Download Dorsoventral patterning by the Chordin

This is a reformatted version of an article to appear in Dev. Biol. (2015); http://dx.doi.org/10.1016/j.ydbio.2015.05.025
Dorsoventral patterning by the Chordin-BMP pathway:
a unified model from a pattern-formation perspective for Drosophila,
vertebrates, sea urchins and Nematostella
Hans Meinhardt
Max Planck Institute for Developmental Biology
Spemannstr. 35, D- 72076 Tübingen
http://www.eb.tuebingen.mpg.de/meinhardt; [email protected]
1. INTRODUCTION
Conserved from Cnidarians to vertebrates, the
dorsoventral (DV) axis is patterned by the ChordinBMP pathway. However, the functions of the pathway´s components are very different in different
phyla. By modeling it is shown that many observations can be integrated by the assumption that BMP,
acting as an inhibitory component in more ancestral
systems, became a necessary and activating component for the generation of a secondary and antipodallocated signaling center. The different realizations
seen in vertebrates, Drosophila, sea urchins and Nematostella allow reconstruction of a chain of modifications during evolution. BMP-signaling is proposed to be based on a pattern-forming reaction of
the activator-depleted substrate type in which BMPsignaling acts via pSmad as the local self-enhancing
component and the depletion of the highly mobile
BMP-Chordin complex as the long-ranging antagonistic component. Due to the rapid removal of the
BMP/Chordin complex during BMP-signaling, an oriented transport and ‘shuttling´ results, although only
ordinary diffusion is involved. The system can be
self-organizing, allowing organizer formation even
from near homogeneous initial situations. Organizers may regenerate after removal. Although connected with some losses of self-regulation, for large
embryos as in amphibians, the employment of maternal determinants is an efficient strategy to make sure
that only a single organizer of each type is generated. The generation of dorsoventral positional information along a long-extended anteroposterior (AP)
axis cannot be achieved directly by a single patchlike organizer. Nature found different solutions for
this task. Corresponding models provide a rationale
for the well-known reversal in the dorsoventral patterning between vertebrates and insects.
In all bilaterally-symmetrical organisms the dorsoventral (DV) patterning is achieved by the Chordin-BMP
pathway that form signaling centers at antipodal positions (Reversade and De Robertis, 2005; Bier, 2011).
Although well conserved during evolution, the actual
functions of the components seem to be very different.
For instance, Chordin and BMP (respectively Sog and
Dpp in Drosophila) are transcribed in vertebrates and
Drosophila at exclusive domains, while in sea urchins
and Nematostella these are produced at overlapping positions. How can the expression region of one component shift from one side to the other, leaving the expression of another component in place?
Pattern-forming reactions allow the generation of selfregulating signaling centers that act as organizing region
for setting up the primary embryonic body axes. Using
a single organizer at one terminal position of a morphogenetic field would lead to a shallow or low-level signal
distribution at the antipodal position. The employment
of two specific organizers, one at each terminal position,
allows a more reliable fate determination over the entire
field. Usually one of these organizers acts as the primary
system, forcing the secondary system to appear at a distance. In the present paper it is shown that emphasizing
the role of the pattern-forming capabilities allows formulation of a set of closely related models for patterning
along the DV axis in different phyla, suggesting a scenario by which the different realizations evolved. In the
presumably more ancestral Nematostella system (and
in feather bud formation), BMP acts as a long-ranging
inhibitory component, restricting the size of an organizing region; Chordin as an activating and BMP as an inhibitory component are expressed in partially overlapping regions. BMP became involved once more in the
formation of a secondary center, in which the roles are
reversed: BMP became a necessary and activating component for the secondary antipodal BMP-pSmad signal1
ing. BMP is required and becomes removed from larger
surroundings for the generation of a local signal. Due to
a long-ranging inhibitory action of the primary Chordindependent system, the secondary BMP-signaling center
can only emerge at a distance from the primary center;
two different centers form at antipodal positions.
According to the currently prevailing view, the initial
steps in establishing organizing regions are achieved by
maternally-supplied determinants, not by self-organizing
pattern-forming reactions. Indeed, pre-localized determinants play a crucial role in the most-studied model systems. In amphibians, the animal-vegetal axis is maternally fixed and the well-known cortical rotation displaces
material from the vegetal pole to a more equatorial position, determining in this way the future dorsal side by
initiating the formation of the Spemann organizer (reviewed in (Harland and Gerhart, 1997; Niehrs, 2004;
De Robertis, 2009) ). Suppression of this translocation or the removal of the organizer abolishes axis formation. Likewise, maternal determinants are required
to initiate early fish development (Abrams and Mullins,
2009). In Drosophila, the DV-symmetry break results
from the translocation of the nucleus from the posterior
tip of the oocyte (Moussian and Roth, 2005; Reeves and
Stathopoulos, 2009). Even if maternal determinants are
involved, several questions remain. For instance, in vertebrates, the Spemann-type organizer seems to be necessary to set up both the AP and DV axes. How can a single organizer organize two axes that are perpendicular to
each other? Why are maternal determinants needed in
amphibians but not in the chick or in the mouse?
Even in systems in which localized determinants play
a crucial role, strong indications exist that reactions are
involved that are in principle able to generate patterns
de-novo in a self-regulatory way. In a sandwich-like coculture of dissociated animal and vegetal amphibian cells
clusters of notochord-, somite- and neural tube-like structures are formed, clearly indicating the formation of organizing regions (Nieuwkoop, 1992), although in this procedure any maternally-imposed asymmetry is removed.
Development can proceed normally in amphibians, chick
and fish after removal of a substantial fraction of the organizer (Cooke, 1975; Psychoyos and Stern, 1996; Shih
and Fraser, 1996; Saùde et al., 2000). After cutting
an early chick blastodisk into two or three fragments,
complete embryos can develop in each fragment (Lutz,
1949), even if the fragment does not contain the incipient
organizer at the posterior marginal zone. The fact that
any cell of an eight-cell mouse embryo can give rise to a
complete embryo shows that no localized maternal determinants are required, although some asymmetries may
be imposed by the sperm entry (Bedzhov and ZernickaGoetz, 2014, Takaoka and Hamada, 2012). A strong indication that organizer formation in vertebrates depends
on a pattern-forming reaction comes from the transient
nature of gene activation in the organizer. As gastrulation proceeds, cells move through the organizer; first
gaining and later losing activation of organizer-specific
genes (Joubin and Stern, 1999). The organizing region
maintains an approximately constant size although the
cells that it consists of change over time, with cells entering and departing the region. Self-regulation along the
DV axis after longitudinal fragmentation also has been
demonstrated for sea urchins (Hörstadius and Wolsky,
1936), Planarians (Molina et al., 2007; Reddien et al.,
2007; Orii and Watanabe, 2007) and for some insects
(Sander, 1971).
There are several attempts to model the DV patterning. For amphibians the Chordin-BMP interaction and
the molecular basis of its self-regulation has been elaborated (Reversade and De Robertis, 2005; De Robertis,
2009). This analysis revealed that, in addition to the Spemann organizer, a second signaling center is present at
the ventral side. This has been overlooked for a long
time since upon transplantation these ventral cells do
not behave as expected for an organizer; their transplantation to the dorsal side is without effect (Smith and
Slack, 1983), much in contrast to the classical SpemannMangold transplantation. The interaction of the dorsal
and ventral center was compared with a seesaw (Reversade and De Robertis, 2005); dorsal and ventral components are in a balanced steady state and manipulations
that lead to an enhancement or decline in one system
have the opposite effect in the other antipodal system.
In another type of model the dorsoventral patterning
is discussed in terms of the ‘French Flag´ concept, assuming that a source and a sink region generates a gradient (Wolpert, 1969; Umulis et al., 2006). In this view,
the fact that early removal of the ventral half in amphibians leads to well-proportioned embryos requires that the
steepness of the signal gradient is regulated to maintain
the terminal concentrations in the smaller field (Umulis
and Othmer, 2013; Ben-Zvi et al., 2014). Since removal
of the Spemann-organizer leads to a collapse of DV patterning, the Spemann organizer is frequently assumed to
be a static signaling source that produces a fixed amount
of Chordin (Ben-Zvi et al., 2008). However, a French Flag
type of model cannot account for early patterning events
in the mouse or in the chick as long as no explanation
is provided how the source and the sink regions are established. In recent models the so-called ‘shuttling´, the
facilitated transport of BMP by Chordin plays a major role
for the localization of BMP-signaling in Drosophila and
vertebrate embryos (Eldar et al., 2002; Mizutani et al.,
2005; Ben-Zvi et al., 2008).
After a brief general introduction into pattern-forming
reactions it will be shown how known molecular components can be integrated to explain not only the distribution of the signalling substances but also how the organizers, the source- and the sink-regions become established. By constructing minimum models the intention is
not to account for all of the many known molecular details
but to unravel the underlying logic of this very essential
step in early development.
2
2. How to make an organizer: pattern-forming
reactions
depletion of the substrate in a larger surroundings. In this
reaction scheme a net flow becomes established towards
the activated region although molecules move only randomly by diffusion; the activator maximum resembles a
powerful sink for the required substrate (SFig. 2).
Many patterning processes in the non-living world
depend on such a type of interaction. For instance, a
sand dune forms behind a wind shelter due to a selfenhancing piling-up. This process depends on the ‘shuttling´ of loose sand corns over long distances by the
blowing wind. The depletion of the loose sand from the
air by local deposition counteracts the self-enhancement
in larger surroundings, leading eventually to dynamically
stable peaks.
It is easy to see that the BMP/Dpp -signaling follows
this activator - depleted substrate scheme (Fig. 1). In
Drosophila, by binding to their receptors, Dpp ligands initiate a self-enhancing reaction by pMAD activation and
transcriptional regulation via medea, zerknüllt and other
components (Wang and Ferguson, 2005; Mizutani et al.,
2005). To close the autocatalytic loop, a transcriptional
activation of a co-receptor was assumed downstream of
the DPP signaling (Wang and Ferguson, 2005). Dpp and
Sog can form rapidly diffusing complexes (Holley et al.,
1996), satisfying in this way the condition that the component removed in the self-enhancing process is of long
range. Sog becomes locally degraded by Tolloid, causing
the release of the ligand at the receptor allowing signaling, internalization and removal. A longer-ranging competition for the complex was already proposed (Umulis
et al., 2006). Since the activated region generates a
very effective sink for the rapidly diffusing complex, this
scheme provides a straightforward explanation for the
‘shuttling´ (Eldar et al., 2002) of Dpp by Sog and for the
oriented movement towards the region of Dpp signaling
although only ordinary diffusion is involved.
In the wasp Nasonia, BMP patterning occurs although Chordin is absent (Özüak et al., 2014). In the
model, if BMP is diffusible on its own, the generation of
localized BMP-signaling by the activator-depletion mechanism does not require Chordin (SFig. 2). Indispensible,
however, would be an alternative asymmetry that determines where the BMP-signaling should occur.
Pattern formation from initially more or less uniform
situations requires reactions that combine local selfenhancement and long-ranging inhibition (Gierer and
Meinhardt, 1972; Meinhardt, 1982, 2008). A straightforward realization of our general principle consists of
a local-acting activator whose autocatalytic production is
antagonized by a long-ranging inhibitor. In an extended
field a homogeneous distribution is unstable since a
small elevation of the activator will increase further due
to the self-enhancement. The concomitantly produced
long-ranging inhibitor restricts the level and extension of
emerging maxima of activator and inhibitor production.
Eventually stable concentration maxima emerge that can
act as signaling centers, i.e., as organizers (Supp Fig. 1).
Regeneration of partially or completely removed organizers is a standard regulatory feature of such reactions
since after removal of the activator-producing region, the
remnant inhibitor fades away until the autocatalytic activator production starts again and maximum becomes
restored.
The possibility to generate patterns by the interaction
of two substances that diffuse with different rates was
discovered by Alan Turing (Turing, 1952). However, almost all interactions of this reaction-diffusion type are
unable to generate any pattern, except if the condition
of local self-enhancement and long-ranging inhibition is
satisfied. This crucial condition is not inherent in Turing´s
seminal paper although one can interpret his equations
in this way (Meinhardt, 2012a).
The Nodal/Lefty interaction is an example that displays the predicted properties (Supp. Fig. 1). In
sea urchins Nodal is responsible for the generation of
the oral opening (Duboc et al., 2004) and, by inducing
Chordin and BMP, for generating the dorsoventral patterning (Lapraz et al., 2009). In amphibians, Nodal is
required for mesoderm formation and provides therewith
the precondition for organizer formation in the blastoporal
ring. The theoretically expected non-linearity in the selfenhancement is realized by a dimerization of Nodal when
bound to the receptor. The inhibitor Lefty has a much
longer range than the activator (Sakuma et al., 2002;
Müller et al., 2012), blocks dimerization of the Nodal receptors and abolishes in this way the self-enhancement.
4. The formation of the Dpp stripe in
Drosophila provides insights for the logic behind
the observed complexity
3. The activator - depleted substrate
mechanism and the BMP-signaling
The formation of narrow stripes with high Dpp-signaling
implies that the signaling cells can inhibit the onset of
Dpp signaling in more ventrally located adjacent cell.
Why such an inhibition does not take place along the
AP extension, causing a disintegration of the stripe into
patches? Most of the published models treat DV patterning only as a one-dimensional process such that this
problem does not show up. According to the model,
stripe-like instead of patch-like distributions are formed
Alternatively, stable patterns can also emerge if the local
self-enhancing reaction is antagonized by the depletion
of a diffusible substrate or co-factor that is necessary
to accomplish the self-enhancing reaction (Gierer and
Meinhardt, 1972). Again, a homogeneous distribution is
unstable. A stable steady state is reached if a maximum
can no longer increase in height or extension due to the
3
Figure 1: Fig. 1: Simulation of the formation of a narrow stripe of Dpp signaling in Drosophila based on an activator-depleted
substrate mechanism (Gierer and Meinhardt, 1972). (A) Schematic expression patterns of Sog (red), Dpp (light blue) and, at the
dorsal-most position, Dpp-pMAD signaling (dark blue) (Wang and Ferguson, 2005; Mizutani et al., 2005). (B) Simulation: Dppsignaling is a self-enhancing process involving pMAD and other components that is antagonized by the depletion of Dpp. On
its own, due to the low diffusion of Dpp, a moderate plateau but no signaling peaks can emerge. Sog mobilizes Dpp by forming
diffusible complexes (blue) that activate and become removed by the self-enhancing Dpp signaling (dark blue). Due to the additional
inhibitory influence of Sog, Dpp signaling occurs only at a distance from the Sog source (for equation and details, see supplementary
information). The region of Dpp signaling is a strong sink for the complex, which accounts for the ‘shuttling´ feature (Eldar et al.,
2002). (C) Simulation in a two-dimensional field shows the stripe-like pMAD activation at the dorsal-most position. (D) Reduction
of the Sog production (Sog+/- strain) reduces the inhibition, driving the self-enhancement stronger into saturation, causing a broader
stripe. (E) Increasing Sog production by increasing the Sog copy number leads to narrower stripes. Since the saturation level may
not be reached, the stripe has the tendency to disintegrate into patches, as observed (Wang and Ferguson, 2005). (F) An additional
region of Sog production via an engrailed2 promotor leads, due to its inhibitory action, to a gap in the stripe (Ashe and Levine,
1999). (F) If Dpp is only produced under the engrailed2 promotor, a pMAD patch appears on this stripe (Wang and Ferguson,
2005); the later appearance of an additional weaker maxima is not yet reproduced. (H, I) Illustration for the requirements in the
assumed reaction: a self-enhancing reaction that depends on a diffusible substrate would lead to isolated patches (H). A saturation
of the self-enhancement would lead to multiple stripes with random orientations (Meinhardt, 1995). A single stripe as shown in (C)
requires both saturation and the additional inhibitory influence of Sog.
4
if the self-enhancing reaction shows saturation at high
concentrations (Fig. 1 H, I; SFig. 1). If the upper limit
is reached, a maximum can no longer increase in peak
height. Instead, the spatial extension will increase until an equilibrium is reached. However, activated regions
depend on the proximity of non-activated cells from which
either fresh substrate such as the Dpp/Sog complex can
be obtained or into which an inhibitor can be dumped. A
stripe-like pattern reconciles the seemingly contradictory
requirements, large sizes of the activated region and the
proximity of non-activated cells (Meinhardt, 1989; Meinhardt, 1995). In such stripe-forming systems the width of
the stripes and the distance between two stripes are of
the same order, as it is the case in the proverbial zebra stripes. The distance between the stripes cannot
be increased by increasing the strength of the lateral inhibition since this would lead to a disintegration of the
stripe into patches. Thus, the formation a single stripelike midline organizer is an intricate pattern-forming process, requiring an interference by a second system that
makes sure that only a single stripe is formed although
space for more stripes would be available (Meinhardt,
2004). In Dpp-signaling this issue is solved by an additional inhibitory action of Sog/Chordin, causing only a
single stripe to be formed and that this occurs distant to
the Sog source, i.e., at the dorsal-most position. This
model provides a rationale for the feature of ‘long-range
activation - short range inhibition´ assigned to the Sog
function on the DPP signalling (Ashe and Levine, 1999).
Short range exclusion and long-range activation is an appropriate mechanism that two pattern-forming systems
keep distance from each other without that one system
can override the other (Meinhardt and Gierer, 1980).
A prediction of such a model is that the stripe may
decay into patches if the saturation level is not reached.
This is in agreement with the observations that an increase of the Sog copy number, i.e., an increase of the
inhibition, leads to a narrower Dpp stripe that becomes
less regular (Wang and Ferguson, 2005; Mizutani et al.,
2005) which is reproduced in the simulation (Fig. 1 E).
Other way round, if only a single Sog copy is present, the
reduced inhibition leads to a broader and more regular
stripe (Fig. 1D).
mation by the Chordin/BMP system, the required autocatalysis can result from the mutual inhibition of Chordin
and BMP. An increase of Chordin, for instance, leads
to a decrease of BMP and thus to a further increase of
Chordin as if Chordin were autocatalytic. ADMP (Moos
et al., 1995; Lele et al., 2001), a BMP-type molecule,
can be regarded as the required long-ranging antagonist (Meinhardt, 2000, 2008). ADMP is produced under the same control as Chordin and has a longer range
(Willot et al., 2002; Reversade and De Robertis, 2005).
Such a scheme is in agreement with the observation that
lowering ADMP leads to an enlargement of Chordin expression (Lele et al., 2001) and can cause the induction
of a secondary embryo (Dosch and Niehrs, 2000). In
terms of the model, the long-ranging ADMP can restrict
the extension of Chordin expression either by activating
BMP or more directly by inhibiting Chordin transcription.
This simple system allows organizer formation from initially homogeneous situations, accounts for regeneration
of a region of high Chordin expression after removal and
shows the observed balanced behavior (SFig. 3).
Again, BMP-signaling as indicated by a high pSMAD
level is active only a fraction of the region in which BMP
is transcribed (Fainsod et al., 1994; De Robertis, 2006),
suggesting that a similar sharpening process is involved
as in Drosophila. Combining the BMP/Chordin/ADMP
patterning mechanism (SFig. 3) with the sharpening of
the BMP-signalling mechanism via Smad leads to two
self-regulating signaling centers at antipodal positions
(Fig. 2). The model provides a rationale for why two
long-ranging components, Chordin and ADMP, are produced in the Spemann-type organizer. As mentioned, in
Drosophila Sog has a double function, generating the diffusible Sog/Dpp complex and to localize Dpp signalling to
a maximum distance from the Sog source. To integrate
Chordin into a self-regulating patterning system, a new
function is required for a component that is produced in
the region of Chordin transcription: a long-ranging antagonist that limits the extension of the region in which
Chordin is expressed. ADMP is a corresponding candidate (Moos et al., 1995; Lele et al., 2001). Similarly,
BMP2b has been found to act as an additional inhibitor
that directly downregulates Chordin transcription (Xue et
al., 2014). As discussed further below, a direct inhibitory
role of a BMP-like molecule is presumably an ancestral
feature.
This minimum model accounts already for many observations. Both organizers behave differently upon
transplantation. Transplantation of cells from the dorsal organizer to the antipodal position - the classical
Spemann-Mangold experiment - establishes a new organizing region, usually in an all or nothing mode. The high
Chordin level inhibits BMP-signaling in the surrounding
cells; a new region of high BMP-signaling becomes established half-way between the two organizers (Fig. 2C).
In contrast, transplantation of ventral cells into a dorsal
position remains without effect since Chordin, spread-
5. Formation of two antipodal signaling centers
in the DV-patterning of vertebrates
Chordin/Sog, in insects under the transcriptional control
of a separate pattern-forming system, acts in vertebrates
as a part of an integrated regulatory system. Corresponding schemes with increasing complexity have been
proposed that allow a balanced Chordin-BMP expression
(Reversade and De Robertis, 2005; De Robertis, 2009).
However, not only a balanced expression ratio is required
but these expressions have to be localized at antipodal
positions.
According to a most simple scheme for pattern for5
Figure 2: Fig. 2: Model for the formation of two antipodal organizing regions in amphibians: Chordin became an integrated part
of the pattern-forming system. (A) Final stable distribution of the components. The self-enhancement is achieved by the mutual
inhibition of Chordin- (red) and BMP-transcription; (BMP distribution: light blue; Chordin distribution: brown). The long-ranging
ADMP (green), produced under the same control as Chordin, activates BMP transcription, acting thus as a long-ranging Chordin
inhibitor (SFig. 3). A direct inhibition of Chordin transcription maybe also involved (Xue et al., 2014). The rapidly diffusing BMPChordin complex (blue) fuels and is removed by the self-enhancing BMP signaling via pSmad (dark blue). The inhibitory influence
of Chordin restricts BMP signaling to the antipodal position (see Fig. 1). Maternal determinant (grey) are assumed that bring
Chordin activation above a threshold. (B) Time course. (C) Simulation of the Spemann experiment: transplantation of Chordinexpressing cells (red) to a ventral position triggers a new dorsal organizer and causes a shift of BMP signaling to the center. (D) In
contrast, transplantation of ventral cells to a dorsal position remains without effect; BMP signaling is immediately suppressed by the
strong inhibitory effect of Chordin secreted by the surrounding cells. (E) After bisection, a new pSmad activation reappears in the
dorsal fragment. In contrast, the ventral fragment is unable to regenerate a new dorsal organizer due to the absence of the maternal
determinants. This is different if all cells are competent for organizer formation (SFig. 4). (F-H) simulation in a two-dimensional
field (for equations and parameters, see Supplementary Information).
6
ing from the original organizer or its remains, immediately blocks the Smad activation in the transplanted cell,
which lose, therefore, their specific BMP-signaling activity (Fig. 2D). The asymmetric behavior of the two centers
was regarded as puzzling (De Robertis, 2006) but finds in
this model a straightforward explanation. More complete
models have to include additional long-ranging antagonists of the BMP-signaling such as Bambi and Sizzled
that contribute to the size-regulation of the pSMAD activation (De Robertis and Kuroda, 2004; Paulsen et al.,
2011; Inomata et al., 2008; Inomata et al., 2013).
Organizer formation in amphibians depends on the
cortical rotation that establishes a high β-catenin level at
the dorsal side. In the model it is assumed that such
localized determinants bring the Chordin system over a
threshold level such that the self-enhancement is triggered (Fig. 2A). If this region is completely removed,
for instance, by the removal of the dorsal blastomeres,
the self-enhancement may not be triggered, causing that
the organizer does not regenerate (Fig. 2E). In contrast,
after removal of the ventral half, the BMP-Chordin complex accumulates to such a degree that a new region of
Smad signaling emerges in the smaller field. For this regeneration of a BMP-signaling center neither a change
in the steepness of a gradient nor a change in diffusion
rates is required, in contrast to other models (Umulis and
Othmer, 2013; Ben-Zvi et al., 2014). It should be emphasized that regeneration of one or both terminal organizes
is nothing special. It is the base for regeneration in other
systems such as Planarians or Hydra and can occur in
fragments that are only a very small part of the original
organism.
In this view, localized maternal determinants are employed as a means to suppress supernumerary organizers in huge embryos as given in amphibians (Fig. 2).
Organizer formation is only possible in the restricted region made competent by the determinants. This view is
supported by experiments in which the competence for
organizer formation is elevated ventrally, for instance, by
increasing the β-catenin or Wnt level there (Sokol et al.,
1991; Molenaar et al., 1996). The resulting supernumerary embryos are well proportioned - a further indication
that self-regulation determines strength, extension and
position of the new organizer.
In contrast, if development starts at a small size, only
the two antipodal organizers can be formed even if all
cells are competent. This occurs whenever a certain
size is surpassed (SFig. 4D). Once formed, the dorsal organizer can suppress the activation of a second
dorsal organizer during further growth. If all cells are
competent, a Spemann-type organizer also can regenerate in a fragment that does not contain the organizer
(SFig. 4E), as observed in early chick embryos (Lutz,
1949). At later stages an active inhibition may be required to suppress the formation of supernumerary organizers. In chick development, for instance, an inhibition
spreads from the established organizer that suppresses
the trigger of supernumerary organizers (Bertocchini et
al., 2004). Downregulation of the competence for organizer formation in cells distant to an established organizer
is an efficient strategy to avoid supernumerary organizers in growing systems; Hydra patterning is a further example for this strategy (Meinhardt, 1993, 2012b).
As mentioned, an unambiguous demonstration of the
self-regulatory capabilities of Spemann organizer formation came from an experiment of Peter Nieuwkoop
(Nieuwkoop, 1992). After co-culture of dissociated animal and vegetal amphibian cells, derivatives of the Spemann organizer such as notochord, spinal cord and
somites were induced. According to the model, organizer formation can start without localized determinants
as long as sufficient competent cells are available, even
if they are randomly distributed (Fig. 3). This type of observations cannot be described by models that do not
posses self-organizing properties [e.g. (Zhang et al.,
2007; Ben-Zvi et al., 2008)].
Even after blocking translation of all ventrally-active
BMP genes, a residual DV polarization and localization of Chordin expression remains (Reversade and De
Robertis, 2005). This polarization, however, is completely abolished if also ADMP is suppressed, suggesting that Chordin and ADMP act on their own as a rudimentary pattern-forming system. A self-enhancing component in the Chordin activation that is antagonized by
ADMP directly, i.e. without intermediate BMP activation,
allows an integration of this observation. Indications for
a similar interaction will discussed further below for Nematostella. Such a modification has little effect on the
normal pattern-forming reactions but leads to more clearcut threshold behavior as required for simulating the effects of maternal determinants.
The strong self-enhancement involved in organizer
formation provides a rational for the otherwise puzzling
observation of unspecific induction as has been made
in early organizer research [reviewed in (De Robertis,
2009)]. According to the model, even the leakage of
an inhibitor at a wound could be sufficient to bring the
Chordin system above a threshold, causing the trigger a
new organizer that would have all properties of a natural
organizer. The region antipodal to the organizer is especially prone to unspecific induction due to a low level of
inhibition.
6. The moving organizer, midline formation and
the DV organization proper in vertebrates
It seems most natural that the side antipodal to the dorsal organizer in vertebrates is assigned to be ventral. To
avoid confusions, I followed this convention thus far. Indeed, high BMP levels specify different ventral cell types
in the marginal zone (Mullins et al., 996; Kishimoto et al.,
1997; Dosch et al., 1997; Walmsley et al., 2002). Nevertheless, this assignment is somewhat misleading. Fate
mapping has shown that cells at the side conventionally
7
Figure 3: Fig 3. Indication for self-organization of the DV patterning in amphibians: Nieuwkoop´s experiment and its simulation.
(A, B) Ectodermal cells from animal caps and endodermal cells from the vegetal pole are dissociated. Although localized maternal
determinants no longer exist, after re-aggregation clustered axial structures emerge (B), including notochord (N), neural tube (NT)
and somites (S), indicating the formation of organizers (Nieuwkoop, 1992). (C-E) Simulations: starting with a pattern as shown
in Fig. 2B, (C), after removal of the dorsal and ventral centers (D), cells of such fragments are reassembled in a random fashion.
The formation of new dorsal organizing regions (red) and BMP signalling centers (dark blue) show that local determinants are not
required for initiating pattern formation as long as sufficient competent cells are present. (F) Another random assembly of cells may
lead to different patterns, as observed.
8
Figure 4: Fig. 4: DV patterning and midline formation in amphibians. (A) The generation of DV-positional information requires
the formation a long extended midline (red) as line of reference along the entire AP axis. (B) Induced by the Spemann organizer
(O), the midline is generated by two processes. For the head, the midline is formed by cells from the Spemann organizer that move
underneath the ectoderm, forming the prechordal plate (yellow). (C) For the trunk, cells of the marginal zone move towards the
organizer and elongate the midline (red). (D) In the course of time, axial structures become elongated along the AP axis while the
blastopore, oriented perpendicular to the AP axis, shrinks. Decisive for the DV specification of cells is their distance to the midline
(green arrows) that is induced by the organizer (Meinhardt, 2006, 2008), not their distance to the organizer. The DV axis is not the
line between the Spemann organizer and the antipodal position on the blastopore (red arrow), as frequently assumed in the literature
(e.g., (Ben-Zvi et al., 2008) ). The AP patterning of the trunk occurs by a time-dependent activation of Hox-genes in cells near the
blastopore (1,2,3,...) (Wacker et al., 2004). Cells originally antipodal to the Spemann organizer (tip of red arrows) remain longest
near the marginal zone in which sequential activation of more posterior-specifying HOX genes take place; they form, therefore, most
posterior structures, in agreement with fate mapping (Lane and Sheets, 2002). The DV patterning can only occur after the midline,
i.e., after notochord and floor plate are formed. Thus, the model explains why the DV and AP organization is under the control of
the same developmental clock (Hashiguchi and Mullins, 2013).
declared as ventral end up posteriorly in the tail (Lane
and Sheets, 2002; Agathon et al., 2003). Moreover,
dorsoventral pattering has to work all along the AP axis,
which requires a line of reference with a stripe-like APextension, not a patch-shaped organizer (Fig. 4). Therefore, crucial for the specification of cells along dorsoventral axis is not their distance to the Spemann-type organizer but their distance to the midline that is induced by
the organizer (Meinhardt, 2004, 2006).
The marginal zone in amphibians, the blastopore on
which the Spemann organizer is localized, is the most
posterior structure of the early embryo. Thus, the midline
has to be formed under organizer control in two parts
(Fig. 4). One part results from cells of the organizer that
move underneath the ectoderm, forming the prechordal
plate and thus the prerequisite for generating a reference
line for DV-patterning of the brain. For midline formation
of the trunk, due to the convergence - extension mechanism, cells near the marginal zone move toward the organizer and the incipient midline to form a rod-like axial
structure perpendicular to the blastopore with the notochord and neural tube as the most dorsal structures.
At a particular AP level of the trunk, the proper DV
patterning can only occur after notochord and floor plate
is formed. This occurs in the course of time during the
posterior elongation of the midline (Fig. 4). Recently it
has been shown that the DV patterning is under control of the same developmental clock as the patterning
along the AP axis (Hashiguchi and Mullins, 2013). This
is a straightforward consequence of the proposed model
since first the midline has to be formed before the signal that specifies the distance from the midline can be
generated or interpreted (Fig. 4). Graded BMP signaling has been shown also to be responsible for regionspecific gene activation after gastrulation (Nguyen et al.,
1998; Steventon et al., 2009). To emphasize it again, according to the model proposed, the DV patterning is not
accomplished by the two antipodal organizers within the
marginal zone of the early embryo, as it is assumed in
several recent models (Ben-Zvi et al., 2008; Inomata et
al., 2013) but by distance of the cells from the midline
that is induced by the dorsal organizer.
Usually the formation of a complete amphibian embryo after early removal of the ventral half is interpreted
as indication of an excellent size regulation along the DV
axis (Ben-Zvi et al., 2008). However, as shown by Cooke
(Cooke, 1981), size regulation does not occur along the
DV but along the AP axis. If cells are removed from the
so-called ventral side, the somites and the embryos as
the whole have a significant shorter AP- but the normal
DV-extension. Thus, the embryo becomes shorter, but
not slimmer. The molecular mechanism is not yet fully
understood (Lauschke et al., 2013).
Even classical observations clearly demonstrate that
the size regulation along the DV axis is restricted. After induction of a second Spemann organizer, the heads
9
of the two embryos are usually complete and well separated while parts of the trunks and the tails are fused.
In terms of the model, at the beginning of gastrulation,
the marginal zone is large and the two incipient midlines
have a large distance. The gradients do not overlap and
the DV patterns of the heads are complete. Later in development, however, the marginal zone shrinks in favor of
axial elongation (Fig. 4); the two midlines become closer
and closer; the gradient systems overlap and the trunks
become fused, clearly indicating that the DV patterning
does not scale. In terms of the model, for the formation of complete embryos after tissue removal it is crucial
that missing organizers regenerate. However, the overlap of the resulting gradients nevertheless can lead to
fused structures. Regeneration of organizers and scaling of gradients are two different processes.
the observed regulation. As shown in Fig. 5, regeneration of organizing regions can occur even if both the dorsal and the ventral sites are removed. In sea urchins,
BMP ligands are diffusible on their own, without complex
formation (Lapraz et al., 2009) In this case, the formation
of diffusible Chordin/BMP complexes is not necessarily
required for the mechanism to work; diffusible BMP ligands would be sufficient. However, the employment of
diffusible complexes enlarges substantially the distances
over which the mechanism can work.
8. Chordin-BMP patterning in Nematostella:
an ancestral mode?
One of the evolutionary earliest systems that display a
patterning perpendicular to the primary (oral-aboral) axis
is the Chordin-BMP patterning in the sea anemone Nematostella. Both Chordin and BMP appear first at the oral
opening and become subsequently shifted to an off-axis
position (Finnerty et al., 2004; Rentzsch et al., 2006; Matus et al., 2006; Saina et al., 2009; Leclère and Rentzsch,
2014; Genikhovich et al., 2015). Even after the shift,
Chordin and BMP remain partially superimposed. The
superposition of Chordin/BMP is reminiscent of the situation in sea urchins discussed above and similar to the
Chordin/ADMP expression in vertebrates (Saina et al.,
2009). The oral organizer is generated by the Wnt pathway (Kusserow et al., 2005).
Many regulatory features can be explained by assuming that in Nematostella the Chordin-BMP patterning
works essentially as an activator-inhibitor system (Fig.
6). BMP, produced under Chordin control, acts as inhibitor, restricting the maximum level and the extension
of the Chordin peak. This inhibitory action of BMP occurs in in cooperation with RGM that presumably acts
as a BMP co-receptor (Leclère and Rentzsch, 2014).
This scheme is in accordance with the observation that
blocking of BMP- (Saina et al., 2009) or RGM-translation
(Leclère and Rentzsch, 2014) leads to a dramatic increase of Chordin transcription since the inhibitory function of BMP is lost. BMP, however, is certainly not the
only inhibitor in Chordin patterning since blocking of BMP
transcription by morpholinos leads to a dramatic increase
but not to a ubiquitous Chordin expression. Moreover, at
later stages, BMP remains spatially restricted in the endoderm although Chordin expression occurs essentially
in the ectoderm.
In terms of the model, the symmetry break and offaxis activation of the Chordin system is achieved as follows. First, a long-ranging activating influence of the
primary WNT system leads to a trigger of Chordin expression at the oral pole. Subsequently, a more localized quenching at the oral pole achieved, for instance,
by an enhancement of the BMP inhibition in the presence of WNT, causes that the activation of the Chordin
system becomes more favored in a zone that surrounds
the oral organizer. The pattern-forming feature of the
7. Applications to the DV organization of sea
urchins
The oral opening of sea urchin embryos is formed at a
lateral position halfway between the animal pole and the
Wnt-expressing cells at the vegetal pole. The oral-aboral
axis formation is initially labile; slight asymmetries are
sufficient for orientation. For instance, unilateral oxygen
depletion is sufficient to orient the emerging pattern (Czihak, 1963);(Coffman et al., 2004).The oral-aboral axis is
highly regulative; embryos fragmented along the animalvegetal axis can form normal embryos. This regeneration
may be connected with a polarity reversal in one fragment (Hörstadius and Wolsky, 1936). Meanwhile it has
been shown that the oral opening is under Nodal/Lefty
control (Duboc et al., 2004) which is known to work as
an activator-inhibitor system (Schier, 2009; Müller et al.,
2012). All these properties, the ability to regenerate, the
initial sensitivity to minute asymmetries and the polarity
reversal in originally non-activated fragments are properties of pattern-forming systems (Meinhardt, 1982).
Chordin and BMP are also involved in the DV organization of sea urchins, although in an unusual way. Nodal
controls the transcription of both Chordin and BMP; the
oral side is conventionally declared as ventral. Although
synthesized ventrally, BMP-signaling as indicated by pSmad activation takes place at the dorsal side (Lapraz et
al., 2009). Again, the purpose of the system is to establish a secondary signaling center at the antipodal position. This is easily integrated into the model proposed
(Fig. 5). At the side of Nodal-controlled BMP synthesis
BMP-signaling is repressed by the high Chordin level. At
antipodal position the inhibition by Chordin is low enough
such that the self-enhancing BMP-signaling via pSmad
is triggered. Obviously a huge net transport takes place
from the ventral to the dorsal side due to sink function
for BMP at the position of BMP-signalling. The position of BMP-synthesis is not critical since, due to the
rapid diffusion of the Chordin-BMP complex, it is available also at distant positions. The model accounts for
10
Figure 5: Fig. 5: Model for the DV organization in sea urchins. BMP and Chordin are transcribed under Nodal control while
BMP-signalling occurs antipodal to the side BMP production (Duboc et al., 2004; Lapraz et al., 2009). (A-E) Simulation in a onedimensional field: the activator-inhibitor system Nodal (green, A) / Lefty (not shown, see SFig. 1) generates a high Nodal peak
that controls BMP and Chordin transcription. BMP (light blue, B) and Chordin (brown, C) form a diffusible complex (blue, D).
At the antipodal position where the inhibitory effect of Chordin is low, the self-enhancing BMP signalling via Smad triggers (dark
blue, E) that leads to a removal of BMP, Chordin and the complex. The extension of the Smad activation is restricted due to the
depletion of the complex. The self-regulatory capability is illustrated by pattern regeneration after a later removal of both organizing
regions. Since degradation of the complex occurs almost exclusively together with the BMP- signalling, without a region of BMP
signaling the complex accumulates in the system until the BMP-signaling triggers. (F) Final stable steady state in a two-dimensional
simulation. The BMP transport has been recently modeled in a more detailed way (van Heijster et al., 2014) (for equations see
Supplementary Information).
11
Figure 6: Fig. 6: Model for early pattern formation in Nematostella. (A) Schematic drawing of the expression patterns of Wnt
(green) defining the oral pole, Chordin (red) and pSmad signalling (blue) at opposite off-axis positions. (B-E) Simulation in a linear
field: Wnt triggers the self-enhancing Chordin activation (red); BMP (light blue) acts as long-ranging inhibitor. The higher inhibition
of BMP in the presence of WNT leads to a shift of Chordin- and BMP transcription to an off-axis position (C). pSmad activation
(dark blue) is driven by a long-ranging BMP molecule (blue) generated under Chordin control. Due to the long-ranging inhibitory
influence of Chordin, this occurs at the opposite side, similar as in sea urchins (Fig. 5). (F) Final steady state in a two-dimensional
simulation, oral view. (G) If BMP is blocked by morpholinos, Chordin transcription increases dramatically since the inhibition is no
longer functional; no symmetry break takes place, as observed (Saina et al., 2009). (H, I) Morpholino injections into two adjacent
blastomeres at the four cell stage (Leclère and Rentzsch, 2014) provide strong support for the proposed interaction. Injection of
Chordin morpholinos (H) reduces the self-enhancement of Chordin in the injected half (reduction is indicated by the density of the
pink background). Chordin activation occurs in the non-injected half, forcing the pSMAD activation to occur at the injected side
(H). In contrast, injections of BMP- or RGM-morpholinos lead to a reduced inhibition of the Chordin self-enhancement. Chordin
activation occurs in the injected and pSmad activation in the non-injected side (I), in agreement with the observations (for equations
see Supplementary Information).
12
Chordin/BMP system makes sure that the Chordin activation becomes restricted to a patch and does not remain a ring that surrounds the organizer (Fig. 6). Again,
BMP signalling and pSMAD activation occurs at an antipodal position (Fig. 6). This model accounts for observations made if BMP translation is blocked by morpholinos (Saina et al., 2009). First, since one of the inhibitors
is lost, Chordin transcription increases dramatically in the
entire competent zone until saturation is reached. Secondly, no shift to an off-axis position occurs since the elevated quenching of Chordin activation via BMP/WNT cooperation at the oral center is no longer functional (Fig.
6G). The model is compatible with the observations that
overexpression of Chordin leads to ectopic overexpression of the BMP message even if the BMP translation
is blocked. The addition of foreign BMP represses not
only Chordin but also BMP transcription (Saina et al.,
2009). The model describes that Chordin activation occurs with a predictable polarity after blocking Chordin- or
BMP-translation in parts of early embryos (Leclère and
Rentzsch, 2014) (Fig. 6 H-I). Other aspects are not yet
included; for instance, that Chordin activation becomes
eventually restricted to the ectoderm while BMP activation resides in a somewhat larger region in the endoderm
(Rentzsch et al, 2006; Matus et al., 2006a).
Chordin patterning is already involved in the patterning of the radial-symmetric Hydra. It appears transiently
in bud formation and is one of the earliest indicators for
head regeneration (Rentzsch et al., 2007). Not unlike the
situation in Nematostella, Chordin transcription becomes
subsequently shifted to a sub-hypostomal position and
remains in newly-formed tentacles as a periodic pattern.
Smad is ubiquitous expressed in the body column except of the terminal ends (Hobmayer et al., 2001) and is
thus presumably not under positive control of an organizer. The function of Chordin in Hydra is yet unknown.
Eventually, the pattern around the oral-aboral axis in
Nematostella, generated under the control of the Chordin
system, consists of a periodic pattern of endodermal
folds, the so called mesenteries. On a first inspection,
the generation of this periodic pattern seems to be unnecessarily complex, forming first an off-axis patch-like
organizer that induces a second organizer at an antipodal position, which, in turn, provides a scaffold for the
periodic pattern. In contrast, in Hydra the periodic pattern - related to tentacle formation around the oral-aboral
axis - is generated directly. From the model, these intermediate steps in Nematostella are necessary. The periodic (tentacle-) pattern in hydra consists of spots around
the oral pol. In Nematostella however, a periodic stripelike pattern has to be generated with an oral-aboral extension of the stripes. This cannot be achieved directly
by the Hydra-type mechanism since direct stripe formation would lead to a stripe around the oral opening, not
to stripes along the oral-aboral axis. A possible mechanism for the formation of stripes that have the correct
orientation is to form first an off-center patch-like activa-
tion that has an inhibitory influence on a stripe-forming
system, allowing only a single stripe at the contralateral
side (Meinhardt, 1989;, 2004) that can be used as a
scaffold to generate a periodic stripe-like pattern around
the oral-aboral axis (Berking and Herrmann, 2007). This
seems to be what is realized in Nematostella. A stripe of
GDf5-like expression and nested expression of Hox8 and
HoxE appear opposite to the patch-like Chordin expression (Saina et al., 2009; Leclère and Rentzsch, 2014;
Genikhovich et al., 2015).
This model suggests that in Nematostella some components are still missing. Required is a (direct or indirect) self-enhancement in the Chordin transcription, as
it was already suggested for to cope with some observation for the Spemann-organizer as mentioned above.
Further, the experiments indicate that BMP downregulates Chordin transcription locally, i.e., outside the region
where BMP-signaling occurs. The huge overproduction
of Chordin after blocking BMP transcription indicates that
this interaction is rather direct and not controlled by a
separate pattern-forming reaction as in sea urchins. The
molecular basis is unknown.
9. A possible evolutionary scenario
The presumably ancestral activator-inhibitor type of
Chordin-BMP patterning in Hydra suggests an interesting evolutionary scenario. In Nematostella, BMP obtained a second function: not only restricting Chordin
expression but providing the prerequisites for a further
pattern-forming system at antipodal position, realized by
pSmad signaling. Both functions may be achieved by
different BMP´s. Also Chordin obtained a double function; controlling BMP transcription that limits its own
self-enhancement and, by its inhibitory function on the
BMP/Smad signaling, it causes the latter to appear at a
distance from the Chordin source. BMP acts as inhibitor
also in other system, for instance, in the initiation of avian
feathers (Jung et al., 1998; Noramly and Morgan, 1998)
and, at a later stage, in the signaling that separates barbs
from each other (Harris et al., 2005).
Later in evolution, perhaps for a better separation of
the multiple functions, Chordin transcription became under control of separate pattern-forming systems such as
Nodal in sea urchins or the nuclear Dorsal gradient in
Drosophila. This liberated BMP from the inhibitory function; the location of BMP transcription became unimportant since, due the mobility of the Chordin/BMP complex,
BMP became essentially available everywhere. With a
BMP transcription outside of the region of Chordin transcription as in Drosophila, the region of BMP expression
became closer to the region in which the secondary BMP
patterning via pSmad should occur. This led to shorter
distances that have to be bridged by shuttling and enabled thus more extended embryonic fields. In vertebrates, a mixture of both systems seems to be preserved:
Chordin together with BMP2b and presumably ADMP as
13
antagonists acts as a primary DV-pattern-forming system
that enables the secondary center at a distance. In this
view, the formation of the Spemann organizer is close to
the ancestral mode as observed in Nematostella. The
locally antagonistic action of Chordin and BMP expression, employed already in Nematostella for the symmetry break, was presumably reemployed in vertebrates to
enhance the required self-enhancement by a double inhibition.
To generate positional information along the longextended AP axis, the vertebrate solution, i.e., the use
of a moving dorsal organizer to generate a dorsal midline
(Fig. 4), is not the only mechanism that evolved. In insects, the midline is formed ventrally due to an inhibition
from the dorsal 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 (Chen et al.,
2000) is an impressive example for this theoretically predicted mode (Meinhardt, 1989). Likewise, in a spider,
a clump of BMP-expressing cells, the cumulus, moves
from the center of the germ disk, the blastopore, towards
the periphery - a posterior-to-anterior movement. The
position at the anterior periphery determines the future
dorsal side. The midline proper, however, is not formed
dorsally behind the moving cumulus but at the ventral
side. A BMP-based inhibition, spreading from the cumulus, focus Chordin expression and thus midline formation to a narrow ventral stripe (Akiyama-Oda and Oda,
2006). The much discussed DV-VD reversal between
vertebrates and insects (Arendt and Nübler-Jung, 1994)
was proposed to have its origin in these different modes
of midline formation, invented during early evolution of
bilateral-symmetric body patterning (Meinhardt, 2004).
In protostomes, a dorsal organizer repels the midline that
appears, therefore, ventrally; it has from the beginning
the full AP extension but sharpens in the course of time.
In contrast, in deuterostomes, the dorsal organizer elongates the midline that appears, therefore, at the dorsal
side. The midline has from the beginning a narrow DV
extension but becomes elongated in the course of time.
These are not the only mechanisms. In planarians, for
instance, a dorsal-ventral confrontation seems to be the
precondition to form the anterior and posterior organizing
regions (Meinhardt, 2004).
activation in sea urchins between the animal and vegetal pole are examples. In these cases, the restriction of
the inducing signal to its final shape, its specific localization on a ring-shaped competent region and its regeneration after removal indicates the involvement of genuine
pattern-forming reactions. Such patterning cannot be explained by a model of the ‘French Flag´ type.
As shown in the present paper, many observations
in the DV patterning of higher organisms can be integrated by the assumption that the formation of BMPsignaling centers results from pattern-forming reactions
of the activator-depletion type; the self-enhancing BMPsignaling is antagonized by the depletion of the mobile
Chordin or Chordin-BMP complex in the surroundings.
Evolutionary, BMP-signaling could be originally involved
in performing a long-ranging inhibitory effect as seen today in Nematostella or in the localization of feather buds.
By obtaining an additional mandatory role it was co-opted
for the generation of a secondary (or tertiary) antipodal
signaling center.
In addition to the symmetry break by the BMPChordin system, the transformation of a patch-like into
a stripe-like organizing region was an important further
step in the evolution of long-extended bilateral-symmetric
animals. As shown, nature found different solutions
for this subtle patterning task, which were presumably
causal for a separation into different phyla and for the DV
reversal.
Although many molecular details are still unknown,
by exploring interactions from the perspective of patternforming reactions it was possible to unravel common
principles in reactions that use the same components but
that look overtly very different. Thus, modeling provides
a powerful tool to integrate disparate-appearing observations.
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16
Supplementary information
1. Mathematical formulation of the model for Chordin-BMP patterning in vertebrates
The equations below describe the interactions as used in the simulations. The equations
describe the concentration changes per time unit of Chordin transcription (T), the secreted
Chordin (C), BMP (B), the Chordin-BMP complex (X) and the BMP signalling via Smad (S).
Calculating repetitively the concentration changes in a short time interval and adding these to
the actual concentrations allow calculating the total time course. As mentioned, these models
are minimum models. For instance, the cooperation by different types of BMP molecules is
ignored. Since many more components are involved no attempt is made to relate the
parameters in the model to particular biophysical parameters. Important are relative time
constants, global or local actions and relative diffusion ranges. The crucial test is that the
minimum models mirror the observed dynamics. A distinction between transcription and the
distribution of the secreted factor is only made if these components are employed in different
ways
In the equations, substances are denoted with capital letters, parameters with Greek letters, 
are production rate,  removal rates,  Michaelis-Menten-type constants that limits
production rates if the level of an inhibitory substance becomes very low,  describe crossreactions between different components, are low baseline production rates that can initiate a
self-enhancing process, the term  leads to a saturation of the self-enhancement at high
concentration and enables thus the formation of stripes, D are the diffusion rates.
2. Simulations for vertebrates
Equation 1 describes the Chordin transcription (T) that is inhibited by BMP () and ADMP
(A). The mutual inhibition of Chordin and BMP acts as the self-enhancing process. A baseline
production results from the maternal determinant M that can be space-dependent as indicated
in grey in the Fig. 2 and SFig. 4:
T
T   T M
 2T



T

D

(1)
T
T
( T  B 2 ) ( TA  A2 )
t
x 2
Numerical constants used: T = 0.005 + 1% fluctuations; T = 0.0005; T = 0.1; TA
= 0.4;T = 0.005; DT = 0.003.
ADMP is assumed to have a direct inhibitory influence on the Chordin transcription. The term
TA is responsible that the system displays a threshold behavior, i.e., for a trigger at a low T
level. If TA is high, T can only trigger if the maternal determinants M are above a certain
level.
The concentration change of the diffusible Chordin (C) depends on its production rate (CT),
on the removal rate due to forming the complex with BMP, (- BCBC) which depends on both
the B and the C concentration, on its decay (-CC) and on its diffusion
C
 2C
  CT   X B C  C C  DC 2
(2)
t
x
Numerical constants used: c = 0.006; X = 0.001; C = 0.005; DC = 0.2.
ADMP is assumed to be under the same control as the Chordin transcription:
1
A
2 A
  AT   A A  DA 2
t
x
Numerical constants used A = 0.008; A = 0.008; DA = 0.2000.
(3)
The assumed concentration change in the BMP distribution of reads as follows
 SB B ( S 2   S ) 
B
B
2 B 
(4)

  X B C   B B  DB 2  

2
B T
t
x
 (1  S S ) (1   S C ) 
Numerical constants used for Fig. 2 and SFig.4: B = 0.005; SB = 0; B = 0.1; B =
0.005; X = 0.001; DB = 0.003.
The BMP production (B) is inhibited in the region of high Chordin transcription (T); BMP is
removed due to the formation of the Chordin-BMP complex (XBC) and by a normal
degradation. The last term describes that some BMP signaling also can take place in the
absence of Chordin (if SB > 0); this term is not important for the normal steady state and not
used in the vertebrate simulations; it can lead to a baseline BMP signaling in the absence of
Chordin (as observed in Drosophila).
The change of the BMP-Chordin complex X is given by its production rate, the removal due
to the BMP signaling via Smad (see equation 6) and the normal decay; the production term of
the complex, xBC corresponds to the removal terms in the equation (2) and (4) for B and C.
X
 X (S2  S )
2 X
  X B C  SX


X

D
X
X
t
(1  S S 2 ) (1   S C )
x 2
(5)
Numerical constants used: X = 0.001; X = 0; DX = 0.2; for the second term, the
depletion of X by BMP-signaling, see equation (6)
BMP signaling via Smad (S) is self-enhancing and depends on the BMP-Chordin complex X
that becomes depleted in this process; the term S C in the denominator describes the
inhibition of Smad activation by Chordin in order that the Chordin- and BMP-signaling
centers keep distance:
S
( SX X   SB B) ( S 2   S )
2S



S

D
(6)
S
S
t
(1  S S 2 ) (1   S C )
x 2
Numerical constants used: XS = 0.001; SB = 0; S = 0.2; S = 0; S = 5;
S = 0.001; DS = 0.002. The term (1 + s S2) in the denominator leads to a saturation at
high S levels that is required for stripe formation.
3. Simulation for Drosophila
The model for Dpp/Sog patterning in Drosophila is somewhat simpler since Sog is only
transcribed in a given region under control of an independent pattern-forming system. The
concentration change of the diffusible Sog/Chordin (C) depends on its production rate (CM),
on the removal rate due to forming the complex with BMP, (- BCBC), on its decay (-CC)
and on its diffusion; M is an indicator whether Sog is transcribed (M = 1) or not ( M = 0); M =
0.5 or 2.0 is if a single or a duplicated copy number of the Sog gene is assumed (Fig. 1 D, E).
M is indicated in red in the plots Fig. 1. This leads to the following change of Sog/Chordin per
time unit:
2
C
 2C
  C M   X B C  C C  DC 2
(7)
t
x
Numerical constants used C = 0.01; X = 0.01, C = 0.005; DC = 0.2.
The synthesis of Dpp/BMP is suppressed in regions in which Sog is transcribed (high M)
B
B
 B (S2  S )
2B

 SB


B
C


B

D
(8)
X
B
B
t
1  BM
(1  S S 2 )
x 2
Numerical constants used: B = 0.003; B = 30; X = 0.001; B = 0.0005; DB = 0.001; for
the second term, see equation (10).
The equations for the change of the BMP-Chordin complex X are almost the same as given
above except that Chordin has no direct inhibitory influence on the removal rate of the
complex.
X
 X (S2  S )
2 X
  X B C  SX


X

D
(9)
X
X
t
(1  S S 2 )
x 2
Numerical constants used: X = 0.001; S = 0.1;S = 0.2;X = 0.0; DX = 0.2; for the
second term see below.
The equation for the signaling is the same as give above for vertebrates.
S
( SX X   SB B) ( S 2   S )
2S



S

D
(10)
S
S
t
(1  S S 2 ) (1   S C )
x 2
Numerical constants used: SX = 0.005; SB = 0.001; S = 0.1;S = 5;S = 0.002;
DX = 0.001
Different in the Drosophila model is that the inhibition by Chordin [1 / (1 + S C)] influences
only the signaling, not the removal of  and C (equation 8 and 9). Only with this change the
stripe of Dpp/BMP signaling shrinks upon an increase of Chordin copy numbers. Otherwise
an inhibition of BMP signaling would also lead to a reduction in the removal rate of the
complex, causing an increase in the concentration of the complex X. This, in turn, would
compensate the increase in the inhibition.
4. Simulations for sea urchins
The main difference to the interactions described above is that both BMP and Chordin are
under control of Nodal that resembles together with Lefty a separate pattern-forming system
of the activator - inhibitor type. As well known, Nodal (N) production is self-enhancing
(Schier, 2009; Müller et al., 2012). The non-linearity results from the required dimer
formation. The production is inhibited by Lefty (L). Lefty production is under the same
control as Nodal.
N
 (N 2  N )
2 N
 N


N

D
N
N
t
L (1  N N 2 )
x 2
L

t
(11)
2L
(12)
x 2
Numerical constants used: N = 0.002; N = 0; N = 0.002; DN = 0.003 L = 0.003;
L = 0.003; DL = 0.4 (0.2 for simulations in two-dimensional fields). The same type
of equation was used for the simulation of the SFig. 1.
 L ( N 2   N )   L L  DL
3
Chordin and BMP production are under Nodal control:
C
 2C
  C N   X B C  C C  DC 2
(13)
t
x
B
 B (S2  S )
2B
  B N  SB


B
C


B

D
(14)
X
B
B
t
(1  S S 2 )
x 2
Numerical constants used: C = 0.02; X = 0.005, C = 0.001; DC = 0.02;
B = 0.02; SB = 0.002; S = 0.3; S = 0.05; B = 0.002; DB = 0.01.
The formation of the BMP-Chordin complex X and BMP-signaling S is similar to that given
for vertebrates:
X
2 X
  X B C   SX X ( S 2   S )   X X  DX
(15)
t
x 2
S
 SX X ( S 2   S )
 2S

  S S  DS 2
(16)
t
(1  S C )
x
Numerical constants used: X = 0.01; X = 0; DX = 0.2; XS = 0.005; S = 5;
S = 0.005; DS = 0.002.
5. Simulations for Nematostella
The following minimum model is the attempt to account for the observation made by
(Finnerty et al., 2004); (Rentzsch et al., 2006); (Matus et al., 2006); (Saina et al., 2009);
(Leclère and Rentzsch, 2014); (Genikhovich et al., 2015).
In Nematostella, the oral opening forms the primary organizing region, realized by the WNT
pathway (Kusserow et al., 2005). It is assumed to work as an activator-inhibitor system, W
and I. A candidate for the inhibitor I could be a molecule of the WNT family, modified to
allow long-ranging diffusion (Bartscherer et al, 2008; Meinhardt, 2012b). A similar reaction
type as for Nodal / Lefty (see equations equation 11 and 12) is assumed. Detailed modeling of
Cnidarian patterning is provided elsewhere (Meinhardt, 2012b).
W
 (W 2   W )
 2W
 W
 WW  DW
t
I
x 2
(17)
I

t
(18)
 IW 2   I I  DI
2I
 I
x 2
Numerical constants used: W = 0.003; W = 0.001; W = 0.001; DW = 0.001 I =
0.002; I = 0.002; I = 0.002; DI = 0.2; I = 0.0002. For initiation, in the central cell
an elevated Wnt level was assumed (Fig. 6B).
The fact that Chordin expression occurs not in a ring surrounding the oral opening but a in a
discrete off-axis patch indicates that Chordin/BMP represents a second pattern-forming
system. Blocking BMP transcription by morpholinos leads to a dramatic increase but not to a
ubiquitous expression of Chordin, suggesting that BMP acts as inhibitor but is not the only
inhibitor. To obtain the required pattern-forming capabilities, it is assumed that Chordin
transcription is a self-enhancing process accomplished by a local-acting molecule T. The
molecular basis is as yet unknown, the self-enhancement may be indirect. The production of
the diffusible Chordin C is proportional to the rate of Chordin transcription T.
4
T (T 2   T I )
T
 2T



T

D
T
T
t
( T  C  T B   BW BW ) (1  vT T 2 )
x 2
(19)
C

t
(20)
 C T  C C  DC
 2C
x 2
The following numerical constants were used for Figs. 6F-I: T = 0.001 with 1% random
fluctuations; T = 0.1: T = 0.002; T = 1; BW = 0.025; T = 0.001; DT = 0.003;
C = 0.0015; C = 0.0015; DC = 0.2.
The trigger of the Chordin transcription by the WNT system is achieved by a basic activation
accomplished by the long-ranging component of the Wnt system (T I). Chordin transcription
is assumed to be inhibited by the secreted Chordin (C). Since this inhibition is linear, it cannot
fully restrict Chordin transcription to a patch; this requires a further inhibition that is assumed
to be under the same control as the BMP transcription (B). Since this substance is assumed to
be under direct control of B, the level of B itself is used for simplicity (term B B). A direct
non-linear inhibition by Chordin could appear more reasonable but the dramatic Chordin
increase after BMP morpholinos argue against such a scheme.
The shift of the Chordin maximum to an off-axis position and the symmetry break is achieved
by an enhanced inhibition of Chordin transcription by BMP in the presence of Wnt (term
BWBW in the denominator). More generally, an organizing region can be forced to move by a
second inhibition that acts more locally and has a longer time constant, causing a local
quenching of a maximum shortly after its generation and the escape of the maximum into an
adjacent position (Meinhardt and Klingler, 1987). A saturation term T limits Chordin
transcription at high levels; it is responsible for the extent of Chordin transcription in the
absence of the BMP-dependent inhibition, i.e., if the term TB vanishes. A Michaelis-Menten
type constant T is responsible for a limitation of Chordin transcription in the absence of all
inhibitions; it has also the effect that Chordin activation occurs only if the WNT level is above
a threshold.
Usually the region of BMP transcription is larger than that of Chordin transcription. Thus,
assumed is that diffusible Chordin molecules controls BMP transcription.
B
2 B
  B C 2   B B  DB 2
(21)
t
x
For Figs. 6F-I the following numerical constants were used: B = 0.01; C = 0.01;
DB = 0.1
Since Chordin has a long range, the inhibition by BMP is also of long range. Since the BMP
production depends in a non-linear way on the diffusible Chordin, the region of BMP
transcription is narrower than the expected Chordin distribution. This non-linearity is required
for the correct balance of the self-enhancement of Chordin (term TB in equation 19).
BMP has a triple function, to restrict Chordin expression by a long-ranging inhibition, to shift
the Chordin expression away from the oral opening for symmetry breaking and to provide the
prerequisites for the pSmad signaling at the opposite site. This combination leads to a
characteristic problem in the simulations. BMP-signaling is connected with a removal of BMP
molecules that would, in turn, lower the inhibition that is required to restrict Chordin
transcription. Thus, a trigger of pSmad activity would lead to a dramatic increase of Chordin
5
transcription. To avoid such instabilities, two components are assumed to be produced under
the same control as BMP transcription. First, a short-ranging and more direct acting
component that accomplishes the inhibition of Chordin but does not contribute to the BMPsignaling as mentioned above; for simplicity B has been used directly for the Chordin
inhibition (term TB in equation 19). Secondly, the long-ranging BMP ligand (to be called
B ) is required for the antipodal BMP signaling; its removal during BMP signaling has
essentially no influence on the restriction of Chordin transcription.
B

t
 B B   S B ( S 2   S )   B B  DB
2 B
x 2
For Figs. 6F-I the following numerical constants were used:
DB
(22)
 B = 0.001;  B = 0.0001;
= 0.2; S = .001 plus 1% random fluctuations (see equation 23).
The BMP ligand B is produced proportional to the rate of BMP transcription B, assumed to be
diffusible on its own (as has been shown to be the case in sea urchins) and removed by the
BMP signaling. The equation for the BMP signaling via pSMAD is essentially the same as
given above for vertebrates. The term S C describes the inhibition of Chordin on the pSmad
signaling
S B ( S 2   S )
S
2S

  S S  DS 2
(23)
t
1 S C
x
For Figs. 6F-I the following numerical constants were used: S = 0.001 plus 1% random
fluctuations; S = 0.2 S = 5.S = 0.001; DS = 0.0002
Taking together, basic features of Nematostella patterning can be described by seven
equations, two for the generation of the Wnt organizer, two for Chordin- and BMPtranscription, two for the corresponding secreted molecules and one for pSmad signaling. This
highly simplified system accounts for the generation of a Chordin maximum, for the
symmetry break and the shift of the Chordin maximum to an off-center position, the
generation of a BMP signaling center at the opposite site, the vast increase of Chordin and the
absence of the symmetry break after treatment with BMP-morpholinos and for the predictable
polarization after morpholino treatment in parts of the early embryo (Fig. 6). The simulations
provided in (Genikhovich et al., 2015)are certainly more detailed. The attempt in the model
described is to include pattern formation and symmetry break as part of the dynamic system.
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5. Supplementary figures
SFig 1. Pattern formation by activator-inhibitor systems – simulation of some Nodal patterns
as examples. (A) A patch-like organizer can emerge if the inhibitor has a long range that
covers the total field, the activator shows some diffusion and no saturation is involved. In a
small field, the maximum appears preferentially at a marginal position since this requires
space for a single slope only. In this way, an initially homogeneous field of cells obtains a
polarity. This pattern resembles nodal activation in the sea urchin (Duboc et al., 2004). (B)
Stripes are preferentially formed if the activator shows some diffusion and the selfenhancement is limited by some saturation, i.e., if the activator concentration has an upper
bound. To localize the activation to the outer border a minor preference is sufficient (insert).
The activation via the upstream Mxtx2 is presumably responsible for this bias (Xu et al.,
2012). The ring-shaped nodal activation is involved in mesoderm formation and is thus a
prerequisite to form the Spemann-organizer. (C) Under the same condition but in the absence
of this bias, stripes are also formed, but these would have a random orientation.
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SFig. 2: Pattern formation by the activator - depleted substrate mechanism – the proposed
elementary process in BMP-signaling. (A) The long-ranging inhibition can result from a
depletion of a rapidly diffusing component (light blue; BMP ligand) that is necessary for a
short-ranging self-enhancing reaction via an activator (pSmad- signaling, dark blue) (Gierer
and Meinhardt, 1972; Meinhardt, 1982). Depending on the field size, multiple peaks can be
formed that emerge at variable position. (B) An elementary model for the formation of two
antipodal organizers. An activator-inhibitor system generates a primary organizer (green). The
long-ranging inhibitor (red) not only restricts the extension of the primary organizer but, due
to its inhibitory influence on the secondary activator-depletion system, it restricts the
activation of the latter. A single maximum emerges at the largest possible distance.
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SFig 3: A minimal model for the formation of the dorsal organizer. (A) The necessary selfenhancement is realized by a double inhibition of BMP (light blue) and Chordin (red). The
more rapidly diffusing ADMP (brown), produced under the same control as Chordin,
activates BMP and exerts therewith a long-ranging inhibition of Chordin transcription
(Meinhardt, 2000). (B) Pattern formation can start from an initially homogeneous situation.
(C) The organizer regenerates after removal. (D) Overall elevation of BMP leads to a
lowering of Chordin. (E) Ectopic increase of ADMP leads to a lowering of Chordin and of
BMP. (F) An increase of ADMP by ectopic elevation of Chordin leads to a lowering of BMP
(Reversade and De Robertis, 2005);(Lele et al., 2001). The long-ranging effect of ADMP may
also result from a direct transcriptional repression of Chordin, as it is observed for BMP2b
(Xue et al., 2014). Together with ADMP as the inhibitory component, a direct self-enhancing
component in the Chordin activation (dashed lines) would allow a residual pattern formation
even if all ventral BMP’s are knocked down, as observed (Reversade and De_Robertis, 2005)
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SFig. 4: DV-pattern formation in the vertebrates system if all cells are competent, i.e., in the
absence of local determinants. (A) In large fields, the danger would be high that more than
one organizer (red) is formed. In this case a symmetrical pattern could result as it is observed
after injection experiments with diverse organizer-promoting components that increase the
competence everywhere (Sokol et al., 1991); (Molenaar et al., 1996). (B) A certain
asymmetry in the competence (grey distribution) may be sufficient to form a single organizer
only. In this example, the region of the elevated competence is larger than that of the
emerging organizer showing the extension of the organizer is self-regulating and does not
depend on the extension of the maternal determinants. The reduced competence can be
nevertheless sufficient that a ventral fragment also regenerates; a transient broader Chordin
activation could lead to a temporary quenching of pSMAD activation. (C) In smaller fields,
only a single organizer is possible; the orientation of the emerging patterns is random. (D) In
small but growing fields, a polar pattern is formed if a certain size is exceeded; this pattern is
maintained during further growth. Supernumerary organizers that could appear during further
growth (E) can be prevented if cells distant to the organizer loose their competence
(Meinhardt, 2012b). If all cells are competent, after fragmentation of a polar field as shown in
(D), each fragment can regenerate the missing organizer as observed in early chick
development (Lutz, 1949). This may be connected with polarity reversal in the fragment not
containing the primary organizer, as observed in sea urchins (Hörstadius and Wolsky, 1936).
Additional References used in the Supplementary information:
Meinhardt, H., and Klingler, M. (1987). A model for pattern formation on the shells of
molluscs. J Theor Biol 126, 63–89.
Xu, C., Fan, Z. P., Müller, P., Fogley, R., DiBiase, A., Trompouki, E., Unternaehrer, J.,
Xiong, F., Torregroza, I., Evans, T., et al. (2012). Nanog-like regulates endoderm formation
through the Mxtx2-Nodal pathway. Dev Cell 22, 625–638.
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