Simulations of Cell Behavior on Substrates of Variegated Stiffness and Architecture - Computer Models in Biomechanics - page 38

Fig. 3.6 Average force per
post F avg exertedbyasquare
cell in steady state versus its
edge length L plotted for post
stiffness values k = 2, 10, 25
and 100 nN / µm

We note that the results of our simulations for cells on posts confirm that the
average force generated by the cell is higher on stiffer substrates, and reaches a
limit value beyond a critical value of substrate stiffness. This trend is consistent
with our findings in the simulations for cells adhered on flat substrates, as presented
in the previous section (Fig. 3.2 (b)).
Tan et al. ( 2003 ) observed in experiments that the average force per post for a
given post stiffness increases with cell size, and therefore with the number of posts
to which the cell is adhered. Simulations by Deshpande et al. ( 2007 ) found the same
trend, and they attributed this feature to the fact that a cell contracting on many posts
senses a stiffer system than one contracting on a few posts. Deshpande et al. ( 2007 )
pointed out that this trend occurs despite the fact that many of the posts under well-
spread cells engaging many posts are only lightly laden, due to the fact that these
posts are in the central region of the cell where the cell stress is relatively uniform
(see Fig. 3.4 (c)). To further explore the effect of cell size on cellular contractility,
we study how the average force per post varies with cell edge length for four post
stiffnesses, with results shown in Fig. 3.6 . We note that the cells engage 3

× 3, 4 × 4,

6 14 posts as they get larger. For each cell size the

average force per post increases with post stiffness. Furthermore, as the smallest cell
size is increased, the trend, the same for all post stiffnesses, is that the average force
per post increases. In the case of the cell on the most compliant posts, this trend
is monotonic. However, in all other cases, a peak in the average force per post is
reached at an intermediate cell size, beyond which the average force per post falls.
The trend in which the average force per post increases with cell size, also ob-
served by Deshpande et al. ( 2007 ), reflects the fact that a cell engaging more posts
is interacting with a stiffer system. Since a stiffer environment induces in the cell a
more robust cytoskeleton, and a higher level of contractile stress, the force per post
goes up as the cell size increases. The trend in which the force per post declines as

× 6, 8 × 8, 11 × 11 and 14 ×