Simulations of Cell Behavior on Substrates of Variegated Stiffness and Architecture - Computer Models in Biomechanics - page 39

the cell size increases reflects the fact that a cell engaging a larger number of posts
has a larger number that are lightly laden because they are near the center of the cell
in the region of uniform cell stress. Since an increasing number of posts has negli-
gible force applied to them, the force per post goes down as the cell size increases.
The results in Fig. 3.6 indicate that the former trend dominates for small cells en-
gaging a small number of posts, but as the cell size increases, the latter trend takes
over. The results in Fig. 3.6 also show that the transition point for these opposite
trends depends on the stiffness of the posts. In a stiff environment, the changeover
occurs at smaller cell size, whereas in a more compliant environment, a larger cell
size is required for the transition.
3.5 Concluding Remarks
A biochemomechanical model is employed for modeling cell behavior in complex
and diverse extracellular settings, and the effects of substrate stiffness, architecture
of the substrate, and cell area are studied. Both on flat gel and micro-post substrates,
cell contractility and focal adhesion assembly intensify as the stiffness of the envi-
ronment is increased. The results of our simulations match key experimental data
in the literature. We verify some well-established features regarding cell behavior
in response to substrate stiffness-namely, (a) the intracellular force generation ma-
chinery exerts higher forces on stiffer substrates, (b) cells form larger and stronger
focal adhesions on stiffer substrates, and (c) cells on stiffer substrates have more
pronounced cytoskeletons in the form of higher concentrations of stress fibers. The
response we have identified comes about because a stiff substrate presents resistance
to the cell as it tries to contract, an effect that stabilizes a high degree of stress fiber
polymerization and focal adhesion development. Such highly developed intracellu-
lar machinery then delivers a high level of traction to the substrate. We also find that
monotonic increase of the stiffness of the substrate does not cause a monotonic en-
hancement of the cellular contractile machinery; an asymptote is reached at a critical
value of substrate stiffness beyond which further enhancement of the cell contractile
system ceases. Such a behavior is hinted at in the results from several experimental
studies, such as that of Saez et al. ( 2005 ), but a conclusive dataset for a wide range
of substrate stiffness values is currently unavailable. Our results not only agree qual-
itatively with many experimental findings, but have been calibrated quantitatively to
the average force per post from Saez et al. ( 2005 ), where the stiffness of the posts
is varied. This step enables us to assert that the cell model parameters used in our
study are representative of the epithelial cells explored by Saez et al. ( 2005 ). The
horseshoe focal adhesions on the post tops that we obtain in our simulations match
the experimental images obtained by Tan et al. ( 2003 ) and Chen et al. ( 2003 ). Such
results give us encouragement to believe that our model captures many elements of
the contractile and adhesive behavior of cells, and may prove useful, eventually, in
a wider setting of cell biology, medicine and disease.