Biomedical Engineering Reference
In-Depth Information
Figure 1.8.
Timelapse of a symmetry-breaking event (white arrow head) preceding
actin-based movement of a bead. Actin is marked with a fluorophore and the samples
are observed in epifluorescence. The first three images were taken 21, 24, and 40
minutes after start of incubation. The last image shows the developed comet. Bar,
10
μ
m. Images are taken from [39]. (Copyright 2005 National Academy of Sciences,
U.S.A.).
The main conclusions are similar to the one obtained before. For instance
the symmetry-breaking onset time is again proportional to the sphere radius,
since
e
0
,
e
2
and
e
∗
are. This expectation is indeed born out by experiment
[40]. Furthermore, if the friction is very high, the spherical steady state can
be reached much before symmetry is actually broken. This will happen in
particular if the gel is dense, an expectation also born out by experiment.
There are several other implicit simplifications in the above presentation:
we have considered only one elastic modulus, without specifying whether it
corresponds to compression or shear or a combination of them. A proper
description is possible by the use of a covariant description of the gel [37]. Ac-
tually, the very geometry of the polymerization/cross-linking process implies
that the gel should be anisotropic as well, but keeping this feature adds in
complexity without bringing further understanding to the question.
A more important limitation comes from the hidden assumption that the
gel density is constant throughout the gel and that all depolymerization is lo-
cated at its external surface. In fact, it is known that the gel density decreases
exponentially in a
Listeria
comet, over length scales comparable to the comet
total length (i.e., several tens of microns [19]). One could be tempted to argue
that this length scale is much larger than the one we discuss here and forget
about this slow bulk depolymerization. It would, however, be a wrong argu-
