Biomedical Engineering Reference
In-Depth Information
between Dicty and other chemotaxing cells with regard to the exact role of
differing connector elements - for example, cdc42 is important in neutrophils
and fibroblasts to sharply define the pseudopod [49], but Dicty has no obvious
cdc42 homologue. Anyone who wishes to make a model of this process would
be well advised to keep up with the extremely rapidly evolving experimental
data, as relevant information arrives every month.
As mentioned earlier, ecient chemotaxis requires not only the formation
of a pseudopod in the correct direction but the active suppression of later
pseudopods that would otherwise form. This is accomplished at least partially
by myosin reinforcement of the actin cortex, preventing cell extension. Myosin
attraction to the cortex is governed by phosphorylation, which appears to rely
on internal cAMP-activating protein kinase A (PKA). A different isoform of
myosin acts not as a stiffener but instead as an active motor to pull the rear of
the cell forward. Mutants with various changes in the differing myosins have,
as expected, a variety of motility defects.
How all these pieces work together to finally determine the sequence of
cell shapes is far from being solved. There have been some attempts to write
down equations for actin-based motility of other types of cells [50, 51], but
these are very phenomenological and need extensive development and testing.
One requirement for progress is an understanding of the forces arising from
the lipid membrane itself. Historically, membrane dynamics has been stud-
ied in liposomes, i.e., protein-free vesicles surrounded by lipid double layers.
These systems can undergo large shape deformations (such as vesicle budding)
and there is an ongoing effort to create computational tools that can handle
what turns out to be a complicated free surface problem coupling fluid flow
to membrane elasticity. A very promising direction is afforded by adapting
the phase-field approach, which now dominates computational studies of free
surface problems during thermodynamic phase changes [52, 53, 54, 55], to this
problem.
The idea behind the phase-field method is the replacement of the sharp
interface (in this case, the cell membrane) by a diffuse self-consistently de-
termined interface in an auxiliary “phase” field
φ
. The creation of such a
boundary is accomplished by a double well potential
V
(
φ
)=
V
0
φ
2
1
2
−
The energy associated with the interface is encoded by adding terms to this
free energy that depend on the gradient of
φ
. In its original application, the
only such term was surface energy. For membranes, on the other hand, the
most important term is the bending energy contribution
2
B
d
2
sκ
2
, where
κ
is the local mean curvature and
B
is a bending modulus. Misbah has shown
how to modify the phase-field model to include bending energies, and has
applied his ideas to the deformations of vesicles due to imposed flow [56].
To our knowledge, no one has yet tried using this natural approach to
model and simulate cell shape dynamics. One diculty, of course, is that the
1
