Invagination and Evagination: The Making and Shaping of Folds and Tubes - Mechanisms of Morphogenesis - page 204

FIGURE 18.2 Bending of a cell sheet of finite thickness (t) requires cells, if they are not to pull apart, to change
from being rectangular in outline to being wedge-shaped with (for this direction of bend) constricted apices and
wide basal surfaces.

becoming reduced and their basal diameter expanded ( Figure 18.2 , bottom). At one level, this
is just a matter of geometry. For a cell sheet of thickness t invaginating to form a symmetrical
depression, the area of the basal surface of a cell must exceed that of the apical by a factor of
[(r t) 2 /r 2 ], where r is the radius of the apical curve, if cells are not to pull apart. For a 'typical'

epithelium 10 m m thick, the apical surface of which has invaginated axially to form a 30 m m
radius depression, the difference between apical and basal surface areas will be of the order
of 75 percent (for an orthogonal invagination, in which cells become wedge-shaped across
one dimension only, the difference in area would be 33 percent for the same radius of
curvature).
This difference in apical and basal areas could be forced by the laws of geometry on to an
epithelial sheet already being bent passively by an outside force. Alternatively, if epithelial
cells generated apical constriction and/or basal expansion actively, by their own internal
mechanisms, this would force the sheet to invaginate; this fact was realized over a century
ago, and was proposed as a local mechanism for large-scale epithelial shape change. 1,2 Given
the concentration of adhesive junctions, actin microfilaments and contractile myosin-actin
complexes at the apical end of a typical epithelial cell, active constriction of the apex (rather
than active expansion of the basal side) seems the most plausible mechanism for driving
invagination. Furthermore, modelling of this mechanism, using an analogue system of
rods and elastic bands, confirms its potential. 2

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