Biology Reference
In-Depth Information
CHAPTER
26
Mechanical and Mathematical
Mod els of Morphogen esis
The purpose of this chapter is to illustrate methods of modelling morphogenesis, both phys-
ically and mathematically, and to provide examples of howmodelling has provided important,
counter-intuitive insights into how cellular events shape tissue-scale behaviour. It is not
intended to provide enough detail to turn a wet-lab biologist into a modeller (there are MSc
courses for that), but it may at least provide a biologist with enough insight into how models
work so that theyare better able toengagewithmodelling experts formore fruitful collaboration.
The examples all address morphogenesis of epithelia and endothelia. These present the
greatest challenge for modellers and therefore provide excellent illustrations of the tech-
niques that can be used. The challenge arises from the fact that 'epithelium' is a tissue-level
definition and it can be argued that a lone epithelial cell is not really 'epithelial' at all. 1 From
this, it follows that any successful attempt to model epithelial morphogenesis must pay close
attention to the relationships between neighbouring cells and the way that forces propagate
across the whole population: modelling isolated, independent entities are not enough.
PHYSICAL MODELS
The relatively simple nature of the forces that are thought to drive some kinds of epithelial
morphogenesis, for example, tensile forces generated by actin and myosin and compressive
resistance of matrix components, provided early encouragement for researchers to make
literally physical models.
One of the most informative amongst us used a combination of brass rods, short tubes,
pegs and elastic bands to model epithelial invagination in amphibian embryos. The model
was published by W.H. Lewis in 1947 2 but substantial credit for it must go to the physicist
Park Miller, who designed and constructed the apparatus in response to Lewis coming to
him with the developmental problem. It consisted of a series of brass rods that had short
pegs projecting axially from their ends, and two more pegs projecting outwards from oppo-
site sides of the middle of each rod ( Figure 26.1 a). The rods symbolized lateral cell-cell
boundaries in a cross section of the tissue, and were laid out parallel to one another on
a flat table. Short lengths of tube, of the type commonly used to connect a Bunsen burner
to a gas tap, ran between the centre pegs of adjacent rods and acted as compression elements
 
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