Biology Reference
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displaced by any inwards movement of a fjord will be contact inhibited and will therefore
pay little or no attention to chemotactic gradients. They will therefore not oppose any
displacement they suffer away from the centre of the island into a 'headland' next to the fjord
(
Figure 26.9
d). Furthermore, while cells right at the tip of the fjord of the bay will still push
inwards, those on the side will now push at an angle that is a compromise between pushing
towards the centre of the island and pushing towards the midline of the headland, which will
be a closer source of chemoattractant (
Figure 26.9
d). The fjord therefore both widens and
deepens, cells deeper inside the island offering little resistance to being displaced outwards
because they are contact inhibited and respond to pressures but not chemotactic gradients.
The headlands tend to narrow and, because cells cannot pile up on one another, the head-
lands become longer. This amplifies the distortion of the local chemotactic gradient, and
the fjords deepen and the headlands become long peninsulas. The same process happening
along the edge of a peninsula creates side-branches, and the positive chemotaxis tends to join
these up to make a plexus.
Merks and colleagues
19
went on to test the implication of their model in a real biological
system: culture of endothelia from mouse allantois. Normally, they make a plexus but, if the
experimenters inhibited the function of VE-cadherin, a cell-adhesion molecule assumed by
them to mediate detection of contact and thus contract inhibition, the cells simply made
islands. This is not definitive proof of the theory (VE-cadherin does many things and its
loss may have changed the cells in many different ways), but it is at least suggestive. It is
always difficult to prove something just by inhibiting function of molecules, and more satis-
factory evidence will probably come from synthetic biological approaches that place engin-
eered features in cells that do not already have them (see Chapter 27).
The important impact of this exercise in modelling is that it suggests something counter-
intuitive. Most cell biologists find it natural to assume that contact inhibition of locomotion
tends to resist the formation of invasive branches, while freedom from contact inhibition
results in invasion. Many classic papers on cancer metastasis, for example, make this
assumption,
20
and even recent papers refer to the finding that molecules that promote contact
inhibition also promote invasion, as a 'paradox'.
21
In systems that are positively auto-
chemotactic, this model suggests that the opposite is the case and that functional contact in-
hibition drives invasive ramification. This is unlikely to be a universal feature of branching
systems (endothelia are currently thought to be unusual in having mutual chemotactic attrac-
tion: epithelial branches tend to avoid each other rather than converge and connect as endo-
thelia do). Nevertheless, the research illustrates howmodelling can correct a 'common-sense'
misapprehension.
Finite Element Models
Superficially, finite element models have much in common with Cellular Potts models.
Cells are again considered to be composed of a plurality of underlying, internally
homogenous pieces. In finite element molecules, these are usually triangles rather than
grid squares, and the triangles that represent a given cell typically all meet at its centre
(
Figure 26.10
), although they do not have to; indeed, when the model is intended to operate
only at tissue scales and cell behaviour is irrelevant (as it is for some theories of morphogen-
esis that rely on tissue-level mechanics) there may not be a need for the elements to conform
