ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

geometry of the cell and ECM degradation can independently impact the movement of
cells. In this study, we examined a model that follows the approach of Harjanto and
Zaman [6], and investigated how cell shape and size can independently influence
mesenchymal cell migration. Focal adhesion mechanical properties that were
independent or dependent on cell shape were considered.
3. METHODS
The geometry of the cell was modeled as an ellipsoid. The semi-axis of the cell that was
aligned with the direction of motion was given by bcell and acell was used to refer to the
semi-axes in the transverse directions. Since the model was axisymmetric with respect
to the centerline of the cell (r = 0) that was parallel to the direction of cell motion (zdirection),
only half of an ellipse was constructed in COMSOL Multiphysics 4.2.
Rotating this 2D slice with respect to r = 0 would result in the ellipsoid. A schematic of
the different geometries is provided in Fig. 1.
Figure 1. Schematic of the cell geometry and traction distribution for the case where
(a) fcell = bcell/acell = 2 or (b) fcell = 0.5.
The expressions for the cell–ECM traction and drag forces applied on the surface of the
cell as well as the equation that governed the degradation of the matrix followed the
approach we described earlier in [9]. For the present study, we computed an adhesion
coefficient of βadh = 600 nm 2 /molecule by using 0.6 as the ratio of traction to substrate
stiffness [10] and an average bound receptor cell surface concentration of 1,000
molecule/µm 2 . The initial receptor and substrate cell surface concentrations were set at
10,000 molecule/µm 2 in the simulations [11], and the Young’s modulus of the cell was
1 kPa. All of the other parameters were the same as those given in our earlier paper [9].
Simulations were used to study the effects of the cell shape and size on cell migration as
the ECM degradation coefficient (α) was varied. The aspect ratio of the cell,
fcell = bcell/acell, was used to characterize the cell shape, and the values that used were
fcell = 0.5, 0.75, 1, 1.5, and 2. In this set of simulations, the cross-sectional area of the
cell was kept constant and equal to that where acell = bcell = 25 µm, which was
1,963.5 µm 2 . The traction was normal to the cell surface in each case [10]. A schematic
of the traction distributions for different cell shapes can be seen in Fig. 1. It was
assumed that βadh = 600 nm 2 /molecule for fcell = 1, and the adhesion coefficient was
increased with bcell using the data reported by Rape, et al. where it was shown that cell
shape influences adhesions and tractions [12]. For comparison purposes, simulations
were also conducted for the case where the adhesion coefficient was fixed at