increases with the size of a cell, a behavior that can be rationalized by recog-
nition that a larger cell pulls on more posts, so experiencing a stiffer environment.