Download Models for patterning primary embryonic body axes: the role of

This is a reformatted version of an article appeared in Seminars Cell Dev. Biol. 2015 doi:10.1016/j.semcdb.2015.06.005
Models for patterning primary embryonic body axes: the role of
space and time
Hans Meinhardt
Max Planck Institute for Developmental Biology
Spemannstr. 35, D- 72076 Tübingen
http://www.eb.tuebingen.mpg.de/meinhardt; [email protected]
Models for the generation and interpretation of spatial patterns are discussed. Crucial for these processes is an intimate link between self-enhancing
and antagonistic reactions. For spatial patterning,
long-ranging antagonistic reactions are required
that restrict the self-enhancing reactions to generate organizing regions. Self-enhancement is also
required for a permanent switch-like activation of
genes. This self-enhancement is antagonized by
the mutual repression of genes, making sure that in
a particular cell only one gene of a set of possible
genes become activated - a long range inhibition in
the ‘gene space’. The understanding how the main
body axes are initiated becomes more straightforward if the evolutionary ancestral head/brain pattern and the trunk pattern is considered separately.
To activate a specific gene at particular concentration of morphogenetic gradient, observations are
compatible with a systematic and time-requiring
‘promotion’ from one gene to the next until the local concentration is insufficient to accomplish a
further promotion. The achieved determination is
stable against a fading of the morphogen, as required to allow substantial growth. Minor modifications lead to a purely time-dependent activation
of genes; both mechanisms are involved to pattern
the anteroposterior axis. A mutual activation of cell
states that locally exclude each other accounts for
many features of the segmental patterning of the
trunk. A possible scenario for the evolutionary invention of segmentation is discussed that is based
on a reemployment of interactions involved in asexual reproduction.
Development of a higher organism starts, as a rule
with a single cell and proceeds, of course, under the
control of genes. Since the genetic material is essentially the same in every cell, a central question is
how the correct arrangement of differentiated cells is
achieved. A most important step on the way from the
fertilized egg to an adult organism is the setting up of
the primary body axes, anteroposterior (AP) and mediolateral/ dorsoventral (DV). In this process, organizing
regions - small nests of cells that act as sources or
sinks of signalling molecules - play an important role.
The Spemann organizer is a prominent example. This
organizer is usually regarded as the only organizer that
exists in vertebrates, raising the question how a single organizer can specify the cells along the two major body axes that are oriented perpendicular to each
other. Moreover, DV patterning has to occur along the
long extended AP axis. This task cannot be accomplished by a patch-like organizer directly. A local signalling source would lead to a conical positional information profile with a constant slope into all directions,
which is clearly insufficient to specify the DV axis. Models will be discussed that account for the generation
and alignment of the main body axes.
The formation of organizing regions requires interactions in which local self-enhancement and longrange inhibition is involved, discussed in detail elsewhere [1, 2, 3]. The interaction of the self-enhancing
Nodal with the antagonistically acting Lefty is an example [4, 5]. Such interactions can generate patterns in
an initially homogeneous assembly of cells. For embryos that start with a large size such as the amphibian
embryo, the employment of maternal determinants is
an appropriate strategy. By making only a small part
of the embryo competent for organizer formation, localized determinants only allow a single organizer to be
formed. Maternal determinants are not required if development starts as a small nest of cells such as it is
the case in mouse or chick development. In this case,
Key words: Pattern formation / gene activation / segmentation / main body axes / interpretation of gradients
1
the self-regulatory features of pattern-forming reactions
allow complete development in fragments even if the
organizer is removed [6]. The formation of several embryos after early fragmentation of a chicken embryo is
an example [7].
The generation of organizing regions requires communication between cells. If based on diffusion, the
range of this signalling is restricted to short distances.
Thus, these patterns can only be generated at small
scales during early stages of development and have
to be converted into a pattern of stable cell determinations by activating particular genes. The activities of
these genes have to be maintained even if the evoking signals are no longer available. Complementary to
models for setting up positional information for the body
axes, models for the stable activation of genes under
the influence of the resulting signal distributions will be
discussed. It will be shown that activation of the correct
gene at a particular position is a time-requiring process.
induce neuronal tissue in the overlying ectoderm [13].
The prechordal plate is the precondition to form the
midline, the dorsal-most structure from which the distance of the cells is measured, so to say, a reference
line. In contrast, for midline formation of the trunk, cells
near the blastopore (marginal zone) move towards the
organizer (node), causing a conversion a ring perpendicular to the AP axis into a rod-like structure parallel to
the AP axis. This process will be discussed further below in more details. The two very different functions of
the organizer become established very early by a subdivision into a head- and a tail-organizer [14].
Frequently the Spemann-organizer is assumed to
provide the positional information for organizing the AP
axis [14]. In the view of the model proposed, this conclusion is partially misleading and results from the fact
that most AP-markers are absent if the organizer is
missing. However, most of these markers are neuronal markers that disappear if no midline is formed.
Thus, the loss of anterior AP markers in the absence
of the organizer is caused by a non-functional DV patterning. In this relation a very instructive set of experiments has been done by Ober and Schulte-Merker
in the zebra fish [15]. By removing required maternal components, they obtained embryos reliably devoid
of any organizer. To visualize the AP patterning they
removed all BMP signalling, allowing in this way the
expression of neuronal markers. Genes like Otx and
Krox20 were expressed at nearly normal positions but
in a completely radially-symmetric way, illustrating that
the activation of the anterior AP genes do not require
the organizer. However, as discussed further below,
the organizer plays a crucial role in the AP patterning
of the trunk by terminating the time-dependent posteriorization.
1. Axes formation in two steps: the head and
the trunk
Understanding of the patterning along the main body
axes of vertebrates is much facilitated if it is realized
that different mechanisms are involved in patterning the
head and in the trunk. This is true for both the patterning along the AP and the DV axes. Several observations suggest that the AP pattern in the brain is under
control of a Wnt gradient that is generated at the blastopore/marginal zone [8, 9, 10]; (reviewed in [11]). The
region of forebrain formation has the largest distance to
the blastopore and emerges at a low WNT concentration, suggesting that the forebrain is the default state.
Thus, the first steps in the AP patterning of the brain
can be regarded as an example where a morphogen
gradient accomplishes posteriorization by gene activation in a concentration- and thus position-depending
manner. In contrast, the AP patterning of the trunk is
achieved by a sequential posterior elongation. In cells
close to the blastopore but with the exemption of the organizer region, new Hox genes become activated in a
sequential way, causing specification of more and more
posterior structures - a time-dependent process [12];
(Durston and Zhu, this issue). Although both mechanisms overtly look very different, as shown below, modelling revealed that gene activation under the influence
of a static gradient has also a strong time-dependent
component, suggesting that interpretation of a gradient,
e.g., in the brain and the time-dependent posteriorization in the trunk shares common elements.
Pronounced differences between brain and trunk
patterning also exist for the patterning of the DV axis.
For the patterning of amphibian brain it is crucial that
cells derived from the Spemann organizer move underneath the ectoderm, forming the prechordal plate and
2. The separation of axes formation into a
brain- and a trunk-part has an evolutionary
justification
Coelenterates are assumed to represent a basal
branch of the metazoan evolutionary tree. A comparison of the gene expression patterns in the
radial-symmetric freshwater polyp Hydra - a muchinvestigated Coelenterate - and homologous genes in
higher organisms suggested that the body column of
an ancestral sac-like creature with a single opening
evolved into the brain of higher organisms; the ancestral oral-aboral pattern evolved in the head/brain APpattern [16]. Wnt and Brachyury are expressed at the
tip of the hypostome and at the most posterior region
in higher organisms, suggesting that, in contrast to
a naı̈ve expectation, the so-called Hydra head is the
most-posterior structure, corresponding to the blastopore in higher organisms (Fig. 1). This view is sup2
Fig. 1: Generation of the primary body axes and a near-Cartesian coordinate system. (A-C) The body pattern of an ancestral radial-symmetric
organism (A), generated under control of a Wnt-driven organizer (green) at the oral opening (blastopore), is assumed to represent the ancestral
AP axis, corresponding to the brain-part of the AP axis in contemporary higher organisms. The pattern of the freshwater polyp Hydra (B)
is assumed to be a living fossil of this ancestral pattern. This ancestral body pattern evolved into the pattern as seen in the early vertebrate
gastrula, giving rise to fore- and midbrain (Otx, blue) and the heart (Nkx2.5, pink). (D-J) The secondary DV axis requires a stripe-like line of
reference along the entire AP axis. Nature found different solution for this intricate patterning problem that is intimately linked to the induction
of mesoderm (pink). In vertebrates (E-G), mesoderm is induced at the most posterior position, i.e., at the oral opening that was enlarged
to a huge ring. The induction of the Spemann-Organizer on this ring is necessarily connected with a symmetry break and the generation of
bilaterality. The midline for the brain is generated dorsally with the movement of organizer-derived cells underneath the ectoderm (yellow)
[13]. The midline of the trunk results from a ring-to-rod transformation (see Fig. 2). The simulation (G) shows a stripe-like midline that
is induced by a moving patch-like signaling center. A second organizer (blue), induced but repelled by the midline, can lead to a left-right
symmetry break [108]. (H-J) In contrast, in insects and in the spider, signaling from the dorsal side (yellow) represses mesoderm and midline
formation. Ventrally a narrow signal with a stripe-like AP-extension induces first mesoderm and then the ventral midline that specifies the
DV-patterning. The simulation (J) shows a stripe-like ventral midline (pink) that results from the repression emanating from a dorsal signaling
center (green). These different mechanisms are assumed to be at the core of the DV-VD reversal in vertebrates and insects [35].
3
ported by the expression patterns of several genes.
Otx, a gene characteristic for the fore- and midbrain
in vertebrates, is expressed in the whole body column
of hydra except of the hypostome and the foot [17].
The posterior border of Otx expression, located in hydra between the tentacles and the hypostome, became
an important secondary organizer in vertebrates, the
midbrain-hindbrain border. In other words, the posterior end of ancestral organism was at a position that
corresponds in today’s animal to the midbrain/hindbrain
border. This is in agreement with the expression of an
Aristaless-related gene in Hydra at the tentacle zone
[18] and in Xenopus in the telen- and diencephalon
[19]. In this view, the aboral side of Cnidarians, e.g.,
the foot in hydra evolved into the most anterior part
of the brain. This fits the expression of six3/6 in Nematostella [20] on the one hand and in vertebrates [21]
and insects [22] on the other. Usually, heart formation
in higher organisms is initiated at a very anterior position. The (anterior) hydra foot is under the control of
the same master gene as the vertebrate heart, Nkx2.5,
suggesting a common ancestry for these two so differently looking organs [23]. Indeed, the hydra foot acts
already as a pump for circulating the gastric fluid.
This scenario provides a rationale why brain formation of insects and vertebrates is under control of
closely related genes [24, 25,26], although their common ancestor certainly did not had an evolved brain;
these expression patterns are the relicts from an ancestral body pattern.
The trunk is an evolutionary later invention and, as
the rule, is also formed later during individual development of an organism. This view is supported by the
observation that Hydra does not posses the 3’-5’ Hox
gene sequence typical for trunk patterning [27]. With
the insertion of the trunk, the posterior organizer realized by Wnt/Brachyury obtained an increasing distance
from the original position at the posterior Otx border.
The midbrain/hindbrain organizer can be regarded as a
replacement that remains at the position of the original
organizer. In his gastrea concept, Ernst Haeckel [28]
proposed already that development of higher organisms generally proceed through a gastrula-like stage.
The scenario I propose modifies this view by postulating that this gastrea stage is equivalent not to the whole
body but only to the brain.
ting up of the oral-aboral axis in the radially-symmetric
Hydra by the Wnt-Brachyury system [29, 30] and its
conservation in higher systems [31, 32] for the organization of the AP axis suggest that the WNT pathway
was involved in organizing an ancestral axial system.
Its self-organizing properties are well investigated in the
Cnidarian system and are theoretically well understood
[33]. This originally small organizer evolved in vertebrates into a large ring, the blastopore. A possible reason for this enlargement could be that this signalling
system became also engaged in mesoderm formation
(Fig. 1). Thus, the geometry of the early AP organizer
in vertebrates is a large ring, not a localized patch as
usual. This could be the reason why this ancestral organizer was often not regarded as such, in contrast to
the patch-like Spemann organizer.
To specify positional information in a twodimensional field, two reference lines are required
to set up a near Cartesian coordinate system, so to
say, an X and a Y axis. Especially for the patterning
of the DV- (or mediolateral-) axis, a stripe-like array
of signalling cells have to generated that extends
along the entire AP axis. The generation of such
an organizing line is an intricate pattern-forming
problem. Stripe-like patterns can be generated if
the self-enhancing component of a pattern-forming
reaction saturates at high concentrations [34]. Due
to this upper bound, the activation has a lower peak
height but obtains a larger extension. Stripes are the
preferred pattern since the activated regions are large
but, nevertheless, non-activated regions are nearby
into which, for instance, the inhibitor can be dumped.
On its own, however, this mechanism would lead to
a periodic stripe pattern as seen in the proverbial zebra stripes. The formation of a single solitary stripe requires cooperation with a second pattern-forming system that makes sure that only a single stripe can
emerge. It was proposed that different mechanism for
midline formation evolved (Fig. 1) [35]. In vertebrates,
the secondary Spemann-type organizer, localized on
the much-enlarged blastopore, initiates and elongates
midline formation in two directions, towards anterior by
giving rise of the prechordal plate and towards posterior
due to the ring-to-rod conversion (Fig. 2). Thus, unusually, for the positional specification of a cell not the distance to the organizer but the distance to the stripe-like
midline induced by the organizer, i.e., to the notochord
and floor plate is decisive [36]. Since the organizer is
dorsally located, the midline emerges also dorsally, has
from the beginning a narrow DV extension but becomes
elongated in the course of time. Since posterior elongation of the midline requires time, the reference line
for DV patterning also emerges in the course of time
with the same pace. This view provides a straightforward explanation why AP and DV patterning in the trunk
3. The generation of the two main body axes
and their correct alignment as a self-organizing
process
Although frequently regarded as the only existing organizer, the Spemann-type organizer in vertebrates,
based on the Chordin-BMP interaction, is neither the
only nor, evolutionary, the earliest organizer. The set4
Fig. 2: Different modes for the ring-to-rod conversion in amphibian and chick development [36]. (A-C) The early amphibian gastrula corresponds to an ancestral body pattern (see Fig. 1). During trunk formation a sequential posteriorization takes place in cells near the blastopore
by activating HOX genes (1, 2, 3..) [12]; (Durston and Zhu, this volume). Cells move towards the organizer (red arrow), leaving the most
posterior zone in which the sequential posteriorization takes place and obtain therewith their final determination. Note that the DV or mediolateral determination can only take place after the corresponding part of the midline is formed; accounting for the observation that AP and DV
determination is under the control of the same developmental clock [37]; (Mullins et al., this volume). Cells antipodal to the organizer (blue
arrow), classically assigned as being ventral, form posterior structures since they remain longest in the zone of posterior transformation. (D-F)
In the chick the ancestral sac-like arrangement became distorted to a near flat disk. The entire outer border (red) resembles the blastopore, a
view supported by the early β-catenin expression there [109]. As in amphibians, the organizer forms on this blastopore. As shown by Gräper
[110], cells at the left and at the right of the organizer move in a ‘polonaise movement’ over the yolk, a movement that can be regarded as
a ‘partial epiboly’ [36]. This leads to a hair-pin like deformation of the blastopore, the primitive streak. In contrast to the notion in many
textbooks, there is no anterior movement of the organizer [110]. Later the organizer (node) moves over the deformed blastopore like the handle
of a zipper. Thus, in amphibians, the ring-to-rod transformation occurs in parallel with posteriorization, relative movement of the organizer and
shrinkage of the blastopore. In the chick, the ring-to-rod transformation occurs first; the movement of the node starts only afterwards.
5
is under control of the same developmental clock [37],
(Mullins et al., this issue). At a particular AP level, the
DV pattern can only be generated after the corresponding part of the midline is generated (Fig. 2). This also
solves some confusion concerning ‘ventral’ in the early
amphibian embryo. Frequently the region antipodal to
the dorsal organizer is declared as ventral. Fate mapping has shown, however, that these cells form the most
posterior structure [38, 39]. In terms of the model, cell
antipodal to the organizer remain longest in the zone
where sequential posteriorization takes place (Fig. 2 B,
C).
In insects and spiders the situation is completely
different. An inhibition spreading from a dorsal signaling center restricts midline formation to the ventral side.
The midline has from the beginning the full AP extension of the embryo but sharpens in the course of time
to a narrow ventral line. The sharpening of the Dorsal transcription in Tribolium [40] is an impressive example for this theoretically predicted mode [41]. In a
spider, a clump of BMP-expressing cells, the cumulus,
move from the center of the germ disk, the blastopore,
towards the periphery - a posterior-to-anterior movement - defining in this way the dorsal side. The midline proper, however, is not formed dorsally behind the
moving cumulus but ventrally due to a cumulus-BMPmediated inhibition of Chordin. Chordin expression and
thus midline formation is focused to a narrow ventral
stripe at maximum distance from the cumulus [42]. The
much discussed DV-VD reversal between vertebrates
and insects [43] was proposed to have its origin in these
different modes of midline formation, invented during
early evolution of bilateral-symmetric body patterning
[35]. In protostomes, a dorsal organizer repels the midline that appears, therefore, ventrally. In contrast, in
deuterostomes, the dorsal organizer elongates the midline that appears, therefore, at the dorsal side.
Most remarkably, these different modes of midline formation are intimately connected with the invention and positioning of mesoderm. In vertebrates, the
mesoderm is formed around the large blastopore at a
most posterior position. A reason for this enlargement
could be that a sufficient number of cells can be specified as mesodermal. In contrast, in insects, mesoderm
is initiated by a newly generated stripe-like signal that
stretches from anterior to posterior; it precedes the formation of the ventral midline and occurs under control
of a different set of genes. These basically different
mechanisms for mesoderm and midline formation suggest that different mechanisms evolved for generating
a bilaterally-symmetric body plan in originally more or
less radial-symmetric organisms. These early differences are in contrast to the concept of an urbilaterian
as a unique bilaterally-symmetric ancestor.
It should also be noted that this view is very different
from the amphistomy concept according to which the
blastopore is closed in a slit-like manner [44]. According to this view, in protostomes the mouth, in deuterostomes the anus remained open. However, in insects
and spiders the blastopore is not involved in the localization of the ‘slit’ at which mesoderm invaginates. In
vertebrates, the blastopore does not close in a slit-like
manner but resembles more a ring that shrinks due to
the preferential removal of material at the site of the
organizer, a closing noose. For a system that was regarded as a prototypical example for a closing slit, the
onychophoran blastopore, it was recently shown that
the posterior end of the slit is not coincident with the
blastopore [45].
4. The role of Wnt antagonists in the view of
the proposed mode of axes formation
There is a surprising diversity of Wnt antagonist, inspiring Brown and Moon to entitle a review “Wnt signaling:
why is everything so negative?” [46]. In terms of the
model, Wnt antagonists are required in several steps for
proper cell specification [36]; (see also Sokol, this volume).The Wnt pathway is crucially involved in amphibians to trigger the Spemann organizer in the marginal
zone. However, due to the posteriorizing nature of the
WNT signal, it is necessary to rapidly switch off Wnt signaling in the organizer shortly after organizer formation.
If not, organizer-derived prechordal plate cells would
carry a posteriorizing activity into the region that should
form the most anterior structure, the forebrain, which
requires low Wnt signalling. Indeed, forebrain formation is lost if the Wnt inhibition in the organizer by Dkk-1
is non-functional [47]. Further, it is necessary to maintain Wnt-signaling restricted to the marginal zone although these cells also ingress; otherwise there would
be no localized source to set up the Wnt gradient. In
the fish, for instance Dkk-1 is expressed first in the organizer and extends later throughout the germ ring [48].
Thus, Dkk-1 could be involved in restricting Wnt to parts
of the marginal zone in spite of the ingression. Analogously, in the ancestral hydra system Dkk seems also
to be involved keeping Wnt signalling localized at the
oral opening [33]. A third expected function of Wnt antagonists is to accomplish a necessary delay in the in
the sequential posteriorization; this will be discussed
further below.
5. From totipotent to differentiated cells: not
as in Waddington’s morphogenetic landscape
Waddington [49] used a well-known analogy to illustrate his view how cell fates become more and more
restricted on the way from the totipotent fertilized egg to
a terminally-differentiated cells: a sphere rolls down in
a valley; new hills within existing valleys lead to branch
6
points at which the sphere has to make a decision; it
can only take the one or the other path. At the end of
its journey the sphere will end up in one of the many
valleys, one of the possible alternative stable states.
This analogy, however, is misleading. It suggests
that the decisions are made at unstable points; the
decision for the one or the other possibility would occur essentially by chance and is essentially irreversible.
Such a mechanism would not be robust. If the position
of a new valley-separating hill would be slightly shifted,
all cells would end up in one valley only. Cell differentiation is achieved by activation of genes under the
influence of transcription factors. At such a delicate situation, a minute change in the ability of transcription
factors to activate the one or the other gene would have
dramatic effects. In Waddington’s analogy, the majority
of cells would end up at the same side; there would be
no chance to obtain differently determined cells in the
correct ratio. Also the situation that precedes the decision would have a decisive impact; a slight deviation
form the correct initial situation would lead to a catastrophic imbalance.
It is not only important that eventually differently determined cells are formed in a correct proportion; they
have to emerge at the correct positions. The frequently
observed ability to regenerate lost structures emphasizes that in many situations later corrections are possible, in contrast to Waddington’s analogy. Nature solved
this sensitivity problem by making decisions not at instable points where minute shifts would have dramatic
and irreversible consequences. To use Waddington’s
analogy, one strategy is that for a particular determination process, all cells start in a particular valley. By
morphogenetic signals, a certain fraction of cells at particular positions are shifted ‘over the hill’ into an adjacent valley. In other words, a determination process
can start with the activation of a default gene. A morphogenetic signal, if high enough and available for a
sufficient time, can lead to the activation of a ‘higher’
gene, which is usually connected with a repression
of the previously-active gene. Mechanisms that allow
such gene activation under the control of a graded morphogen distribution will be discussed in the next section.
A second mechanism involves feedback mechanisms. To use Waddington’s analogy once again, if too
many spheres went to the right valley, the probability increases that other spheres go preferentially to the left.
A corresponding mechanism requires that determining gene activities not only exclude each other locally
(e.g., within the same cell) but mutually support each
other on a longer range. This interaction allows balanced and patterned distributions of differentiated cells
with strong self-regulatory capabilities. The engrailedwingless-hedgehog interaction involved in segmenta-
tion is a typical example of such an interaction; it will
be discussed further below.
This list is not exhaustive. In many cases, fate determination is closely connected to cell division; in each
daughter cell a different set of transcription factors becomes activated - clearly a non-random decision mechanism.
6. Switch-like gene activations by positive
autoregulatory feedback loops
A stable switch-like activation of a single gene can result from a non-linear saturating autocatalytic feedback
of a gene product on the activation of its own gene
(Fig. 3) [50, 51, 2]. The condition of non-linearity is
satisfied if gene activation is not accomplished by the
transcription factor itself but by a dimer. This requirement is easy to understand. At low concentration the
chance of finding a partner for building a dimer is low.
Therefore, the normal first-order decay is dominating
and gene activation will decrease further. If the morphogen signal has an additional activating influence on
this gene activation, with increasing signalling strength,
the rate of dimerization will increases too. From a
certain threshold level onwards, the rate of the nonlinear auto-activation becomes larger than the first order decay rate; gene activation will become stronger
until a saturation level is reached. In other words, under morphogen control gene activation can switch from
an OFF- into an ON-state. This switch requires time
since a certain concentration of the gene product has to
be reached before the activation becomes irreversible.
Due to the positive feedback, the activation can (but
need not) remain in the ON state even if the signal is no
longer available (Fig. 3). The required autoregulation
can be direct but also can be realized by an inhibition
of an inhibition of two transcription factors [2].
7. Gene activation by a graded distribution: a
time-requiring process
According to a classical view and most clearly formulated by Wolpert in his positional information concept
[52], a graded distribution of a morphogen causes an
ordered activation of several genes in a concentrationdependent response. This raises the question how
cells can measure the local concentrations with such a
precision. At particular positions different genes should
reliably be activated in adjacent cells although the differences in the morphogen concentrations are minute.
An analysis of ligation experiments made by Klaus
Sander in the early seventies with non-Drosophila insects [53] suggested that cells do not obtain their final
determination in a single step; instead, they are stepwise ‘promoted’ from one state to the next until the signal concentration is insufficient to accomplish a further
7
Fig. 3: Model for stable activation of a gene under the influence of a morphogen signal. (A) A gene with a non-linear saturating feedback on
its own activation. (B) Such feedback can lead two stable steady states (dg/dt = 0), one at a low and one at a high activation of the gene (red
and blue circles). Whenever the gene activation is higher than the instable steady state (yellow circle), the change is positive; the activation
increases further until the upper steady state is reached. In the presence of an inducing morphogen that causes an additional production of the
gene activator (green curve), only the high steady state may exist (pink circle) leading to the switch from low to high activation that will be
maintained even after the signal is gone [50, 2]. (C) Simulation of gene activation (red) under the control of a gradient (green). All cells that
are above a certain threshold switch into the activated state and remain there even if the gradient is later removed (blue arrow). Note that cells
just above the threshold level need much longer to accomplish the switch. (D) If the saturation of the self-enhancement occurs at a lower level
of activation (higher κ in equation 1, BOX1), the high steady state in the absence of the signal may no longer exist; the switching remains but
the activation ceases after signal removal. The activation of Monopterus under Auxin control [111] is an example.
8
Figure 4: Model for the space-dependent activation of several genes under the control of a morphogenetic gradient. Genes are assumed whose
gene products have a positive non-linear feedback on the activation of their own gene. They compete with each other for activity (Box 1;
equation 2). In a given cell, only one of the alternative genes can be fully active [51, 55, 2]. (A) Starting with activation of a default gene 1
(blue), the genes 2, 3 and 4 become activated in the course of time. Regions with sharp borders are formed. A later reduction of the morphogen
(green to red distribution) remains without effect. The sequential activation of genes proceeds faster in regions of high signal concentration,
which leads to the apparent wave-like movement of gene activities as observed in neural tube determination [56]. Activation of new genes
occurs only in one direction (distal or posterior transformation). (B) Upon a later increase, gene activation adapts to the new level. (C) After a
premature drop of morphogen level, the activation of the gene that is usually activated close to the source (yellow) may fail since the available
time was insufficient; an example can be found in ref [59]. The pixel density indicates activation of particular genes. (D) The unidirectional
promotion allows arbitrary growth without that cells lose their achieved determination (local gene activation indicated by the height of the
bars). (E, F) At an early stage, cells could be too close to the source and the signal so high that activation of the default gene (blue) is lost (E).
A fading maternal antagonist such as Cerberus [112, 113, 114] (yellow,) could delay the promotion until a sufficient extension is achieved; the
activation of the default gene is maintained (F).
9
step [54]. The situation may be compared with a barrel
at the base of a staircase that is lifted up by a flood.
The level at which the barrel comes to rest depends
on the highest level of the flood. A later fading of the
flood remains without effect; a later even higher flood
can deposit the barrel at an even higher level. A corresponding model for gene activation [51, 55, 2] predicted
the following components (Fig. 4):
BOX 1: Models for gene activation under
morphogen control
A switch-like activation of a gene is possible if the
gene product g has a non-linear self-activating feedback on the activation of its own gene [50] (Fig. 3):
cg 2
∂g
− rg + m
=
∂t
1 + κg 2
1
1. A set of genes exists that could be active at a particular stage. The genes have a positive non-linear
feedback on their own activation. The auto-activation
may be realized by a mutual repression of two genes.
2. The activations of such genes are locally exclusive.
For instance, in a particular cell only one gene of the
set can be active.
3. Gene activation starts with a particular default gene.
4. The morphogenetic signal leads to a sequential activation of ‘higher’ genes. Each further step requires
a higher signal concentration and requires a certain
time to activate the subsequent feedback loop. This
time-consuming promotion comes to rest if the local
signal concentration is insufficient to accomplish a
further step.
Equation 2 describes an interaction that allows the
activation of several genes under the influence of a
graded signal m (Fig. 4). A set of genes whose gene
products feed back on the activation of their own gene
compete with each other for activity; the sum term
in the denominator is responsible for the local exclusion; each active gene has an inhibitory influence on
the other genes, including a self-inhibition that leads
to an upper bound in the self-activation. A particular
gene i, i = 1....n becomes activated by the preceding
gene i − 1 in collaboration with the signal m:
ci gi2 + bi gi−1 m
∂gi
Pn
=
− ri gi
∂t
i=1 ci gi
2
Such a mechanism has regulatory properties as experimentally observed. A once achieved gene activation can be stable against a lowering of the signal concentration (Fig. 4). This is a most important feature
since embryos grow (or are subdivided in more and
more cells). Thus, due to the increasing distance between a particular cell and the signaling source, the
local concentration at a particular cell will decrease.
Which of the ever-changing concentration a cell should
measure? The answer given by this model: a cell
measures the highest concentration to which it was exposed at least for a certain time. Due to time averaging and the restriction to unidirectional changes, this
mechanism reduces inherently possible perturbations
by noise in the gradient or in the interpretation machinery.
The predicted stepwise activation has a remarkable
consequence [51, 55] that is now well-known for gene
activation under hedgehog control in the neural tube
[56, 57]. Those genes that are eventually activated at
a distance from the signaling source, i.e., the gene that
requires the lowest signal concentration, become first
activated close to the source at the ventral center, i.e.,
close to the hedgehog-signaling notochord. Later, new
genes become activated at this position that quenches
the activity of the previously activated genes. Gene activation appears to become shifted in a wave-like manner. This shifting reflects only the increasing time required to reach the finally stable activation; it does not
depend on signaling between adjacent cells: the cells
listen only to the local morphogen concentration (Fig.
There are several possibilities to make sure that the
activation of each subsequent gene requires a higher
morphogen concentration. One possibility is that
genes which are less sensitive for the morphogen are
better in the autoregulation. In the equation above,
this requires ci+1 > ci ; (i = gene number; i = 1 corresponds to the default gene; the gene with a higher
number requires a higher morphogen concentration
for its activation). Due to this condition, with each
activation of a subsequent gene, the denominator increases. This has the consequence that the activation
of each further gene requires an even higher signal
concentration. Such an increasing negative feedback
has been observed during neural tube patterning [56].
Under this condition the influence of the signal m in
the activation of the subsequent gene, bi, can remain
essentially the same.
Alternatively, the self-enhancement can remain the
about the same for all genes, but the activating influence of the signal becomes lower with the activation
of a subsequent gene, i.e., bi+1 < bi , causing also
that the signal m has to be higher to achieve a further
step. In both cases, although the signal is smoothly
graded, there is an all-or-nothing response in the activation of the particular genes. This stepping trough
requires time. However, a too-low signal concentration cannot be compensated by a longer exposure of
the responding cell.
10
4). The correct neighborhood depends solely on the
interpretation of the graded signal. This has the consequence that mismatches caused by transplantation at
later stages might be neither detected nor repaired.
A systematic change in the threshold level was predicted in order that the stepwise activation of genes
comes to rest if the morphogen concentration is insufficient to accomplish a further step [51, 55]. Possible
mechanisms are outlined in BOX 1, including that the
activation of a subsequent gene has a negative effect
on the sensitivity. Recently such an increasing negative feedback has been described; the sensitivity for
the hedgehog signal become reduced by upregulation
of patched [56]. For Nodal signaling observations are
available that support both a threshold model and timerequiring dose model (reviewed in [58]). According to
the model proposed, these are just two sides of the
same coin. A certain threshold concentration is required to activate a particular gene, but this activation
is not achieved at once but requires substantial time.
A too-low signal level cannot be compensated by elongating the time of exposure. Also evidence for the predicted behavior that a premature removal of the morphogen source causes that the ‘higher’ genes may not
be activated (Fig. 4C) has been observed, in this case
experimentally achieved by an inhibition of Nodal signaling [59].
A characteristic feature of such systems is that a
once obtained determination can be changed only in
a unidirectional way (distal or posterior transformation).
Therefore, upon transplantation from a region of high
to a region of low concentration, the cells maintain their
already achieved determination. In contrast, after a
low-to-high transplantation, the cells change their determination according to the new level. Strong evidence
for such a unidirectional promotion exists for the hindbrain [60, 61], in the commitment of CNS progenitors
along the dorsoventral axis of Drosophila neuroectoderm [62], and for the response to activin signalling in
the early amphibian gastrula - called there a ‘ratchet’ like behavior [63]. A stepwise posterior transformation
was proposed for the AP-specification in the anterior
neural tube [64]. The involvement of one gene in the
activation of the subsequent gene - a crucial feature for
time-dependent gene activation - has been also shown
in the specification of neural crest cells [65].
The described stepwise promotion is not the only
mechanism that allows the interpretation of a gradient.
An alternative possibility works as follows: If the morphogen has an activating influence on a particular gene
at low and an inhibitory influence at high concentrations, there is an optimal concentration for the activation
of that gene. Other genes of the set have other optimal
levels for activation. Although these activating profiles
are smooth, sharp borders are formed due to the mu-
tual repression of the genes. A characteristic feature of
such a mechanism is that if one gene is missing due to
a mutation, the expression regions of both adjacently
expressed genes expands, indicating that there is no
lower threshold. This is the situation in the activation of
gap genes in Drosophila [66, 67].
This model for the activation of a particular gene
has an interesting formal similarity to pattern formation
in space. In the latter, e.g., for organizer formation, a
particular region has to become activated; the remaining region has to be suppressed. In gene activation,
one gene should become activated while alternative
genes should be repressed. Thus, the activation of a
particular gene can be regarded as a patterning process in the ‘gene space’. Reproducible development is
achieved by a specific coupling between pattern formation in space and pattern formation between alternative
genes.
8. Models for segmentation and the sequential
activation of HOX genes in insects
With a head alone, rapid swimming is impossible. Thus,
the addition of a long extended trunk was a major evolutionary achievement. Characteristic for many phyla is
a segmented trunk. Segments are clearly a periodic
structure, manifested, for instance, by the alternation of
anterior and posterior compartments. Superimposed
is a sequential activation pattern of HOX genes, enabling that individual segments undergo specific developments. Both patterns are precisely in register.
In contrast to Drosophila, in many species the periodic pattern emerges in the course of time during
posterior outgrowth, suggesting that segmentation is
based on genuine pattern-forming reactions. Already
an inspection of morphological structures suggests that
the periodic pattern consists of adjacent narrow stripes
with a short extension along the AP but a long DV extension. To account for a periodic pattern of narrow
stripes we proposed the mechanism of Mutual activation of locally exclusive cell states [68, 2]. A particular
cell type needs cells of another cell type in close proximity. Both cell types provide mutual support for each
other. Narrow adjacent stripes are the preferred pattern
since the long common border allows an efficient mutual stabilization (Fig. 5). The shortly later discovered
engrailed-wingless-hedgehog interaction in segmentation provided direct support. The gene engrailed (en),
the key gene for posterior compartmental specification,
is autocatalytically activated. Via the diffusible molecule
hedgehog (hh), en activates the gene wingless (wg)
that is crucial for the anterior compartment (reviewed
in [69]). The gene cuD, on which wingless-expression
depends, is involved in the local exclusion of en and wg
expression [70]. The gene sloppy paired contributes to
the wg-autoregulation. The wg protein can reach adja11
Fig. 5: Mutual activation of locally exclusive cell states: a basic mechanism in segmentation. (A) Prototypical reaction scheme: two feedback
loops locally exclude each other but activate each other on a longer range [68]. The engrailed-wingless-hedgehog system has turned out to be
of this type [76]. (B) Such a system has pattern-forming capabilities, forming preferentially narrow stripes. (C) Small asymmetries such as a
gradient from a posterior organizer can orient the emergent stripes. (D) With growth at the posterior pole (right), the periodic pattern can be
elongated. Whenever the extension of a particular specification becomes too large, it will switch to the other specification (blue arrow). Thus,
the most posterior cells oscillate - a feature that important for a model of somite formation (Fig. 7).
In this respect it is interesting that engrailed and some
other homeobox genes can be actively exchanged between cells [75].
In contrast to a simple alternation between two
states ....APAPAP.... segments have an internal polarity. For this reason I proposed that, in addition to the
anterior and posterior compartment, at least one additional element, termed S, must be present, such that a
sequence ....SAP/SAP/SAP/.... results. The region S
separates one A-P pair from the next [2]. Now it is generally assumed that the AP pattern of each parasegment is founded by four differently determined cells
(see [76]). Four cells also establish the parasegments
in crustaceans [77]). A subdivision into three or more
compartments has the consequence that only one A/P
border exists per segment. This is important since the
A/P border was proposed to generate a precondition to
form imaginal disks and thus legs or wings [78].
cent cells via vesicle transport and is required there to
stabilize en [71, 72]. As expected from the theory, the
en gene activity requires an active wg gene in its neighbourhood and vice versa, although both genes are transcribed in non-overlapping regions.
Such a mechanism has interesting features appropriate to describe segmentation (Fig. 5). Narrow stripes
can emerge spontaneously. To obtain stripes with an
orientation perpendicular to the AP axis, almost any
asymmetry resulting from the posterior organizing region is sufficient. During posterior outgrowth, more
stripes will be added. This can be connected with an
oscillation at the posterior pole. For example, whenever the size of cells with anterior compartmental specification exceeds a critical limit, a switch to a posterior
specification will occur in the posterior region, and vice
versa. In other words, posterior outgrowth leads to a
periodic change between two (or more) specifications
at the most posterior position (Fig. 5D). The on-offon activation of the hairy gene in the Spider is an example [73]. If stripes obtain a certain width due to an
overall growth, the central part of a thicker stripe can
change its activation, leading to a split. For instance,
in Tribolium the initial even-skipped stripes split at a
later stage [74]. A small diffusion of the self-enhancing
components makes stripes more robust against disintegration into patches or into a salt-and pepper pattern.
9. Formation of a precise number of different
segments during terminal outgrowth
Segments are not only a periodic pattern, but they obtain different specifications, known to be under control
of the HOX gene (reviewed in [79]). Classical observations have shown that the number of segments is precisely controlled. The polychaet Clymenelly torquata,
12
Fig. 6: Model for HOX gene activation in insects in register with the compartmental specification during posterior outgrowth. Assumed
are three compartmental specifications, A (red), P (green) and S (blue) that activate each other in a cyclic way. During outgrowth, a regular
sequence ...A,P,S,A,P,S... emerges (see also Fig. 5). With an at least threefold subdivision, each periodic unit has an intrinsic polarity and only
one AP border per (para-)segment, the precondition that only one wing or leg per segment is formed [78]. To achieve Hox gene activation
in register, a component is assumed to be produced in the anterior compartment that activates of next HOX gene, but its actual activation
is blocked. After a switch to the posterior specification, this activation is no longer blocked but the corresponding component is no longer
produced; the available component concentration allows only a single switch. Thus, a transition from one HOX gene to the next can only occur
with an A-to-P transition in the compartmental specification [2]. (A-D) snapshots at subsequent time points. In (B), the system is ready to
switch from A to P at the posterior position. Shortly later (C), this transition is achieved and the next HOX gene is active (blue arrows) [2].
13
for instance, has 22 segments. If posterior segments
are removed, regeneration occurs such that eventually
22 segments will be present independent of the number
of segments removed [80]. In the leech, initially more
than the final 32 segments might be formed. The surplus segments are later removed by programmed cell
death [81, 82]. These observations indicate that some
sort of counting mechanism exists. In an early model
I proposed that the oscillation between compartmental
specifications at the outgrowing posterior pole is used
to drive the activation of new specifying HOX-genes [2],
similar as the periodic movement of a pendulum drives
the sequential advancement of the pointer of a grandfather’s clock. Each full cycle leads to the advancement by one and only one unit - a stop and go mechanism. Fig. 6 shows a simulation. According to our
present knowledge, this early model has to be modified and extended because particular HOX genes are
known to be active in several segments. However, there
are segment-specific cis-regulatory units on the chromosome, which are separated by chromosomal insulators [83,84, 85] In terms of the model, each oscillatory
cycle may cause the advancement from one such insulator to the next, suggesting that a certain number of
insulators have to be passed until the activation of the
subsequent HOX gene takes place.
moves from anterior to posterior that initiates somite
formation. In addition, an oscillation was assumed;
each full activation causes for a short period the suppression of somite formation and thus the separation of
one somite from the next. The frequency of the oscillation was assumed to depend on the overall size
of the embryo, the smaller the embryo the higher the
frequency. Assuming a constant velocity of the wave,
this would lead to a regulation of A-P extension of
the somites in relation to the total size of the embryo.
Cooke found shortly later that the frequency of the oscillation is not size-dependent, but the clock and wave
front model was born. Cooke and Zeeman did not formulate their model in a mathematical way. However,
such a model can be easily provided by the toolkits of
pattern-forming reactions (Fig. 7A).
Already in the early eighties it became clear that the
clock and wave front model was not tenable in this form.
Important information in this pre-molecular time came
from heat shock experiments [90]. After a short heat
shock - much shorter then the time required to from a
somite - about fife additional somites formed in an unperturbed manner, indicating that these somites were
already determined. In later-formed somites, characteristic perturbations occurred such as partial Y-shaped
splits of somites into two or to an incomplete border between two somites (Fig. 7B). Such an irregularity is frequently followed by a second irregularity that compensates partially the first, allowing that subsequent somite
formation can return to normal. In my view, this is a
strong indication that a component of spatial patterning is involved that attempts to maintain a certain spatial wavelength. This feature has been disregarded in
many contemporary models but has found recently direct experimental support. Somite formation has been
observed in cell culture in the absence of any waves
[91].
To maintain the posterior oscillation in a model for
somite formation I proposed that an oscillation between
two states takes place in the posterior portion of the vertebrate embryo [2, 92]. In contrast to the insect case
(Fig. 5) the oscillation was proposed to be no longer
restricted to the posterior pole but to extend anteriorly
up to region in which somite formation occurs. The
mechanism explained above for segmental patterning
in space (Fig. 5) also can act as an oscillator (Fig. 7).
For instance, if only A cells are present, the P-cell state
will get strong support, while the support of the A state
by cells in the P state is missing. Thus, cells will switch
from A to P and, for the same reason, later back to A.
In other words, the cells will oscillate between the two
states (Fig. 7C). How can the transition from a posterior oscillating into an anterior stable spatial pattern be
enforced? Imagine that initially only one A region exists
at the anterior end, the remaining cells are all in the P
10. Somite formation: the conversion of a
periodic pattern in time into a periodic pattern
in space
In contrast to insects, segmentation in vertebrates
takes place in the mesoderm. In the hemichordate Amphioxus somites form similar as in short germ insects
in a growth zone at the posterior pole [86]. In contrast, in higher vertebrates, somite formation occurs at
a considerable distance from the posterior pole by a sequential separation from a non-segmented presomitic
mesoderm (PSM) in an anterior-to-posterior sequence.
Somite formation has been reviewed extensively [87,
88] (see also the article of Oates in this volume). Therefore, the following remarks are restricted to some historical notes in somite modeling and to inherent parallels
to insect segmentation.
The first model for somite formation has been proposed by Cooke and Zeeman [89]. Their ‘clock and
wave front model’ was name-giving for many later models. It has an interesting background. In careful experiments Jonathan Cooke found that removal of material
from the ventral side of an amphibian embryo leads to
shorter embryos. Thus, most remarkable, the AP, not
the DV extension of the somites became smaller, although the material was removed from the ventral side.
In an attempt to find an explanation, Cooke and Zeeman considered a model according to which a wave
14
Fig. 7: Different concepts in oscillation-driven models of somite formation. (A) A mathematically-formulated version of the ‘clock and wave
front model’ of Cooke and Zeeman [89]. Similar as in an infection wave, a wave is generated by a self-enhancing activator (dark green) and
a non-diffusible inhibitor (red) that has a longer half life. The diffusion of the activator leads to the wave-like spread [115], showing up in the
time record as an oblique line. The wave triggers the irreversible activation of a gene causing somite formation (brown) in a switch-like manner
(see Fig. 3). A similar assumption was made for the oscillation; a more rapid spread of both components (blue and light green) leads to a
global synchronization. A burst in the oscillation blocks gene activation for somite formation, leading to a separation between two somites. (B)
Experiments of Elsdale and Pearson [90] have shown that characteristic perturbations can occur after a short heat shock. If a somite becomes
too large, a partial border will be inserted or an existing border can split, suggesting that a pattern-forming mechanism is involved that has an
inherent spatial wave length. (C) The mutual activation mechanism (Fig. 5) can work as an oscillator. An A region (red) next to a P region
(green) is stabilized, the remaining P cells switch to the A state, forming a new stable A-region, and so on. With each full cycle, one new stable
A-P pair is added. During later terminal growth, further A-P pairs can be added without oscillations, allowing a smooth transition between
both modes. (D) Model of somite formation based on posterior oscillations between two cell states [2, 92]. Oscillation becomes arrested and
stable patters are formed whenever the level of a gradient (pink) drops below a certain level, determining the AP level at which stable patterns
emerge. The gradient is now known to be FGF [96]. The mechanism, proposed in 1982, predicted correctly many unexpected features that
were later experimentally observed [93].
15
activities towards anterior appeared counter-intuitive,
it was the only mechanism I found to be compatible
with classical observations and to have some relations
to the model derived for insect segmentation. It took
fifteen years until essential points of this model were
shown to be correct [93, 94]. It turned out that the
model predicted correctly that there is
BOX 2: Time-dependent gene activation
For the purely time-dependent gene activation it is assumed that each active gene i produce a component pi
that has an activating influence on the activation of the
subsequent gene: The region in which posterior transformation can take place is restricted, for instance,
due to the requirement of a high BMP/Brachyury concentration [100]. This signal s in cooperation with the
signal pi produced by presently active gene drives the
activation of the subsequent gene:
∂pi
= αgi − βi pi
∂t
1. An out of phase oscillation between two activities
(one turned out to involve components of the Wnt
pathway [94]).
2. Each of these alternating activities gives rise to one
half-somite. The existence of half-somites was also
a prediction since this feature has been shown only
two years later [95].
3. A gradient assumed to control the posterior maintenance versus the anterior block of oscillation; it
turned out that this gradient is realized by FGF [96].
3
The region in which posterior transformation can take
place is restricted, for instance, due to the requirement
of a high BMP/Brachyury concentration [100]. This
signal s in cooperation with the signal pi produced
by presently active gene drives the activation of the
subsequent gene:
2
ci+1 gi+1
+ bpi s
∂gi+1
Pn
=
− ri+1 gi+1
∂t
i=1 ci gi
Although the model predicted the essential and unexpected elements correctly, it was frustrating for me
that in the seminal experimental paper the model was
quoted as follows [93]: “Our results also argue against
models in which a reaction-diffusion mechanism patterns the rostral PSM into two states that lead to the
segregation of alternating anterior and posterior somitic
compartments (Meinhardt, 1986)” [92]. There was no
discussion that the main features were correctly predicted.
In the model I proposed there is only a moderate slowing down of the waves on their way towards
anterior; there is a rather abrupt separation between
still oscillating cells and cells that obtained their anterior/posterior half-somitic specification (Fig. 7D). This
is in contrast to what was later observed [97]. However,
as expected from the model, it was found that cells stop
oscillation in discrete groups, not in a continuous wavelike process that moves towards posterior [98]. This is
not surprising since in nonlinear oscillations it is to be
expected that cells either go through another cycle or
stop. Any model according to which an oscillation can
be arrested at an arbitrary phase of the cycle is molecularly not realistic. An interesting feature not yet understood is that the slowing down of the wave is connected
with an increase in the amplitude [98].
It should be emphasized that the 1982-model [2]
was very different from the original clock and wave front
model [89]. In the latter there are no waves moving
from posterior towards anterior that come to rest in the
somite-forming zone; the oscillation was assumed to
separate two somites, not being involved in the formation of half-somites. Thus, the original clock and wave
front model predicted a completely different mechanism
with little resemblance to what was later found.
4
Although models for gene activation under the influence of a morphogen gradient and the time-dependent
gene activation share many formal similarities, the actual mechanisms are presumably more different. The
first process depends on a direct activation of transcriptional feedback loops. In the second, the activation of HOX genes, on the opening of chromatin
regions play a decisive role [116]. In this model, a
newly activated gene suppresses completely the previously activated gene (Fig. 8). In reality, the switching
off is not as abrupt.
state. The direct P-neighbors of the A-cells are stabilized, while the other will switch to the alternative state.
With each complete cycle one new pair of A/P specifications is added. In the course of time the region
of stable periodic patterning would enlarge on the expense of regions in which cells still oscillate. To obtain
a first border and to get a regular and size-regulated
pattern, I assumed that a gradient with a high posterior
point exist; in a region of high concentration the oscillation is maintained. Thus, formation of a stable pattern
needs a low gradient level as given at a certain distance from the posterior pole. The posterior-spreading
front where somite formation occurs is an indirect consequence of the sequential stabilization, not of an independent wave-forming mechanism as in the ‘Clock and
wave front’ mechanism.
Although the posterior oscillation and spread of this
16
sequent HOX-gene (BOX 2). It is only produced in the
region where the signal from the AP-organizer is high,
i.e., close to the organizer (the restriction to the nonorganizer mesoderm is ignored in this one-dimensional
simulation). While models of this kind can be easily
constructed, so far it is unknown how both the periodic pattern of the somites and the sequential pattern
of Hox-gene activation can be brought so precisely into
register.
What terminates the time-dependent posteriorization? Although mainly involved in the DV patterning by
midline formation, the Spemann-type organizer plays a
crucial role also in the AP patterning of the trunk by
being involved in the termination of the time-dependent
posteriorization. This is an unusual function of an organizer since, as the rule, the strength of an organizerderived signal determines the fate of a cell. In amphibians, cells of the non-organizer mesoderm move
towards the organizer and join the elongating midline
(Fig. 2). Due to this movement, cells leave the zone
in which posterior transformation takes place, obtaining
in this way their final AP determination. As mentioned
above, after removal of the organizer, the anterior neuronal genes were almost normally expressed in fishes
mutant for BMP [15]. The AP pattern of the trunk, however, was completely missing. This is in agreement with
the view that, due to the absence of the organizer, cells
were unable to escape from the posteriorization until
the most terminal determination is reached.
Fig. 8: Simulation of space- and time-dependent gene activation
for the regionalizing the AP axis. (A-C) Genes in the anterior part
are activated by a promotion of under the influence of a gradient
(red) generated by an organizer (green), as described in Fig. 4. Assumed is an activator-inhibitor system; the inhibitor (red) has a double function, keeping the organizer localized and act by its longer
range as signal for gene activation. Gene activations are indicated
by pixel densities. To achieve a time-dependent gene activation of
the more posterior genes 4 to 8, whenever the terminal signal is
high enough, each gene produces a component that activates the
subsequent gene (BOX 2). The accumulation of this component is
decisive when the next switch will occur. Thus, the time-based posteriorization is restricted to a region near the organizer; in the more
anterior region the determination is fixed. (D) If growth would be
arrested in a stage as shown in (B), the posterior transformation
would proceed autonomously until the most posterior gene is activated. (E) If the time-dependent posteriorization would not work,
only the anterior (head-) genes can be activated.
12. A possible scenario for the evolutionary
invention of segmentation: giving up complete
separation during asexual reproduction
Segmentation, the metameric repetition of body parts,
was certainly a fundamental evolutionary invention, for
instance, to allow rapid swimming. Many proposals for
its evolutionary origin has been put forward [101]. Although segmentation in insects and vertebrates share
some common features, it is still controversially discussed whether both processes have a common evolutionary origin [102, 103].
Segmentation emerged and was lost several times
during evolution, suggesting that segmentation was derived from mechanisms that were available early in evolution in non-segmented animals for a different purpose. Here I propose that one of the preceding mechanisms was asexual reproduction. Primitive organism
are usually organized by two organizing regions, one at
each pole, head/tail or aboral/oral. One way of asexual reproduction is the insertion of a new tail (T) - head
(H) pair, (T/H), somewhere in the body column, converting H—–T pattern into a pattern H—T/H–T pattern,
followed by a separation at the new T/H border; leading
two organisms with identical polarity. Such a separa-
11. Time-dependent activation of HOX-genes
Ironically, one of the reasons to predict the oscillation the possibility to achieve a precise sequential activation
of HOX genes in relation to the periodic pattern - seems
no longer tenable. In mutants that have a longer oscillation frequency, the next HOX gene becomes activated
after a certain time, not after a particular number of oscillations [99]. Also both processes take place in different regions of the developing embryo. New HOX-genes
are activated the horseshoe-shaped region around the
blastopore excluding the midline and organizer [100].
In contrast, oscillations and waves occur at the dorsal
midline, i.e., in a complementary region.
The sequential promotion model as proposed for
the interpretation of a gradient (Fig. 4) can be extended
in a straightforward manner to achieve a sequential
‘promotion’ in the course of time. For the simulation Fig.
8 it was assumed that the anterior genes are activated
under gradient control as described above. For the
more posterior genes, each (HOX-) gene produces a
component that has an activating influence on the sub17
Fig. 9: A hypothetical scenario for the evolutionary invention of segmentation by modification of asexual reproduction. (A) The anteroposterior
axis of ancestral organisms is organized by two organizing regions, one for anterior (head, pink, left) and one for posterior (tail, green), realized
e.g., by the WNT-pathway. To reproduce asexually, a new pair of tail/head organizers becomes inserted, followed by a separation that gives rise
to two complete animals. (B) For segmentation, the insertion of the Wnt-expressing regions was maintained that forms, not accidentally, the
most posterior part of each parasegment. In contrast, the head signal was replaced by a signal ‘beginning of the trunk’ (e.g., engrailed, red). The
separation into individual animals became replaced by the generation of metameric structures that no longer separate from the parental body.
The sequential insertion of Wnt signals in short germ insects [106] follows the proposed scheme. (C, D) A system at the borderline between
asexual reproduction and segmentation, the strobilation of Aurelia [107]. In the polyp stage (C) a repetitive structures is generated that leads to
the shedding off of juvenile Medusas (D); (figure C and D kindly supplied by Barbara Siefker).
tion occurs spontaneously, for instance, in the flatworm
Stenostonum incaudatum [104].
According to this view, crucial for the transition from
asexual reproduction to segmentation was the replacement of the tail/head insertion by another pair that didn’t
led to a separation. Wnt is involved in both the formation of the posterior terminal end of animals and in the
formation of the most posterior part of parasegments
[105]. This suggests that the Wnt pathway was originally involved in the determination of the posterior pole.
Whenever asexual reproduction should occur by insertion of a new tail-head pair, a Wnt activity has to be
triggered somewhere between head and tail (Fig. 9A).
The insertion of new Wnt regions during growth of short
germ insects [106] is proposed to be conserved from
this ancestral process. It is the expected pattern of
a terminal gene that was once involved in asexual reproduction and that became subsequently adopted for
segmentation (Fig. 9). For segmentation, the insertion of a new WNT activity occurs whenever sufficient
space is available between the terminal Wnt expression and the already established Wnt regions [106], a
feature that is explicable in a straightforward manner by
our toolkit of pattern-forming reactions.
In insects the most anterior part of each parasegment is specified by the engrailed gene. engrailed (see
[76] for review) has no function in the determination of
the anterior-most structures in any organism. In vertebrates it is activated at the mid/hindbrain border, i.e.,
at a region that can be regarded as the most anterior part of the trunk. This suggests that the insertion
of tail/head pairs for asexual reproduction became replaced by pairs of signals for end/begin of primordial
trunks. The physical separation of the animals was replaced by the formation of metameric units; the integrity
of the anteroposterior axis became maintained.
A possible link between asexual reproduction and a
segmentation-like process can be seen in the strobilation process of asexual reproduction in some Cnidaria.
Aurelia aurata (Scyphozoa) forms first a polyp. Starting at the tentacle region a repetitive pattern is formed
that is overtly very reminiscent of a segmented structure (Fig, 9C) [107] A substantial part of the polyp
around the foot remains non-segmented. Later, these
metameric units are released as individual ephyra (Fig.
9D), the juvenile form of the medusa (jellyfish). Extrapolating the situation from hydra [16] the non-segmented
part around the foot is the anterior part of the organism. It is a common feature of many segmented animals that only the posterior part becomes segmented.
The tentacle-bearing part at which the ‘segmentation’
starts is posterior. In this case, the segmentation does
18
not take place in a posterior growth zone but, unusually, by trigger of an alternating repetitive pattern at a
posterior position that spreads towards anterior.
Thus, it is proposed that, as sexual reproduction became the dominant mode of reproduction, asexual reproduction became obsolete and was modified to an
incomplete separation as seen in today’s segmentation. The evolutionary advantage is clear. The repetitive segmental organization can provide the scaffold,
e.g., for muscle and neuronal organization to allow a
coordinated movement. During further evolution some
of the segments could specialize to take over particular
functions including sexual reproduction.
[2] Meinhardt H. Models of Biological Pattern Formation. Acad Press
London, available at
http://www.eb.tuebingen.mpg.de/meinhardt/82-book
[3] Meinhardt H. Models of biological pattern formation: from elementary steps to the organization of embryonic axes. Curr Top Dev
Biol 2008;81:1-63.
[4] Schier AF. Nodal Morphogens. Cold Spring Harb Perspect Biol
Doi101101cshperspecta003459 2009:0000.
[5] Müller P, Rogers KW, Jordan BM, Lee JS, Robson D, Ramanathan
S, et al. Differential diffusivity of Nodal and Lefty underlies a
reaction-diffusion patterning system. Science 2012;336:721-4.
[6] Meinhardt H. Dorsoventral patterning by the Chordin-BMP pathway: a unified model from a pattern-formation perspective for
Drosophila, vertebrates, sea urchins and Nematostella. Dev Biol
2015: doi:10.1016/j.semcdb.2015.06.005
[7] Lutz H. Sur la production expérimentale de la polyembryonie et de
la monstruosité double chez les oiseaux. ArchAnat Micro Morph
1949;38:79-144.
[8] Kiecker C, Niehrs C. A morphogen gradient of wnt/β-catenin signalling regulates anteroposterior neural patterning in Xenopus.
Development 2001;128:4189-201.
[9] Nordström U, Jessell TM, Edlund T. Progressive induction of
caudal neural character by graded Wnt signaling. Nat Neurosci
2002;5:525-32.
[10] Dorsky RI, Itoh M, Moon RT, Chitnis A. Two tcf3 genes cooperate
to pattern the zebrafish brain. Development 2003;130:1937-47.
[11] Green D, Whitener AE, Mohanty S, Lekven AC. Vertebrate nervous system posteriorization: Grading the function of Wnt signaling. Dev Dyn 2015;244:507-12.
[12] Wacker SA, Jansen HJ, McNulty CL, Houtzager E, Durston AJ.
Timed interactions between the Hox expressing non-organiser
mesoderm and the Spemann organiser generate positional information during vertebrate gastrulation. Dev Biol 2004;268:207-19.
[13] Kiecker C, Niehrs C. The role of prechordal mesendoderm in
neural patterning. Curr Opin Neurobiol 2001;11:27-33.
[14] Zoltewicz JS, Gerhart JC. The Spemann Organizer ofXenopusIs
Patterned along Its Anteroposterior Axis at the Earliest Gastrula
Stage. Dev Biol 1997;192:482-91.
[15] Ober EA, Schulte-Merker S. Signals from the yolk cell induce
mesoderm, neuroectoderm, the trunk organizer, and the notochord in zebrafish. Dev Biol 1999;215:167-81.
[16] Meinhardt H. The radial-symmetric hydra and the evolution of the
bilateral body plan: an old body became a young brain. BioEssays
2002;24:185-91.
[17] Smith KM, Gee L, Blitz IL, Bode HR. CnOtx, a member of the
Otx gene family, has a role in cell movement in hydra. Dev Biol
1999;212:392-404.
[18] Smith KM, Gee L, Bode HR. Hyalx, an aristaless-related
gene, is involved in tentacle formation in hydra. Development
2000;127:4743-52.
[19] Miura H, Yanazawa M, Kato K, Kitamura K. Expression of a novel
aristaless related homeobox gene arx in the vertebrate telencephalon, diencephalon and floor plate. Mech Dev 1997;65:99109.
[20] Sinigaglia C, Busengdal H, Lecl?re L, Technau U, Rentzsch F.
The bilaterian head patterning gene six3/6 controls aboral domain
development in a Cnidarian. PLoS Biol 2013; doi: 10.1371/journal.pbio.1001488.
[21] Oliver G, Mailhos A, Wehr R, Copeland NG, Jenkins NA, Gruss
P. Six3, a murine homologue of the sine oculis gene, demarcates
the most anterior border of the developing neural plate and is expressed during eye development. Development 1995;121:404555.
[22] Blanco J, Pauli T, Seimiya M, Udolph G, Gehring WJ. Genetic
interactions of eyes absent, twin of eyeless and orthodenticle
regulate sine oculis expression during ocellar development in
Drosophila. Dev Biol 2010;344:1088-99.
[23] Shimizu H, Fujisawa T. Peduncle of Hydra and the heart of
higher organisms share a common ancestral origin. Genesis
2003;36:182-6.
13. Conclusion
In pre-molecular times, classical observations provided
a very informative set of regulatory features. To find
possible molecular interactions we formulated hypothetical molecular interactions that described the production, spread, removal and the mutual regulatory interferences between the components in a mathematical
way. By simulating patterning processes on the computer it turned out that the classical observations were
very restrictive. Differences between the observed and
model-expected regulatory features allowed reformulating the hypotheses and checking again; the models
evolved. If a particular model was then able to describe
even more details than originally envisioned, the models found increasing confidence. These models are, of
course, minimum models; they describe what is at least
required to accomplish a particular step. The minimum
models however, provide a basis to understand what is
going on. Self-enhancing reactions combined with antagonistic reactions are the driving force in these selforganizing processes, both in spatial patterning and in
space-depending gene activation. With the advent of
the molecular techniques, it turned out that most of
these models were close to what is actually realized.
An intimate interaction between theory and observation
contributed substantially in most branches of natural
sciences to the progress. Theories and mathematically
formulated models are now an accepted tool in developmental biology, bridging the gap between the observations on the one hand and underlying principles on
the other. By accepting theories, developmental biology became a normal branch of science.
Acknowledgment I wish to express my thanks to Alfred
Gierer. Much of the basic work on pattern formation
emerged from a fruitful collaboration and exchange of
ideas over many years.
14. References
[1] Gierer A, Meinhardt H. A theory of biological pattern formation.
Kybernetik 1972;12:30-9.
19
[24] Hirth F, Kammermeier L, Frei E, Walldorf U, Noll M, Reichert H.
An urbilaterian origin of the tripartite brain: developmental genetic
insights from Drosophila. Development 2003;130:2365-73.
[25] Lowe CJ, Wu M, Salic A, Evans L, Lander E, Stange-Thomann N,
et al. Anteroposterior patterning in hemichordates and the origins
of the chordate nervous system. Cell 2003;113:853-65.
[26] Sprecher SG, Reichert H. The urbilaterian brain: developmental insights into the evolutionary origin of the brain in insects and
vertebrates. Arthropod Struct Dev 2003;32:141-56.
[27] Kamm K, Schierwater B, Jakob W, Dellaporta SL, Miller DJ. Axial patterning and diversification in the cnidaria predate the hox
system. Curr Biol 2006;16:920-6.
[28] Haeckel E. The Gastraea-theory, the phylogenetic classification
of the animal kingdom and the homology of the germ lamellae. Q
J Micr Sci 1874;14:142-65.
[29] Hobmayer B, Rentzsch F, Kuhn K, Happel CM, Cramer von Laue
C, Snyder P, et al. Wnt signalling molecules act in axis formation
in the diploblastic metazoan hydra. Nature 2000;407:186-9.
[30] Holstein TW, Hobmayer E, Technau U. Cnidarians: an evolutionarily conserved model system for regeneration? Dev Dyn
2003;226:257-67.
[31] Wu LH, Lengyel JA. Role of caudal in hindgut specification
and gastrulation suggests homology between Drosophila amnioproctodeal invagination and vertebrate blastopore. Development
1998;125:2433-42.
[32] Martin BL, Kimelman D. Wnt signaling and the evolution of embryonic posterior development. Curr Biol 2009;19:R215-9.
[33] Meinhardt H. Modeling pattern formation in hydra - a route
to understand essential steps in development. Int J Dev Biol
2012;56:447-62.
[34] Meinhardt H. Growth and patterning - dynamics of stripe formation. Nature 1995;376:722-3.
[35] Meinhardt H. Different strategies for midline formation in bilaterians. Nat Rev Neurosci 2004;5:502-10.
[36] Meinhardt H. Primary body axes of vertebrates: generation of a
near-Cartesian coordinate system and the role of Spemann-type
organizer. Dev Dyn 2006;235:2907-19.
[37] Hashiguchi M, Mullins MC. Anteroposterior and dorsoventral patterning are coordinated by an identical patterning clock. Development 2013;140:1970-80.
[38] Lane MC, Sheets MD. Rethinking axial patterning in amphibians.
Dev Dyn 2002;225:434-47.
[39] Agathon A, Thisse C, Thisse B. The molecular nature of the zebrafish tail organizer. Nature 2003;424:448-52.
[40] Chen G, Handel K, Roth S. The maternal nf-kappa b/dorsal gradient of tribolium castaneum: dynamics of early dorsoventral patterning in a short-germ beetle. Development 2000;127:5145-56.
[41] Meinhardt H. Models for positional signalling with application to
the dorsoventral patterning of insects and segregation into different cell types. Dev Suppl 1989; 169-80
[42] Akiyama-Oda Y, Oda H. Axis specification in the spider embryo:
dpp is required for radial-to-axial symmetry transformation and
sog for ventral patterning. Development 2006;133:2347-57.
[43] Arendt D, Nübler-Jung K. Inversion of dorsoventral axis. Nature
1994;371:26-26.
[44] Arendt D, Nübler-Jung K. Dorsal or ventral - similarities in fate
maps and gastrulation patterns in annelids, arthropods and chordates. Mech Dev 1997;61:7-21.
[45] Janssen R, Jorgensen M, Lagebro L, Budd GE. Fate and nature
of the onychophoran mouth-anus furrow and its contribution to the
blastopore. Proc R Soc B-Biol Sci 1805 101098rspb20142628
2015:0000.
[46] Brown JD, Moon RT. Wnt signaling - why is everything so negative? Curr Opin Cell Biol 1998;10:182-7.
[47] Kazanskaya O, Glinka A, Niehrs C. The role of Xenopus dickkopf1 in prechordal plate specification and neural patterning. Development 2000;127:4981-92.
[48] Hashimoto H, Itoh M, Yamanaka Y, Yamashita S, Shimizu
T, Solnica-Krezel L, et al. Zebrafish dkk1 functions in fore-
brain specification and axial mesendoderm formation. Dev Biol
2000;217:138-52.
[49] Waddington CH. The strategy of the genes. Geo Allen Unwin
Lond 1957:0000.
[50] Meinhardt H. Morphogenesis of lines and nets. Differentiation
1976;6:117-23.
[51] Meinhardt H. Space-dependent cell determination under the control of a morphogen gradient. J Theor Biol 1978;74:307-21.
[52] Wolpert L. Positional information and the spatial pattern of cellular differentiation. J Theor Biol 1969;25:1-47.
[53] Sander K. Pattern formation in longitudinal halves of leaf hopper
eggs (Homoptera) and some remarks on the definition of “Embryonic regulation.” Wilhelm Roux Arch 1971;167:336-52.
[54] Meinhardt H. A model of pattern formation in insect embryogenesis. J Cell Sci 1977;23:117-39.
[55] Meinhardt H. Models for the generation and interpretation of gradients. Cold Spring Harb Perspect Biol 2009; doi: 10.1101/cshperspect.a001362.
[56] Ribes V, Briscoe J. Establishing and interpreting graded Sonic
Hedgehog signaling during vertebrate neural tube patterning: the
role of negative feedback. Cold Spring Harb Perspect Biol 2009,
doi: 10.1101/cshperspect.a002014.
[57] Balaskas N, Ribeiro A, Panovska J, Dessaud E, Sasai N,
Page KM, et al. Gene regulatory logic for reading the Sonic
Hedgehog signaling gradient in the vertebrate neural tube. Cell
2012;148:273-84.
[58] Dubrulle J, Jordan BM, Akhmetova L, Farrell JA, Kim SH,
Solnica-Krezel L, et al. Response to nodal morphogen gradient
is determined by the kinetics of target gene induction. Elife 2015
http://dx.doi.org/10.7554/eLife.05042.
[59] Gritsman K, Talbot WS, Schier AF. Nodal signaling patterns the
organizer. Development 2000;127:921-32.
[60] Gould A, Itasaki N, Krumlauf R. Initiation of rhombomeric HoxB4
expression requires induction by somites and a retinoic acid pathway. Neuron 1998;21:39-51.
[61] Grapin-Botton A, Bonnin MA, Sieweke M, Le Douarin NM.
Defined concentrations of a posteriorizing signal are critical for
MadB/Kreisler segmental expression in the hindbrain. Development 1998;125:1173-81.
[62] Udolph G, Lüer K, Bossing T, Technau GM. Commitment of CNS
progenitors along the dorsoventral axis of Drosophila neuroectoderm. Science 1995;269:1278-81.
[63] Gurdon JB, Harger P, Mitchell A, Lemaire P. Activin signalling and
response to a morphogen gradient. Nature 1994;371:487-92.
[64] Nieuwkoop PD. Activation and organization of the central
nerveous system in amphibians. III Synthesis of a new working
hypothesis. J Exp Zool 1952;120:83-108.
[65] Simões-Costa M, Bronner ME. Insights into neural crest development and evolution from genomic analysis. Genome Res
2013;23:1069-80.
[66] Jäckle H, Tautz D, Schuh R, Seifert E, Lehmann R. Crossregulatory interactions among the gap genes of Drosophila. Nature 1986;324:668-70.
[67] Meinhardt H. Hierarchical inductions of cell states: a model for
segmentation in Drosophila. J Cell Sci Suppl 1986;4:357-81.
[68] Meinhardt H, Gierer A. Generation and regeneration of sequences of structures during morphogenesis. J Theor Biol
1980;85:429-50.
[69] Ingham P, Hidalgo A. Regulation of wingless transcription in the
Drosophila embryo. Development 1993;117:283-91.
[70] Eaton S, Kornberg T. Repression of cubitus interruptus Dominant
expression in the posterior compartment by engrailed. Genes Dev
1990;4:1074-83.
[71] Baker NE. Molecular cloning of sequences from wingless, a segment polarity gene in Drosophila the spatial distribution of a transcript in embryos. Embo J 1987;6:1765-74.
[72] Van den Heuvel M, Nusse r, Jonston P, Lawrence P. Distribution
of the wingless gene product in Drosophila embryos: a protein
involved in cell cell communication. Cell 1989;59:739-49.
20
[73] Damen WGM, Weller M, Tautz D. Expression patterns of hairy,
even-skipped, and runt in the spider cupiennius salei imply that
these genes were segmentation genes in a basal arthropod. Pnas
2000;97:4515-9.
[74] El-Sherif E, Averof M, Brown SJ. A segmentation clock operating
in blastoderm and germband stages of Tribolium development.
Development 2012;139:4341-6.
[75] Maizel A, Tassetto M, Filhol O, Cochet C, Prochiantz A, Joliot A.
Engrailed homeoprotein secretion is a regulated process. Development 2002;129:3545-53.
[76] Ingham PW. Segment polarity genes and cell patterning within
the Drosophila body segment. Curr Op Gen Dev 1991;1:261-7.
[77] Scholtz G, Patel NH, Dohle W. Serially homologous engrailed
stripes are generated via different cell lineages in the germ band
of amphipod crustaceans (malacostraca, peracarida). Int J Dev
Biol 1994;38:471-8.
[78] Meinhardt H. Cell determination boundaries as organizing regions for secondary embryonic fields. Dev Biol 1983;96:375-85.
[79] Mallo M, Alonso CR. The regulation of hox gene expression during animal development. Development 2013;140:3951-63.
[80] Moment GB. Simultaneous anterior and posterior regeneration
and other growth phenomena in maldanid polychaetes. J Exp
Zool 1951;117:1-13.
[81] Fernandez J, Stent GS. Embryonic-development of the hirudinid
leech hirudo-medicinalis - structure, development and segmentation of the germinal plate. J Embryol Exp Morphol 1982;72:71-96.
[82] Shankland M. Leech segmentation - cell lineage and the formation of complex body patterns. Dev Biol 1991;144:221-31.
[83] Drewell RA, Bae E, Burr J, Lewis EB. Transcription defines the
embryonic domains of cis-regulatory activity at the Drosophila
bithorax complex. Pnas 2002;99:16853-8.
[84] Estrada B, Casares F, Busturia A, Sanchez-Herrero E. Genetic
and molecular characterization of a novel iab-8 regulatory domain
in the abdominal-b gene of Drosophila melanogaster. Development 2002;129:5195-204.
[85] Maeda RK, Karch F. The bithorax complex of Drosophila an exceptional Hox cluster. Curr Top Dev Biol 2009;88:1-33.
[86] Schubert M, Holland LZ, Stokes MD, Holland ND. Three amphioxus wnt genes (amphiwnt3, amphiwnt5, and amphiwnt6) associated with the tail bud: the evolution of somitogenesis in chordates. Dev Biol 2001;240:262-73.
[87] Aulehla A, Herrmann BG. Segmentation in vertebrates: clock
and gradient finally joined. Genes Dev 2004;18:2060-7.
[88] Hubaud A, Pourquié O. Signalling dynamics in vertebrate segmentation. Nat Rev Molec Cell Biol 2014;15:709-21.
[89] Cooke J, Zeeman EC. A clock and wavefront model for control of
the number of repeated structures during animal morphogenesis.
J Theor Biol 1976;58:455-76.
[90] Elsdale T, Pearson M. Somitogenesis in amphibia. II. Origins in
early embryogenesis of two factors involved in somite specification. J Embryol Exp Morphol 1979;53:245-67.
[91] Dias AS, de Almeida I, Belmonte JM, Glazier JA, Stern CD.
Somites without a clock. Science 2014;343:791-5.
[92] Meinhardt H. Models of segmentation. In: Somites in developing
embryos (R.Bellairs, D.A.Edie, J.W. Lash, Edts), Nato ASI Series
A, Vol 118, pp 179-189,
[93] Palmeirim I, Henrique D, Ish-Horowicz D, Pourquie O. Avian hairy
gene-expression identifies a molecular clock linked to vertebrate
segmentation and somitogenesis. Cell 1997;91:639-48.
[94] Aulehla A, Wehrle C, Brand-Saberi B, Kemler R, Gossler A, Kanzler B, et al. Wnt3a plays a major role in the segmentation clock
controlling somitogenesis. Dev Cell 2003;4:395-406.
[95] Keynes RJ, Stern CD. Segmentation in the vertebrate nervous
system. Nature 1984;310:786-9.
[96] Naiche LA, Holder N, Lewandoski M. Fgf4 and fgf8 comprise the wavefront activity that controls somitogenesis. Pnas
2011;108:4018-23.
[97] Dale JK, Maroto M, Dequeant ML, Malapert P, McGrew M,
Pourquié O. Periodic notch inhibition by lunatic fringe underlies
the chick segmentation clock. Nature 2003;421:275-8.
[98] Shih NP, François P, Delaune EA, Amacher SL. Dynamics of the
slowing segmentation clock reveal alternating two-segment periodicity. Development 2015;142:1785-93.
[99] Schröter C, Oates AC. Segment number and axial identity in a
segmentation clock period mutant. Curr Biol 2010;20:1254-8.
[100] Wacker SA, McNulty CL, Durston AJ. The initiation of Hox gene
expression in Xenopus laevis is controlled by Brachyury and BMP4. Dev Biol 2004;266:123-37.
[101] Clark RB. Dynamics in Metazoan Evolution: The origin of the
ceolom and segments. Clarendon Press Oxf 1964:0000.
[102] Erwin DH, Davidson EH. The last common bilateral ancestor.
Development 2002;129:3021-32.
[103] Chipman AD. Parallel evolution of segmentation by co-option of
ancestral gene regulatory networks. Bioessays 2010;32:60-70.
[104] Sonneborn TM. Genetic studies on Stenostonum incaudatum
(nov.sec.). J.expZo?logy 1930;57:57-108.
[105] Martinez Arias A, Lawrence PA. Parasegments and compartments in the Drosophila embryo. Nature 1985;313:639-42.
[106] Nagy LM, Carroll SB. Conservation of wingless patterning functions in the short germ embryos of Tribolium castaneum. Nature
1994;367:460-2.
[107] Kroiher M, Siefker B, Berking S. Induction of segmentation in
polyps of aurelia aurita (Scyphozoa, Cnidaria) into medusae and
formation of mirror-image medusa anlagen. Intern J Dev Biol
2000;44:485-90.
[108] Meinhardt H. Organizer and axes formation as a self-organizing
process. Int J Dev Biol 2001;45:177-88.
[109] Roeser T, Stein S, Kessel M. Nuclear β-catenin and the development of bilateral symmetry in normal and LiCl-exposed chick
embryos. Development 1999;126:2955-65.
[110] Gräper L. Die Primitiventwicklung des Hähnchens nach
stereokinematographischen Untersuchungen, kontrolliert durch
vitale Farbmarkierng und verglichen mit der Entwicklung anderer
Wirbeitiere. Wilhelm Roux Arch EntwMech Organ 1929;116:382429.
[111] Lau S, De Smet I, Kolb M, Meinhardt H, Jürgens G. Auxin triggers a genetic switch. NatCell Biol 2011;13:611-5.
[112] Belo JA, Bouwmeester T, Leyns L, Kertesz N, Gallo M, Follettie
M, et al. Cerberus-like is a secreted factor with neuralizing activity expressed in the anterior primitive endoderm of the mouse
gastrula. Mech Dev 1997;68:45-57.
[113] Silva AC, Filipe M, Kuerner KM, Steinbeisser H, Belo JA. Endogenous Cerberus activity is required for anterior head specification in Xenopus. Development 2003;130:4943-53.
[114] Kuroda H, Wessely O, De Robertis EM. Neural induction in
Xenopus: requirement for ectodermal and endomesodermal signals via Chordin, Noggin, β-catenin, and Cerberus. PLoS Biol
2004;DOI: 10.1371/journal.pbio.0020092.
[115] Meinhardt H. The Algorithmic Beauty of Sea Shells. 4nd Enlarg
Ed Programs CD Springer Heidelb N Y 2009.
[116] Noordermeer D, Duboule D. Chromatin architectures and hox
gene collinearity. Epigenetics Dev 2013;104:113-48.
[117] Fuchs B, Wang W, Graspeuntner S, Li Y, Insua S, Herbst EM,
Dirksen P, Böhm AM, Hemmrich G, Sommer F, Domazet-Loso
T, Klostermeier UC, Anton-Erxleben F, Rosenstiel P, Bosch TC,
Khalturin K. Regulation of polyp-to-jellyfish transition in Aurelia
aurita. 2015;Curr Biol. 24:263-73
21