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4. The bulls-eye target of bands can reduce its energy by deforming
into a hollow tube, as shown in Fig. 5.4B, C. This shape change would
occur because it reduces the area of contact between adjacent bands.
But, because of its elasticity, the epithelium resists out-of-plane bend-
ing. Its ¬nal equilibrium shape, therefore, corresponds to the mini-
mum of the total energy, which incorporates both the adhesive and
elastic contributions.
5. The result of the interplay of forces described above is a ˜˜leg”
consisting of a tubular epithelium arranged in a sequence of bands.
The shape of this tube represents a compromise between an elongate
shape that minimizes contact between bands (that is, maximizes the
total work of adhesion) and a squat shape that minimizes the strain in
the hypodermis (Fig. 5.5). The adhesion energy is expressed in terms
of the interfacial energy de¬ned in Eq. 5.2. Since no a priori infor-
mation exists on the number of adhesion bands in the imaginal disc,
the authors assumed to be a function varying continuously along
the developing leg segment. The elastic energy can be obtained by
adding the contributions for each band using the curvature energy
given in Eq. 2.5. Again, instead of a ¬nite number of bands, a con-
tinuous approximation was used. Minimization of the total energy
predicted that each arthropod leg segment has a cylindrical shape of
length L and radius R, and led to an experimentally testable relation-
ship between these quantities,
1 R
= a + b. (5.6)

Balance of
Lower adhesion energy, Lower strain energy,
adhesion and strain
greater strain energy greater adhesion energy
Fig. 5.5 Shaping of a leg segment
in the Mittenthal“Mazo model.
The middle panel represents a
compromise between maximizing
the work of adhesion and
minimizing the strain. (After
Mittenthal and Mazo, 1983.)

Here a and b are constants. This ˜˜scaling relationship” between L and
R provides a relatively good ¬t to the measurements on the different
leg segments in Drosophila.
As instructive as it is, the Mittenthal--Mazo model clearly neglects
a number of considerations required for a satisfactory understand-
ing of epithelial morphogenesis. In the model the imaginal disc is
assumed to consist of bands of cells with differential adhesive prop-
erties, but the origin of this differential adhesion is not addressed.
The model is based solely on the idea that the balance between strain
and adhesion can determine the shape of the epithelium, which is
treated as a continuous medium. Thus it ignores the possibility of
active and passive shape changes of individual cells.
The following detailed description of certain features of gastrulat-
ion will indicate why more elaborate models of epithelial morphogen-
esis, which explicitly address some of the above issues, are required.

The formation and rearrangement of distinct tissue layers during the
establishment of the body plan in the early development of animals
involves about half a dozen distinct kinds of cell behavior, only a sub-
set of which occur in the embryo of any given species. Each set of
movements that constitute gastrulation depends on a prior ˜˜pattern
formation” event that designates a subpopulation of the blastula™s
cells as having a distinctive character relative to the others (see Chap-
ter 7). Often, but not always, the distinctive character is an adhesive
differential whereby the subpopulation is either more or less cohe-
sive than the originating blastula cells. The pattern-formation process
that brings differentially adhesive cells into a speci¬c spatial arrange-
ment in a pregastrula does not, in principle, require anything beyond
straightforward physics. Even if these cells arise in a purely random
fashion, cell sorting alone can cause them to localize in a single re-
gion of the embryo. This, indeed, is how the arrangement of cells that
precedes morphogenesis is generated in the model of Mittenthal and
Mazo (1983) discussed above. Gravity, another purely physical force,
can also lead indirectly to a nonuniform pregastrulation arrangement
of different cell subpopulations (Allaerts, 1991). In the Xenopus egg,
for example, the sedimentation of dense yolk platelets creates a gra-
dient that causes the cells that contain these platelets after cleavage
(the ˜˜vegetal pole” cells) to have physical and biochemical properties
that differ from the (˜˜animal pole”) cells that do not contain them
(Gerhart et al., 1981; Neff et al., 1983, 1984) (see Chapter 7).
In most embryos, however, other pattern-forming mechanisms,
some depending on the spatially asymmetric introduction of mole-
cules into the forming egg by maternal tissues and others on the self-
organizing properties of cell aggregates (based on their biochemical
activities and ability to transmit signals; see Chapter 7), will guaran-
tee that the cells of the late blastula are heterogeneous.

Fig. 5.6 Cell movements and
tissue rearrangements involved in
different forms of gastrulation.
Most organisms employ a
combination of one or more of
these basic processes.



The basic categories of gastrulation-related cell rearrangements
all follow from these initial regional differences in cell phenotype
(Fig. 5.6). In invagination, a hollow single-layered embryo develops one
or two additional layers by the folding inward of a portion of its
surface under the guidance of a differentiated subpopulation of cells
with distinct adhesive and/or motile properties. In delamination, a solid
embryo that has thus far developed into a form with two distinct but
attached cell layers acquires an internal space (shown in brown) by
physical separation of the layers. In ingression, cells in a subpopulation
having changed adhesive and/or motile properties move individually
or in groups into the interior of a hollow embryo. In epiboly, one of
the two embryo cell layers comes to partially envelop the other by
actively spreading around it. In involution, cells move under the edge
of an existing tissue layer, thereby forming a new layer.
Once gastrulation is under way, the layers of the now multilay-
ered embryo are assigned speci¬c names: the ˜˜ectoderm” refers to the
outermost layer and the ˜˜endoderm” to the innermost. In diploblastic
forms such as hydra and jelly ¬sh, these two layers give rise to all sub-
sequent differentiated tissues of the body. In vertebrates, for example,
the ectoderm gives rise to the skin and nervous tissue and the endo-
derm gives rise to the lining of the intestine and its derivatives, such
as the liver and pancreas. For triploblastic forms such as sea urchins
and humans the movements of gastrulation result in a third layer,
interpolated between the other two. This is called the ˜˜mesoderm,”
and in vertebrates is ultimately the source of the ˜˜middle” tissues of
the body -- the skeleton, blood and muscles.
Convergence and extension amount to a cell rearrangement, utilized
in the gastrulation of some species, that encompasses several distinct
cell activities. It involves the simultaneous narrowing and elonga-
tion of a tissue primordium, such as that initiated by the process

of invagination in sea urchin or amphibian embryos. Later in this
chapter we will present a physical interpretation of this widespread
but somewhat puzzling (from both a cell-biological and a physical
standpoint) tissue rearrangement.

Gastrulation in the sea urchin
Gastrulation has been extensively studied in the sea urchin, an inver-
tebrate from the wider group known as echinoderms (Hardin, 1996;
Ettensohn, 1999). The advantages of using this organism stem from
the easy availability of experimental material (thousands of eggs are
released from single females on stimulation and can be fertilized on
demand) and the transparency of the embryo through many succes-
sive stages, which allows for easy visual access. In the early sea urchin
blastula, at about the 60-cell stage, various pattern-forming events, in-
volving multiple direct (rather than long-range) cell--cell interactions
cued by preexisting molecular nonuniformities in the uncleaved zy-
gote, lead to the generation (not irreversible at this point) of radially
symmetric tiers of cells with distinct cell fates (Fig. 5.7). By the 128-cell
stage the embryo has formed a single-layered blastula with an in-
ternal cavity, the blastocoel (see Chapter 2). Several cell cycles later
(by the ninth or tenth cycle, depending on the species) the blastula
hatches out of its con¬ning fertilization envelope and, as a hollow
ball consisting of about 1000 cells, is ready to begin gastrulation.
The multiple cell types arising from these local interactions repre-
sent alternative states of gene regulation produced by autoregulatory
networks of transcription factors like those discussed in Chapter 3
(Davidson, E. H., 2001; Davidson, E. H., et al., 2002; Oliveri et al., 2002).
Once hatched from its fertilization envelope, the spherical blas-
tula undergoes a series of morphological changes comprising gastru-
lation. First the cells of its base, or ˜˜vegetal,” end begin to thicken
and ¬‚atten. Next, as a result of reduced adhesion to neighboring cells
and increased af¬nity for the basal lamina lining the blastocoel (Wes-
sel and McClay, 1987), a small population of cells at the center of
this vegetal plate, the primary mesenchyme cells, begin to ingress
into the blastocoel and extend long ¬lopodia, which attach to the
inner surface of the blastula. The branched structures formed by the
primary mesenchyme cells, their ¬lopodia, and their secreted extra-
cellular matrix eventually become the skeleton of the sea urchin larva
(Fig. 5.7).
The remaining cells of the vegetal plate then rearrange to ¬ll in
the gaps left by the ingressing primary mesenchyme (Fig. 5.7). A series
of biosynthetic changes in this region cause both the inner and outer
layers of the extracellular matrix to change their physical properties
and, in consequence, the plate invaginates about one-fourth to one-
half the way into the blastocoel, by a process that has been likened
to the thermal bending of a bimetallic strip (Lane et al., 1993).
In the following sections we describe simpli¬ed quantitative mod-
els for aspects of sea urchin gastrulation. Our objective is to illus-
trate how elementary physical considerations can lead to the observed
complex cellular pattern. The combination of the various models in

Animal pole 8 cells
4 cells
16 cells

32 cells
Vegetal pole





Mouth Mouth




Large micromeres
Small micromeres

Fig. 5.7 Gastrulation in the sea urchin embryo, leading to the formation of the
swimming larva, termed a “pluteus.” The cell and tissue rearrangements that occur at
the various stages are described in the text. Cells indicated by particular colors at early
stages map into structures indicated by the same colors, at later stages. The lower box
depicts a “fate map” in which the origin of tissues in the larva are traced back to speci¬c
cell populations at the 64-cell stage. (After Wolpert, 2002.)

conjunction with additional experimental details should eventually


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