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be induced (Nieuwkoop, 1973, 1992).
The formation of the body axis in vertebrates also exhibits another
unusual feature: while it occurs in an apparently symmetrical fash-
ion, with the left and right sides of the embryo seemingly equivalent
to one another, at some point this symmetry is broken. Genes such as
nodal and Sonic hedgehog start being expressed differently on the two
sides of the embryo, and the whole body eventually assumes a partly
asymmetric morphology, particularly with respect to internal organs
such as the heart.
In his pioneering paper on reaction--diffusion systems Turing
(1952) demonstrated that such systems have inherent pattern-forming
potential, with a particular propensity to exhibit symmetry break-
ing across more than one axis. In the following, we present the
180 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


application of this framework by Meinhardt to axis formation in ver-
tebrates and the breaking of symmetry around these axes.

Meinhardt™s models for axis formation
and symmetry breaking
Viewed from the perspective of physics, early development, during
which the organism acquires its ¬nal shape, is a series of symmetry-
breaking events starting from a highly symmetrical spheroidal egg
and arriving at a body with a much lower degree of symmetry. The
understanding of symmetry breaking has long occupied physicists
because it underlies the striking phenomena of phase transitions.
Phase transitions are typically accompanied by a reduction in sym-
metry. A well-known example will illustrate this point. In a paramag-
net, molecules are elementary magnets, each with its own random
orientation. These can be aligned in an external magnetic ¬eld, but
once the ¬eld is turned off the molecules continue their uncorrelated
existence and the system shows no net magnetization. Upon decreas-
ing the temperature, however, a critical point is reached below which
the elementary magnets couple. If they are now aligned by an ex-
ternal ¬eld, they remain aligned even after the ¬eld is turned off:
the paramagnet changes to a ferromagnet. The originally perfectly
isotropic, featureless system, with a net magnetization of zero in ev-
ery direction, gradually self-organizes into a ˜˜pattern.” It becomes
anisotropic, characterized by a single axis de¬ned by the direction of
its net magnetization.
It took great efforts to decipher the mechanism responsible for
the paramagnet--ferromagnet and similar phase transitions. At high
temperatures, the thermal energy (proportional to the absolute tem-
perature T , see Chapter 1), which causes strong ¬‚uctuations and tends
to disorient the molecules, dominates over the interaction energy be-
tween neighbors. With decreasing temperature, the thermal energy
diminishes and the interaction energy can more effectively compete
with it: adjacent molecules align and gradually induce others to fol-
low suit. Short-range correlations become ampli¬ed and, as a conse-
quence, the system responds to external in¬‚uences (e.g., an imposed
magnetic ¬eld) in a collective manner. The message from this exam-
ple is that symmetry breaking, with its macroscopic manifestation,
may be induced from a microscopic localized source (e.g., individual
molecules in a paramagnet) as a consequence of competition between
antagonistic driving forces.
Can our knowledge of the physical mechanisms underlying phase
transitions provide insight into the generation of developmental axes?
We may consider the various uncommitted cells in the early embryo
to be analogous to the molecules with random magnetic orientation.
Organizers, such as the vegetal pole, the ˜˜Nieuwkoop center” (Fig. 7.9),
and the Spemann organizer, may be considered as analogous to the
local sources whose in¬‚uence, under permissive conditions, is prop-
agated through progressive interactions between cells in such a way
that a pattern, and eventually an axis, may be induced to form. While
7 PATTERN FORMATION: SEGMENTATION, AXES, AND ASYMMETRY 181


thermal ¬‚uctuations are not relevant in early development, the states
of cells in a developmental ˜˜¬eld” (a term often used in embryology
in analogy with its use in physics; Gilbert, 2003) are susceptible to
in¬‚uences by adjacent cells and diffusible signals. Speci¬c competing
processes analogous to thermal randomization and magnetic dipole
interactions may therefore be responsible for the formation of axes.
Meinhardt hypothesized (Meinhardt, 2001; see also Meinhardt and
Gierer, 2000) that the expression levels of known genes involved in
axis formation (e.g., VegT, FGF, brachyury, β-catenin, etc.) are outcomes
and indicators of such biochemical competition. Below we summarize
his reaction--diffusion-based model of symmetry breaking and axis
formation in amphibians.
1. The ¬rst goal that a model of axis formation must achieve is
to generate an organizer de novo. Biochemically, this is re¬‚ected in a
pattern of high local concentrations and graded distributions of one
or more signaling molecules, which can be produced by the coupling
of a self-enhancing feedback loop, acting over a short range, and a
competing inhibitory reaction, acting over a longer range. Meinhardt
proposed a simple system acting in the xy plane (representing two-
dimensional sections of the embryo) that consists of a positively au-
toregulatory activator (with concentration A(x, y; t)) and an inhibitor
(with concentration I (x, y; t)). The activator controls the production
of the inhibitor, which in turn limits the production of the activa-
tor. This process can be described by the following reaction--diffusion
system (Meinhardt, 2001)
‚A ‚2 A ‚2 A A2 + I A
= DA + +s ’ kA A (7.9a)
‚t ‚ x2 ‚ y2 I (1 + s A A 2 )
‚I ‚2 I ‚2 I
= DI +2 + s A2 ’ kI I + I I . (7.9b)
‚t ‚ x2 ‚y
The terms proportional to A 2 specify that the feedback of the activa-
tor to its own production and that of the inhibitor is in both cases
nonlinear. The factor s > 0 describes positive autoregulation, the ca-
pability of a molecule to induce positive feedback and regulate its
own synthesis. This may occur by purely chemical means (˜˜autocata-
lysis”), which is the mechanism originally considered by Turing (1952).
More generally, in living tissues, positive autoregulation occurs if a
cell™s exposure to a factor that it has secreted causes it to make more
of the same factor (Van Obberghen-Schilling et al., 1988). The inhibitor
slows down the production of the activator (by the 1/I factor in the
second term in Eq. 7.9a). Both activator and inhibitor diffuse and de-
cay with respective diffusion coef¬cients D A , D I and rate constants
k A , k I . The small baseline inhibitor concentrations I A and I I can ini-
tiate activator self-enhancement or suppress its onset, respectively, at
low values of A. The factor s A , when present, leads to the saturation
of positive autoregulation. Once the positive autoregulatory reaction
is under way, it leads to a stable self-regulating pattern in which the
activator is in dynamic equilibrium with the surrounding cloud of
the inhibitor.
182 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


2. The various organizers and subsequent inductive interactions
leading to symmetry breaking, axis formation and the appearance
of the three germ layers in amphibians during gastrulation can all
be modeled, in principle, by the reaction--diffusion system de¬ned by
Eqs. 7.9a, b or by the coupling of several such systems. The biologi-
cal relevance of such reaction--diffusion models depends on whether
there exist molecules that can be identi¬ed as activator--inhibitor
pairs. Meinhardt™s model starts with a default state, which consists
of ectodermal tissue. Patch-like activation generates the ¬rst ˜˜hot
spot,” the vegetal pole organizer, which induces endoderm formation
(a simulation is shown in Fig. 7.11A). A candidate for the diffusible ac-
tivator in the corresponding self-enhancing loop for endoderm speci¬-
cation is the TGF-β-like factor Derriere, which activates the transcrip-
tion factor VegT (Sun et al., 1999). Evidence for the existence of an
inhibitor is more circumstantial. VegT expression remains localized
to the vegetal pole, but this is not because the surrounding cells lack
the competence to produce VegT (Clements et al., 1999). Subsequently,
a second feedback loop forms a second hot spot in the vicinity of the
¬rst, in the endoderm. This is identi¬ed with the Nieuwkoop cen-
ter, an organizing region, which appears in the rostro-vegetal quad-
rant of the blastula (see Fig. 7.9) at around the 32-cell stage (Gimlich,
1985, 1986). A candidate for the second self-enhancing loop is the
molecular assembly of the Wnt-pathway (including β-catenin), a ubiq-
uitous early developmental signaling cascade (Fagotto et al., 1997).
Meinhardt made the interesting suggestion that the inhibitor for
this second loop might be the product of the ¬rst loop (i.e., the
vegetal pole organizer). As a result of this local inhibitory effect,
the Nieuwkoop center is displaced from the pole (see the simula-
tion in Fig. 7.11B). With the formation of the Nieuwkoop center the
spherical symmetry of the embryo is broken. In Meinhardt™s model
this symmetry breaking ˜˜propagates” and thus forms the basis of
further symmetry breakings, in particular left--right asymmetry (see
below).
3. The vegetal pole and the Nieuwkoop center are examples of the
localized spot-like patterns generated by activator--inhibitor reaction--
diffusion systems in Eqs. 7.9a, b (with s A = 0). Such systems can also in-
duce the full zonal separation of cells with ectodermal, endodermal,
and mesodermal speci¬cation into stripes (if s A > 0) and with this es-
tablish the dorsoventral axis (which, according to the new axis assign-
ments, coincides with the animal--vegetal axis, as discussed above).
This is achieved by using several competing feedback loops in such a
way that in any cell only one of these loops can be active. For a real-
istic description of pattern formation, loops that are able to induce
spots and zones must be coupled (Fig. 7.11C).
4. By secreting several diffusible factors, the Nieuwkoop center
induces the formation of the Spemann--Mangold organizer (Harland
and Gerhart, 1997). Interestingly, if the second feedback loop, respon-
sible for the Nieuwkoop center, is not included in the model then two
Spemann--Mangold organizers appear, symmetrically with respect to
7 PATTERN FORMATION: SEGMENTATION, AXES, AND ASYMMETRY 183



A B




D
C




Fig. 7.11 Pattern formation in the reaction“diffusion model of Meinhardt.
(A) Induction of the vegetal pole organizer. Left: The interaction of an autocatalytic
activator, the TGF-β-like factor Derriere (red), and a long-ranging inhibitor (whose
production it controls and which, in turn, limits the activator™s production), creates an
unstable state in an initially near-uniform distribution of the substances (the inhibitor is
not shown). Middle and right: A small local elevation in the activator concentration above
steady-state levels triggers a cascade of events governed by Eqs. 7.9, a further increase in
the activator due to autocatalysis, the spread of the concomitantly produced surplus of
inhibitor into the surrounding area, where it suppresses activator production (middle),
and the establishment of a new stable state in which the activator maximum (at the hot
spot) is in a dynamic equilibrium with the surrounding cloud of inhibitor (right). The
right-hand panel also shows the near-uniform distribution of the activator (green) in the
second reaction“diffusion system, discussed in B. (B) Induction of the Nieuwkoop center.
Once the ¬rst hot spot has formed, it activates a second self-enhancing feedback loop.
The production of the activator (green) in this reaction is inhibited by the vegetal pole
organizer itself. As a consequence, the Nieuwkoop center is displaced from the pole.
(C) The zonal separation of ectoderm, endoderm, and mesoderm. The competition of
several positive feedback loops ensures that in one cell only one of these loops is active.
As the results indicate, reaction“diffusion systems can produce not only spot-like
organizers but also zones. Endoderm (red) forms, in the way shown in A, from a default
ectodermal state (blue). The mesodermal zone (green; it forms by the involvement of
the FGF“brachyury feedback loop, Schulte-Merker and Smith, 1995) develops a
characteristic width from the additional self-inhibitory in¬‚uence in Eqs. 7.9. (D) Induction
of the Spemann“Mangold organizer. The activation of an organizing region (yellow)
within the still-symmetric mesodermal zone would imply a competition over relatively
long distances. In such a case, Eqs. 7.9 lead to the occurrence of two organizing regions,
a biologically unacceptable result. The strong asymmetry shown in B prevents this and
suggests a reason for the existence of the Nieuwkoop center. (Reprinted from
Meinhardt, 2001, with permission from the University of the Basque Country Press.)




the animal--vegetal axis, and no symmetry breaking occurs (Fig. 7.11D).
With the formation of the Spemann--Mangold organizer the develop-
mental process is in full swing. The organizer triggers gastrulation,
in the course of which the germ layers acquire their relative positions
and the notochord forms. This long thin structure marks the midline
of the embryo, and this midline itself inherits organizer function and
184 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


eventually establishes the primary embryonic axis, the rostral--caudal
or anterior--posterior (AP) axis.
Spatial information for the AP axis is already contained in the
pregastrula, as soon as the Spemann--Mangold organizer forms. The
reason is that the organizer is subdivided into head and trunk organ-
izers, the activities of which are associated with speci¬c gene prod-
ucts. The differential activation of the head and trunk organizer is
achieved by the Nieuwkoop center, which establishes a gradient in a
TGF-β-like morphogen. At the low concentration end of this gradient,
away from the Nieuwkoop center, the genes for the trunk organizer
(e.g., Xnot, the Xenopus homologue of zebra¬sh floating head; Danos
and Yost, 1996) are activated. Near the Nieuwkoop center, where the
morphogen concentration is high, genes of the head organizer (e.g.,
goosecoid; Gritsman et al., 2000) are turned on. The inhibitor of the ac-
tivator for the head organizer is the activator of the trunk organ-
izer and vice versa. A simulation of midline formation based on
Meinhardt™s model is shown in Fig. 7.12.
5. Finally, the breaking of left--right symmetry can be understood
as again a competition between already existing and newly develop-
ing self-enhancing loops, similarly to the formation of the Nieuwkoop
center and prospective germ layer zones. The molecule that best ful¬ls
the role of the ˜˜left” activator in Meinhardt™s model is the product
of the nodal gene, so called because it is expressed around Hensen™s
node, the avian and mammalian counterpart of the Spemann--
Mangold organizer, as well as around the Spemann--Mangold orga-
nizer itself (Weng and Stemple, 2003). The Nodal protein, which is
a diffusible, positively autoregulatory, member of the TGF-β super-
family, induces expression from the embryonic midline of another
TGF-β-related molecule, Lefty, and Lefty antagonizes Nodal produc-
tion ( Juan and Hamada, 2001; Branford and Yost, 2002; Yamamoto
et al., 2004). Because Nodal and Lefty are antagonistic diffusible sig-
nals that differ in the range of their activities (Chen and Schier,
2002; Branford and Yost, 2002; Sakuma et al., 2002), the ingredients
for a symmetry-breaking event along the primary embryonic axis are
present (Solnicka-Krezel, 2003).
Interestingly, although the major molecular players involved in
symmetry breaking in the frog and the mouse appear to be the same,
in the chicken, another popular experimental system for studying
axis formation, things appear to be quite different. In this species,
when Nodal is initially expressed in Hensen™s node, it is already spa-
tially asymmetric (Pagan-Westphal and Tabin, 1998). The asymmetry
in expression thus appears at a relatively earlier stage than in the frog
or mouse and is unlikely to be induced by a diffusible signal (Dathe

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( 66 .)



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