Biology Reference
In-Depth Information
FIGURE 26.10
Typical finite element models represent cells as a series of triangles (in this diagram, the cell
membranes are indicated by thicker lines).
to living cells at all. As in Cellular Potts models, triangles are associated with attributes (some
direct, such as their shape; others, treated as 'energy' terms, are more abstract). Again, these
energy terms are brought together in a Hamiltonian function. The main difference between
the models is that while Cellular Potts models operate on very local scales, common finite
element models evolve to minimize
global
energy.
An interesting example of a finite element approach to understanding basic epithelial
mechanics has come from a very close collaboration between wet-lab experiments and
computer simulation.
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The hypothesis being addressed was that forces at cell boundaries
dominate the forces within an epithelium (and that modelling boundaries would only there-
fore be a 'safe' thing to do). The experimental system used was the early embryo of
Drosophila
melanogaster
, during dorsal closure (Chapter 17). At this stage, the outside of the embryo is
a simple, easily-observed epithelium.
The computer model used finite elements to represent a two-dimensional patch of tightly
packed cells, the patch being constrained in a rectangular 'container' to which the cells at the
edge connected. The cells were polygonal in plan view, similar to those in
Figure 26.10
. All
versions of the computer model included 'energy' terms, representing tension along cell
interfaces, and area constraints. Some versions of the model also included internal viscosities
and tensions, or visco-elastic 'rods' along the cell boundaries. The model would be allowed to
evolve to stability, then a small 'hole'
d
smaller than a cell
d
would be created at a random
place in the epithelium. The hole could carry neither tension nor compression, so would alter
the balance of forces near it; the resulting movements of all parts of the sheet would then be
studied.
The wet-lab system used careful observation of cells before and after a high-powered laser
was used to 'shoot' a small hole right through the epithelial sheet, either in the middle of
a cell or near, or at, the boundary. The predictions of the computer models run with different
