Dorsoventral Patterning by the Chordin-BMP Pathway: a Unified Model from a Pattern-Formation Perspective for Drosophila, Vertebrates, Sea Urchins and Nematostella

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 Tubingen¨ http://www.eb.tuebingen.mpg.de/meinhardt; [email protected]

Conserved from Cnidarians to vertebrates, the 1. INTRODUCTION dorsoventral (DV) axis is patterned by the Chordin- In all bilaterally-symmetrical organisms the dorsoven- BMP pathway. However, the functions of the path- tral (DV) patterning is achieved by the Chordin-BMP way´s components are very different in different pathway that form signaling centers at antipodal posi- phyla. By modeling it is shown that many observa- tions (Reversade and De Robertis, 2005; Bier, 2011). tions can be integrated by the assumption that BMP, Although well conserved during evolution, the actual acting as an inhibitory component in more ancestral functions of the components seem to be very different. systems, became a necessary and activating compo- For instance, Chordin and BMP (respectively Sog and nent for the generation of a secondary and antipodal- Dpp in Drosophila) are transcribed in vertebrates and located signaling center. The different realizations Drosophila at exclusive domains, while in sea urchins seen in vertebrates, Drosophila, sea urchins and Ne- and Nematostella these are produced at overlapping po- matostella allow reconstruction of a chain of mod- sitions. How can the expression region of one compo- ifications during evolution. BMP-signaling is pro- nent shift from one side to the other, leaving the expres- posed to be based on a pattern-forming reaction of sion of another component in place? the activator-depleted substrate type in which BMP- Pattern-forming reactions allow the generation of self- signaling acts via pSmad as the local self-enhancing regulating signaling centers that act as organizing region component and the depletion of the highly mobile for setting up the primary embryonic body axes. Using BMP-Chordin complex as the long-ranging antago- a single organizer at one terminal position of a morpho- nistic component. Due to the rapid removal of the genetic field would lead to a shallow or low-level signal BMP/Chordin complex during BMP-signaling, an ori- distribution at the antipodal position. The employment ented transport and ‘shuttling´ results, although only of two specific organizers, one at each terminal position, ordinary diffusion is involved. The system can be allows a more reliable fate determination over the entire self-organizing, allowing organizer formation even field. Usually one of these organizers acts as the primary from near homogeneous initial situations. Organiz- system, forcing the secondary system to appear at a dis- ers may regenerate after removal. Although con- tance. In the present paper it is shown that emphasizing nected with some losses of self-regulation, for large the role of the pattern-forming capabilities allows formu- embryos as in amphibians, the employment of mater- lation of a set of closely related models for patterning nal determinants is an efficient strategy to make sure along the DV axis in different phyla, suggesting a sce- that only a single organizer of each type is gener- nario by which the different realizations evolved. In the ated. The generation of dorsoventral positional infor- presumably more ancestral Nematostella system (and mation along a long-extended anteroposterior (AP) in feather bud formation), BMP acts as a long-ranging axis cannot be achieved directly by a single patch- inhibitory component, restricting the size of an organiz- like organizer. Nature found different solutions for ing region; Chordin as an activating and BMP as an in- this task. Corresponding models provide a rationale hibitory component are expressed in partially overlap- for the well-known reversal in the dorsoventral pat- ping regions. BMP became involved once more in the terning between vertebrates and insects. formation of a secondary center, in which the roles are reversed: BMP became a necessary and activating com- ponent for the secondary antipodal BMP-pSmad signal- 1 ing. BMP is required and becomes removed from larger gaining and later losing activation of organizer-specific surroundings for the generation of a local signal. Due to genes (Joubin and Stern, 1999). The organizing region a long-ranging inhibitory action of the primary Chordin- maintains an approximately constant size although the dependent system, the secondary BMP-signaling center cells that it consists of change over time, with cells enter- can only emerge at a distance from the primary center; ing and departing the region. Self-regulation along the two different centers form at antipodal positions. DV axis after longitudinal fragmentation also has been According to the currently prevailing view, the initial demonstrated for sea urchins (Horstadius¨ and Wolsky, steps in establishing organizing regions are achieved by 1936), Planarians (Molina et al., 2007; Reddien et al., maternally-supplied determinants, not by self-organizing 2007; Orii and Watanabe, 2007) and for some insects pattern-forming reactions. Indeed, pre-localized determi- (Sander, 1971). nants play a crucial role in the most-studied model sys- There are several attempts to model the DV pattern- tems. In amphibians, the animal-vegetal axis is mater- ing. For amphibians the Chordin-BMP interaction and nally fixed and the well-known cortical rotation displaces the molecular basis of its self-regulation has been elab- material from the vegetal pole to a more equatorial po- orated (Reversade and De Robertis, 2005; De Robertis, sition, determining in this way the future dorsal side by 2009). This analysis revealed that, in addition to the Spe- initiating the formation of the Spemann organizer (re- mann organizer, a second signaling center is present at viewed in (Harland and Gerhart, 1997; Niehrs, 2004; the ventral side. This has been overlooked for a long De Robertis, 2009) ). Suppression of this transloca- time since upon transplantation these ventral cells do tion or the removal of the organizer abolishes axis for- not behave as expected for an organizer; their trans- mation. Likewise, maternal determinants are required plantation to the dorsal side is without effect (Smith and to initiate early fish development (Abrams and Mullins, Slack, 1983), much in contrast to the classical Spemann- 2009). In Drosophila, the DV-symmetry break results Mangold transplantation. The interaction of the dorsal from the translocation of the nucleus from the posterior and ventral center was compared with a seesaw (Rever- tip of the oocyte (Moussian and Roth, 2005; Reeves and sade and De Robertis, 2005); dorsal and ventral compo- Stathopoulos, 2009). Even if maternal determinants are nents are in a balanced steady state and manipulations involved, several questions remain. For instance, in ver- that lead to an enhancement or decline in one system tebrates, the Spemann-type organizer seems to be nec- have the opposite effect in the other antipodal system. essary to set up both the AP and DV axes. How can a sin- In another type of model the dorsoventral patterning gle organizer organize two axes that are perpendicular to is discussed in terms of the ‘French Flag´ concept, as- each other? Why are maternal determinants needed in suming that a source and a sink region generates a gra- amphibians but not in the chick or in the mouse? dient (Wolpert, 1969; Umulis et al., 2006). In this view, Even in systems in which localized determinants play the fact that early removal of the ventral half in amphib- a crucial role, strong indications exist that reactions are ians leads to well-proportioned embryos requires that the involved that are in principle able to generate patterns steepness of the signal gradient is regulated to maintain de-novo in a self-regulatory way. In a sandwich-like co- the terminal concentrations in the smaller field (Umulis culture of dissociated animal and vegetal amphibian cells and Othmer, 2013; Ben-Zvi et al., 2014). Since removal clusters of notochord-, somite- and neural tube-like struc- of the Spemann-organizer leads to a collapse of DV pat- tures are formed, clearly indicating the formation of orga- terning, the Spemann organizer is frequently assumed to nizing regions (Nieuwkoop, 1992), although in this pro- be a static signaling source that produces a fixed amount cedure any maternally-imposed asymmetry is removed. of Chordin (Ben-Zvi et al., 2008). However, a French Flag Development can proceed normally in amphibians, chick type of model cannot account for early patterning events and fish after removal of a substantial fraction of the or- in the mouse or in the chick as long as no explanation ganizer (Cooke, 1975; Psychoyos and Stern, 1996; Shih is provided how the source and the sink regions are es- and Fraser, 1996; Saude` et al., 2000). After cutting tablished. In recent models the so-called ‘shuttling´, the an early chick blastodisk into two or three fragments, facilitated transport of BMP by Chordin plays a major role complete embryos can develop in each fragment (Lutz, for the localization of BMP-signaling in Drosophila and 1949), even if the fragment does not contain the incipient vertebrate embryos (Eldar et al., 2002; Mizutani et al., organizer at the posterior marginal zone. The fact that 2005; Ben-Zvi et al., 2008). any cell of an eight-cell mouse embryo can give rise to a After a brief general introduction into pattern-forming complete embryo shows that no localized maternal deter- reactions it will be shown how known molecular compo- minants are required, although some asymmetries may nents can be integrated to explain not only the distribu- be imposed by the sperm entry (Bedzhov and Zernicka- tion of the signalling substances but also how the orga- Goetz, 2014, Takaoka and Hamada, 2012). A strong in- nizers, the source- and the sink-regions become estab- dication that organizer formation in vertebrates depends lished. By constructing minimum models the intention is on a pattern-forming reaction comes from the transient not to account for all of the many known molecular details nature of gene activation in the organizer. As gastru- but to unravel the underlying logic of this very essential lation proceeds, cells move through the organizer; first step in early development. 2 2. How to make an organizer: pattern-forming depletion of the substrate in a larger surroundings. In this reactions reaction scheme a net flow becomes established towards the activated region although molecules move only ran- Pattern formation from initially more or less uniform domly by diffusion; the activator maximum resembles a situations requires reactions that combine local self- powerful sink for the required substrate (SFig. 2). enhancement and long-ranging inhibition (Gierer and Many patterning processes in the non-living world Meinhardt, 1972; Meinhardt, 1982, 2008). A straight- depend on such a type of interaction. For instance, a forward realization of our general principle consists of sand dune forms behind a wind shelter due to a self- a local-acting activator whose autocatalytic production is enhancing piling-up. This process depends on the ‘shut- antagonized by a long-ranging inhibitor. In an extended tling´ of loose sand corns over long distances by the field a homogeneous distribution is unstable since a blowing wind. The depletion of the loose sand from the small elevation of the activator will increase further due air by local deposition counteracts the self-enhancement to the self-enhancement. The concomitantly produced in larger surroundings, leading eventually to dynamically long-ranging inhibitor restricts the level and extension of stable peaks. emerging maxima of activator and inhibitor production. It is easy to see that the BMP/Dpp -signaling follows Eventually stable concentration maxima emerge that can this activator - depleted substrate scheme (Fig. 1). In act as signaling centers, i.e., as organizers (Supp Fig. 1). Drosophila, by binding to their receptors, Dpp ligands ini- Regeneration of partially or completely removed orga- tiate a self-enhancing reaction by pMAD activation and nizers is a standard regulatory feature of such reactions transcriptional regulation via medea, zerknullt¨ and other since after removal of the activator-producing region, the components (Wang and Ferguson, 2005; Mizutani et al., remnant inhibitor fades away until the autocatalytic ac- 2005). To close the autocatalytic loop, a transcriptional tivator production starts again and maximum becomes activation of a co-receptor was assumed downstream of restored. the DPP signaling (Wang and Ferguson, 2005). Dpp and The possibility to generate patterns by the interaction Sog can form rapidly diffusing complexes (Holley et al., of two substances that diffuse with different rates was 1996), satisfying in this way the condition that the com- discovered by Alan Turing (Turing, 1952). However, al- ponent removed in the self-enhancing process is of long most all interactions of this reaction-diffusion type are range. Sog becomes locally degraded by Tolloid, causing unable to generate any pattern, except if the condition the release of the ligand at the receptor allowing signal- of local self-enhancement and long-ranging inhibition is ing, internalization and removal. A longer-ranging com- satisfied. This crucial condition is not inherent in Turing´s petition for the complex was already proposed (Umulis seminal paper although one can interpret his equations et al., 2006). Since the activated region generates a in this way (Meinhardt, 2012a). very effective sink for the rapidly diffusing complex, this The Nodal/Lefty interaction is an example that dis- scheme provides a straightforward explanation for the plays the predicted properties (Supp. Fig. 1). In ‘shuttling´ (Eldar et al., 2002) of Dpp by Sog and for the sea urchins Nodal is responsible for the generation of oriented movement towards the region of Dpp signaling the oral opening (Duboc et al., 2004) and, by inducing although only ordinary diffusion is involved. Chordin and BMP, for generating the dorsoventral pat- In the wasp Nasonia, BMP patterning occurs al- terning (Lapraz et al., 2009). In amphibians, Nodal is though Chordin is absent (Oz¨ uak¨ et al., 2014). In the required for mesoderm formation and provides therewith model, if BMP is diffusible on its own, the generation of the precondition for organizer formation in the blastoporal localized BMP-signaling by the activator-depletion mech- ring. The theoretically expected non-linearity in the self- anism does not require Chordin (SFig. 2). Indispensible, enhancement is realized by a dimerization of Nodal when however, would be an alternative asymmetry that deter- bound to the receptor. The inhibitor Lefty has a much mines where the BMP-signaling should occur. longer range than the activator (Sakuma et al., 2002; Muller¨ et al., 2012), blocks dimerization of the Nodal re- 4. The formation of the Dpp stripe in ceptors and abolishes in this way the self-enhancement. Drosophila provides insights for the logic behind 3. The activator - depleted substrate the observed complexity mechanism and the BMP-signaling The formation of narrow stripes with high Dpp-signaling implies that the signaling cells can inhibit the onset of Alternatively, stable patterns can also emerge if the local Dpp signaling in more ventrally located adjacent cell. self-enhancing reaction is antagonized by the depletion Why such an inhibition does not take place along the of a diffusible substrate or co-factor that is necessary AP extension, causing a disintegration of the stripe into to accomplish the self-enhancing reaction (Gierer and patches? Most of the published models treat DV pat- Meinhardt, 1972). Again, a homogeneous distribution is terning only as a one-dimensional process such that this unstable. A stable steady state is reached if a maximum problem does not show up. According to the model, can no longer increase in height or extension due to the stripe-like instead of patch-like distributions are formed 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: Dpp- signaling 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 mation by the Chordin/BMP system, the required auto- concentrations (Fig. 1 H, I; SFig. 1). If the upper limit catalysis can result from the mutual inhibition of Chordin is reached, a maximum can no longer increase in peak and BMP. An increase of Chordin, for instance, leads height. Instead, the spatial extension will increase un- to a decrease of BMP and thus to a further increase of til an equilibrium is reached. However, activated regions Chordin as if Chordin were autocatalytic. ADMP (Moos depend on the proximity of non-activated cells from which et al., 1995; Lele et al., 2001), a BMP-type molecule, either fresh substrate such as the Dpp/Sog complex can can be regarded as the required long-ranging antago- be obtained or into which an inhibitor can be dumped. A nist (Meinhardt, 2000, 2008). ADMP is produced un- stripe-like pattern reconciles the seemingly contradictory der the same control as Chordin and has a longer range requirements, large sizes of the activated region and the (Willot et al., 2002; Reversade and De Robertis, 2005). proximity of non-activated cells (Meinhardt, 1989; Mein- Such a scheme is in agreement with the observation that hardt, 1995). In such stripe-forming systems the width of lowering ADMP leads to an enlargement of Chordin ex- the stripes and the distance between two stripes are of pression (Lele et al., 2001) and can cause the induction the same order, as it is the case in the proverbial ze- of a secondary embryo (Dosch and Niehrs, 2000). In bra stripes. The distance between the stripes cannot terms of the model, the long-ranging ADMP can restrict be increased by increasing the strength of the lateral in- the extension of Chordin expression either by activating hibition since this would lead to a disintegration of the BMP or more directly by inhibiting Chordin transcription. stripe into patches. Thus, the formation a single stripe- This simple system allows organizer formation from ini- like midline organizer is an intricate pattern-forming pro- tially homogeneous situations, accounts for regeneration cess, requiring an interference by a second system that of a region of high Chordin expression after removal and makes sure that only a single stripe is formed although shows the observed balanced behavior (SFig. 3). space for more stripes would be available (Meinhardt, Again, BMP-signaling as indicated by a high pSMAD 2004). In Dpp-signaling this issue is solved by an ad- level is active only a fraction of the region in which BMP ditional inhibitory action of Sog/Chordin, causing only a is transcribed (Fainsod et al., 1994; De Robertis, 2006), single stripe to be formed and that this occurs distant to suggesting that a similar sharpening process is involved the Sog source, i.e., at the dorsal-most position. This as in Drosophila. Combining the BMP/Chordin/ADMP model provides a rationale for the feature of ‘long-range patterning mechanism (SFig. 3) with the sharpening of activation - short range inhibition´ assigned to the Sog the BMP-signalling mechanism via Smad leads to two function on the DPP signalling (Ashe and Levine, 1999). self-regulating signaling centers at antipodal positions Short range exclusion and long-range activation is an ap- (Fig. 2). The model provides a rationale for why two propriate mechanism that two pattern-forming systems long-ranging components, Chordin and ADMP, are pro- keep distance from each other without that one system duced in the Spemann-type organizer. As mentioned, in can override the other (Meinhardt and Gierer, 1980). Drosophila Sog has a double function, generating the dif- A prediction of such a model is that the stripe may fusible Sog/Dpp complex and to localize Dpp signalling to decay into patches if the saturation level is not reached. a maximum distance from the Sog source. To integrate This is in agreement with the observations that an in- Chordin into a self-regulating patterning system, a new crease of the Sog copy number, i.e., an increase of the function is required for a component that is produced in inhibition, leads to a narrower Dpp stripe that becomes the region of Chordin transcription: a long-ranging an- less regular (Wang and Ferguson, 2005; Mizutani et al., tagonist that limits the extension of the region in which 2005) which is reproduced in the simulation (Fig. 1 E). Chordin is expressed. ADMP is a corresponding can- Other way round, if only a single Sog copy is present, the didate (Moos et al., 1995; Lele et al., 2001). Similarly, reduced inhibition leads to a broader and more regular BMP2b has been found to act as an additional inhibitor stripe (Fig. 1D). that directly downregulates Chordin transcription (Xue et al., 2014). As discussed further below, a direct inhibitory 5. Formation of two antipodal signaling centers role of a BMP-like molecule is presumably an ancestral in the DV-patterning of vertebrates feature. This minimum model accounts already for many ob- Chordin/Sog, in insects under the transcriptional control servations. Both organizers behave differently upon of a separate pattern-forming system, acts in vertebrates transplantation. Transplantation of cells from the dor- as a part of an integrated regulatory system. Corre- sal organizer to the antipodal position - the classical sponding schemes with increasing complexity have been Spemann-Mangold experiment - establishes a new orga- proposed that allow a balanced Chordin-BMP expression nizing region, usually in an all or nothing mode. The high (Reversade and De Robertis, 2005; De Robertis, 2009). Chordin level inhibits BMP-signaling in the surrounding However, not only a balanced expression ratio is required cells; a new region of high BMP-signaling becomes es- but these expressions have to be localized at antipodal tablished half-way between the two organizers (Fig. 2C). positions. In contrast, transplantation of ventral cells into a dorsal According to a most simple scheme for pattern for- position remains without effect since Chordin, spread- 5 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 BMP- Chordin 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 Chordin- expressing 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, immedi- the trigger of supernumerary organizers (Bertocchini et ately blocks the Smad activation in the transplanted cell, al., 2004). Downregulation of the competence for orga- which lose, therefore, their specific BMP-signaling activ- nizer formation in cells distant to an established organizer ity (Fig. 2D). The asymmetric behavior of the two centers is an efficient strategy to avoid supernumerary organiz- was regarded as puzzling (De Robertis, 2006) but finds in ers in growing systems; Hydra patterning is a further ex- this model a straightforward explanation. More complete ample for this strategy (Meinhardt, 1993, 2012b). models have to include additional long-ranging antago- As mentioned, an unambiguous demonstration of the nists of the BMP-signaling such as Bambi and Sizzled self-regulatory capabilities of Spemann organizer for- that contribute to the size-regulation of the pSMAD ac- mation came from an experiment of Peter Nieuwkoop tivation (De Robertis and Kuroda, 2004; Paulsen et al., (Nieuwkoop, 1992). After co-culture of dissociated ani- 2011; Inomata et al., 2008; Inomata et al., 2013). mal and vegetal amphibian cells, derivatives of the Spe- Organizer formation in amphibians depends on the mann organizer such as notochord, spinal cord and cortical rotation that establishes a high β-catenin level at somites were induced. According to the model, orga- the dorsal side. In the model it is assumed that such nizer formation can start without localized determinants localized determinants bring the Chordin system over a as long as sufficient competent cells are available, even threshold level such that the self-enhancement is trig- if they are randomly distributed (Fig. 3). This type of ob- gered (Fig. 2A). If this region is completely removed, servations cannot be described by models that do not for instance, by the removal of the dorsal blastomeres, posses self-organizing properties [e.g. (Zhang et al., the self-enhancement may not be triggered, causing that 2007; Ben-Zvi et al., 2008)]. the organizer does not regenerate (Fig. 2E). In contrast, Even after blocking translation of all ventrally-active after removal of the ventral half, the BMP-Chordin com- BMP genes, a residual DV polarization and localiza- plex accumulates to such a degree that a new region of tion of Chordin expression remains (Reversade and De Smad signaling emerges in the smaller field. For this re- Robertis, 2005). This polarization, however, is com- generation of a BMP-signaling center neither a change pletely abolished if also ADMP is suppressed, suggest- in the steepness of a gradient nor a change in diffusion ing that Chordin and ADMP act on their own as a rudi- rates is required, in contrast to other models (Umulis and mentary pattern-forming system. A self-enhancing com- Othmer, 2013; Ben-Zvi et al., 2014). It should be empha- ponent in the Chordin activation that is antagonized by sized that regeneration of one or both terminal organizes ADMP directly, i.e. without intermediate BMP activation, is nothing special. It is the base for regeneration in other allows an integration of this observation. Indications for systems such as Planarians or Hydra and can occur in a similar interaction will discussed further below for Ne- fragments that are only a very small part of the original matostella. Such a modification has little effect on the organism. normal pattern-forming reactions but leads to more clear- In this view, localized maternal determinants are em- cut threshold behavior as required for simulating the ef- ployed as a means to suppress supernumerary organiz- fects of maternal determinants. ers in huge embryos as given in amphibians (Fig. 2). The strong self-enhancement involved in organizer Organizer formation is only possible in the restricted re- formation provides a rational for the otherwise puzzling gion made competent by the determinants. This view is observation of unspecific induction as has been made supported by experiments in which the competence for in early organizer research [reviewed in (De Robertis, organizer formation is elevated ventrally, for instance, by 2009)]. According to the model, even the leakage of increasing the β-catenin or Wnt level there (Sokol et al., an inhibitor at a wound could be sufficient to bring the 1991; Molenaar et al., 1996). The resulting supernumer- Chordin system above a threshold, causing the trigger a ary embryos are well proportioned - a further indication new organizer that would have all properties of a natural that self-regulation determines strength, extension and organizer. The region antipodal to the organizer is espe- position of the new organizer. cially prone to unspecific induction due to a low level of In contrast, if development starts at a small size, only inhibition. the two antipodal organizers can be formed even if all cells are competent. This occurs whenever a certain 6. The moving organizer, midline formation and size is surpassed (SFig. 4D). Once formed, the dor- the DV organization proper in vertebrates sal organizer can suppress the activation of a second dorsal organizer during further growth. If all cells are It seems most natural that the side antipodal to the dor- competent, a Spemann-type organizer also can regen- sal organizer in vertebrates is assigned to be ventral. To erate in a fragment that does not contain the organizer avoid confusions, I followed this convention thus far. In- (SFig. 4E), as observed in early chick embryos (Lutz, deed, high BMP levels specify different ventral cell types 1949). At later stages an active inhibition may be re- in the marginal zone (Mullins et al., 996; Kishimoto et al., quired to suppress the formation of supernumerary orga- 1997; Dosch et al., 1997; Walmsley et al., 2002). Nev- nizers. In chick development, for instance, an inhibition ertheless, this assignment is somewhat misleading. Fate spreads from the established organizer that suppresses 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 along the AP axis (Hashiguchi and Mullins, 2013). This and Sheets, 2002; Agathon et al., 2003). Moreover, is a straightforward consequence of the proposed model dorsoventral pattering has to work all along the AP axis, since first the midline has to be formed before the sig- which requires a line of reference with a stripe-like AP- nal that specifies the distance from the midline can be extension, not a patch-shaped organizer (Fig. 4). There- generated or interpreted (Fig. 4). Graded BMP signal- fore, crucial for the specification of cells along dorsoven- ing has been shown also to be responsible for region- tral axis is not their distance to the Spemann-type orga- specific gene activation after gastrulation (Nguyen et al., nizer but their distance to the midline that is induced by 1998; Steventon et al., 2009). To emphasize it again, ac- the organizer (Meinhardt, 2004, 2006). cording to the model proposed, the DV patterning is not The marginal zone in amphibians, the blastopore on accomplished by the two antipodal organizers within the which the Spemann organizer is localized, is the most marginal zone of the early embryo, as it is assumed in posterior structure of the early embryo. Thus, the midline several recent models (Ben-Zvi et al., 2008; Inomata et has to be formed under organizer control in two parts al., 2013) but by distance of the cells from the midline (Fig. 4). One part results from cells of the organizer that that is induced by the dorsal organizer. move underneath the ectoderm, forming the prechordal Usually the formation of a complete amphibian em- plate and thus the prerequisite for generating a reference bryo after early removal of the ventral half is interpreted line for DV-patterning of the brain. For midline formation as indication of an excellent size regulation along the DV of the trunk, due to the convergence - extension mecha- axis (Ben-Zvi et al., 2008). However, as shown by Cooke nism, cells near the marginal zone move toward the or- (Cooke, 1981), size regulation does not occur along the ganizer and the incipient midline to form a rod-like axial DV but along the AP axis. If cells are removed from the structure perpendicular to the blastopore with the noto- so-called ventral side, the somites and the embryos as chord and neural tube as the most dorsal structures. the whole have a significant shorter AP- but the normal At a particular AP level of the trunk, the proper DV DV-extension. Thus, the embryo becomes shorter, but patterning can only occur after notochord and floor plate not slimmer. The molecular mechanism is not yet fully is formed. This occurs in the course of time during the understood (Lauschke et al., 2013). posterior elongation of the midline (Fig. 4). Recently it Even classical observations clearly demonstrate that has been shown that the DV patterning is under con- the size regulation along the DV axis is restricted. Af- trol of the same developmental clock as the patterning ter induction of a second Spemann organizer, the heads 9 of the two embryos are usually complete and well sep- the observed regulation. As shown in Fig. 5, regenera- arated while parts of the trunks and the tails are fused. tion of organizing regions can occur even if both the dor- In terms of the model, at the beginning of gastrulation, sal and the ventral sites are removed. In sea urchins, the marginal zone is large and the two incipient midlines BMP ligands are diffusible on their own, without complex have a large distance. The gradients do not overlap and formation (Lapraz et al., 2009) In this case, the formation the DV patterns of the heads are complete. Later in de- of diffusible Chordin/BMP complexes is not necessarily velopment, however, the marginal zone shrinks in favor of required for the mechanism to work; diffusible BMP lig- axial elongation (Fig. 4); the two midlines become closer ands would be sufficient. However, the employment of and closer; the gradient systems overlap and the trunks diffusible complexes enlarges substantially the distances become fused, clearly indicating that the DV patterning over which the mechanism can work. does not scale. In terms of the model, for the forma- tion of complete embryos after tissue removal it is crucial 8. Chordin-BMP patterning in Nematostella: that missing organizers regenerate. However, the over- an ancestral mode? lap of the resulting gradients nevertheless can lead to fused structures. Regeneration of organizers and scal- One of the evolutionary earliest systems that display a ing of gradients are two different processes. patterning perpendicular to the primary (oral-aboral) axis is the Chordin-BMP patterning in the sea anemone Ne- 7. Applications to the DV organization of sea matostella. Both Chordin and BMP appear first at the oral urchins opening and become subsequently shifted to an off-axis position (Finnerty et al., 2004; Rentzsch et al., 2006; Ma- The oral opening of sea urchin embryos is formed at a tus et al., 2006; Saina et al., 2009; Leclere` and Rentzsch, lateral position halfway between the animal pole and the 2014; Genikhovich et al., 2015). Even after the shift, Wnt-expressing cells at the vegetal pole. The oral-aboral Chordin and BMP remain partially superimposed. The axis formation is initially labile; slight asymmetries are superposition of Chordin/BMP is reminiscent of the situ- sufficient for orientation. For instance, unilateral oxygen ation in sea urchins discussed above and similar to the depletion is sufficient to orient the emerging pattern (Cz- Chordin/ADMP expression in vertebrates (Saina et al., ihak, 1963);(Coffman et al., 2004).The oral-aboral axis is 2009). The oral organizer is generated by the Wnt path- highly regulative; embryos fragmented along the animal- way (Kusserow et al., 2005). vegetal axis can form normal embryos. This regeneration Many regulatory features can be explained by as- may be connected with a polarity reversal in one frag- suming that in Nematostella the Chordin-BMP patterning ment (Horstadius¨ and Wolsky, 1936). Meanwhile it has works essentially as an activator-inhibitor system (Fig. been shown that the oral opening is under Nodal/Lefty 6). BMP, produced under Chordin control, acts as in- control (Duboc et al., 2004) which is known to work as hibitor, restricting the maximum level and the extension an activator-inhibitor system (Schier, 2009; Muller¨ et al., of the Chordin peak. This inhibitory action of BMP oc- 2012). All these properties, the ability to regenerate, the curs in in cooperation with RGM that presumably acts initial sensitivity to minute asymmetries and the polarity as a BMP co-receptor (Leclere` and Rentzsch, 2014). reversal in originally non-activated fragments are proper- This scheme is in accordance with the observation that ties of pattern-forming systems (Meinhardt, 1982). blocking of BMP- (Saina et al., 2009) or RGM-translation Chordin and BMP are also involved in the DV organi- (Leclere` and Rentzsch, 2014) leads to a dramatic in- zation of sea urchins, although in an unusual way. Nodal crease of Chordin transcription since the inhibitory func- controls the transcription of both Chordin and BMP; the tion of BMP is lost. BMP, however, is certainly not the oral side is conventionally declared as ventral. Although only inhibitor in Chordin patterning since blocking of BMP synthesized ventrally, BMP-signaling as indicated by pS- transcription by morpholinos leads to a dramatic increase mad activation takes place at the dorsal side (Lapraz et but not to a ubiquitous Chordin expression. Moreover, at al., 2009). Again, the purpose of the system is to estab- later stages, BMP remains spatially restricted in the en- lish a secondary signaling center at the antipodal posi- doderm although Chordin expression occurs essentially tion. This is easily integrated into the model proposed in the ectoderm. (Fig. 5). At the side of Nodal-controlled BMP synthesis In terms of the model, the symmetry break and off- BMP-signaling is repressed by the high Chordin level. At axis activation of the Chordin system is achieved as fol- antipodal position the inhibition by Chordin is low enough lows. First, a long-ranging activating influence of the such that the self-enhancing BMP-signaling via pSmad primary WNT system leads to a trigger of Chordin ex- is triggered. Obviously a huge net transport takes place pression at the oral pole. Subsequently, a more local- from the ventral to the dorsal side due to sink function ized quenching at the oral pole achieved, for instance, for BMP at the position of BMP-signalling. The posi- by an enhancement of the BMP inhibition in the pres- tion of BMP-synthesis is not critical since, due to the ence of WNT, causes that the activation of the Chordin rapid diffusion of the Chordin-BMP complex, it is avail- system becomes more favored in a zone that surrounds able also at distant positions. The model accounts for the oral organizer. The pattern-forming feature of the 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 one- dimensional 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 (Leclere` 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 ac- tion that has an inhibitory influence on a stripe-forming tivation becomes restricted to a patch and does not re- system, allowing only a single stripe at the contralateral main a ring that surrounds the organizer (Fig. 6). Again, side (Meinhardt, 1989;, 2004) that can be used as a BMP signalling and pSMAD activation occurs at an an- scaffold to generate a periodic stripe-like pattern around tipodal position (Fig. 6). This model accounts for obser- the oral-aboral axis (Berking and Herrmann, 2007). This vations made if BMP translation is blocked by morpholi- seems to be what is realized in Nematostella. A stripe of nos (Saina et al., 2009). First, since one of the inhibitors GDf5-like expression and nested expression of Hox8 and is lost, Chordin transcription increases dramatically in the HoxE appear opposite to the patch-like Chordin expres- entire competent zone until saturation is reached. Sec- sion (Saina et al., 2009; Leclere` and Rentzsch, 2014; ondly, no shift to an off-axis position occurs since the ele- Genikhovich et al., 2015). vated quenching of Chordin activation via BMP/WNT co- This model suggests that in Nematostella some com- operation at the oral center is no longer functional (Fig. ponents are still missing. Required is a (direct or indi- 6G). The model is compatible with the observations that rect) self-enhancement in the Chordin transcription, as overexpression of Chordin leads to ectopic overexpres- it was already suggested for to cope with some obser- sion of the BMP message even if the BMP translation vation for the Spemann-organizer as mentioned above. is blocked. The addition of foreign BMP represses not Further, the experiments indicate that BMP downregu- only Chordin but also BMP transcription (Saina et al., lates Chordin transcription locally, i.e., outside the region 2009). The model describes that Chordin activation oc- where BMP-signaling occurs. The huge overproduction curs with a predictable polarity after blocking Chordin- or of Chordin after blocking BMP transcription indicates that BMP-translation in parts of early embryos (Leclere` and this interaction is rather direct and not controlled by a Rentzsch, 2014) (Fig. 6 H-I). Other aspects are not yet separate pattern-forming reaction as in sea urchins. The included; for instance, that Chordin activation becomes molecular basis is unknown. eventually restricted to the ectoderm while BMP activa- tion resides in a somewhat larger region in the endoderm 9. A possible evolutionary scenario (Rentzsch et al, 2006; Matus et al., 2006a). Chordin patterning is already involved in the pattern- The presumably ancestral activator-inhibitor type of ing of the radial-symmetric Hydra. It appears transiently Chordin-BMP patterning in Hydra suggests an interest- in bud formation and is one of the earliest indicators for ing evolutionary scenario. In Nematostella, BMP ob- head regeneration (Rentzsch et al., 2007). Not unlike the tained a second function: not only restricting Chordin situation in Nematostella, Chordin transcription becomes expression but providing the prerequisites for a further subsequently shifted to a sub-hypostomal position and pattern-forming system at antipodal position, realized by remains in newly-formed tentacles as a periodic pattern. pSmad signaling. Both functions may be achieved by Smad is ubiquitous expressed in the body column ex- different BMP´s. Also Chordin obtained a double func- cept of the terminal ends (Hobmayer et al., 2001) and is tion; controlling BMP transcription that limits its own thus presumably not under positive control of an orga- self-enhancement and, by its inhibitory function on the nizer. The function of Chordin in Hydra is yet unknown. BMP/Smad signaling, it causes the latter to appear at a Eventually, the pattern around the oral-aboral axis in distance from the Chordin source. BMP acts as inhibitor Nematostella, generated under the control of the Chordin also in other system, for instance, in the initiation of avian system, consists of a periodic pattern of endodermal feathers (Jung et al., 1998; Noramly and Morgan, 1998) folds, the so called mesenteries. On a first inspection, and, at a later stage, in the signaling that separates barbs the generation of this periodic pattern seems to be un- from each other (Harris et al., 2005). necessarily complex, forming first an off-axis patch-like Later in evolution, perhaps for a better separation of organizer that induces a second organizer at an antipo- the multiple functions, Chordin transcription became un- dal position, which, in turn, provides a scaffold for the der control of separate pattern-forming systems such as periodic pattern. In contrast, in Hydra the periodic pat- Nodal in sea urchins or the nuclear Dorsal gradient in tern - related to tentacle formation around the oral-aboral Drosophila. This liberated BMP from the inhibitory func- axis - is generated directly. From the model, these inter- tion; the location of BMP transcription became unimpor- mediate steps in Nematostella are necessary. The peri- tant since, due the mobility of the Chordin/BMP complex, odic (tentacle-) pattern in hydra consists of spots around BMP became essentially available everywhere. With a the oral pol. In Nematostella however, a periodic stripe- BMP transcription outside of the region of Chordin tran- like pattern has to be generated with an oral-aboral ex- scription as in Drosophila, the region of BMP expression tension of the stripes. This cannot be achieved directly became closer to the region in which the secondary BMP by the Hydra-type mechanism since direct stripe forma- patterning via pSmad should occur. This led to shorter tion would lead to a stripe around the oral opening, not distances that have to be bridged by shuttling and en- to stripes along the oral-aboral axis. A possible mech- abled thus more extended embryonic fields. In verte- anism for the formation of stripes that have the correct brates, a mixture of both systems seems to be preserved: orientation is to form first an off-center patch-like activa- Chordin together with BMP2b and presumably ADMP as 13 antagonists acts as a primary DV-pattern-forming system activation in sea urchins between the animal and vege- that enables the secondary center at a distance. In this tal pole are examples. In these cases, the restriction of view, the formation of the Spemann organizer is close to the inducing signal to its final shape, its specific localiza- the ancestral mode as observed in Nematostella. The tion on a ring-shaped competent region and its regener- locally antagonistic action of Chordin and BMP expres- ation after removal indicates the involvement of genuine sion, employed already in Nematostella for the symme- pattern-forming reactions. Such patterning cannot be ex- try break, was presumably reemployed in vertebrates to plained by a model of the ‘French Flag´ type. enhance the required self-enhancement by a double in- As shown in the present paper, many observations hibition. in the DV patterning of higher organisms can be inte- To generate positional information along the long- grated by the assumption that the formation of BMP- extended AP axis, the vertebrate solution, i.e., the use signaling centers results from pattern-forming reactions of a moving dorsal organizer to generate a dorsal midline of the activator-depletion type; the self-enhancing BMP- (Fig. 4), is not the only mechanism that evolved. In in- signaling is antagonized by the depletion of the mobile sects, the midline is formed ventrally due to an inhibition Chordin or Chordin-BMP complex in the surroundings. from the dorsal side. The midline has from the begin- Evolutionary, BMP-signaling could be originally involved ning the full AP extension of the embryo but sharpens in in performing a long-ranging inhibitory effect as seen to- the course of time to a narrow ventral line. The sharpen- day in Nematostella or in the localization of feather buds. ing of the Dorsal transcription in Tribolium (Chen et al., By obtaining an additional mandatory role it was co-opted 2000) is an impressive example for this theoretically pre- for the generation of a secondary (or tertiary) antipodal dicted mode (Meinhardt, 1989). Likewise, in a spider, signaling center. a clump of BMP-expressing cells, the cumulus, moves In addition to the symmetry break by the BMP- from the center of the germ disk, the blastopore, towards Chordin system, the transformation of a patch-like into the periphery - a posterior-to-anterior movement. The a stripe-like organizing region was an important further position at the anterior periphery determines the future step in the evolution of long-extended bilateral-symmetric dorsal side. The midline proper, however, is not formed animals. As shown, nature found different solutions dorsally behind the moving cumulus but at the ventral for this subtle patterning task, which were presumably side. A BMP-based inhibition, spreading from the cumu- causal for a separation into different phyla and for the DV lus, focus Chordin expression and thus midline forma- reversal. tion to a narrow ventral stripe (Akiyama-Oda and Oda, Although many molecular details are still unknown, 2006). The much discussed DV-VD reversal between by exploring interactions from the perspective of pattern- vertebrates and insects (Arendt and Nubler-Jung,¨ 1994) forming reactions it was possible to unravel common was proposed to have its origin in these different modes principles in reactions that use the same components but of midline formation, invented during early evolution of that look overtly very different. Thus, modeling provides bilateral-symmetric body patterning (Meinhardt, 2004). a powerful tool to integrate disparate-appearing observa- In protostomes, a dorsal organizer repels the midline that tions. 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 elon- References gates the midline that appears, therefore, at the dorsal Abrams, E.W., Mullins, M.C., 2009. Early zebrafish development: it´s in side. 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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 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 TMTT  T 22TTTD 2 (1) tBA()()TTA  x

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 CC2 TBCCD   (2) txCX C C2 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 AA2 TAD (3) txAA A2 Numerical constants used A = 0.008; A = 0.008; DA = 0.2000.

The assumed concentration change in the BMP distribution of reads as follows 2 2 BB B  SBBS() S  XBBBC B D 22  (4) tTBSS  x (1  SC )(1  ) 

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.

22 X SXXS() S X XXXBC22  X D (5) tSCx(1SS )(1 )

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: 22 SXBS()()SX SB  S  S 22SSSD (6) tSCx(1SS )(1 ) 

Numerical constants used: XS = 0.001; SB = 0; S = 0.2; S = 0; S = 5; 2 S = 0.001; DS = 0.002. The term (1 + s S ) 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 CC2 MBCCD   (7) txCX CC2 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) 22 B BSBSBS()  B 22 XBBBC B D (8) tM1(1)BS  S  x

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. 22 X SXXS() S X XXXBC22  X D (9) tSx(1 S ) 

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. 22 SXBS()()SX SB  S  S 22SSSD (10) tSCx(1SS )(1 ) 

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.

22 NNNN()  N 22NNND (11) tL(1 N N )  x LL2 ()NLD2 (12) txLNLL2 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.

3 Chordin and BMP production are under Nodal control: CC2 NBCCD   (13) txCX CC2 22 B SBBS() S  B BXBBNBCBD22   (14) tS(1 S )  x

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 BC X() S2   X D (15) txXSXSXX2 22 SXSSX() S  S SSSD 2 (16) tC(1S )  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).

WW()22  W WW WD (17) tIWW x2 II2  WID2  (18) txIIII2

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

22 TTTT()TI 22TTTD (19) tCBBWvTx()(1)TTBWT  CC2 TCD (20) txCCC2

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 CBD2 (21) txBBB2 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 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.

B 2 B BBS()2   BD (22) txBBBSS 2

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

DB = 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 SSSSBS() SSSD 2 (23) tC1 S  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 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.

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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 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.

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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 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.

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