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

Shown in Fig. 2(b) is a plot of the average speed for the case where the adhesion
coefficient was dependent on bcell. The adhesion coefficient for fcell = 0.5, 0.75, 1, 1.5,
and 2 was multiplied by approximately 0.62, 0.83, 1, 1.29, and 1.54, respectively, in the
simulations. For the case where fcell was greater than one, the maximum cell speed
occurred at a higher degradation coefficient when βadh increased with bcell than when βadh
was constant. When fcell was less than one, the cell speed shifted in the direction towards
the lower degradation coefficients. These shifts were greater when fcell deviated further
from one. Since the adhesion coefficient increased with fcell, the cell was able to achieve
optimal migration speed at a lower ECM density for fcell > 1. Lower matrix densities
corresponded to higher values of α.
Another way to understand these shifts is by using the acquired data for the computed
tractions. Figure 2(c) shows the traction as a function of the degradation coefficient for
different cell aspect ratios. Note that this is for the case when the adhesion coefficient
was increased with bcell. For the different aspect ratios where βadh (and the traction) was
independent of bcell, the traction distributions corresponded with the case where fcell = 1.
For each aspect ratio, the cell required a certain level of traction in order to achieve the
maximum migration speed. This could either occur with a higher adhesion coefficient
(provided by an increase in bcell) and lower ECM density or vice versa.
Figure 3. Plot of the average cell speed as a function of the matrix degradation coefficient for an aspect
ratio of one and cell sizes of 25, 35, and 55 µm.
Figure 3 shows the simulation results of the average speed for spherical cells (fcell = 1)
with different sizes of bcell = 25, 35, and 55 µm. For this set of data, the adhesion
coefficient and traction increased with bcell. As a result, as the cell size increased, a lower
ECM density was sufficient to provide enough support for the cell to achieve its optimal
migration speed. Note that there was no change in the magnitude as the cell size was
altered. For the case where the adhesion coefficient was fixed at 600 nm 2 /molecule, the
cell speed exhibited no changes as the cell grew larger.
5. DISCUSSION
In this study, we investigated how cell shape can impact proteolysis-based cell
migration. Quantitative information is provided in terms of how both the aspect ratio of
the cell and the extent of degradation are required to determine the traction that the cell
exerts on its environment as well as the resulting migration speed. In general, the results
show that cells that are longer in the direction of migration do not need to secrete as
many MMPs and are able to move through a denser matrix. As the matrix becomes