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separation of immiscible ¬‚uids and have been shown to follow that
process quantitatively as well (Beysens et al., 2000). Similar experi-
ments have been performed with numerous pairs of different em-
bryonic tissues (Armstrong, 1989; Foty et al., 1996). In each case the
sorted pattern corresponded to a con¬guration in which the more
cohesive tissue was surrounded by the less cohesive one. The cohe-
sivity of many of these tissues has been quanti¬ed by measuring
their surface tension (i.e., the interfacial tension with the surround-
ing tissue-culture medium) with a speci¬cally designed parallel plate
tensiometer (Foty et al., 1996). (See Chapter 2 for the relation between
surface tension and cohesivity.)
The sorted patterns exhibit a hierarchical relationship consistent
with the values of the tissue surface tensions (Fig. 4.6) as predicted by
the DAH. The sorting of two cell populations that are identical except
for having been genetically manipulated to express differing num-
bers of N-cadherin molecules on their surfaces (as their only CAMs)
(Fig. 4.7) illustrates how a 50% difference in the quantitative expres-
sion of cell-surface adhesive molecules leads to a dramatic difference
in tissue behavior -- i.e., the establishment of immiscible tissue lay-
ers. Cell sorting as a liquid-like phenomenon is thus readily studied
in vitro. Can we use this physical phenomenon to extract useful quan-
titative insights into cell behaviors that are relevant to early develop-
mental processes such as the Drosophila oocyte--follicle-cell interaction
described above?
In the state of lowest energy in a sorting experiment, cells with
the higher number of CAMs must be surrounded by adhesively similar
cells, because such a con¬guration allows for the maximum number
of CAM bonds to be formed (Fig. 4.8). To reach this state, cells in
96 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO




Fig. 4.8 Schematic illustration of adhesion in a mixture of two cell populations with
differential expression of homophilic CAMs. The small bars ending in small circles
symbolize CAMs. To minimize the con¬gurational energy, high expressers tend to group
together to bene¬t from all available bonds. The arrangement on the left has lower
energy than that on the right. Compare with Fig. 4.7.




the initial random mixture of the two cell types must move around
until they ¬nd their respective partners. This motion is driven by
cytoskeletal rearrangement powered by metabolic energy, in contrast
with the motion of liquid particles (which is driven by thermal ¬‚uc-
tuations, see Chapter 2). The surprising outcome is that this biologi-
cal mechanism, despite the complexity of the underlying machinery,
drives the cellular system to its lowest energy state, as characterized
by purely physical parameters such as surface and interfacial ten-
sions. For cells to move, they have to break adhesive bonds with their
immediate neighbors and reform bonds as they ¬nd new partners.
This amounts to a frictional force experienced by the cells. The cor-
responding friction coef¬cient, µ, is a characteristic property of the
cellular environment, which relates the velocity v of the cell™s motion
to the force F under which the motion takes place (see Chapter 1),
µ = F/v. In the sorting process this force is generated by the energy
difference between the sorted and unsorted con¬gurations. Using di-
mensional analysis (as introduced in Chapter 1), and the Bell model,
we can now relate µ, a physical parameter whose value can be experi-
mentally determined, to important variables that characterize the
biological state of cells in an aggregate and which are all but impos-
sible to measure directly (Forgacs et al., 1998).
From its de¬nition, the unit of µ is N s/m. The more CAMs a cell
has on its surface the stronger is its tendency to adhere to its neigh-
bors and the more dif¬cult it will be for it to arrive at a lower energy
state by changing its neighbors. Thus µ ∝ N , N being the number
of CAMs per unit area of the membrane. The stronger the adhesive
bonds the cell forms the more dif¬cult it will be to break them, so
we have also µ ∝ E , E being the energy of a single bond. The longer
these bonds last the more they hinder the motion of a cell; hence
furthermore µ ∝ „ , where „ is the lifetime of a bond (see the Bell
equation, Eq. 4.11). Combining the above observations, we arrive at
4 CELL ADHESION, COMPARTMENTALIZATION, AND LUMEN FORMATION 97


µ ∝ NE„ . The units of the three quantities on the right-hand side of
this relation are, respectively, m’2 , J = N m, and seconds; thus di-
mensional analysis suggests that in the combination NE„ we have
taken into account all the relevant parameters that may in¬‚uence
the friction coef¬cient, and so µ = aNE„ where a is a dimensionless
constant.
The Bell model, through Eq. 4.10, allows us to ¬x the value of a,
since a must be related to the fraction of receptors that are bound, the
only ones we need to consider in the above analysis (see also Howard,
2001). A similar dimensional analysis for tissue surface tension leads
to σ = bNE, where b is a constant related to the difference in the frac-
tion of bound CAMs between cells at the surface and in the bulk of
the tissue (Forgacs et al., 1998). In relation to the Drosophila oocyte--
follicle-cell interaction described earlier in this chapter, we now have
predictive criteria, in terms of measurable parameters such as the
relative number of DE-cadherin molecules on the two cell types, that
could rigorously establish whether the observed terminal cell arrange-
ment is fully accounted for by differential adhesion.
In the case of sorting involving the two genetically engineered cell
populations shown in Fig. 4.7, the surface concentrations of receptors
are not equal, N 1 = N 2 , and therefore µ is not uniform across the
aggregate. The time evolution of the sorting pattern in this case will
be governed by µ = a max(N 1 , N 2 ) E „ , that is, by the more cohesive
cells.
Surface tensions and friction coef¬cients have been determined
experimentally for a number of natural tissue types (Foty et al., 1994;
1996) and tumors (Foty and Steinberg, 1997; Steinberg and Foty, 1997;
Forgacs et al., 1998), as well as for aggregates of genetically trans-
formed cells with varying levels of cadherin or integrin expression
(Ryan et al., 2001; Robinson et al., 2003; Foty and Steinberg, 2005).
Sorting experiments (Figs. 4.5--4.7) have been performed to verify the
consistency of the obtained surface tension values (Foty et al., 1996;
Beysens et al., 2000). Using the results of dimensional analysis in con-
junction with physical models, the measured tensions and friction
constants provide quantitative information on such molecular param-
eters as the lifetime of the bonds between CAMs and the energy of
these bonds. Since this type of measurement involves large numbers
of cells the results obtained re¬‚ect conditions comparable to those
in tissues. Therefore when compared with single molecular studies,
in which typically CAMs are considered under non-physiological con-
ditions, the signi¬cance of factors such as the cytoskeleton or the
interaction between CAMs on the same cell can be assessed.


Perspective
Cell adhesion is the de¬ning characteristic of multicellular organisms
and the nature and strength of cell bonding is a major determinant
98 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


of tissue properties. Cells in embryos have the unique feature of be-
ing bound to each other by forces that are neither so strong as to
resist relative movement (as in mature organisms) or so weak as to
disperse, and they therefore constitute tissues that behave like vis-
coelastic materials. Physical models can account for many aspects of
the reversible cell--cell interactions seen in developing systems, as well
as for certain self-organizing consequences of differential adhesion
such as boundary formation via sorting, engulfment behavior, and
the internal spaces (i.e., lumens) within tissues containing polarized
cells.
Chapter 5




Epithelial morphogenesis:
gastrulation and neurulation

In the previous chapters we have followed the process of rapid cell
divisions in the early embryo until the formation of the blastula, ini-
tially a solid mass of cells poised to develop into the structurally and
functionally differentiated organism. Adhesive differentials along the
surfaces of individual cells of the early blastula, the blastomeres, drive
the formation of spaces or lumens (see Fig. 4.2) within the embryos of
most species. As a result, the typical blastula acquires a geometrically
simple closed spheroidal structure that consists of a single cell layer
enclosing the hollow blastocoel.
By the time the blastula has developed, the embryo already con-
tains, or begins to generate, a number of differentiated cell types (see
Chapter 3). Insofar as these cell types have or acquire distinct physi-
cal (adhesive, contractile) properties, compartmentalization or other
forms of regional segregation start taking place. This regionalization,
accompanied by the collective movement of the resulting cell masses,
gives rise in most cases to embryos consisting of two major cell layers,
referred to as ˜˜germ layers,” along with some subsidiary populations
of cells.
The various modes of cell rearrangement by which a solid or
single-layered blastula becomes multilayered are known collectively
as gastrulation. In ˜˜diploblastic” animals, such as sponges and coelen-
terates (hydra, jelly¬sh), gastrulation is complete when the two germ
layers, the outer ectoderm, and inner endoderm, are established. Fur-
ther cell specialization occurs within these two main layers and any
subsidiary cell populations. For other, ˜˜triploblastic,” animals such
as insects, echinoderms (e.g., sea urchins, star¬sh), and vertebrates
(e.g., frogs, humans), the initial binary segregation results in a ˜˜pre-
gastrula,” which sets the stage for the next phase of the developmen-
tal process, establishment of a third germ layer, the mesoderm, and,
in those triploblasts that contain one, the primordium of the axial
skeleton (the vertebral column). This later set of processes is often
referred to, narrowly, as gastrulation, but we will use the term to en-
compass all the cell and tissue movements leading to both two and
three layers. Gastrulation is followed, in species with an axial ner-
vous system (e.g., vertebrates, the subphylum to which humans and
100 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


other mammals belong), by neurulation, the formation of the tubular
rudiment of the nerve cord.
Both gastrulation and neurulation involve the folding and reshap-
ing of epithelial sheets. During gastrulation the blastula is deformed
and reorganized in a sequence of steps, often involving the narrow-
ing and elongation of internal and external embryonic tissues. (This
latter set of tissue-reshaping movements is termed ˜˜convergence and
extension.”) The resulting forms have a central ˜˜primary” axis. In neu-
rulation, the central zone of the gastrula™s surface ectoderm forms an
elongated ˜˜neural tube” that parallels the primary axis. Although the
tissue movements and rearrangements underlying gastrulation and
neurulation lead to dramatically different outcomes, from a physical
standpoint both sets of processes employ similar mechanisms and are
subject to similar constraints.


Physical properties of epithelia
In Chapter 4 we described the physical bases of adhesion and the
consequences of differential adhesion in epithelioid tissues, that is,
tissues made up of cells in direct contact with one another via
their membrane-adhesion proteins or associated surface coats (gly-
cocalyces). This chapter is concerned with a subset of these tissues,
referred to as ˜˜epithelia.” In these tissues cells still make direct con-
tact with one another, but only along their lateral surfaces. The cells
are therefore ˜˜polarized.” The apical and basal surfaces of such cells
do not adhere to adjacent cells of the same type but rather to extra-
cellular matrices known as basal laminae (see Fig. 4.1) or to other cell
types, tissue ¬‚uids, or acellular matrices. For example, the outer sur-
faces of many blastulae are in contact with specialized matrices called
egg envelopes or ˜˜jelly coats” (Dumont and Brummett, 1985), and
their inner surfaces are in contact with blastocoelic ¬‚uid. By express-
ing adhesive proteins in a polar fashion (that is, on some portions
of the cells but not others), epithelioid tissues can generate internal
spaces (lumens) or, under appropriate conditions, form themselves
into ˜˜two-dimensional” epithelial cell sheets. The apical and basal
surfaces of epithelia are sometimes referred to as ˜˜free surfaces.” (In
physics this term is usually reserved for surfaces in contact with the
vacuum, something never encountered in biology).
As we discussed earlier, the fact that attachments between embry-
onic epithelioid cells are weak and short-lived causes the tissues they
comprise to behave like liquids. This is the case for many tissues in
the embryo, including planar epithelia. The basal laminae underlying
many epithelia, however, are stiff and have decided elastic properties.
The epithelia of early embryos and developing organs are therefore
unique in that they behave like liquids in the plane but like elastic
sheets when deformed out of the plane. This unusual combination
of properties largely accounts for the ability of these tissue sheets to
undergo a wide range of morphological changes, including bending,
5 EPITHELIAL MORPHOGENESIS: GASTRULATION AND NEURULATION 101


eversion, invagination, and placode, cyst, and tubule formation
(Gierer, 1977; Mittenthal and Mazo, 1983; Newman 1998a; see below).
Epithelial folding is perhaps the most typical morphogenetic phe-
nomenon in early development, giving rise to the complex shapes
and forms of the early embryo and eventually the organs (Gierer,
1977). The parameter that quanti¬es the extent of folding of a sheet
is its local average curvature C, introduced in Chapter 2 (see the text
following Eq. 2.2). Bending a sheet from its equilibrium con¬gura-
tion (determined by its spontaneous curvature C0 ) requires energy,
the bending or curvature energy (see Eq. 2.5). Thus the initiation of
gastrulation and neurulation, which involve epithelial folding at pre-
cise locations along the blastula and gastrula, imply alterations in
speci¬c physical properties of cells at those locations relative to their
neighbors.
It is clear that the physical characteristics of individual cells (e.g.,
spontaneous elongation or ¬‚attening) are determined by the molec-
ular content and organization of their cytoplasm and microenviron-
ment. The molecular composition of cells is the consequence of dif-
ferential gene expression, which itself is in¬‚uenced by many factors
(e.g., intercellular communication and cell adhesion). But molecules
by themselves do not determine cell and tissue shape; physical pro-
cesses do. Morphogenetic processes such as gastrulation and neuru-
lation can only arise from the coordinated interplay of physical and
genetic mechanisms. For such processes to occur, the biochemically
excitable cells that constitute the epithelia involved must develop spa-
tial variations in their physical properties, i.e., ˜˜self-organize.” They
do this by interacting with one another directly and/or with diffusible
or otherwise propagating signals, thereby establishing patterned ar-
rangements of differentiated cell types (see Chapter 7).
Our objective in this chapter is to characterize the physical prin-
ciples that come into play in the behavior of embryonic epithelia. By
considering the viscoelastic and adhesive properties of cells and tis-
sues, described in previous chapters in the geometric context of the
early embryo, we will show (within the limits of necessarily simpli-
¬ed models) how certain morphological changes emerge during the
early stages of development. We will rely heavily on the well-justi¬ed
assumption that an epithelial structure, the blastula for example,

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