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eq
of adhering CAMs, Nb , will vanish. This happens when the curves (as functions of
Nb ) determined by the ¬rst term and the second term (without the minus sign)
in Eq. B4.1a become tangential.
Mathematically, this condition is expressed by equating the derivatives of the
two terms with respect to Nb , yielding
γ Fc γ Fc
2K (N ’ Nb ) = 1 ’ .
exp (B4.1b)
k B T Nb k B T Nb
The solution of this equation for Nb is then inserted into the right-hand side
of Eq. B4.1a, which when equated to zero determines the critical detachment
force F c . Owing to the complicated form of these equations this program can be
carried out only numerically. Using for example γ = 0.59 nm (Baumgartner et al.,
2000), for a large range of K N values one obtains for the critical force per bond
f c = F c /N ≈ 40 pN.
For forces larger than F c , bonds break rapidly and Bell™s model provides the
time at which Nb becomes zero. This time is obtained from Eq. B4.1a, in which the
¬rst term can now be neglected. Within a good approximation (for F > F c )
exp (’γ F /k B T N)
tdetach (F ) ≈ . (B4.1c)
k ’ (1 + γ F /k B T N)
The above analysis can be used to estimate the critical forces and times of detach-
ment of cells for any experimental situation.



Differential adhesion of embryonic tissues
One of the most dramatic morphogenetic processes exhibited by em-
bryonic cells is sorting, the ability of cells of distinct types to seg-
regate into distinct tissues that do not intermix at their common
boundary. Cells of the prospective central nervous system, for exam-
ple, must differentiate, segregate from prospective skin cells, and, in a
concerted fashion, fold inward along the dorsal surface (i.e., the back)
of the embryo. If this process fails to occur properly the spinal cord
remains open to the body surface, resulting in a condition known as
˜˜spina bi¬da.” A half-century ago Holtfreter and colleagues provided
insight on how this is accomplished (Townes and Holtfreter, 1955).
They dissociated tissues such as nervous system and skin primordia
into single cells and then mixed them together randomly. Although
all the cells were able to adhere to one another, they did so to differ-
ent degrees. After random wandering within the cell mixture, skin
and neural progenitor cells found their respective counterparts and
formed ¬rst islands and then two distinct, uniform, regions, in which
the skin cells surrounded a central sphere of neural cells. In a similar
fashion, an initially random mixture of endodermal and ectodermal
cells, derived from the two tissue layers of the invertebrate Hydra,
sorted themselves out in such a way that the endodermal cells wound
4 CELL ADHESION, COMPARTMENTALIZATION, AND LUMEN FORMATION 91


up at the center of the aggregate and the ectodermal cells came to
surround them, precisely their relationship in the intact organism
(Technau and Holstein, 1992; Rieu et al., 2000).
Steinberg (1963) postulated that cells of different origin adhere
to each other with different strengths. Furthermore, in analogy with
immiscible liquids such as oil and water, mixtures of such cells un-
dergo a process of phase separation in which the ¬nal con¬guration
corresponds to the minimum of interfacial and surface free energies.
(Here the cells play a role analogous to the molecules of a liquid).
This ˜˜differential adhesion hypothesis” (DAH) was expressed in quan-
titative terms, by Phillips and coworkers (Phillips, 1969; Heintzelman
et al., 1978), based on a geometric analysis of the surface and interfa-
cial tension of immiscible droplets of liquid (Israelachvili, 1991; see
Chapter 2 for a more complete version of this analysis). According
to the DAH, the ¬nal ˜˜phase-separated” state of two adjacent tissues
is an equilibrium con¬guration not dependent on the pathway by
which it was reached. That is, it will be the same whether arrived at
by the fusion of two intact fragments of tissue or by the sorting out
of their respective cells from a binary mixture (Fig. 4.5A). Another im-
plication of the DAH is that tissue engulfment relationships should
form a hierarchy (Fig. 4.6): if tissue A engulfs tissue B and B engulfs C
in separate experiments, it follows that A will engulf C if that experi-
ment is performed. Finally, the DAH predicts that the values of tissue
surface tensions (see below) should fall into a quantitative order that
corresponds to the engulfment hierarchy. Each of these predictions of
the DAH has been amply con¬rmed experimentally (Steinberg, 1963;
1978; 1998; Armstrong, 1989; Mombach et al., 1995; Foty et al., 1994,
1996; Duguay et al., 2003).
According to the DAH, any pair of tissues, not only those that
contact each other in normal development, will undergo phase sepa-
ration and sorting, provided that their cells are capable of rearrang-
ing and that one of the tissues is more cohesive than the other (see
Figs. 4.6 and 4.7). This was con¬rmed in a decisive fashion in an exper-
iment in which mouse L cells, which do not normally express CAMs,
were genetically engineered to express P-cadherin (i.e., placental cad-
herin; Steinberg and Takeichi, 1994). Two populations of cells were
prepared -- high expressers and low expressers -- and when intermixed
they sorted themselves out, the high expressers ending up in the in-
terior of the aggregate as predicted on thermodynamic grounds. (The
result of a similar experiment is shown in Fig. 4.7.)

Embryonic tissues as liquids
In Chapter 2 we noted that while the shape of an individual cell
could be described in terms of a surface-tension-like quantity termed
the ˜˜cortical tension,” it is inaccurate to consider individual cells as
exhibiting a true surface tension. The reason for this is that the cell
surface -- its plasma membrane -- does not consist of the same ma-
terial as the interior of the cell and will not therefore automatically
92 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO




SORTING FRAGMENT FUSION




SPREADING
COALESCENCE




EQUILIBRIUM

A




B

Fig. 4.5 (A) Different paths by which two immiscible liquids or cell aggregates
(composed of cells with differing adhesive properties) may arrive at the same equilibrium
state. The path on the left shows sorting, or nucleation, which proceeds through the
gradual coalescence of groups of cells. The path on the right corresponds to engulfment,
which occurs through spreading. (After Steinberg, 1978.) (B) The time evolution of
sorting in a mixture of chicken embryonic pigmented epithelial (dark) and neural retinal
(light) cells. The images show the equatorial section of a three-dimensional spheroidal
aggregate. The left-hand, middle, and right-hand panels correspond respectively to 17,
42, and 73 hours after the initiation of sorting. The diameter of the sorted con¬guration
is around 200 microns. (After Beysens et al., 2000.)




increase or decrease its area as the cell experiences external forces.
With tissues the story is different: in many cases a true surface ten-
sion can be de¬ned. An aggregate of cells coheres by virtue of adhesive
forces between its cells rather than by a distinct bounding layer. New
surface can potentially be created from the interior by the movement
of cells to the surface and surface can be lost by cells moving inward.
A tissue will have the ability to increase or decrease its surface
in this fashion if its cells are individually mobile and can easily slip
4 CELL ADHESION, COMPARTMENTALIZATION, AND LUMEN FORMATION 93


EQUILIBRIUM
SURFACE
TISSUE CONFIGURATION
TENSION
(dyne/cm)
Limb bud
20.1




Pigmented
12.6
epithelium



Heart 8.5




4.6
Liver




Retina 1.6




Fig. 4.6 The correspondence between equilibrium cellular patterns and values of
surface tension for ¬ve embryonic chicken tissues. On the right are shown the
con¬gurations generated by cell sorting or aggregate fusion that occur when adjacent
tissues in the surface tension hierarchy are combined and allowed to rearrange in vitro
(see Fig. 4.5). Cells from the two tissue sources were stained with contrasting
¬‚uorescent markers. In each case, the more cohesive cell population, as quanti¬ed by its
surface tension, was engulfed by the less cohesive cell population (Foty et al., 1996).




Fig. 4.7 Sorting of two genetically transformed Chinese hamster ovary cell
populations with ∼50% difference in N-cadherin expression. On the left, the
con¬guration four hours after mixing. On the right, the fully sorted con¬guration after
24 hours (Forgacs and Foty, 2004).
94 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


past one another. In most tissues of the mature body this will not
be the case. Mature epithelial tissues consist of cells that have elabo-
rate, specialized, connections to one another. Mature connective tis-
sues are embedded in complex extracellular matrices that similarly
impede their mobility. Embryonic tissues (along with healing and re-
generating tissues, and many types of tumors) are exceptional in that
their cells can rearrange in response to external stresses on the tissue
mass, although it may take of the order of hours for them to do so
and for the tissue to assume its new equilibrium shape. With such a
capability, tissues can be modeled by physical laws that pertain to liq-
uids since, like any nonliving liquid, they are cohesive materials with
independently mobile subunits (Steinberg and Poole, 1982). The cells
within ˜˜liquid” tissues execute their random movements under the
power of cell metabolism and an intrinsic motile machinery rather
than by the thermal agitation undergone by the smaller-scale molec-
ular subunits of nonliving liquids (see Chapter 1). These distinctions
in scale and source of random motion, however, turn out to make no
difference when sorting phenomena are being interpreted (Mombach
et al., 1995; Foty et al., 1996; Rieu et al., 1998; Beysens et al., 2000;
Duguay et al., 2003).
Differential adhesion clearly dictates the sorting behavior and the
engulfment hierarchy in experimentally manipulated tissue fusions
and cell mixtures. This does not necessarily mean that it acts during
development to guide tissue assembly. That it does in some cases has
been demonstrated in a series of in vivo experiments (Godt and Tepass,
1998; Gonzalez-Reyes and St Johnston, 1998). The anterior--posterior
axis of the Drosophila embryo originates from two symmetry-breaking
steps during early oogenesis. Each oocyte arises within a cyst of 16 in-
terconnected cells that are formed by four incomplete cell divisions.
The one cell of these 16 that becomes the oocyte then comes to lie
posterior to the other 15 cells of the cyst in an enclosure called the fol-
licle, thereby de¬ning the polarity of the axis. Godt and Tepass (1998)
and Gonzalez-Reyes and St Johnston (1998) showed independently that
during this cell rearrangement the oocyte adheres to the cells of the
follicle that express the highest amounts of DE-cadherin. The position-
ing of the oocyte, moreover, requires cadherin-dependent adhesion be-
tween these two cell types, since the oocyte is frequently misplaced
when DE-cadherin is removed from either the ˜˜germ-line” cells that
give rise to the oocyte or the posterior follicle cells. Analogous studies
of the development of the Drosophila retina similarly demonstrate the
role of differential adhesion in cell patterning (Hayashi and Carthew,
2004).
As these and other experiments have shown, differential adhesion
results from the varying expression of cell adhesion molecules in dif-
ferent cell types (Friedlander et al., 1989). There are numerous cases in
development in which boundaries are established in response to pat-
terning signals and in which the cells on one side of such a boundary
do not mix with cells on the other side (Blair, 2003). Examples include
4 CELL ADHESION, COMPARTMENTALIZATION, AND LUMEN FORMATION 95


the development of compartmental subdivisions within the wings
and other surface structures of Drosophila (Garcia-Bellido, 1975; Crick
and Lawrence, 1975), the formation of segmental boundaries during
development of the vertebrate body axis (Meier, 1984; Palmeirim et al.,
1997) and hindbrain (Guthrie and Lumsden, 1991; see Chapter 7), and
the formation of mesenchymal condensations during vertebrate limb
development (Newman, 1977; Newman and Tomasek, 1996; Hall and
Miyake, 2000) (see Chapter 6). In each case, local sorting appears to be
involved in keeping the boundaries distinct when they are ¬rst estab-
lished. The challenge for a model of sorting is to relate the physical
quantities, such as surface tension, to biological properties character-
izing the adhesion complex in terms of speci¬c CAMs.


The physics of cell sorting
The change over time of the con¬guration of an originally random
mixture of embryonic chicken neural retinal and pigmented epithe-
lial cells is shown in Fig. 4.5B. The evolution of the cellular pat-
tern and the ¬nal equilibrium state qualitatively resemble the phase

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( 66 .)



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