Biology Reference
In-Depth Information
traces of detergent) greatly inhibits branching.
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The pressure difference that drives viscous
fingering can come from elevated pressure in the low-viscosity fluid or from reduced pres-
sure in the surrounding high-viscosity one (place a drop of glycerol between two microscope
slides, press them together to spread the drop into a disc, then peel them apart: as the fluid
pressure drops as you pull the slides apart, air will make viscous fingers as it invades). If (and
this is a big 'if') the action of surface tension in organ culture is to pressurize the middle of the
thin organ rudiment and to spread the outside out, lowering its internal pressure conditions
would be conducive to viscous fingering, assuming of course that the epithelium has a lower
effective viscosity than its surrounding matrix-rich mesenchyme.
Other arguments weigh against the idea that epithelial branching happens by viscous
fingering. The first is the need for pressure. The obvious biological source of this is cell prolif-
eration, a feature of mammalian branching epithelia (Chapter 19). The problem is that when
proliferation is blocked in salivary gland epithelium, branching still takes place to produce
a very small, but still branched, 'bonsai' salivary tree.
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This suggests that internal pressure
is not a driving force for branching, although the experiment is not completely clear-cut since
it blocked DNA synthesis but not necessarily cell growth. The second argument against
viscous fingering is the tendency for the cells at the tips of actively branching epithelia to
show specializations
d
of gene expression,
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e
12
of proliferation rate
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and of cytoskeletal
organization.
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The essence of 'pure' viscous fingering is that it requires no special local activ-
ities; the process is so simple that an unstructured liquid, or even a gas, can be used to
perform it. The presence of specialization of both cell state and behaviour at branching
tips suggests that something else, more complex, must be going on such as the possibilities
discussed in Chapter 19.
Whatever the current balance of these arguments, it is probably a mistake to ask whether
something is mediated by biochemical systems
or
biophysical ones, since morphogenesis is
almost always likely to rely on both.
COM
PUTER MODELS OF EPITHELIAL MORPHOGEN
ESIS
Computer models of epithelial behaviour fall into three main classes according to the way
that cellular properties are encoded for mathematical manipulation.
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These classes are: (1)
agent-based models, (2) cellular Potts models, and (3) finite element models.
Explicitly Mechanical, Agent-Based Models
In typical agent-based models, different cells are treated as independent objects ('agents')
and properties change discontinuously across the epithelium, belonging as they do to indi-
vidual cells. Mutual cell boundaries are usually represented by a series of short, straight
segments with the properties of springs, the segments being connected to each other at
vertices so that each cell is completely surrounded (
Figure 26.4
). The vertices do not corre-
spond exactly to any underlying biological structure, but are just a computing convenience
so that the membrane can be modelled as a series of straight lines. Each cell has a notional
internal pressure that pushes outwards at each vertex point. This pressure is determined
by the difference between a cell's actual area (in a two-dimensional model of the epithelial
