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 MeinhardtMax Planck Institute for Developmental Biology

Spemannstr. 35, D- 72076 Tubingenhttp://www.eb.tuebingen.mpg.de/meinhardt; hans.meinhardt@tuebingen.mpg.de

Conserved from Cnidarians to vertebrates, thedorsoventral (DV) axis is patterned by the Chordin-BMP pathway. However, the functions of the path-way´s components are very different in differentphyla. By modeling it is shown that many observa-tions can be integrated by the assumption that BMP,acting as an inhibitory component in more ancestralsystems, became a necessary and activating compo-nent for the generation of a secondary and antipodal-located signaling center. The different realizationsseen in vertebrates, Drosophila, sea urchins and Ne-matostella allow reconstruction of a chain of mod-ifications during evolution. BMP-signaling is pro-posed to be based on a pattern-forming reaction ofthe activator-depleted substrate type in which BMP-signaling acts via pSmad as the local self-enhancingcomponent and the depletion of the highly mobileBMP-Chordin complex as the long-ranging antago-nistic component. Due to the rapid removal of theBMP/Chordin complex during BMP-signaling, an ori-ented transport and ‘shuttling´ results, although onlyordinary diffusion is involved. The system can beself-organizing, allowing organizer formation evenfrom near homogeneous initial situations. Organiz-ers may regenerate after removal. Although con-nected with some losses of self-regulation, for largeembryos as in amphibians, the employment of mater-nal determinants is an efficient strategy to make surethat only a single organizer of each type is gener-ated. The generation of dorsoventral positional infor-mation along a long-extended anteroposterior (AP)axis cannot be achieved directly by a single patch-like organizer. Nature found different solutions forthis task. Corresponding models provide a rationalefor the well-known reversal in the dorsoventral pat-terning between vertebrates and insects.

1. INTRODUCTIONIn all bilaterally-symmetrical organisms the dorsoven-tral (DV) patterning is achieved by the Chordin-BMPpathway that form signaling centers at antipodal posi-tions (Reversade and De Robertis, 2005; Bier, 2011).Although well conserved during evolution, the actualfunctions of the components seem to be very different.For instance, Chordin and BMP (respectively Sog andDpp in Drosophila) are transcribed in vertebrates andDrosophila at exclusive domains, while in sea urchinsand Nematostella these are produced at overlapping po-sitions. How can the expression region of one compo-nent shift from one side to the other, leaving the expres-sion of another component in place?

Pattern-forming reactions allow the generation of self-regulating signaling centers that act as organizing regionfor setting up the primary embryonic body axes. Usinga single organizer at one terminal position of a morpho-genetic field would lead to a shallow or low-level signaldistribution at the antipodal position. The employmentof two specific organizers, one at each terminal position,allows a more reliable fate determination over the entirefield. Usually one of these organizers acts as the primarysystem, forcing the secondary system to appear at a dis-tance. In the present paper it is shown that emphasizingthe role of the pattern-forming capabilities allows formu-lation of a set of closely related models for patterningalong the DV axis in different phyla, suggesting a sce-nario by which the different realizations evolved. In thepresumably more ancestral Nematostella system (andin feather bud formation), BMP acts as a long-ranginginhibitory component, restricting the size of an organiz-ing region; Chordin as an activating and BMP as an in-hibitory component are expressed in partially overlap-ping regions. BMP became involved once more in theformation of a secondary center, in which the roles arereversed: BMP became a necessary and activating com-ponent for the secondary antipodal BMP-pSmad signal-

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ing. BMP is required and becomes removed from largersurroundings for the generation of a local signal. Due toa long-ranging inhibitory action of the primary Chordin-dependent system, the secondary BMP-signaling centercan only emerge at a distance from the primary center;two different centers form at antipodal positions.

According to the currently prevailing view, the initialsteps in establishing organizing regions are achieved bymaternally-supplied determinants, not by self-organizingpattern-forming reactions. Indeed, pre-localized determi-nants play a crucial role in the most-studied model sys-tems. In amphibians, the animal-vegetal axis is mater-nally fixed and the well-known cortical rotation displacesmaterial from the vegetal pole to a more equatorial po-sition, determining in this way the future dorsal side byinitiating the formation of the Spemann organizer (re-viewed in (Harland and Gerhart, 1997; Niehrs, 2004;De Robertis, 2009) ). Suppression of this transloca-tion or the removal of the organizer abolishes axis for-mation. Likewise, maternal determinants are requiredto initiate early fish development (Abrams and Mullins,2009). In Drosophila, the DV-symmetry break resultsfrom the translocation of the nucleus from the posteriortip of the oocyte (Moussian and Roth, 2005; Reeves andStathopoulos, 2009). Even if maternal determinants areinvolved, several questions remain. For instance, in ver-tebrates, the Spemann-type organizer seems to be nec-essary to set up both the AP and DV axes. How can a sin-gle organizer organize two axes that are perpendicular toeach other? Why are maternal determinants needed inamphibians but not in the chick or in the mouse?

Even in systems in which localized determinants playa crucial role, strong indications exist that reactions areinvolved that are in principle able to generate patternsde-novo in a self-regulatory way. In a sandwich-like co-culture of dissociated animal and vegetal amphibian cellsclusters of notochord-, somite- and neural tube-like struc-tures are formed, clearly indicating the formation of orga-nizing regions (Nieuwkoop, 1992), although in this pro-cedure any maternally-imposed asymmetry is removed.Development can proceed normally in amphibians, chickand fish after removal of a substantial fraction of the or-ganizer (Cooke, 1975; Psychoyos and Stern, 1996; Shihand Fraser, 1996; Saude et al., 2000). After cuttingan 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 incipientorganizer at the posterior marginal zone. The fact thatany cell of an eight-cell mouse embryo can give rise to acomplete embryo shows that no localized maternal deter-minants are required, although some asymmetries maybe imposed by the sperm entry (Bedzhov and Zernicka-Goetz, 2014, Takaoka and Hamada, 2012). A strong in-dication that organizer formation in vertebrates dependson a pattern-forming reaction comes from the transientnature of gene activation in the organizer. As gastru-lation proceeds, cells move through the organizer; first

gaining and later losing activation of organizer-specificgenes (Joubin and Stern, 1999). The organizing regionmaintains an approximately constant size although thecells that it consists of change over time, with cells enter-ing and departing the region. Self-regulation along theDV axis after longitudinal fragmentation also has beendemonstrated for sea urchins (Horstadius 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 pattern-ing. For amphibians the Chordin-BMP interaction andthe molecular basis of its self-regulation has been elab-orated (Reversade and De Robertis, 2005; De Robertis,2009). This analysis revealed that, in addition to the Spe-mann organizer, a second signaling center is present atthe ventral side. This has been overlooked for a longtime since upon transplantation these ventral cells donot behave as expected for an organizer; their trans-plantation to the dorsal side is without effect (Smith andSlack, 1983), much in contrast to the classical Spemann-Mangold transplantation. The interaction of the dorsaland ventral center was compared with a seesaw (Rever-sade and De Robertis, 2005); dorsal and ventral compo-nents are in a balanced steady state and manipulationsthat lead to an enhancement or decline in one systemhave the opposite effect in the other antipodal system.

In another type of model the dorsoventral patterningis discussed in terms of the ‘French Flag´ concept, as-suming that a source and a sink region generates a gra-dient (Wolpert, 1969; Umulis et al., 2006). In this view,the fact that early removal of the ventral half in amphib-ians leads to well-proportioned embryos requires that thesteepness of the signal gradient is regulated to maintainthe terminal concentrations in the smaller field (Umulisand Othmer, 2013; Ben-Zvi et al., 2014). Since removalof the Spemann-organizer leads to a collapse of DV pat-terning, the Spemann organizer is frequently assumed tobe a static signaling source that produces a fixed amountof Chordin (Ben-Zvi et al., 2008). However, a French Flagtype of model cannot account for early patterning eventsin the mouse or in the chick as long as no explanationis provided how the source and the sink regions are es-tablished. In recent models the so-called ‘shuttling´, thefacilitated transport of BMP by Chordin plays a major rolefor the localization of BMP-signaling in Drosophila andvertebrate embryos (Eldar et al., 2002; Mizutani et al.,2005; Ben-Zvi et al., 2008).

After a brief general introduction into pattern-formingreactions it will be shown how known molecular compo-nents can be integrated to explain not only the distribu-tion of the signalling substances but also how the orga-nizers, the source- and the sink-regions become estab-lished. By constructing minimum models the intention isnot to account for all of the many known molecular detailsbut to unravel the underlying logic of this very essentialstep in early development.

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2. How to make an organizer: pattern-formingreactions

Pattern formation from initially more or less uniformsituations requires reactions that combine local self-enhancement and long-ranging inhibition (Gierer andMeinhardt, 1972; Meinhardt, 1982, 2008). A straight-forward realization of our general principle consists ofa local-acting activator whose autocatalytic production isantagonized by a long-ranging inhibitor. In an extendedfield a homogeneous distribution is unstable since asmall elevation of the activator will increase further dueto the self-enhancement. The concomitantly producedlong-ranging inhibitor restricts the level and extension ofemerging maxima of activator and inhibitor production.Eventually stable concentration maxima emerge that canact as signaling centers, i.e., as organizers (Supp Fig. 1).Regeneration of partially or completely removed orga-nizers is a standard regulatory feature of such reactionssince after removal of the activator-producing region, theremnant inhibitor fades away until the autocatalytic ac-tivator production starts again and maximum becomesrestored.

The possibility to generate patterns by the interactionof two substances that diffuse with different rates wasdiscovered by Alan Turing (Turing, 1952). However, al-most all interactions of this reaction-diffusion type areunable to generate any pattern, except if the conditionof local self-enhancement and long-ranging inhibition issatisfied. This crucial condition is not inherent in Turing´sseminal paper although one can interpret his equationsin this way (Meinhardt, 2012a).

The Nodal/Lefty interaction is an example that dis-plays the predicted properties (Supp. Fig. 1). Insea urchins Nodal is responsible for the generation ofthe oral opening (Duboc et al., 2004) and, by inducingChordin and BMP, for generating the dorsoventral pat-terning (Lapraz et al., 2009). In amphibians, Nodal isrequired for mesoderm formation and provides therewiththe precondition for organizer formation in the blastoporalring. The theoretically expected non-linearity in the self-enhancement is realized by a dimerization of Nodal whenbound to the receptor. The inhibitor Lefty has a muchlonger range than the activator (Sakuma et al., 2002;Muller et al., 2012), blocks dimerization of the Nodal re-ceptors and abolishes in this way the self-enhancement.

3. The activator - depleted substratemechanism and the BMP-signaling

Alternatively, stable patterns can also emerge if the localself-enhancing reaction is antagonized by the depletionof a diffusible substrate or co-factor that is necessaryto accomplish the self-enhancing reaction (Gierer andMeinhardt, 1972). Again, a homogeneous distribution isunstable. A stable steady state is reached if a maximumcan no longer increase in height or extension due to the

depletion of the substrate in a larger surroundings. In thisreaction scheme a net flow becomes established towardsthe activated region although molecules move only ran-domly by diffusion; the activator maximum resembles apowerful sink for the required substrate (SFig. 2).

Many patterning processes in the non-living worlddepend on such a type of interaction. For instance, asand dune forms behind a wind shelter due to a self-enhancing piling-up. This process depends on the ‘shut-tling´ of loose sand corns over long distances by theblowing wind. The depletion of the loose sand from theair by local deposition counteracts the self-enhancementin larger surroundings, leading eventually to dynamicallystable peaks.

It is easy to see that the BMP/Dpp -signaling followsthis activator - depleted substrate scheme (Fig. 1). InDrosophila, by binding to their receptors, Dpp ligands ini-tiate a self-enhancing reaction by pMAD activation andtranscriptional regulation via medea, zerknullt and othercomponents (Wang and Ferguson, 2005; Mizutani et al.,2005). To close the autocatalytic loop, a transcriptionalactivation of a co-receptor was assumed downstream ofthe DPP signaling (Wang and Ferguson, 2005). Dpp andSog can form rapidly diffusing complexes (Holley et al.,1996), satisfying in this way the condition that the com-ponent removed in the self-enhancing process is of longrange. Sog becomes locally degraded by Tolloid, causingthe release of the ligand at the receptor allowing signal-ing, internalization and removal. A longer-ranging com-petition for the complex was already proposed (Umuliset al., 2006). Since the activated region generates avery effective sink for the rapidly diffusing complex, thisscheme provides a straightforward explanation for the‘shuttling´ (Eldar et al., 2002) of Dpp by Sog and for theoriented movement towards the region of Dpp signalingalthough only ordinary diffusion is involved.

In the wasp Nasonia, BMP patterning occurs al-though Chordin is absent (Ozuak et al., 2014). In themodel, if BMP is diffusible on its own, the generation oflocalized BMP-signaling by the activator-depletion mech-anism does not require Chordin (SFig. 2). Indispensible,however, would be an alternative asymmetry that deter-mines where the BMP-signaling should occur.

4. The formation of the Dpp stripe inDrosophila provides insights for the logic behind

the observed complexityThe formation of narrow stripes with high Dpp-signalingimplies that the signaling cells can inhibit the onset ofDpp signaling in more ventrally located adjacent cell.Why such an inhibition does not take place along theAP extension, causing a disintegration of the stripe intopatches? Most of the published models treat DV pat-terning only as a one-dimensional process such that thisproblem does not show up. According to the model,stripe-like instead of patch-like distributions are formed

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Figure 1: Fig. 1: Simulation of the formation of a narrow stripe of Dpp signaling in Drosophila based on an activator-depletedsubstrate mechanism (Gierer and Meinhardt, 1972). (A) Schematic expression patterns of Sog (red), Dpp (light blue) and, at thedorsal-most position, Dpp-pMAD signaling (dark blue) (Wang and Ferguson, 2005; Mizutani et al., 2005). (B) Simulation: Dpp-signaling is a self-enhancing process involving pMAD and other components that is antagonized by the depletion of Dpp. Onits own, due to the low diffusion of Dpp, a moderate plateau but no signaling peaks can emerge. Sog mobilizes Dpp by formingdiffusible complexes (blue) that activate and become removed by the self-enhancing Dpp signaling (dark blue). Due to the additionalinhibitory influence of Sog, Dpp signaling occurs only at a distance from the Sog source (for equation and details, see supplementaryinformation). 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) Reductionof the Sog production (Sog+/- strain) reduces the inhibition, driving the self-enhancement stronger into saturation, causing a broaderstripe. (E) Increasing Sog production by increasing the Sog copy number leads to narrower stripes. Since the saturation level maynot be reached, the stripe has the tendency to disintegrate into patches, as observed (Wang and Ferguson, 2005). (F) An additionalregion 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 theassumed reaction: a self-enhancing reaction that depends on a diffusible substrate would lead to isolated patches (H). A saturationof 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.

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if the self-enhancing reaction shows saturation at highconcentrations (Fig. 1 H, I; SFig. 1). If the upper limitis reached, a maximum can no longer increase in peakheight. Instead, the spatial extension will increase un-til an equilibrium is reached. However, activated regionsdepend on the proximity of non-activated cells from whicheither fresh substrate such as the Dpp/Sog complex canbe obtained or into which an inhibitor can be dumped. Astripe-like pattern reconciles the seemingly contradictoryrequirements, large sizes of the activated region and theproximity of non-activated cells (Meinhardt, 1989; Mein-hardt, 1995). In such stripe-forming systems the width ofthe stripes and the distance between two stripes are ofthe same order, as it is the case in the proverbial ze-bra stripes. The distance between the stripes cannotbe increased by increasing the strength of the lateral in-hibition since this would lead to a disintegration of thestripe into patches. Thus, the formation a single stripe-like midline organizer is an intricate pattern-forming pro-cess, requiring an interference by a second system thatmakes sure that only a single stripe is formed althoughspace for more stripes would be available (Meinhardt,2004). In Dpp-signaling this issue is solved by an ad-ditional inhibitory action of Sog/Chordin, causing only asingle stripe to be formed and that this occurs distant tothe Sog source, i.e., at the dorsal-most position. Thismodel provides a rationale for the feature of ‘long-rangeactivation - short range inhibition´ assigned to the Sogfunction on the DPP signalling (Ashe and Levine, 1999).Short range exclusion and long-range activation is an ap-propriate mechanism that two pattern-forming systemskeep distance from each other without that one systemcan override the other (Meinhardt and Gierer, 1980).

A prediction of such a model is that the stripe maydecay into patches if the saturation level is not reached.This is in agreement with the observations that an in-crease of the Sog copy number, i.e., an increase of theinhibition, leads to a narrower Dpp stripe that becomesless 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, thereduced inhibition leads to a broader and more regularstripe (Fig. 1D).

5. Formation of two antipodal signaling centersin the DV-patterning of vertebrates

Chordin/Sog, in insects under the transcriptional controlof a separate pattern-forming system, acts in vertebratesas a part of an integrated regulatory system. Corre-sponding schemes with increasing complexity have beenproposed that allow a balanced Chordin-BMP expression(Reversade and De Robertis, 2005; De Robertis, 2009).However, not only a balanced expression ratio is requiredbut these expressions have to be localized at antipodalpositions.

According to a most simple scheme for pattern for-

mation by the Chordin/BMP system, the required auto-catalysis can result from the mutual inhibition of Chordinand BMP. An increase of Chordin, for instance, leadsto a decrease of BMP and thus to a further increase ofChordin as if Chordin were autocatalytic. ADMP (Mooset al., 1995; Lele et al., 2001), a BMP-type molecule,can be regarded as the required long-ranging antago-nist (Meinhardt, 2000, 2008). ADMP is produced un-der 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 thatlowering ADMP leads to an enlargement of Chordin ex-pression (Lele et al., 2001) and can cause the inductionof a secondary embryo (Dosch and Niehrs, 2000). Interms of the model, the long-ranging ADMP can restrictthe extension of Chordin expression either by activatingBMP or more directly by inhibiting Chordin transcription.This simple system allows organizer formation from ini-tially homogeneous situations, accounts for regenerationof a region of high Chordin expression after removal andshows the observed balanced behavior (SFig. 3).

Again, BMP-signaling as indicated by a high pSMADlevel is active only a fraction of the region in which BMPis transcribed (Fainsod et al., 1994; De Robertis, 2006),suggesting that a similar sharpening process is involvedas in Drosophila. Combining the BMP/Chordin/ADMPpatterning mechanism (SFig. 3) with the sharpening ofthe BMP-signalling mechanism via Smad leads to twoself-regulating signaling centers at antipodal positions(Fig. 2). The model provides a rationale for why twolong-ranging components, Chordin and ADMP, are pro-duced in the Spemann-type organizer. As mentioned, inDrosophila Sog has a double function, generating the dif-fusible Sog/Dpp complex and to localize Dpp signalling toa maximum distance from the Sog source. To integrateChordin into a self-regulating patterning system, a newfunction is required for a component that is produced inthe region of Chordin transcription: a long-ranging an-tagonist that limits the extension of the region in whichChordin is expressed. ADMP is a corresponding can-didate (Moos et al., 1995; Lele et al., 2001). Similarly,BMP2b has been found to act as an additional inhibitorthat directly downregulates Chordin transcription (Xue etal., 2014). As discussed further below, a direct inhibitoryrole of a BMP-like molecule is presumably an ancestralfeature.

This minimum model accounts already for many ob-servations. Both organizers behave differently upontransplantation. Transplantation of cells from the dor-sal organizer to the antipodal position - the classicalSpemann-Mangold experiment - establishes a new orga-nizing region, usually in an all or nothing mode. The highChordin level inhibits BMP-signaling in the surroundingcells; a new region of high BMP-signaling becomes es-tablished half-way between the two organizers (Fig. 2C).In contrast, transplantation of ventral cells into a dorsalposition remains without effect since Chordin, spread-

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Figure 2: Fig. 2: Model for the formation of two antipodal organizing regions in amphibians: Chordin became an integrated partof the pattern-forming system. (A) Final stable distribution of the components. The self-enhancement is achieved by the mutualinhibition of Chordin- (red) and BMP-transcription; (BMP distribution: light blue; Chordin distribution: brown). The long-rangingADMP (green), produced under the same control as Chordin, activates BMP transcription, acting thus as a long-ranging Chordininhibitor (SFig. 3). A direct inhibition of Chordin transcription maybe also involved (Xue et al., 2014). The rapidly diffusing BMP-Chordin complex (blue) fuels and is removed by the self-enhancing BMP signaling via pSmad (dark blue). The inhibitory influenceof Chordin restricts BMP signaling to the antipodal position (see Fig. 1). Maternal determinant (grey) are assumed that bringChordin activation above a threshold. (B) Time course. (C) Simulation of the Spemann experiment: transplantation of Chordin-expressing cells (red) to a ventral position triggers a new dorsal organizer and causes a shift of BMP signaling to the center. (D) Incontrast, transplantation of ventral cells to a dorsal position remains without effect; BMP signaling is immediately suppressed by thestrong inhibitory effect of Chordin secreted by the surrounding cells. (E) After bisection, a new pSmad activation reappears in thedorsal fragment. In contrast, the ventral fragment is unable to regenerate a new dorsal organizer due to the absence of the maternaldeterminants. This is different if all cells are competent for organizer formation (SFig. 4). (F-H) simulation in a two-dimensionalfield (for equations and parameters, see Supplementary Information).

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ing from the original organizer or its remains, immedi-ately blocks the Smad activation in the transplanted cell,which lose, therefore, their specific BMP-signaling activ-ity (Fig. 2D). The asymmetric behavior of the two centerswas regarded as puzzling (De Robertis, 2006) but finds inthis model a straightforward explanation. More completemodels have to include additional long-ranging antago-nists of the BMP-signaling such as Bambi and Sizzledthat contribute to the size-regulation of the pSMAD ac-tivation (De Robertis and Kuroda, 2004; Paulsen et al.,2011; Inomata et al., 2008; Inomata et al., 2013).

Organizer formation in amphibians depends on thecortical rotation that establishes a high β-catenin level atthe dorsal side. In the model it is assumed that suchlocalized determinants bring the Chordin system over athreshold level such that the self-enhancement is trig-gered (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 thatthe organizer does not regenerate (Fig. 2E). In contrast,after removal of the ventral half, the BMP-Chordin com-plex accumulates to such a degree that a new region ofSmad signaling emerges in the smaller field. For this re-generation of a BMP-signaling center neither a changein the steepness of a gradient nor a change in diffusionrates is required, in contrast to other models (Umulis andOthmer, 2013; Ben-Zvi et al., 2014). It should be empha-sized that regeneration of one or both terminal organizesis nothing special. It is the base for regeneration in othersystems such as Planarians or Hydra and can occur infragments that are only a very small part of the originalorganism.

In this view, localized maternal determinants are em-ployed as a means to suppress supernumerary organiz-ers in huge embryos as given in amphibians (Fig. 2).Organizer formation is only possible in the restricted re-gion made competent by the determinants. This view issupported by experiments in which the competence fororganizer formation is elevated ventrally, for instance, byincreasing the β-catenin or Wnt level there (Sokol et al.,1991; Molenaar et al., 1996). The resulting supernumer-ary embryos are well proportioned - a further indicationthat self-regulation determines strength, extension andposition of the new organizer.

In contrast, if development starts at a small size, onlythe two antipodal organizers can be formed even if allcells are competent. This occurs whenever a certainsize is surpassed (SFig. 4D). Once formed, the dor-sal organizer can suppress the activation of a seconddorsal organizer during further growth. If all cells arecompetent, a Spemann-type organizer also can regen-erate 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 re-quired to suppress the formation of supernumerary orga-nizers. In chick development, for instance, an inhibitionspreads from the established organizer that suppresses

the trigger of supernumerary organizers (Bertocchini etal., 2004). Downregulation of the competence for orga-nizer formation in cells distant to an established organizeris an efficient strategy to avoid supernumerary organiz-ers in growing systems; Hydra patterning is a further ex-ample for this strategy (Meinhardt, 1993, 2012b).

As mentioned, an unambiguous demonstration of theself-regulatory capabilities of Spemann organizer for-mation came from an experiment of Peter Nieuwkoop(Nieuwkoop, 1992). After co-culture of dissociated ani-mal and vegetal amphibian cells, derivatives of the Spe-mann organizer such as notochord, spinal cord andsomites were induced. According to the model, orga-nizer formation can start without localized determinantsas long as sufficient competent cells are available, evenif they are randomly distributed (Fig. 3). This type of ob-servations cannot be described by models that do notposses self-organizing properties [e.g. (Zhang et al.,2007; Ben-Zvi et al., 2008)].

Even after blocking translation of all ventrally-activeBMP genes, a residual DV polarization and localiza-tion of Chordin expression remains (Reversade and DeRobertis, 2005). This polarization, however, is com-pletely abolished if also ADMP is suppressed, suggest-ing that Chordin and ADMP act on their own as a rudi-mentary pattern-forming system. A self-enhancing com-ponent in the Chordin activation that is antagonized byADMP directly, i.e. without intermediate BMP activation,allows an integration of this observation. Indications fora similar interaction will discussed further below for Ne-matostella. Such a modification has little effect on thenormal pattern-forming reactions but leads to more clear-cut threshold behavior as required for simulating the ef-fects of maternal determinants.

The strong self-enhancement involved in organizerformation provides a rational for the otherwise puzzlingobservation of unspecific induction as has been madein early organizer research [reviewed in (De Robertis,2009)]. According to the model, even the leakage ofan inhibitor at a wound could be sufficient to bring theChordin system above a threshold, causing the trigger anew organizer that would have all properties of a naturalorganizer. The region antipodal to the organizer is espe-cially prone to unspecific induction due to a low level ofinhibition.

6. The moving organizer, midline formation andthe DV organization proper in vertebrates

It seems most natural that the side antipodal to the dor-sal organizer in vertebrates is assigned to be ventral. Toavoid confusions, I followed this convention thus far. In-deed, high BMP levels specify different ventral cell typesin the marginal zone (Mullins et al., 996; Kishimoto et al.,1997; Dosch et al., 1997; Walmsley et al., 2002). Nev-ertheless, this assignment is somewhat misleading. Fatemapping has shown that cells at the side conventionally

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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 maternaldeterminants 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 shownin 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 notrequired for initiating pattern formation as long as sufficient competent cells are present. (F) Another random assembly of cells maylead to different patterns, as observed.

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Figure 4: Fig. 4: DV patterning and midline formation in amphibians. (A) The generation of DV-positional information requiresthe 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 moveunderneath the ectoderm, forming the prechordal plate (yellow). (C) For the trunk, cells of the marginal zone move towards theorganizer and elongate the midline (red). (D) In the course of time, axial structures become elongated along the AP axis while theblastopore, 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 theline 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 theblastopore (1,2,3,...) (Wacker et al., 2004). Cells originally antipodal to the Spemann organizer (tip of red arrows) remain longestnear the marginal zone in which sequential activation of more posterior-specifying HOX genes take place; they form, therefore, mostposterior 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 ofthe same developmental clock (Hashiguchi and Mullins, 2013).

declared as ventral end up posteriorly in the tail (Laneand 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 AP-extension, not a patch-shaped organizer (Fig. 4). There-fore, crucial for the specification of cells along dorsoven-tral axis is not their distance to the Spemann-type orga-nizer but their distance to the midline that is induced bythe organizer (Meinhardt, 2004, 2006).

The marginal zone in amphibians, the blastopore onwhich the Spemann organizer is localized, is the mostposterior structure of the early embryo. Thus, the midlinehas to be formed under organizer control in two parts(Fig. 4). One part results from cells of the organizer thatmove underneath the ectoderm, forming the prechordalplate and thus the prerequisite for generating a referenceline for DV-patterning of the brain. For midline formationof the trunk, due to the convergence - extension mecha-nism, cells near the marginal zone move toward the or-ganizer and the incipient midline to form a rod-like axialstructure perpendicular to the blastopore with the noto-chord and neural tube as the most dorsal structures.

At a particular AP level of the trunk, the proper DVpatterning can only occur after notochord and floor plateis formed. This occurs in the course of time during theposterior elongation of the midline (Fig. 4). Recently ithas been shown that the DV patterning is under con-trol of the same developmental clock as the patterning

along the AP axis (Hashiguchi and Mullins, 2013). Thisis a straightforward consequence of the proposed modelsince first the midline has to be formed before the sig-nal that specifies the distance from the midline can begenerated or interpreted (Fig. 4). Graded BMP signal-ing has been shown also to be responsible for region-specific gene activation after gastrulation (Nguyen et al.,1998; Steventon et al., 2009). To emphasize it again, ac-cording to the model proposed, the DV patterning is notaccomplished by the two antipodal organizers within themarginal zone of the early embryo, as it is assumed inseveral recent models (Ben-Zvi et al., 2008; Inomata etal., 2013) but by distance of the cells from the midlinethat is induced by the dorsal organizer.

Usually the formation of a complete amphibian em-bryo after early removal of the ventral half is interpretedas indication of an excellent size regulation along the DVaxis (Ben-Zvi et al., 2008). However, as shown by Cooke(Cooke, 1981), size regulation does not occur along theDV but along the AP axis. If cells are removed from theso-called ventral side, the somites and the embryos asthe whole have a significant shorter AP- but the normalDV-extension. Thus, the embryo becomes shorter, butnot slimmer. The molecular mechanism is not yet fullyunderstood (Lauschke et al., 2013).

Even classical observations clearly demonstrate thatthe size regulation along the DV axis is restricted. Af-ter induction of a second Spemann organizer, the heads

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of the two embryos are usually complete and well sep-arated 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 midlineshave a large distance. The gradients do not overlap andthe DV patterns of the heads are complete. Later in de-velopment, however, the marginal zone shrinks in favor ofaxial elongation (Fig. 4); the two midlines become closerand closer; the gradient systems overlap and the trunksbecome fused, clearly indicating that the DV patterningdoes not scale. In terms of the model, for the forma-tion of complete embryos after tissue removal it is crucialthat missing organizers regenerate. However, the over-lap of the resulting gradients nevertheless can lead tofused structures. Regeneration of organizers and scal-ing of gradients are two different processes.

7. Applications to the DV organization of seaurchins

The oral opening of sea urchin embryos is formed at alateral position halfway between the animal pole and theWnt-expressing cells at the vegetal pole. The oral-aboralaxis formation is initially labile; slight asymmetries aresufficient for orientation. For instance, unilateral oxygendepletion is sufficient to orient the emerging pattern (Cz-ihak, 1963);(Coffman et al., 2004).The oral-aboral axis ishighly regulative; embryos fragmented along the animal-vegetal axis can form normal embryos. This regenerationmay be connected with a polarity reversal in one frag-ment (Horstadius and Wolsky, 1936). Meanwhile it hasbeen shown that the oral opening is under Nodal/Leftycontrol (Duboc et al., 2004) which is known to work asan activator-inhibitor system (Schier, 2009; Muller et al.,2012). All these properties, the ability to regenerate, theinitial sensitivity to minute asymmetries and the polarityreversal in originally non-activated fragments are proper-ties of pattern-forming systems (Meinhardt, 1982).

Chordin and BMP are also involved in the DV organi-zation of sea urchins, although in an unusual way. Nodalcontrols the transcription of both Chordin and BMP; theoral side is conventionally declared as ventral. Althoughsynthesized ventrally, BMP-signaling as indicated by pS-mad activation takes place at the dorsal side (Lapraz etal., 2009). Again, the purpose of the system is to estab-lish a secondary signaling center at the antipodal posi-tion. This is easily integrated into the model proposed(Fig. 5). At the side of Nodal-controlled BMP synthesisBMP-signaling is repressed by the high Chordin level. Atantipodal position the inhibition by Chordin is low enoughsuch that the self-enhancing BMP-signaling via pSmadis triggered. Obviously a huge net transport takes placefrom the ventral to the dorsal side due to sink functionfor BMP at the position of BMP-signalling. The posi-tion of BMP-synthesis is not critical since, due to therapid diffusion of the Chordin-BMP complex, it is avail-able also at distant positions. The model accounts for

the observed regulation. As shown in Fig. 5, regenera-tion of organizing regions can occur even if both the dor-sal and the ventral sites are removed. In sea urchins,BMP ligands are diffusible on their own, without complexformation (Lapraz et al., 2009) In this case, the formationof diffusible Chordin/BMP complexes is not necessarilyrequired for the mechanism to work; diffusible BMP lig-ands would be sufficient. However, the employment ofdiffusible complexes enlarges substantially the distancesover which the mechanism can work.

8. Chordin-BMP patterning in Nematostella:an ancestral mode?

One of the evolutionary earliest systems that display apatterning perpendicular to the primary (oral-aboral) axisis the Chordin-BMP patterning in the sea anemone Ne-matostella. Both Chordin and BMP appear first at the oralopening and become subsequently shifted to an off-axisposition (Finnerty et al., 2004; Rentzsch et al., 2006; Ma-tus et al., 2006; Saina et al., 2009; Leclere and Rentzsch,2014; Genikhovich et al., 2015). Even after the shift,Chordin and BMP remain partially superimposed. Thesuperposition of Chordin/BMP is reminiscent of the situ-ation in sea urchins discussed above and similar to theChordin/ADMP expression in vertebrates (Saina et al.,2009). The oral organizer is generated by the Wnt path-way (Kusserow et al., 2005).

Many regulatory features can be explained by as-suming that in Nematostella the Chordin-BMP patterningworks essentially as an activator-inhibitor system (Fig.6). BMP, produced under Chordin control, acts as in-hibitor, restricting the maximum level and the extensionof the Chordin peak. This inhibitory action of BMP oc-curs in in cooperation with RGM that presumably actsas a BMP co-receptor (Leclere and Rentzsch, 2014).This scheme is in accordance with the observation thatblocking of BMP- (Saina et al., 2009) or RGM-translation(Leclere and Rentzsch, 2014) leads to a dramatic in-crease of Chordin transcription since the inhibitory func-tion of BMP is lost. BMP, however, is certainly not theonly inhibitor in Chordin patterning since blocking of BMPtranscription by morpholinos leads to a dramatic increasebut not to a ubiquitous Chordin expression. Moreover, atlater stages, BMP remains spatially restricted in the en-doderm although Chordin expression occurs essentiallyin the ectoderm.

In terms of the model, the symmetry break and off-axis activation of the Chordin system is achieved as fol-lows. First, a long-ranging activating influence of theprimary WNT system leads to a trigger of Chordin ex-pression at the oral pole. Subsequently, a more local-ized quenching at the oral pole achieved, for instance,by an enhancement of the BMP inhibition in the pres-ence of WNT, causes that the activation of the Chordinsystem becomes more favored in a zone that surroundsthe oral organizer. The pattern-forming feature of the

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Figure 5: Fig. 5: Model for the DV organization in sea urchins. BMP and Chordin are transcribed under Nodal control whileBMP-signalling occurs antipodal to the side BMP production (Duboc et al., 2004; Lapraz et al., 2009). (A-E) Simulation in a one-dimensional field: the activator-inhibitor system Nodal (green, A) / Lefty (not shown, see SFig. 1) generates a high Nodal peakthat 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 (darkblue, E) that leads to a removal of BMP, Chordin and the complex. The extension of the Smad activation is restricted due to thedepletion of the complex. The self-regulatory capability is illustrated by pattern regeneration after a later removal of both organizingregions. Since degradation of the complex occurs almost exclusively together with the BMP- signalling, without a region of BMPsignaling the complex accumulates in the system until the BMP-signaling triggers. (F) Final stable steady state in a two-dimensionalsimulation. The BMP transport has been recently modeled in a more detailed way (van Heijster et al., 2014) (for equations seeSupplementary Information).

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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 linearfield: Wnt triggers the self-enhancing Chordin activation (red); BMP (light blue) acts as long-ranging inhibitor. The higher inhibitionof 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 inhibitoryinfluence of Chordin, this occurs at the opposite side, similar as in sea urchins (Fig. 5). (F) Final steady state in a two-dimensionalsimulation, oral view. (G) If BMP is blocked by morpholinos, Chordin transcription increases dramatically since the inhibition is nolonger functional; no symmetry break takes place, as observed (Saina et al., 2009). (H, I) Morpholino injections into two adjacentblastomeres at the four cell stage (Leclere and Rentzsch, 2014) provide strong support for the proposed interaction. Injection ofChordin morpholinos (H) reduces the self-enhancement of Chordin in the injected half (reduction is indicated by the density of thepink 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. Chordinactivation occurs in the injected and pSmad activation in the non-injected side (I), in agreement with the observations (for equationssee Supplementary Information).

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Chordin/BMP system makes sure that the Chordin ac-tivation becomes restricted to a patch and does not re-main a ring that surrounds the organizer (Fig. 6). Again,BMP signalling and pSMAD activation occurs at an an-tipodal position (Fig. 6). This model accounts for obser-vations made if BMP translation is blocked by morpholi-nos (Saina et al., 2009). First, since one of the inhibitorsis lost, Chordin transcription increases dramatically in theentire competent zone until saturation is reached. Sec-ondly, no shift to an off-axis position occurs since the ele-vated quenching of Chordin activation via BMP/WNT co-operation at the oral center is no longer functional (Fig.6G). The model is compatible with the observations thatoverexpression of Chordin leads to ectopic overexpres-sion of the BMP message even if the BMP translationis blocked. The addition of foreign BMP represses notonly Chordin but also BMP transcription (Saina et al.,2009). The model describes that Chordin activation oc-curs with a predictable polarity after blocking Chordin- orBMP-translation in parts of early embryos (Leclere andRentzsch, 2014) (Fig. 6 H-I). Other aspects are not yetincluded; for instance, that Chordin activation becomeseventually restricted to the ectoderm while BMP activa-tion resides in a somewhat larger region in the endoderm(Rentzsch et al, 2006; Matus et al., 2006a).

Chordin patterning is already involved in the pattern-ing of the radial-symmetric Hydra. It appears transientlyin bud formation and is one of the earliest indicators forhead regeneration (Rentzsch et al., 2007). Not unlike thesituation in Nematostella, Chordin transcription becomessubsequently shifted to a sub-hypostomal position andremains in newly-formed tentacles as a periodic pattern.Smad is ubiquitous expressed in the body column ex-cept of the terminal ends (Hobmayer et al., 2001) and isthus presumably not under positive control of an orga-nizer. The function of Chordin in Hydra is yet unknown.

Eventually, the pattern around the oral-aboral axis inNematostella, generated under the control of the Chordinsystem, consists of a periodic pattern of endodermalfolds, the so called mesenteries. On a first inspection,the generation of this periodic pattern seems to be un-necessarily complex, forming first an off-axis patch-likeorganizer that induces a second organizer at an antipo-dal position, which, in turn, provides a scaffold for theperiodic pattern. In contrast, in Hydra the periodic pat-tern - related to tentacle formation around the oral-aboralaxis - is generated directly. From the model, these inter-mediate steps in Nematostella are necessary. The peri-odic (tentacle-) pattern in hydra consists of spots aroundthe oral pol. In Nematostella however, a periodic stripe-like pattern has to be generated with an oral-aboral ex-tension of the stripes. This cannot be achieved directlyby the Hydra-type mechanism since direct stripe forma-tion would lead to a stripe around the oral opening, notto stripes along the oral-aboral axis. A possible mech-anism for the formation of stripes that have the correctorientation is to form first an off-center patch-like activa-

tion that has an inhibitory influence on a stripe-formingsystem, allowing only a single stripe at the contralateralside (Meinhardt, 1989;, 2004) that can be used as ascaffold to generate a periodic stripe-like pattern aroundthe oral-aboral axis (Berking and Herrmann, 2007). Thisseems to be what is realized in Nematostella. A stripe ofGDf5-like expression and nested expression of Hox8 andHoxE appear opposite to the patch-like Chordin expres-sion (Saina et al., 2009; Leclere and Rentzsch, 2014;Genikhovich et al., 2015).

This model suggests that in Nematostella some com-ponents are still missing. Required is a (direct or indi-rect) self-enhancement in the Chordin transcription, asit was already suggested for to cope with some obser-vation for the Spemann-organizer as mentioned above.Further, the experiments indicate that BMP downregu-lates Chordin transcription locally, i.e., outside the regionwhere BMP-signaling occurs. The huge overproductionof Chordin after blocking BMP transcription indicates thatthis interaction is rather direct and not controlled by aseparate pattern-forming reaction as in sea urchins. Themolecular basis is unknown.

9. A possible evolutionary scenarioThe presumably ancestral activator-inhibitor type ofChordin-BMP patterning in Hydra suggests an interest-ing evolutionary scenario. In Nematostella, BMP ob-tained a second function: not only restricting Chordinexpression but providing the prerequisites for a furtherpattern-forming system at antipodal position, realized bypSmad signaling. Both functions may be achieved bydifferent BMP´s. Also Chordin obtained a double func-tion; controlling BMP transcription that limits its ownself-enhancement and, by its inhibitory function on theBMP/Smad signaling, it causes the latter to appear at adistance from the Chordin source. BMP acts as inhibitoralso in other system, for instance, in the initiation of avianfeathers (Jung et al., 1998; Noramly and Morgan, 1998)and, at a later stage, in the signaling that separates barbsfrom each other (Harris et al., 2005).

Later in evolution, perhaps for a better separation ofthe multiple functions, Chordin transcription became un-der control of separate pattern-forming systems such asNodal in sea urchins or the nuclear Dorsal gradient inDrosophila. This liberated BMP from the inhibitory func-tion; the location of BMP transcription became unimpor-tant since, due the mobility of the Chordin/BMP complex,BMP became essentially available everywhere. With aBMP transcription outside of the region of Chordin tran-scription as in Drosophila, the region of BMP expressionbecame closer to the region in which the secondary BMPpatterning via pSmad should occur. This led to shorterdistances that have to be bridged by shuttling and en-abled thus more extended embryonic fields. In verte-brates, a mixture of both systems seems to be preserved:Chordin together with BMP2b and presumably ADMP as

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antagonists acts as a primary DV-pattern-forming systemthat enables the secondary center at a distance. In thisview, the formation of the Spemann organizer is close tothe ancestral mode as observed in Nematostella. Thelocally antagonistic action of Chordin and BMP expres-sion, employed already in Nematostella for the symme-try break, was presumably reemployed in vertebrates toenhance the required self-enhancement by a double in-hibition.

To generate positional information along the long-extended AP axis, the vertebrate solution, i.e., the useof a moving dorsal organizer to generate a dorsal midline(Fig. 4), is not the only mechanism that evolved. In in-sects, the midline is formed ventrally due to an inhibitionfrom the dorsal side. The midline has from the begin-ning the full AP extension of the embryo but sharpens inthe course of time to a narrow ventral line. The sharpen-ing of the Dorsal transcription in Tribolium (Chen et al.,2000) is an impressive example for this theoretically pre-dicted mode (Meinhardt, 1989). Likewise, in a spider,a clump of BMP-expressing cells, the cumulus, movesfrom the center of the germ disk, the blastopore, towardsthe periphery - a posterior-to-anterior movement. Theposition at the anterior periphery determines the futuredorsal side. The midline proper, however, is not formeddorsally behind the moving cumulus but at the ventralside. A BMP-based inhibition, spreading from the cumu-lus, focus Chordin expression and thus midline forma-tion to a narrow ventral stripe (Akiyama-Oda and Oda,2006). The much discussed DV-VD reversal betweenvertebrates and insects (Arendt and Nubler-Jung, 1994)was proposed to have its origin in these different modesof midline formation, invented during early evolution ofbilateral-symmetric body patterning (Meinhardt, 2004).In protostomes, a dorsal organizer repels the midline thatappears, therefore, ventrally; it has from the beginningthe full AP extension but sharpens in the course of time.In contrast, in deuterostomes, the dorsal organizer elon-gates the midline that appears, therefore, at the dorsalside. The midline has from the beginning a narrow DVextension but becomes elongated in the course of time.These are not the only mechanisms. In planarians, forinstance, a dorsal-ventral confrontation seems to be theprecondition to form the anterior and posterior organizingregions (Meinhardt, 2004).

10. ConclusionCrucial for setting up embryonic axes is the formation oforganizing regions by pattern-forming reactions. Theirself-regulatory features account for many observations,including organizer formation from near-homogeneousinitial situations and their restoration after removal.Pattern-forming reactions are not only decisive to formthe terminal organizers but also to initiate substructures.The activation of Chordin/BMP at a distance from theoral pole in Nematostella or the positioning of the Nodal

activation in sea urchins between the animal and vege-tal pole are examples. In these cases, the restriction ofthe inducing signal to its final shape, its specific localiza-tion on a ring-shaped competent region and its regener-ation after removal indicates the involvement of genuinepattern-forming reactions. Such patterning cannot be ex-plained by a model of the ‘French Flag´ type.

As shown in the present paper, many observationsin the DV patterning of higher organisms can be inte-grated by the assumption that the formation of BMP-signaling centers results from pattern-forming reactionsof the activator-depletion type; the self-enhancing BMP-signaling is antagonized by the depletion of the mobileChordin or Chordin-BMP complex in the surroundings.Evolutionary, BMP-signaling could be originally involvedin performing a long-ranging inhibitory effect as seen to-day in Nematostella or in the localization of feather buds.By obtaining an additional mandatory role it was co-optedfor the generation of a secondary (or tertiary) antipodalsignaling center.

In addition to the symmetry break by the BMP-Chordin system, the transformation of a patch-like intoa stripe-like organizing region was an important furtherstep in the evolution of long-extended bilateral-symmetricanimals. As shown, nature found different solutionsfor this subtle patterning task, which were presumablycausal for a separation into different phyla and for the DVreversal.

Although many molecular details are still unknown,by exploring interactions from the perspective of pattern-forming reactions it was possible to unravel commonprinciples in reactions that use the same components butthat look overtly very different. Thus, modeling providesa powerful tool to integrate disparate-appearing observa-tions.

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16

1

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 cross-reactions 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:

2

2 2 2( ) ( )T T

T TT TA

T M TT D

t B A x

(1)

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

2

2C X C C

C CT BC C D

t x

(2)

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:

2

2

2A A A

A AT A D

t x

(3)

Numerical constants used A = 0.008; A = 0.008; DA = 0.2000. The assumed concentration change in the BMP distribution of reads as follows

22

2 2

( )

(1 ) (1 )SB SB

X B BB S S

B SB BBC B D

t T x S C

(4)

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.

2 2

2 2

( )

(1 ) (1 )SX S

X X XS S

X X S XBC X D

t S C x

(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:

2 2

2 2

( ) ( )

(1 ) (1 )SX SB S

S SS S

S X B S SS D

t S C x

(6)

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 S

2) 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:

3

2

2C X C C

C CM B C C D

t x

(7)

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)

2 2

2 2

( )

1 (1 )B SB S

X B BB S

B B S BBC B D

t M S x

(8)

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.

2 2

2 2

( )

(1 )SX S

X X XS

X X S XBC X D

t S x

(9)

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.

2 2

2 2

( ) ( )

(1 ) (1 )SX SB S

S SS S

S X B S SS D

t S C x

(10)

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.

2 2

2 2

( )

(1 )N N

N NN

N N NN D

t L N x

(11)

22

2( )L N L L

L LN L D

t x

(12)

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.

4

Chordin and BMP production are under Nodal control: 2

2C X C C

C CN BC C D

t x

(13)

2 2

2 2

( )

(1 )SB S

B X B BS

B B S BN BC B D

t S x

(14)

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:

22

2( )X SX S X X

X XBC X S X D

t x

(15)

2 2

2

( )

(1 )SX S

S SS

S X S SS D

t C x

(16)

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).

2 2

2

( )W WW W

W W WW D

t I x

(17)

22

2I I I I

I IW I D

t x

(18)

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.

5

2 2

2 2

( )

( ) (1 )T T

T TT T BW T

T IT TT D

t C B BW v T x

(19)

2

2C C C

C CT C D

t x

(20)

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.

22

2B B B

B BC B D

t x

(21)

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

6

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 BMP-signaling 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.

22

2( )S SB B B

B BB B S B D

t x

(22)

For Figs. 6F-I the following numerical constants were used: B = 0.001; B = 0.0001;

BD = 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

2 2

2

( )

1S S

S SS

B SS SS D

t C x

(23)

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 BMP- transcription, 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.

7

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 self-enhancement 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.

8

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 self-enhancement 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.