Simulations of Cell Behavior on Substrates of Variegated Stiffness and Architecture - Computer Models in Biomechanics - page 34

3.4.1 Finite Element Setup for Cells on Posts

We use square cells having various areas, and model the posts as rigid circular discs
of radius a

1 µm constrained to move in the x 1 - x 2 plane. The displacement d i of
the discs is constrained by a spring of stiffness k (SPRING1 option in ABAQUS)
such that the force P i applied by the cell is P i =

=

kd i . We implement the adhesion
between the cell and the disc surfaces by employing the user-defined interface (UIN-
TER) option in ABAQUS, as before. Adhesions are allowed to form only where the
cell is in contact with the discs. We keep the post area fraction, defined as the ratio
of total surface area of the post-tops in contact with the cell to the total cell area, at
approximately 25 % to match the characteristics of the post-bed used by Saez et al.
( 2005 ).
As in the simulations for cells on flat gel substrates, we commence with stress
free, quiescent cells having neither stress fibers nor significant adhesions, and initi-
ate the computation with a single signal. After transient behavior, a steady state sets
in, with a constant stress state and stress fiber concentration and distribution at any
point in the cell, a constant focal adhesion concentration at any point on the top of a
post, and a constant deflection of the top of each post.

3.4.2 Simulation Results and Discussion

We first address simulations for a square cell of edge length L = 30 µm that covers

an 8 × 8 post array.

3.4.2.1 Focal Adhesion and Stress Fiber Distribution

We consider first highly compliant posts having a spring constant k = 2nN / µm. As

showninFig. 3.3 (a), a plot of the concentration of high affinity integrins in steady
state, focal adhesions form a circular ring on each post with little polarization, and
with relatively low densities of high affinity integrins. We interpret this to mean that
the size of focal adhesions on these posts is small, even though they completely
surround the tops of the posts. We implicate the very low stiffness of the posts
used in this case for this behavior. Such compliant posts offer little resistance to
stress fiber contractility, obviating the generation of tension in the stress fibers and
allowing much depolymerization. The resulting lack of intracellular machinery in
steady state is evident in the low stress fiber concentrations observed for this case,
and in the lack of curvature along the edge of the cell, as depicted in Fig. 3.3 (a). In
Fig. 3.4 (a) we show the distribution of stress fibers for this case, characterized by the
parameter Γ . A modest degree of alignment of stress fibers is evident in this figure,
but the significance of this is reduced by the fact that the stress fiber concentration
at each point in the cell is relatively low. We note that each post top is interacting
individually with the cell region that surrounds it, and there is little mechanical