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velopment of new structures. Although developing tissues need not
contain different cell types in order to undergo morphogenesis, dif-
ferentiation often sets this process in motion. For example, sorting
and tissue engulfment, which together comprise one of the classes
of morphogenetic phenomena discussed earlier, require at least two
populations of cells that are differentiated with respect to their cell-
surface adhesivity.
Cell sorting, however, is unusual among the morphogenetic pro-
cesses dependent on differentiation in that the initial differentiation
event need not be spatially controlled. Recall that the random mix-
ing of two cell types and the fusing of fragments of the tissues from
which they were derived ultimately achieved the same morphological
outcome (Fig. 4.5). Thus, if differentiation in a developing cell mass
occurs in a spatially random manner, so that two cell types with dif-
fering adhesive properties come to be dispersed in a salt-and-pepper
fashion, the ¬nal con¬guration of the eventually phase-separated tis-
sues will always be the same. A case in point is Hydra, a diploblas-
tic, i.e., two-germ-layered, organism (see Chapter 5), which starts out
as a single-layered blastula. The formation of the second germ layer
(i.e., gastrulation) involves the ingression of individual endodermal
cells that apparently arise in a dispersed fashion in the original layer
(Martin et al., 1997).
While this scenario may be informative in revealing the physi-
cal consequences of sorting and the resulting boundaries of immis-
cibility, the emergence of distinct cell types in developing tissues is
rarely spatially random. Indeed, the sorting of a random population
of differentiated cells into well-organized layers will only occur if the
cells are differentiated from one another with respect to adhesivity. If
156 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


cells were to differentiate randomly with respect to other functions,
for example, contractility (as in muscle cells) or electrical excitabil-
ity (as in nerve cells), then sorting into homotypic layers would not
automatically take place. In general, therefore, the acquisition of spa-
tial patterns of differentiated cells in the developing embryo must be
regulated by mechanisms other than spontaneous sorting. The phys-
ical nature of these mechanisms of spatial pattern formation is the
subject of this chapter.
We encountered examples of non-sorting pattern formation when
we discussed gastrulation and neurulation in Chapter 5. Recall that
in each case a spatially heterogeneous distribution of cell states was
needed to set things in motion. In the Drasdo--Forgacs model for gas-
trulation this took the form of a preexisting nonuniformity in the
distribution of certain gene products, on the basis of which cells
near the vegetal pole acquired nonzero spontaneous curvature. In
the Kerszberg--Changeux model for neurulation it took the form of
predetermined gradients of the diffusible molecules BMP and Shh.
Although these models are simpli¬ed representations of the biolog-
ical reality, embryos of most species exhibit spatial nonuniformities
of cell state from the earliest stages of development. This is true even
of mammalian embryos, where it was long thought not to be the case
(see Gardner, 2001).
The term ˜˜gradient,” as used in developmental biology, designates
continuously varying spatial nonuniformities either in cell state (typ-
ically characterized by the cells™ expression levels of a particular gene)
or in the molecular microenvironment of cells that may initially be
in identical states. As an example of the ¬rst meaning, early during
gastrulation in the chicken the caudal genes (which specify a class
of transcription factors) exhibit sequential activation in the newly
formed neural plate and sequential extinction in axial midline struc-
tures along the anterior--posterior axis (Marom et al., 1997). The result-
ing distribution of the caudal products along the embryo is indicative
of spatially varying cell states. Such gradients in gene expression are
outcomes of pattern formation.
As noted, in addition to its use in describing a distribution of cell
states, the term ˜˜gradient” is also used to describe distributions of
molecules in the microenvironment of cells, in particular distribu-
tions of signaling molecules that induce changes in cell state during
development. Thus extracellular gradients of the Xenopus nodal-
related (Xnr) factors, which are secreted by the embryonic ectoderm,
mediate mesoderm induction during the blastula stage (Agius et al.,
2000). The factors that constitute such gradients are referred to as
˜˜morphogens” (a term coined by the mathematician A. M. Turing;
Turing, 1952). There is considerable evidence that diffusible mor-
phogens play important roles throughout development (this topic is
reviewed in Green, 2002).
As we have seen, a new cell pattern may arise by the rearrange-
ment of preexisting cells of different types or by the generation of
new cell types. Morphogenetic pattern formation (or more commonly,
˜˜morphogenesis”) refers to mechanisms that generate new patterns
7 PATTERN FORMATION: SEGMENTATION, AXES, AND ASYMMETRY 157


without generating new cell types (Salazar-Ciudad et al., 2003).
Pattern-forming mechanisms in which new cell types are generated
can be divided into two subcategories, those that generate new cell
types without employing cell--cell signaling, termed cell autonomous
mechanisms, and those that do so by using cell--cell signaling, termed
inductive mechanisms (Salazar-Ciudad et al., 2003). As we will see, each
type of biological pattern formation mechanism can employ a vari-
ety of distinct physical processes. The following sections will describe
examples of each category of pattern formation listed above and il-
lustrate the different ways in which physical mechanisms -- adhesion,
diffusion, oscillatory and other dynamical systems properties -- enter
into our understanding of these phenomena.



Basic mechanisms of cell pattern formation
While most changes in cell pattern during development involve both
morphogenesis (i.e., changes in tissue form and shape; see Chapters
4, 5, and 6) and cell differentiation (i.e., stable changes in cell state;
see Chapter 3), it is useful to focus at ¬rst on mechanisms in which
only one or the other occurs (Salazar-Ciudad et al., 2003) (Fig. 7.1A, B).


Mechanisms that do not generate new cell states
As indicated above, morphogenetic pattern-forming mechanisms (Fig.
7.1A) are de¬ned by their capacity to change the relative arrange-
ment of cells over space without affecting their states. We have con-
sidered already one such morphogenetic mechanism, differential adhe-
sion, which generates pattern by the sorting of preexisting cell types
into homotypic islands.
Other morphogenetic mechanisms that lead to changes in cell pat-
tern without changes in state include oriented cell division or directed
mitosis, in which a tissue elongates in a preferential direction because
of the nonrandom alignment of its cells™ mitotic spindles (Gong et al.,
2004) and migration. Migration can be directionally random, or it can
be random but speeded up by an ambient chemical cue (˜˜chemokine-
sis”), or it can have a preferred direction in relation to a chemical
gradient (chemotaxis) or an insoluble substratum gradient (hapto-
taxis). Note that these cues do not change the cells™ differentiated
states, only their relative positions. Convergent extension, a reshaping
of tissue masses during gastrulation, which involves the mutual in-
tercalation of planar polarized cells without changing their state, is
also such an example. The contraction of individual cells, mediated
by actin--myosin complexes, can have dramatic morphogenetic effects
on neighboring cells and on the tissue as a whole (Beloussov, 1998).
Contraction is propagated in epithelial tissues by direct physical at-
tachment between cells (see, for example, Hutson et al., 2003), and in
mesenchymal tissues by the extracellular matrix. Apoptosis, the pro-
grammed loss of cells, changes the pattern of the cells that remain
behind.
B MECHANISMS GENERATING NEW CELL STATES
(i) Cell autonomous mechanisms




Heterogeneous Asymmetric Mitosis with
egg division mitosis temporal dynamics



(ii) Inductive mechanisms



Hierarchic Emergent




Fig. 7.1 Schematic representation of the basic pattern-forming mechanisms. Panel A
shows morphogenetic mechanisms, which bring cells into new spatial relationships with
one another without generating new cell types. Directed mitosis: consistently oriented
mitotic spindles can reshape a growing tissue. Differential growth: cells dividing at a higher
rate (yellow) can alter tissue shape. Apoptosis: the programmed death of speci¬c cells
(blue) can transform an established pattern into a different one. Migration: a pattern is
altered by the directed migration of cells (blue) to a new location. Differential adhesion: a
change in pattern can result from the grouping of cells with different adhesive properties
(the blue cells are more cohesive than the yellow cells). Condensation: some
mesenchymal cells in a matrix become tightly associated with one another. Contraction:
the contraction of a subset of cells (yellow) can cause the buckling of a tissue. Matrix
modi¬cation: the swelling, new deposition, loss, or molecular modi¬cation of an ECM can
cause budding and other shape changes in a tissue.
(Cont.)
7 PATTERN FORMATION: SEGMENTATION, AXES, AND ASYMMETRY 159



Mechanisms that generate new cell states
There are two major categories of basic pattern-forming mechanisms
that produce patterns by cell differentiation, i.e., by generating
new cell states (Fig. 7.1B): those that do not depend on cell--cell
signaling (cell autonomous mechanisms) and those that do (inductive
mechanisms) (Salazar-Ciudad et al., 2003). Cell autonomous mechanisms
all generate new cell states by employing cell division. In these mech-
anisms, mitosis occurs under conditions that are nonuniform either
in space or in time, causing the daughter cells to exhibit distinct
cell states. In general these cell states may be transient or stable, but
here we consider a new developmental pattern to have formed only
if transient differences in state are converted into stable differences,
i.e., new cell types. As we saw in Chapter 3, this usually occurs by
the establishment of persistent changes at the transcriptional level.
Let us ¬rst consider how cell division can be spatially nonuniform
with respect to cell state. Certain eggs have materials such as yolk or
informational RNAs or proteins transported into them in a spatially
asymmetric fashion during oogenesis (Wikramanayake et al., 1998;
Zhang et al., 1998). When the zygote resulting from this egg under-
goes its ¬rst division, a cellular pattern is automatically formed:
one blastomere will contain greater amounts of the stored material
than the other. In such cases, the initiation of pattern formation is a
passive consequence of an earlier cellular event. Such differences in
cell state may then be converted into differences in cell type (see, for
example, the review by Chan and Etkin, 2001). Another variant of this
cell autonomous patterning mechanism is the preferential transport,
on the basis of intracellular polarity, of materials to one of the daugh-
ter cells during cell division (asymmetric mitosis, Fig. 7.1B). This
mechanism may employ transport along the cytoskeleton by molecu-
lar motors, a general cellular process that has been studied by physical


Panel B shows pattern-forming mechanisms that involve the generation of new cell
states. (i) Cell-autonomous mechanisms produce pattern changes by generating new cell
types without employing cell“cell signaling. Division of a heterogeneous egg: the egg
cytoplasm contains spatially separated sets of different molecules (indicated by different
colors) resulting in distinct blastomeres after cleavage. Asymmetric mitosis: molecules are
differentially transported into the two halves of a dividing cell, resulting in different
daughter cells. Internal temporal dynamics coupled to mitosis: cells which have levels of
molecular determinants that oscillate with a period different from that of the cell cycle
can produce periodic spatial patterns. In the example shown, the green cell (a stem cell)
divides to produce unequal progeny, another green cell and a cell that is yellow or blue,
depending on the state of the regulatory cycle; the latter is out of synchrony with the
cell cycle. This leads to the alternating production of yellow and blue cells (see Newman,
1993 for additional details). (ii) Inductive mechanisms produce changes in pattern by
employing cell“cell signaling to generate new cell types. Hierarchic induction: the inducing
cell (yellow) affects neighboring cells but the induced cells (blue) do not in¬‚uence the
production of the inducing signal. Emergent induction: the inducing cell affects neighboring
cells, which in turn signal back, in¬‚uencing the inducing signal. (Based on Salazar-Ciudad
et al., 2003, with additions.)
160 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


methods (see Howard, 2001). Cell division may also occur under
conditions in which the cell state is nonuniform in time. This requires
that something other than the cell cycle acts as a clock. As we saw in
Chapter 3, the cyclical production of biomolecules can result from
biochemical networks with inherent oscillatory dynamics. According
to the model of Borisuk and Tyson (1998) the cell cycle itself is based
on such a dynamic oscillation. If a regulatory molecule unrelated to
the cell cycle also exhibits oscillatory dynamics then it can act as a
clock, and a cell pattern can emerge from the interplay of the two
oscillations (Newman, 1993; Holtzendorff et al., 2004). Consider, for
example, a population of dividing cells in which one of the daughter
cells eventually becomes converted into one of several new cell types,
and the other daughter remains uncommitted. Such populations are
called ˜˜stem cells.” By itself, stem cell character does not imply any
particular pattern or arrangement of cells. But now if we assume
that the fate of the differentiating daughter cell is determined by
the particular level of a periodically varying regulatory molecule it
contains when it is ˜˜born,” under a certain choice of parameters
a spatially periodic pattern of cells will be generated (mitosis with
temporal dynamics, Fig 7.1B).
Inductive mechanisms, the second category of basic pattern-forming
mechanisms that generate speci¬c cellular con¬gurations by produ-
cing new cell types, do so by employing cell-to-cell signaling (Fig.
7.1B); cell division may or may not be involved. Signaling can be di-
rectly from one cell to an adjacent cell ( juxtacrine signaling) or via
morphogens and other signals that are transmissible across several
cell diameters ( paracrine signaling). The most ubiquitous form of jux-
tacrine signaling during development, the Notch--Delta system, em-
ploys just one cell-surface-bound receptor--ligand pair. The Notch and
Delta proteins, and by implication this signaling system, are consid-
ered to be evolutionarily ancient because of the conservation (i.e., the
limited extent of change) of their sequences over the more than half-
billion years since insects diverged from vertebrates. This system is
used in a wide variety of embryonic contexts to set up cell patterns,
including, as we have seen previously, neurogenesis in the neural
plate (Tiedemann, 1998; see also the discussion of the Kerszberg--
Changeux model in Chapter 5) and in the peripheral nervous system
(Wakamatsu et al., 2000; Morrison et al., 2000), somitogenesis ( Jiang,
Y. J., et al., 2000; Oates and Ho, 2002; see below), left--right asym-
metry (Raya et al., 2003, 2004; see below), muscle cell differentiation
(Umbhauer et al., 2001), and blood vessel formation (Uyttendaele et al.,
2001).
Paracrine-type inductive mechanisms are also widespread during
development (Green, 2002). Typically, these employ morphogens, such
as members of the transforming growth factor, i.e., TGF-β, superfam-

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