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