1 Dynamics of BMP signaling and distribution during zebrafish 2 dorsal-ventral patterning 3 4 5 Autumn P. Pomreinke*, Gary H. Soh*, Katherine W. Rogers*, Jennifer K. Bergmann, Alexander 6 J. Bläßle, and Patrick Müller 7 8 9 Friedrich Miescher Laboratory of the Max Planck Society 10 Systems Biology of Development Group 11 Spemannstraße 39 12 72076 Tübingen, Germany 13 14 *equal contribution 15 16 17 18 Abstract 19 During vertebrate embryogenesis, dorsal-ventral patterning is controlled by the BMP/Chordin 20 activator/inhibitor system. BMP induces ventral fates, whereas Chordin inhibits BMP signaling 21 on the dorsal side. Several theories can explain how the distributions of BMP and Chordin are 22 regulated to achieve patterning, but the assumptions regarding activator/inhibitor diffusion and 23 stability differ between models. Notably, “shuttling” models in which the BMP distribution is 24 modulated by a Chordin-mediated increase in BMP diffusivity have gained recent prominence. 25 Here, we directly test five major models by measuring the biophysical properties of fluorescently 26 tagged BMP2b and Chordin in zebrafish embryos. We found that BMP2b and Chordin diffuse 27 and rapidly form extracellular protein gradients, Chordin does not modulate the diffusivity or 28 distribution of BMP2b, and Chordin is not required to establish peak levels of BMP signaling. 29 Our findings challenge current self-regulating reaction-diffusion and shuttling models and 30 provide support for a graded source-sink mechanism underlying zebrafish dorsal-ventral 31 patterning. 32 33 Introduction 34 The dorsal-ventral axis is one of the earliest coordinate systems established during animal 35 development and divides the embryo into dorsal (back) and ventral (belly) territories. This axis 36 forms under the influence of the BMP/Chordin patterning system. The activator BMP induces the 37 formation of ventral tissues, and BMP signaling is antagonized on the dorsal side by the inhibitor 38 Chordin. There are currently several disparate models that can explain how BMP signaling is 39 restricted to the ventral side (Ben-Zvi et al. 2008, Barkai and Ben-Zvi 2009, Francois et al. 2009, 40 Ben-Zvi et al. 2011b, Inomata et al. 2013, Ramel and Hill 2013, Ben-Zvi et al. 2014), but the 41 underlying biophysical assumptions have not been fully tested. 42 In the “Graded source-sink + mobile BMP model” (Model 1), BMP is produced in a graded, 43 ventrally biased shallow source, and signaling from diffusing BMP is antagonized by binding to 44 its inhibitor Chordin (Figure 1 - figure supplement 1, Table 1). Chordin diffuses from a localized 45 source on the opposing dorsal side and therefore provides a “sink” that inactivates BMP 1

46 molecules diffusing through the embryo, helping to shape the signaling distribution into a 47 gradient that peaks ventrally. The distributions of bmp and chd mRNA in developing embryos are 48 consistent with this idea – initially nearly uniform bmp expression refines to a ventrally biased 49 gradient over time (Ramel and Hill 2013, Zinski et al. 2017), and chd expression is restricted to 50 the dorsal region (Miller-Bertoglio et al. 1997). 51 Similar to Model 1, BMP signaling activity in the “Graded source-sink + immobile BMP model” 52 (Model 2, Figure 1 - figure supplement 1, Table 1) is also restricted by the inhibitor Chordin 53 diffusing from the dorsal side. However, Model 2 assumes that BMP does not diffuse (Ramel and 54 Hill 2013) and that it binds to Chordin with weaker affinity than in Model 1 (see Materials and 55 Methods). Proponents have argued that the close relationships between the graded bmp mRNA 56 distribution, signaling gradient, and target gene expression indicate negligible BMP diffusion 57 during patterning (Ramel and Hill 2013). Consistent with this, BMP4 was unable to induce long- 58 range signaling in Xenopus experiments (Jones et al. 1996), although BMP target genes are 59 induced outside of BMP-expressing clones in zebrafish (Xu et al. 2014). However, measuring the 60 diffusivity of BMP in vivo is the most direct way to determine whether BMP is mobile (Kicheva 61 et al. 2007, Zinski et al. 2017). 62 Although these two relatively simple models are generally supported by biological observations, 63 they do not take into account other regulators known to be crucial for dorsal-ventral patterning, 64 such as the BMP-like ligand ADMP, and Sizzled, an inhibitor of the Chordin protease 65 Tolloid/Xlr. Three models described below include these important dorsal-ventral regulators in 66 addition to BMP and Chordin and have also been shown to explain scale-invariant patterning, a 67 phenomenon in which embryos adjust their development to differently sized patterning fields. 68 The recent “Long-range accumulation and feedback model” (Model 3, Figure 1 - figure 69 supplement 1, Table 1) postulates that BMP and Chordin have equally high mobility, but that 70 dorsal-ventral patterning is controlled by differences in BMP and Chordin protein stability 71 (Inomata et al. 2013). In this model, BMP and ADMP induce the secreted, highly diffusible and 72 stable Chordin protease inhibitor Sizzled. This protects Chordin from proteolysis and promotes 73 its expansion towards the ventral side. Over time the resulting inhibition of BMP signaling leads 74 to decreased Sizzled production, destabilizing Chordin and relieving inhibition of BMP. In this 75 way, an appropriate balance between ventral BMP and dorsal Chordin levels can be established 76 even in differently sized embryos. 77 In the “Self-regulating reaction-diffusion model” (Model 4, Figure 1 - figure supplement 1, Table 78 1), BMP and Chordin both have low diffusivities and equivalent protein stabilities. Interactions 79 with highly mobile ADMP and Sizzled in two coupled reaction-diffusion networks eventually 80 result in the restriction of BMP signaling activity on the ventral side, assuming an initial dorsal 81 Chordin or ventral BMP bias (Francois et al. 2009). Such a system self-regulates even with noisy 82 initial conditions and could provide robustness during embryogenesis – e.g., the ability of 83 developing organisms to withstand noise in gene expression or fluctuating environmental 84 conditions – that can be difficult to explain with other models. 85 Finally, the prominent “Shuttling model” (Model 5, Figure 1 - figure supplement 1, Table 1) 86 postulates that Chordin not only acts as an inhibitor of BMP, but also modulates the mobility and 87 distribution of BMP protein (Ben-Zvi et al. 2008, Barkai and Ben-Zvi 2009, Ben-Zvi et al. 88 2011b, Ben-Zvi et al. 2014). In this model, BMP is poorly diffusive, Chordin is highly diffusive, 89 and BMP mobility increases when bound to Chordin. Cleavage of the BMP/Chordin complex by 90 the uniformly distributed protease Tolloid/Xlr combined with dorsal Chordin flux is thought to 2

91 “shuttle” BMP towards the ventral side by facilitated diffusion over time. In this way, Chordin is 92 responsible for the accumulation of BMP protein on the ventral side, and actively helps establish 93 the subsequent ventral BMP signaling peak. 94 These five conflicting models postulate different diffusion (no diffusion, equal diffusion, 95 differential diffusion, facilitated diffusion) and stability properties of BMP and Chordin proteins 96 (Table 1, Figure 1 - figure supplement 1). However, these biophysical properties have not been 97 fully measured experimentally, in part due to the lack of reagents and techniques to detect active 98 BMP and Chordin in living vertebrate embryos. To test the biophysical tenets of these models, 99 we developed active BMP and Chordin fluorescent fusion proteins, and used a combination of 100 mathematical modeling and quantitative experiments to determine how BMP2b and Chordin 101 gradients form. Additionally, we tested the distinct predictions that the five models make about 102 how BMP signaling changes in the absence of Chordin. We found that i) BMP2b and Chordin 103 proteins have similar stabilities, ii) both BMP2b and Chordin diffuse and form gradients in the 104 extracellular space, and iii) Chordin does not significantly facilitate BMP2b diffusion or play an 105 active role in establishing peak ventral BMP signaling levels. Together, our results are most 106 consistent with dorsal-ventral patterning mediated by Model 1, the “Graded source-sink + mobile 107 BMP” model. 108 109 Results 110 Chordin does not actively establish peak ventral BMP signaling 111 BMP signaling induces phosphorylation and nuclear localization of the transcriptional effectors 112 Smad1/5/9 (Schier and Talbot 2005). To quantitatively measure BMP signaling activity during 113 early dorsal-ventral patterning, we imaged pSmad1/5/9-immunostained zebrafish embryos fixed 114 at different developmental stages using in toto light sheet microscopy, converted pSmad1/5/9 115 signaling activities into information-compressed two-dimensional maps (Schmid et al. 2013), and 116 quantified pSmad1/5/9 intensities along the ventral-dorsal axis (Figure 1A, Materials and 117 Methods). Over the course of approximately 3 h during early zebrafish development, BMP 118 signaling rapidly shifts from a low-level near-uniform distribution to a gradient with peak levels 119 on the ventral side (Figure 1A+B, Movies 1-5) (Tucker et al. 2008), similar to changes in the 120 distribution of bmp2b mRNA over time (Ramel and Hill 2013, Zinski et al. 2017). We simulated 121 pSmad1/5/9 gradient formation kinetics predicted by each of the five models over a similar time 122 period (Figure 1C-G). Our measurements are consistent with the gradient kinetics predicted by 123 Models 1, 2, 4, and 5, whereas the dynamics predicted by Model 3 do not resemble the 124 experimentally observed distributions. 125 All five major models of BMP/Chordin-mediated dorsal-ventral patterning qualitatively explain 126 the formation of a ventral signaling peak, but they assign different roles to the inhibitor Chordin 127 (Figure 2A-E, Table 1, and Figure 1 - figure supplement 1). Models 1 and 2 assume that a dorsal 128 flux of the inhibitor Chordin restricts the range of BMP signaling activity throughout the embryo. 129 They thus predict that in the absence of Chordin, BMP signaling should be expanded throughout 130 the embryo with a small increase in the peak levels on the ventral side (Figure 2A+B). Model 3 131 adds an additional regulatory layer: Here the abundance of Chordin is regulated by feedback 132 interactions that modify its stability and affect ventral BMP signaling levels (Figure 1 - figure 133 supplement 1). Similar to Models 1 and 2, Model 3 also predicts that in the absence of Chordin, 134 BMP signaling should be expanded throughout the embryo (Figure 2C).

3

135 In Model 4, two reaction-diffusion systems involving BMP/Sizzled and Chordin/ADMP are 136 coupled. In a completely homogenous field of cells with no initial expression biases, this self- 137 organizing system would give rise to both ventral and dorsal BMP peaks (Francois et al. 2009). 138 To achieve a single ventral BMP peak, an initial dorsal Chordin or ventral BMP bias is required 139 (see Materials and Methods). Under these conditions, the initial advantage in BMP signaling on 140 the ventral side is amplified by autoregulation of BMP production. Since Chordin inhibits the 141 autoregulation of BMP production, the absence of Chordin leads to a more pronounced ventral 142 BMP peak but has no effect in the rest of the embryo (Figure 2D). Model 4 thus predicts that in 143 the absence of Chordin, pSmad1/5/9 levels would be increased on the ventral but not the dorsal 144 side. 145 In contrast to Models 1-4, Model 5 assigns a more active role to Chordin in promoting the ventral 146 BMP signaling peak. This model proposes that Chordin activity results in increased BMP 147 signaling ventrally: Chordin increases ventral BMP levels by binding to and physically moving 148 BMP protein toward the ventral side. This model therefore predicts that in embryos lacking 149 Chordin, BMP signaling should be lower on the ventral side compared to wild type embryos 150 (Figure 2E). 151 To experimentally test these predictions, we quantitatively measured BMP signaling activity in 152 fixed chordin-/- zebrafish embryos (Movie 6) and their wild type siblings using pSmad1/5/9 153 immunostaining and in toto light sheet microscopy. Strikingly, BMP signaling was increased in 154 dorso-lateral domains in chordin-/- mutants compared to wild type embryos, but BMP signaling 155 on the ventral side was not significantly affected (Figure 2F-H), consistent with the predictions 156 from Models 1-3 and observations in Xenopus and zebrafish embryos (Plouhinec et al. 2013, 157 Zinski et al. 2017), but not with the BMP signaling distributions predicted by Models 4 and 5 158 (Table 1). 159 160 BMP and Chordin fusion proteins diffuse and rapidly form gradients in vivo 161 In order to understand the underlying basis of BMP/Chordin distribution and directly test the 162 biophysical assumptions of the five dorsal-ventral patterning models, we developed fluorescent 163 fusion proteins. We fused superfolder-GFP (sfGFP (Pedelacq et al. 2006)) and the 164 photoconvertible protein Dendra2 (Gurskaya et al. 2006) to zebrafish Chordin and BMP2b, the 165 major BMP ligand regulating zebrafish dorsal-ventral patterning (Kishimoto et al. 1997, Xu et al. 166 2014). Basing our design on previously established fusions with small peptide tags (Cui et al. 167 1998, Degnin et al. 2004, Sopory et al. 2006), we inserted fluorescent proteins to label the mature 168 signaling domains, and obtained fusion proteins that are processed similarly and have similar 169 biological activity as untagged versions or constructs fused to small FLAG tags (Figure 3A-E, 170 Figure 3 - figure supplement 1). Indeed, BMP2b mutants (swr-/-, which are normally severely 171 dorsalized (Kishimoto et al. 1997)) can be rescued by injection of mRNA encoding BMP2b- 172 Dendra2 or BMP2b-sfGFP at levels equivalent to untagged BMP2b (Figure 3C). In these 173 experiments, the injected mRNA should be uniformly distributed, highlighting the important role 174 of Chordin or other antagonists in shaping the graded BMP signaling distribution. 175 To measure the kinetics of BMP and Chordin protein gradient formation, we expressed BMP2b- 176 sfGFP and Chordin-sfGFP from local sources in wild type zebrafish embryos (Müller et al. 2012) 177 and imaged the distribution profiles over time using light sheet microscopy (Figure 3F-I). 178 Importantly, in previous experiments it has been demonstrated that BMP2b clones generated in a 179 similar manner can recapitulate BMP signaling comparable to that observed along the dorsal- 4

180 ventral axis (Xu et al. 2014). Strikingly, both BMP2b-sfGFP and Chordin-sfGFP are secreted and 181 diffuse in the extracellular space (Figure 3F+G, Movies 7+8), in contrast to the proposal of 182 Model 2 that only Chordin – but not BMP – diffuses (Ramel and Hill 2013) (Table 1), and the 183 absence of long-range BMP4 signaling in Xenopus (Jones et al. 1996). Both BMP2b-sfGFP and 184 Chordin-sfGFP rapidly establish concentration gradients over the course of one hour (Figure 185 3H+I), consistent with the rapid patterning of the dorsal-ventral axis during zebrafish 186 development. 187 188 BMP and Chordin fusion proteins have similar stabilities in vivo 189 The gradient formed by Chordin-sfGFP has a moderately longer range than the one formed by 190 BMP2b-sfGFP. For example, 60 min post-transplantation the BMP2b-sfGFP signal drops to 50% 191 of the maximal concentration at a distance of 30-40 µm, whereas the gradient formed by 192 Chordin-sfGFP reaches 50% of its maximal concentration at a distance of 50-60 µm from the 193 source boundary at this time point (Figure 3H+I). This suggests that stability or diffusivity might 194 differ between these proteins (Müller and Schier 2011, Müller et al. 2013). Importantly, Models 3 195 and 5 assume that BMP is more stable than Chordin, whereas the other models assume either 196 similar or unconstrained stabilities (Table 1). 197 To distinguish between these possibilities, we first determined protein stability in living zebrafish 198 embryos using a Fluorescence Decrease After Photoconversion (FDAP) assay (Müller et al. 199 2012, Bläßle and Müller 2015, Rogers et al. 2015). We expressed BMP2b and Chordin fused to 200 the green-to-red photoconvertible protein Dendra2 uniformly in zebrafish embryos, used brief 201 UV exposure to convert the signal from green to red to generate a pulsed protein pool, and 202 monitored the decrease in extracellular red fluorescence over time (Figure 4A+B). For BMP2b- -5 203 Dendra2, we found a clearance rate constant of k1 = (8.9 ± 0.1) x 10 /s (half-life 130 min, Figure - 204 4A). For Chordin-Dendra2, we measured a similar clearance rate constant of k1 = (9.6 ± 0.3) x 10 205 5/s (half-life 120 min, Figure 4B). The similar clearance rate constants suggest that differential 206 protein stabilities cannot account for the different protein distributions of BMP2b and Chordin. 207 Importantly, these results are inconsistent with the differential protein stabilities predicted by 208 Models 3 and 5 (Table 1). 209 210 Diffusivity of BMP and Chordin fusion proteins in vivo 211 Our finding that BMP2b- and Chordin-Dendra2 fusions have similar stabilities (Figure 4A+B) 212 suggests that differences in diffusivity could account for the slight differences in their gradient 213 formation kinetics. Indeed, when we fitted a gradient formation model based on local production, 214 uniform diffusion, and clearance constrained with our measured protein half-lives in a realistic 215 three-dimensional zebrafish embryo-like geometry (Müller et al. 2012) to our measured protein 216 distributions, we obtained the best agreement between model and data with lower diffusivity of 217 BMP2b (4 µm2/s) compared to Chordin (6 µm2/s) (Figure 3 – figure supplement 2A+B). 218 Importantly, the five models assume distinct BMP and Chordin diffusion properties (Table 1, 219 Figure 1 – figure supplement 1), from no BMP diffusion (Model 2) to substantially higher 220 Chordin mobility compared to BMP (Model 5). To directly test these predictions, we determined 221 the effective diffusivities of fluorescently tagged BMP2b and Chordin moving through 222 developing zebrafish embryos. We used a Fluorescence Recovery After Photobleaching (FRAP) 223 assay (Müller et al. 2012) that measures the dynamics of re-appearance of fluorescence in a 224 bleached region in embryos uniformly expressing fluorescent fusion proteins (Figure 4C-E). We 5

225 found effective diffusion coefficients of 2-3 µm2/s for BMPs (BMP2b-Dendra2: 2.0 ± 0.4 µm2/s; 226 BMP2b-sfGFP: 2.6 ± 0.7 µm2/s (similar to (Zinski et al. 2017)) and of 6-7 µm2/s for Chordin 227 (Chordin-Dendra2: 6.0 ± 0.7 µm2/s; Chordin-sfGFP: 7.3 ± 3.9 µm2/s), indicating that slight 228 differences in diffusivities could underlie the differences in protein distributions. This idea is 229 further supported by the agreement between gradients simulated with the measured diffusivities 230 and clearance rate constants and our experimentally determined protein gradients (Figure 3 - 231 figure supplement 2E-H). The measured diffusion coefficients are most consistent with Models 1 232 and 4, which assume either similarly low diffusivities (Model 4) or that BMP has a moderately 233 lower diffusion coefficient than Chordin (Model 1, Table 1). As observed in the BMP2b-sfGFP 234 gradient formation experiment (Figure 3F-I), our FRAP data demonstrates that BMP2b-sfGFP is 235 mobile in vivo, inconsistent with Model 2. 236 Strikingly, local diffusion measurements in very small extracellular volumes far away from cell 237 surfaces using Fluorescence Correlation Spectroscopy (FCS) assays showed that BMP2b-sfGFP 2 238 (free diffusion coefficient: Df = 46 ± 1 µm /s) and Chordin-sfGFP (free diffusion coefficient: Df 239 = 59 ± 2 µm2/s) are similarly mobile over short spatial and temporal scales (Figure 4F), whereas 240 their diffusivity difference only emerges at the global scale when they move across a field of cells 241 (Figure 4E). We hypothesize that the difference between effective diffusivities (measured by 242 FRAP) and local diffusivities (measured by FCS) is due to binding to immobile extracellular 243 molecules, which could serve as diffusion regulators that hinder the mobility of BMP2b and 244 Chordin, similar to what has been proposed for other developmental signals such as Nodal and 245 FGF (Müller et al. 2012, Müller et al. 2013). 246 247 Sizzled, BMP, and Chordin diffusivities are within the same order of magnitude 248 Models 3 and 4 assign important roles to the secreted proteins ADMP and Sizzled in regulating 249 BMP signaling and distribution. Model 3 postulates diffusivities of ADMP and Sizzled 250 equivalent to BMP and Chordin, whereas Model 4 requires approximately 25-fold higher 251 diffusivities of ADMP and Sizzled compared to BMP and Chordin (Table 1). To measure the 252 diffusivities of ADMP and Sizzled and test these assumptions, we developed fluorescent ADMP 253 and Sizzled fusion proteins (see Materials and Methods). Whereas Sizzled fusion proteins had 254 activity comparable to untagged Sizzled (Figure 4 - figure supplement 1A-C), ADMP fusions 255 with sfGFP or FLAG tags inserted 2, 5, or 11 amino acids after the Furin cleavage site were 256 much less active than untagged ADMP (data not shown), and could therefore not be used for 257 diffusion measurements. Using FRAP, we measured an effective diffusion coefficient of 9.7 ± 3.2 258 µm2/s for Sizzled-sfGFP (Figure 4E, Figure 4 - figure supplement 1D). This measurement is 259 consistent with Model 3, but not Model 4, the latter of which requires much higher Sizzled 260 mobility (Table 1). 261 When parameterized with these measured diffusion coefficients and over a ~100-fold range of 262 ADMP diffusion coefficients, Model 3 can form ventral-dorsal gradients over relevant time 263 scales (Figure 4 - figure supplement 1F-J), but the kinetics of gradient formation do not reflect 264 the measurements of pSmad1/5/9 distribution profiles in Figure 1A+B. Moreover, the relatively 265 minor difference between BMP/Chordin and Sizzled diffusivity is not compatible with the 25- 266 fold differential required for Model 4 (Figure 4 – figure supplement 1K-P). 267 268 Chordin does not regulate BMP protein diffusivity or distribution

6

269 Model 5 (Shuttling) postulates that highly diffusive Chordin enhances the mobility of poorly 270 diffusive BMPs (Ben-Zvi et al. 2008). In this model, Chordin is secreted dorsally, binds to 271 relatively immobile BMP, and creates a highly mobile BMP/Chordin complex. This complex 272 then diffuses until Chordin is cleaved by a protease (Xlr), rendering BMP immobile again (Figure 273 1 – figure supplement 1). To investigate whether Chordin is not only an inhibitor of BMP, but 274 also enhances BMP diffusivity, we increased Chordin levels and measured the effective 275 diffusivity of fluorescent BMP2b. In embryos overexpressing Chordin, we did not observe a 276 significant change in the diffusivity of fluorescently tagged BMP2b compared to embryos that 277 did not overexpress Chordin (BMP2b-Dendra2 + Chordin: 2.2 ± 0.2 µm2/s; BMP2b-sfGFP + 278 Chordin: 2.8 ± 0.7 µm2/s; Figure 4G). The ability of Chordin to enhance the diffusivity of BMP, 279 a major tenet of Model 5, is therefore not supported by FRAP data. 280 Model 5 also predicts that Chordin alters the distribution of BMP protein. Over time, the 281 shuttling of BMP by Chordin causes BMP to accumulate away from the Chordin source, 282 resulting in an opposing peak of BMP. Our observation that Chordin does not affect the 283 diffusivity of BMP challenges this view (Figure 4G). However, to directly test whether a Chordin 284 source can alter BMP distribution (Figure 5A+B), we juxtaposed clones of BMP2b-sfGFP- 285 producing cells with clones of cells secreting untagged Chordin and imaged the formation of the 286 BMP2b-sfGFP gradient over time using light sheet fluorescence microscopy (Figure 5C+D, 287 Movies 9-10). Model 5 predicts a steeper BMP2b-sfGFP gradient in the presence of an adjacent 288 Chordin-producing clone compared to a wild type clone (Figure 5A+B). Although BMP2b-sfGFP 289 gradients tend to be slightly steeper in the presence of a neighboring Chordin-expressing clone 290 compared to a non-Chordin-expressing clone (Figure 5D), this minor change is unlikely to 291 account for the formation of a ventral peak in BMP signaling during the short time (hours) 292 required to complete dorsal-ventral patterning (Figure 1A+B). We also failed to observe 293 significant redistribution of BMP in simulations of adjacent BMP and Chordin clones using our 294 measured diffusion coefficients and half-lives (Figure 5E+F). This suggests that shuttling of 295 BMP2b by Chordin is not relevant for the early aspects of dorsal-ventral patterning in zebrafish 296 embryos. 297 298 Discussion 299 The BMP signaling gradient patterns the dorsal-ventral axis during animal development. Five 300 major models can explain how a ventral peak of BMP signaling forms. The biophysical 301 assumptions underlying these models differ widely (Table 1). After experimentally examining 302 these assumptions, our findings lead to four main conclusions. First, Chordin does not play an 303 active role in generating BMP signaling peaks, but only globally inhibits BMP (Figure 2). This is 304 consistent with graded source-sink-type models (e.g. Models 1 and 2) and Model 3, but 305 inconsistent with Models 4 and 5 (Table 1). Interestingly, BMP signaling in the absence of 306 Chordin is not raised on the extreme dorsal side, indicating that other extracellular inhibitors such 307 as Follistatin or Noggin (Umulis et al. 2009) or inhibitors of bmp expression (Koos and Ho 1999, 308 Leung et al. 2003, Ramel and Hill 2013) that were not included in our models might further 309 restrict BMP signaling in these regions. Second, BMP2b and Chordin both diffuse in the 310 extracellular space (Figure 3F-I), challenging models involving immobile BMP (Model 2). Third, 311 fluorescently tagged BMP2b and Chordin have similar local diffusivities (Figure 4F), but on a 312 global scale they move much more slowly through the embryo (Figure 4E). These findings rule 313 out Models 2, 3, and 5, but are consistent with Models 1 and 4. Fourth, Chordin does not 314 significantly affect BMP2b diffusion or protein distribution (Figure 4G, Figure 5), undermining

7

315 shuttling models in this developmental context. Instead, our data is most consistent with Model 1, 316 the graded source-sink model of BMP/Chordin-mediated dorsal-ventral patterning during early 317 zebrafish development. Our conclusions are also consistent with a complementary recent study 318 (Zinski et al. 2017). 319 Notably, shuttling models (e.g. Model 5) have gained prominence in many developmental 320 contexts including scale-invariant patterning (Ben-Zvi et al. 2008, Barkai and Ben-Zvi 2009, 321 Francois et al. 2009, Plouhinec and De Robertis 2009, Ben-Zvi and Barkai 2010, Ben-Zvi et al. 322 2011a, Haskel-Ittah et al. 2012), but the fundamental tenet, i.e., whether putative shuttles such as 323 Chordin change the diffusivity and distribution of signals such as BMP, has not been directly 324 examined. Alternative models that do not invoke Chordin-dependent facilitated BMP diffusion 325 (Model 4) (Francois et al. 2009) or that postulate differential protein stability (Model 3) (Inomata 326 et al. 2013) can also explain scale-invariant patterning. Our data do not provide strong evidence 327 for shuttling of BMP2b at time scales relevant for dorsal-ventral patterning during early zebrafish 328 embryogenesis: We failed to observe a significant modulation of BMP2b-sfGFP or BMP2b- 329 Dendra2 diffusivity or distribution by Chordin (Figure 4G, Figure 5). It is, however, possible that 330 other BMPs (e.g. BMP4, BMP7, ADMP) are shuttled by interactions with Chordin and its 331 protease Tolloid/Xlr. Indeed, tolloid mutants display a mild patterning defect of the ventral tail 332 fin (Connors et al. 1999) that might reflect a requirement for the ventral accumulation of a 333 weakly active, dorsally expressed BMP ligand such as ADMP (Dickmeis et al. 2001, Lele et al. 334 2001). 335 The graded source-sink model (Model 1) that is best supported by our data describes a system in 336 which the graded, ventrally biased distribution of bmp mRNA and the dorsally localized chd 337 mRNA distribution produce opposing sources of extracellular, diffusing BMP and Chordin 338 protein, which together generate the BMP signaling gradient required for proper dorsal-ventral 339 patterning. Notably, this model fails to take other known dorsal-ventral regulators into account 340 (e.g., ADMP, Sizzled, Follistatin, Noggin). Furthermore, approximately one third of bmp2b and 341 chordin mutant embryos can be rescued by apparently uniform bmp and chordin expression, 342 respectively (Kishimoto et al. 1997, Fisher and Halpern 1999) (Figure 3C), arguing against a 343 strong requirement for concurrent opposing BMP and Chordin sources as long as one component 344 of the system is biased (i.e. ventrally biased bmp2b expression with uniform Chordin, or dorsally 345 biased chordin expression with uniform BMP). Thus, further adjustments to the basic Model 1 346 will be required to fully describe dorsal-ventral patterning. 347 Although our results support a role for BMP diffusion in dorsal-ventral patterning, the necessity 348 of signal diffusion for developmental patterning has recently been challenged by several studies 349 (Brankatschk and Dickson 2006, Roy and Kornberg 2011, Alexandre et al. 2014, Dominici et al. 350 2017, Varadarajan et al. 2017). It will be interesting to determine whether BMP diffusion is 351 indeed required for proper patterning using emerging nanobody-mediated diffusion perturbations 352 (Harmansa et al. 2015) or optogenetics-based cell-autonomous modulation of signaling range 353 (Sako et al. 2016). 354 355 Acknowledgements 356 We are grateful to Hans Meinhardt for valuable discussions of BMP/Chordin-mediated dorsal- 357 ventral patterning mechanisms. We thank Edgar Herrera and Luciano Marcon for support with 358 immunostainings, light sheet microscopy, data reconstruction, and helpful discussions. We 359 acknowledge Matteo Pilz and Sarah Keim for technical assistance. This work was supported by

8

360 the Max Planck Society and a Human Frontier Science Program (HFSP) Career Development 361 Award to PM.

9

362 Materials and Methods 363 364 Immunostainings 365 To visualize pSmad1/5/9, wild type TE embryos were dechorionated at the one-cell stage using 1 366 mg/ml of Pronase (Roche, Cat. No. 11 459 643 001). Dechorionated embryos were incubated at 367 28 °C and fixed at different developmental stages in 4% formaldehyde (Roth) in PBS overnight 368 at 4 °C on a shaker. Embryos were then stored in 100% methanol at -20 °C for at least 2 h. All 369 subsequent steps were carried out at room temperature. Embryos were re-hydrated with 70%, 370 50%, and 30% methanol in PBS for 10 min each. The embryos were then washed eight times 371 with PBST (0.1% Tween) for 15 min and blocked twice with blocking solution (10% fetal bovine 372 serum and 1% DMSO in PBST) for 1 h, and incubated with 1:100 anti-pSmad1/5/9 antibody 373 (Cell Signaling Technology, Cat. No. 9511) for 4 h. Embryos were washed with blocking 374 solution for 15 min, washed seven times with PBST, blocked with blocking solution for 1 h, 375 incubated with 1:500 Alexa 488-coupled goat anti-rabbit secondary antibody (Life Technologies, 376 Cat. No. A11008) for 4 h, and washed similarly to the procedure after primary antibody 377 application. Embryos were then counterstained with DAPI solution (0.2 µg/ml in PBST) for 1 h 378 and washed with PBST. Immunostainings were performed using an In situ Pro hybridization 379 robot (Abimed/Intavis). 380 To analyze pSmad1/5/9 distributions in the absence of Chordin, embryos from one pair of 381 chordintt250 (Hammerschmidt et al. 1996) heterozygous parents were collected, fixed, 382 immunostained with anti-pSmad1/5/9 antibody (Cell Signaling Technology, Cat. No. 13820S) as 383 above, and imaged simultaneously to minimize differences between samples. Embryos were 384 treated as described above, except that progeny from chordin+/- incrosses were first 385 permeabilized with ice-cold acetone at -20 °C for 7 min before the re-hydration step. After 386 imaging and DNA extraction (Meeker et al. 2007), progeny from the chordintt250 heterozygote 387 incross were identified as wild type, heterozygous, or homozygous mutant embryos by PCR 388 amplification using the forward primer 5’-TTCGTTTGGAGGACAACTCG-3’ and the reverse 389 primer 5’-AACTCAGCAGCAGAAGTCAATTC-3’ with an initial denaturation step of 94 °C for 390 3 min; 39 cycles of 94 °C for 30 s, 55 °C for 40 s, and 72 °C for 30s; and a final extension at 72 391 °C for 5 min with subsequent digestion with MspI (New England Biolabs, Cat. No. R0106) for 2 392 h. The genotyping assay for the chordintt250 line was designed by the Zebrafish International 393 Resource Center (ZIRC) staff and downloaded from the ZIRC website at http://zebrafish.org. 394 395 Generation of fluorescent BMP2b fusions 396 All constructs were generated by PCR-based methods (Horton et al. 1990), contain the consensus 397 Kozak sequence gccacc 5’ of the start codon, and were inserted into the EcoRI and XhoI sites of 398 the pCS2(+) vector. To generate BMP2b-sfGFP and BMP2b-Dendra2, sequences encoding 399 sfGFP or Dendra2 flanked by LGDPPVAT linkers were inserted two amino acids downstream of 400 the BMP2b Furin cleavage site. Sequences encoding the FLAG tag DYKDDDDK were inserted 401 between the first linker and sfGFP or Dendra2 to generate BMP2b-sfGFP-FLAG and BMP2b- 402 Dendra2-FLAG. To generate BMP2b-FLAG, the FLAG tag was inserted between two 403 LGDPPVAT linkers two amino acids downstream of the BMP2b Furin cleavage site. 404 405 Generation of fluorescent Chordin fusions

10

406 All constructs were generated by PCR-based methods (Horton et al. 1990) and contain the 407 consensus Kozak sequence gccacc 5’ of the start codon. Chordin was inserted into the ClaI site of 408 pCS2(+). All other Chordin-containing constructs were inserted into the EcoRI and XbaI sites of 409 the pCS2(+) vector. To generate Chordin-sfGFP and BMP2b-Dendra2, sequences encoding 410 sfGFP or Dendra2 flanked by LGDPPVAT linkers were inserted immediately 5’ of the Tolloid 411 cleavage site 2. To generate Chordin-FLAG, sequences encoding the FLAG tag DYKDDDDK 412 were inserted immediately 5’ of the Tolloid cleavage site 2 without additional linkers. To 413 generate Chordin-sfGFP-FLAG and Chordin-Dendra2-FLAG, sequences encoding the FLAG tag 414 were inserted between the first linker and sfGFP or Dendra2 of Chordin-sfGFP and Chordin- 415 Dendra2 constructs. 416 417 Generation of fluorescent Sizzled fusions 418 All Sizzled constructs were generated by PCR-based methods (Horton et al. 1990), contain the 419 consensus Kozak sequence gccacc 5’ of the start codon, and were inserted into the EcoRI and 420 XbaI sites of the pCS2(+) vector. To generate Sizzled-sfGFP, sequences encoding sfGFP with an 421 N-terminal LGLG linker were fused to the C-terminus of Sizzled. Sequences encoding the FLAG 422 tag DYKDDDDK were inserted between the LGLG linker and sfGFP to generate Sizzled-sfGFP- 423 FLAG. To generate Sizzled-FLAG, the FLAG tag was fused to the C-terminus of Sizzled 424 separated by an LGLG linker. 425 426 mRNA in vitro synthesis 427 mRNA was generated using SP6 mMessage mMachine kits (Thermo Fisher) after vector 428 linearization with NotI-HF (New England Biolabs, Cat. No. R3189). mRNA was purified using 429 LiCl precipitation or Qiagen RNAeasy kits following the manufacturers’ instructions. 430 431 Phenotypic analysis 432 Scoring of ventralization and dorsalization was executed as previously described (Mullins et al. 433 1996, Kishimoto et al. 1997). Embryos were injected at the one- to two-cell stage with equimolar 434 amounts of BMP2b (1 pg), BMP2b-sfGFP (1.49 pg), and BMP2b-Dendra2 (1.47 pg) mRNA to 435 assess ventralizing activity. At 1 day post-fertilization, BMP2b-injected embryos were classified 436 as weakly ventralized (V1) to strongly ventralized (V4). V1 embryos have reduced eyes but a 437 prominent head. V2 embryos have no eyes, reduction of the head, and expansion of posterior 438 structures such as somites and tail. V3 embryos completely lack head structures and exhibit a 439 further expanded tail and enlarged blood islands. Finally, V4 embryos lack most structures except 440 for a short, protruding, and expanded tail. 441 To assess dorsalizing activity of the Chordin constructs, embryos were injected with equimolar 442 amounts of Chordin (30 pg), Chordin-sfGFP (37 pg), Chordin-Dendra2 (37 pg), and Chordin- 443 FLAG mRNA (30 pg). Embryos were scored at 1 day post-fertilization and classified as weakly 444 dorsalized (C1) to strongly dorsalized (C5) (Kishimoto et al. 1997). C1 embryos lack the ventral 445 tail fin. C2 embryos have a further loss of ventral structures, such as the ventral tail vein, and a 446 bent tail. C3 embryos exhibit a tail that is shortened and twisted. C4 embryos have observable 447 head structures and develop eyes with twisting of the posterior structures above the yolk. C5 448 embryos are fully dorsalized and frequently lyse (Mullins et al. 1996, Kishimoto et al. 1997). 449 450 Rescue of BMP2b (swr-/-) mutants

11

451 Injection of BMP2b mRNA can rescue BMP2b mutants (Kishimoto et al. 1997). To investigate 452 whether tagged BMP2b constructs can rescue swrtc300-/- mutants (Mullins et al. 1996), the 453 rescuing amount of BMP2b mRNA was first determined (1.8 pg), and equimolar amounts of 454 mRNA encoding fluorescent fusion constructs were subsequently injected into the progeny of 455 heterozygous swr+/- mutant incrosses. Embryos with wild type morphology at 24 hpf were 456 anesthetized and mounted in 2% methylcellulose for imaging with an AxioZoom V16 (ZEISS) 457 microscope at 30-33 hpf. To genotype embryos following DNA extraction (Meeker et al. 2007), 458 PCR was performed to amplify a BMP2b fragment with the forward primer 5'- 459 AAAAGCCGAGGAGAAAGCAC-3' and the reverse primer 5'- 460 AGTCCTTCATTGGGGAGATTGTTC-3', and the following thermocycling parameters: An 461 initial denaturation step of 94 °C for 3 min; 39 cycles of 94 °C for 30 s, 58 °C for 40 s, and 72 °C 462 for 40 s; and a final extension at 72 °C for 5 min. PCR amplicons were subsequently digested 463 with HaeIII (New England Biolabs, Cat. No. R0108) at 37 °C for 2 h. The genotyping assay for 464 the swrtc300 line was designed by the Zebrafish International Resource Center (ZIRC) staff and 465 downloaded from the ZIRC website at http://zebrafish.org. 466 467 Preparation of extracellularly enriched fractions for western blotting 468 Extracellularly enriched and cellular fractions from manually deyolked embryos between sphere 469 and dome stage were obtained as described previously (Müller et al. 2012). mRNAs encoding 470 FLAG-tagged constructs were injected at the one- or two-cell stage at equimolar amounts 471 (BMP2b-FLAG: 444 pg, BMP2b-sfGFP-FLAG: 638 pg, BMP2b-Dendra2-FLAG: 630 pg; and 472 Chordin-FLAG: 500 pg, Chordin-sfGFP-FLAG: 620 pg, Chordin-Dendra2-FLAG: 615 pg). For 473 protein samples with BMP2b constructs, fractions from approximately 19 embryos were loaded 474 and resolved by SDS-PAGE using 12% polyacrylamide gels. For protein samples with Chordin 475 constructs, fractions from approximately 17-18 embryos were loaded and resolved in 8% 476 polyacrylamide gels. Proteins were subsequently transferred onto PVDF membranes using a 477 Trans-Blot Turbo Transfer System (Bio-Rad, Cat. No. 170-4272). Membranes were blocked with 478 5% non-fat milk (Roth, Cat. No. T145.2) in PBST (0.1% Tween) and incubated with anti-FLAG 479 antibody (Sigma, Cat. No. F3165) at a concentration of 1:2,000 in non-fat milk in PBST at 4 °C 480 overnight. HRP-coupled donkey anti-mouse secondary antibody (Jackson ImmunoResearch, Cat. 481 No. 715-035-150) was used at concentration of 1:25,000 for 3 h at room temperature. 482 Chemiluminescence was detected using SuperSignal West Dura Extended Duration Substrate 483 (Thermo Fisher, Cat. No. 34075) and imaged with a chemiluminescence imaging system (Fusion 484 Solo, Vilber Lourmat). 485 486 Transplantations 487 To generate clonal sources secreting BMP2b-sfGFP, Chordin-sfGFP, and untagged Chordin 488 (Figures 3 and 5), approximately 50-75 cells were transplanted from sphere stage wild type TE 489 donor embryos expressing these constructs into uninjected, sphere stage sibling host embryos 490 (similar to (Müller et al. 2012)). Transplantations were carried out in 1 x Ringer’s buffer. Cells 491 were explanted from donors, extruded briefly into the buffer to wash away cellular debris and 492 extracellular fluorescent protein, and then transplanted into host embryos. 493 Donor embryos were dechorionated with 1 mg/ml Pronase (Roche, Cat. No. 11 459 643 001) and 494 injected with 1-2 nl injection mix at the one-cell stage. Sibling host embryos were dechorionated 495 together with donors at the one-cell stage, and all embryos were incubated at 28 C until 496 transplantation. Unfertilized or injured embryos were discarded. 12

497 For single (Figure 3) and double (Figure 5) transplantation experiments, BMP2b-sfGFP and 498 Chordin-sfGFP donors were injected with 500 pg mRNA (Figure 3 – figure supplement 1F-H). 499 For double transplantation experiments (Figure 5), embryos received one transplantation from a 500 donor expressing BMP2b-sfGFP and a second transplantation from a donor injected at the one- 501 cell stage with either 50 pg Alexa 546-coupled dextran (10 kDa, Molecular Probes, Cat. No. 502 D22911) or 1000 pg Chordin mRNA + 50 pg Alexa 546-coupled dextran. Alexa 546-coupled 503 dextran was used to mark the location of the second clone. 504 2-10 min post-transplantation, embryos were mounted in 1% low-melting NuSieve GTG agarose 505 (Lonza, Cat. No. 50080) dissolved in embryo medium (250 mg/l Instant Ocean salt dissolved in 506 reverse osmosis water). Embryos were immersed in 40 C molten low melting point agarose, 507 pulled into 1.5 mm glass capillary tubes (ZEISS), and positioned with the animal pole 508 perpendicular to the capillary using a metal probe. Agarose tubes were then suspended in embryo 509 medium, and imaged at room temperature using a ZEISS Lightsheet Z.1 microscope (see Light 510 sheet microscopy section for further imaging details). 511 512 Light sheet microscopy 513 Fluorescence images in Figures 1, 2, 3, and 5, and Figure 3 - figure supplement 1 were obtained 514 using a Lightsheet Z.1 microscope (ZEISS). For fixed, immunostained embryos, samples were 515 mounted into a glass capillary sample holder in 1% low-melting NuSieve GTG agarose (Lonza, 516 Cat. No. 50080) in embryo medium with 0.2 µm dark red fluorescent FluoSpheres (Life 517 Technologies, Cat. No. F8807) diluted 1:200,000 from a 2% solids stock. Embryos were imaged 518 at 0°, 45°, 180° and 225° angles (Schmid et al. 2013) using identical imaging conditions. For 3D 519 reconstruction, an interactive bead-based registration algorithm was used to determine the 520 threshold that most accurately selects the beads (Preibisch et al. 2010). Reconstructed images 521 were converted to 8-bit format using ImageJ, and Imaris software (Bitplane) was used for 3D 522 data visualization and video generation. The videos were cropped using Avidemux 2.6. 523 To visualize the entire embryo in a single image, reconstructed images were first converted to 16- 524 bit files using ImageJ, and equirectangular 2D map projections were then generated (Schmid et 525 al. 2013). The 2D maps were re-aligned into Hammer-Aitoff projections using Hugin panorama 526 photo stitcher software (http://hugin.sourceforge.net) to orient the peak of pSmad1/5/9 intensity 527 to the ventral pole (left in Figure 1 panels) and the trough of pSmad1/5/9 intensity to the dorsal 528 pole (right in Figure 1 panels). For gradient quantifications in Figures 1A+B and 2F-H, the 529 embryo proper was masked using manual polygon selections in Fiji (Schindelin et al. 2012) in 530 order to exclude signal from the yolk syncytial layer and yolk. The “Plot Profile” function in Fiji 531 was then applied to the entire masked image to determine ventral-to-dorsal gradients. The 532 background signal of immunostained embryos was determined by finding the lowest value in the 533 profiles of sphere stage embryos (Figure 1A+B) and the lowest value in the profiles of chordin-/- 534 embryos (Figure 2F+G), respectively. These background values were subtracted from the data 535 sets, and the profiles were normalized to the highest value in each data series. The mean and 536 standard error of the normalized data sets was then calculated piece-wise for every point along 537 the ventral-to-dorsal profile. 538 For transplantation experiments in Figures 3 and 5, imaging began 5 to 20 min post- 539 transplantation and continued for approximately 1 h (see Transplantation section for further 540 details). The following imaging conditions were used: 541 - W Plan-Apochromat 20 x objective, 0.5 x zoom 13

542 - dual side light sheets 543 - 488 nm laser (100 mW) at 6% power (for sfGFP-containing constructs) 544 - 561 nm laser (20 mW) at 5% power (for double transplantations only; to detect Alexa 546 545 signal) 546 - separate exposure to 488/561 nm lasers (in double transplantation experiments only) to avoid 547 cross-talk 548 - exposure time: 250 ms 549 - average light sheet thickness: 6.4 µm 550 - 3 µm intervals between z-slices; 60 slices per embryo (≈180 µm total) 551 - 5 min intervals between imaging 552 Gradients were quantified using maximum intensity projections of 15 z-slices similar to (Müller 553 et al. 2012). A rectangular region of interest abutting the clone with a fixed height of 86.34 μm 554 (corresponding to 189 pixels) and varying widths depending on embryo length was drawn in Fiji 555 (Schindelin et al. 2012), and the average intensity in 0.457 μm strips was calculated from the 556 maximum intensity projections. Background intensity resulting from autofluorescence was 557 measured similarly in uninjected embryos (for single transplantation experiments, n = 4) or in 558 uninjected embryos transplanted with a clone of cells containing Alexa 546-coupled dextran (for 559 double transplantation experiments, n = 2). A single value for background subtraction was 560 determined by calculating the average of the intensity profile values. After subtracting the 561 background value from the experimental intensity profiles, the data was normalized to the value 562 closest to the clonal source boundary. This approach allows for the comparison of the relative 563 gradient range, which is independent of constant production rates. We assume constant 564 production rates over the relatively short time scales of observation (≈80 min). 565 Embryos with low signal-to-noise ratios were excluded from analysis. 566 567 Fluorescence Decrease After Photoconversion (FDAP) experiments 568 FDAP experiments were carried out as described in (Müller et al. 2012, Rogers et al. 2015). 569 Embryos were injected at the one-cell stage with either 60 pg BMP2b-Dendra2 mRNA + 0.5 ng 570 Alexa 488-dextran (3 kDa, Molecular Probes) or 150 pg Chordin-Dendra2 mRNA + 0.5 ng 571 Alexa 488-dextran. To assess background fluorescence, embryos were injected with 0.5 ng Alexa 572 488-dextran only. Embryos were mounted in 1% low melting point agarose in glass-bottom Petri 573 dishes (MatTek Corporation) covered with embryo medium to hydrate the agarose during 574 imaging. 575 FDAP experiments were performed using an LSM 780 (ZEISS) confocal microscope. Pre- 576 conversion and post-conversion images were acquired using an LD C-Apochromat 40x/1.1 NA 577 water immersion objective. A single pre-photoconversion image was first acquired for each 578 sample followed by photoconversion and multiposition time-lapse imaging with 10 min intervals 579 for approximately 300 min. For photoconversion, embryos were illuminated with a Sola SE II 580 LED lamp at 100% power for 30 s through a C-Apochromat 10x/0.45 NA objective and an AHF 581 F36-500 UV filter cube. For both pre- and post-conversion images, Alexa 488 was excited using 582 a 488 nm Argon laser, and a DPSS 561 nm laser was used to excite photoconverted Dendra2. The 583 emission signal between 494 – 576 nm (Alexa 488) and 578 – 696 nm (photoconverted Dendra2) 584 was collected using a 32 channel GaAsP QUASAR detector array. Embryos that produced only 585 low levels of photoconverted Dendra2 signal or whose position shifted significantly over time as 586 well as embryos with non-uniform signal distribution or embryos that died were excluded from

14

587 analysis. Sample numbers: n = 22 for BMP2b-Dendra2 (with n = 17 background embryos); n = 6 588 for Chordin-Dendra2 (with n = 1 background embryo). 589 All experiments were analyzed using PyFDAP (Bläßle and Müller 2015, Rogers et al. 2015), 590 version 1.1.2. PyFDAP extracts the extracellular and intracellular photoconverted Dendra2 signal 591 by masking the Alexa 488 signal, and fits the resulting average intensities with a linear decay 592 model. The ordinary differential equation describing linear protein decay is given by 593 dc 594 kc dt 1 595 596 where c is the concentration of the protein and k1 is its clearance rate constant. We assume that 597 Dendra2 signal is directly proportional to the protein concentration. The analytical solution of 598 this equation is given by

kt1 599 c() t c00 e y 600 601 where c0 is the protein's concentration at t = 0 and y0 is the protein's concentration at t = ∞. The 602 half-life τ of the protein can then be calculated as

603   ln(2) / k 604 605 PyFDAP estimates a lower bound for y0 by computing the maximum relative effect of bleaching 606 Fi,r. For each background data set, the strongest influence of photobleaching was computed by 607 taking the minimum over all differences of background intensity Bj,r background noise Ni and the 608 difference between pre-conversion background intensity Bpre,i,r and noise level. Here r denotes the 609 region under consideration, i.e., extracellular, intracellular, or the entire imaging slice; i indicates 610 the ith dataset, and j counts the background data sets. The average over all b background data sets 611 was then taken to arrive at the mean effect of photobleaching. The factor 612 b  1 Bj, r() t N i 613 Fir,  min  t bj1  B N pre jr, i

614 was used to scale the pre-conversion intensity of the FDAP data set according to

615 y F I  N  N 0i,, ri , r pre i r i i 616 617 This lower bound was then used to constrain a Nelder-Mead simplex algorithm when minimizing

2 618 SSD( I ( tnn ) c ( t )) n 619 620 Fluorescence Recovery After Photobleaching (FRAP) experiments 621 FRAP experiments and data analysis were carried out as previously described (Müller et al. 2012, 622 Müller et al. 2013) using an LSM 780 NLO confocal microscope (ZEISS) and an LD LCI Plan- 15

623 Apochromat 25x water immersion objective. Embryos were injected at the one-cell stage with 30 624 pg of mRNA encoding BMP2b-sfGFP, 60 pg of mRNA encoding BMP2b-Dendra2, 60 pg of 625 mRNA encoding Chordin-sfGFP, 120 pg of mRNA encoding Chordin-Dendra2, or 30 pg of 626 mRNA encoding Sizzled-sfGFP. To analyze the effect of Chordin on BMP2b diffusion, embryos 627 were injected at the one-cell stage with 30 pg of mRNA encoding BMP2b-sfGFP plus 60 or 200 628 pg of mRNA encoding Chordin, or 60 pg of mRNA encoding BMP2b-Dendra2 plus 200 pg of 629 mRNA encoding Chordin. Embryos were mounted in 1% low melting point agarose in glass- 630 bottom Petri dishes (MatTek Corporation) covered with embryo medium to hydrate the agarose 631 during imaging. Embryos with low or non-uniform fluorescence and embryos that died or whose 632 position shifted significantly over time were excluded from analysis. 633 For FRAP data analysis, the fits of a model with uniform production, diffusion, and clearance 634 were constrained with the clearance rate constants of BMP2b-Dendra2 and Chordin-Dendra2 -5 635 fusions measured by FDAP in the present study (BMP2b-Dendra2: k1 = 8.9 x 10 /s; Chordin- -5 636 Dendra2: k1 = 9.6 x 10 /s). Sizzled-sfGFP fits were constrained with the clearance constant 637 measured for BMP2b-Dendra2 assuming similar protein stability. As shown previously, the 638 estimation of diffusion coefficients does not sensitively depend on the values of clearance rate 639 constants if the time scales of observation (here: 50 min) and protein stability (here: 640 approximately 120 min) are similar (Müller et al. 2012). 641 642 Fluorescence Correlation Spectroscopy (FCS) experiments 643 The FCS experiments were done using an LD C-Apochromat 40x/1.1 NA water immersion 644 objective on an LSM 780 NLO confocal microscope (ZEISS). Embryos were injected at the one- 645 cell stage with 30 pg of mRNA encoding BMP2b-sfGFP or 60 pg of mRNA encoding Chordin- 646 sfGFP. Embryos were mounted in 1% low melting point agarose in glass-bottom Petri dishes 647 (MatTek Corporation) and covered with embryo medium to hydrate the agarose during imaging. 648 The fluorophores (sfGFP, Alexa 488) were excited using an Argon 488 nm laser, and the 649 emission light between 494 – 542 nm was collected using a 32-channel GaAsP QUASAR 650 detector array. Before each FCS experiment, the pinhole was aligned and set to 1 Airy unit, and 651 the instrument was calibrated using a solution of 40 nM Alexa 488 dye (Thermo Fisher) in water. 652 For each FCS sample, fluorescence fluctuations were measured for 10 s with 10 repeats, and any 653 irregularities in the 100 s count trace resulting from cellular movements were excluded from 654 analysis. 655 Auto-correlation curves for Alexa 488 were freely fitted to determine the structural parameter as 656 well as the diffusion time, the triplet state fraction, and the triplet state relaxation time of Alexa 657 488 for every experiment. The auto-correlation curves for BMP2b-sfGFP and Chordin-sfGFP 658 were fitted with a fixed structural parameter, fixed triplet state fraction, and fixed triplet 659 relaxation time determined from the Alexa 488 calibration measurements. The curves were fitted 660 using ZEISS ZEN Pro software with a one-component “free diffusion with triplet state 661 correction” model. The first 10-6 seconds lag time for the correlation curve was excluded in the 662 fitting (Yu et al. 2009, Müller et al. 2013). The diffusion coefficient was then calculated by 663 comparing the diffusion time of BMP2b-sfGFP and Chordin-sfGFP with Alexa 488 (reference 664 diffusion coefficient: 435 μm2/s (Petrasek and Schwille 2008)). 665 Since the values of the triplet state fraction and the triplet state relaxation time of sfGFP are 666 unknown and not necessarily identical to those of Alexa 488, we also freely fitted the 667 autocorrelation curves for BMP2b-sfGFP and Chordin-sfGFP with the experimentally measured 668 structural parameter as the only constraint, and determined free diffusion coefficients of D = 35 ± 16

669 2 μm2/s for BMP2b-sfGFP (n = 17 measurements from 4 embryos) and D = 50 ± 3 μm2/s for 670 Chordin-sfGFP (n = 19 measurements from 5 embryos), within a deviation of approximately 20- 671 30% compared to the diffusion coefficients determined by constraining the fits with a fixed 672 structural parameter, fixed triplet state fraction, and fixed triplet relaxation time (D = 46 ± 1 673 μm2/s for BMP2b-sfGFP, and D = 59 ± 2 μm2/s for Chordin-sfGFP; values reported in Figure 4). 674 The similar diffusion coefficients determined by differently constrained fits indicate that the 675 diffusion time measured in our experiments does not sensitively depend on the values of the 676 triplet state fraction and triplet state relaxation time. 677 678 Mathematical modeling of BMP2b-sfGFP and Chordin-sfGFP gradient formation 679 The geometry of the zebrafish blastoderm was approximated by the complement of two spheres 680 with a columnar subdomain placed off-center to represent the signal source region with the same 681 parameters as described in (Müller et al. 2012). Gradient formation was simulated with the 682 source-diffusion-sink model c 683 D 2 c  k c  k t 12s 684 with 1 in the source 685 훿 = { s 0 otherwise 686 687 For Figure 3 - figure supplement 2, the experimental data was fitted with solutions from a 50 x 50 688 parameter grid spanning all possible combinations of 50 diffusion coefficients (logarithmically 689 spaced from 0.1 µm2/s to 50 µm2/s) and 50 clearance rate constants (logarithmically spaced from 690 1 x 10-5/s to 5 x 10-4 ). 691 692 Simulations of previous models 693 The finite element method was used for all numerical simulations. All geometries are one- 694 dimensional representations of embryos. The solution at each time step in the discretized 695 geometries was determined using a sparse LU factorization algorithm (UMFPACK), and the time 696 stepping was computed using a backward Euler step method (Comsol Multiphysics). Simulations 697 in Figure 1C-E,G (Models 1, 2, 3, and 5) were executed for a total of 10080 s (i.e., for 698 approximately 3 h from sphere to shield stage during zebrafish embryogenesis (Kimmel et al. 699 1995)) and read out every 2520 s (i.e., approximately every 42 min at relevant zebrafish stages). 700 The simulation in Figure 1F (Model 4) was executed for a total of 20 time steps near steady state 701 and read out at every fifth time step. 702 The following model descriptions comprise the complete wild type systems. For simulations of 703 chordin mutants the Chordin flux was set to 0 (Models 1, 2, 3, and 5), or the Chordin-dependent 704 terms were removed from the equations and the initial concentration of Chordin was set to 0 705 (Model 4). To focus on the role of Chordin in regulating BMP signaling and distribution, we did 706 not include other negative regulators of BMP such as Noggin and Follistatin (Umulis et al. 2009). 707 For the interpretation of the simulations, we assume that the distribution of free BMPs is 708 correlated with BMP signaling and the distribution of pSmad1/5/9. 709 To facilitate comparison of the models, the distribution profiles of free BMP are shown as a 710 function of relative embryo length, and the solutions were normalized to the ventral-most free 711 BMP concentration at shield stage (i.e., at t = 7560 s for Models 1, 2, 3, and 5, and at t = 15 for 712 Model 4) in wild type simulations. 17

713 714 Model 1: Graded source-sink (mobile BMP)

715 In the graded source-sink model, the BMP source, ρBMP(x), was modeled after the known 716 distribution of bmp2b mRNA between sphere stage and 30% epiboly (Ramel and Hill 2013). The 717 model does not include autoregulation of BMP production since positive feedback only appears 718 to be important for later stages of development (Ramel and Hill 2013, Zinski et al. 2017). 719 Chordin binds BMP irreversibly and acts as a sink. The model was simulated using the following 720 equations: 721 BMP D 2[BMP]  Chd BMP  BMP  (x ) t BMP BMP BMP Chd 722 D 2[Chd] Chd BMP  Chd t Chd Chd ChdBMP D 2[ChdBMP]   Chd BMP  ChdBMP t ChdBMP Chd 723 724 Embryo geometry and boundary conditions 725 Embryo length: 300 x 10-6 m (300 µm, the typical length of the zebrafish blastoderm) 726 Constant Chordin flux from the dorsal boundary: 5 x 10-14 mol/(m2s) 727 No-flux boundary condition for all other species on both ventral and dorsal boundaries 728 729 Parameter values 2 730 DBMP = 2 µm /s (measured in the present study) 2 731 DChd = 7 µm /s (measured in the present study) 2 732 DChdBMP = 7 µm /s -5 733 BMP = 8.9 x 10 /s (measured in the present study) -5 734 Chd = 9.6 x 10 /s (measured in the present study) 735  = 400 x 103 m3/(mol s) -9 -5000x 736 ρBMP(x) = 0.57 x 10 x e (accounting for the inhomogeneous ventrally peaking distribution 737 of bmp2b mRNA in zebrafish embryos) 738 739 Initial conditions 740 BMP initial concentration: 2.85 x 10-8 mol/m3 everywhere (one-twentieth of the concentration 741 used for Xenopus frogs in (Inomata et al. 2013)) 742 Chordin initial concentration: 0 everywhere 743 Chordin-BMP complex initial concentration: 0 everywhere 744 745 Model 2: Graded source-sink (immobile BMP) 746 As for Model 1, the graded source-sink model (immobile BMP) was modeled without 747 autoregulation of BMP production since positive feedback only appears to be important for later 748 stages of development (Ramel and Hill 2013, Zinski et al. 2017). Here , which reflects the 749 binding between Chordin and BMP, is smaller than in Model 1 to obtain a realistic free BMP 750 distribution; using the same value for  as in Model 1 creates an unrealistically steep free BMP 751 gradient. The model was simulated using the following equations: 18

752 BMP Chd BMP  BMP  ()x t BMP BMP Chd 753 D 2[Chd] Chd BMP  Chd t Chd Chd ChdBMP D 2[ChdBMP]   Chd BMP  ChdBMP t ChdBMP Chd 754 755 Embryo geometry and boundary conditions 756 Embryo length: 300 x 10-6 m (300 µm, the typical length of a zebrafish blastoderm) 757 Constant Chordin flux from the dorsal boundary: 5 x 10-14 mol/(m2s) 758 No-flux boundary condition for all other species on both ventral and dorsal boundaries 759 760 Parameter values 2 761 DChd = 7 µm /s (measured in the present study) 2 762 DChdBMP = 7 µm /s -5 763 BMP = 8.9 x 10 /s (measured in the present study) -5 764 Chd = 9.6 x 10 /s (measured in the present study) 765  = 4 x 103 m3/(mol s) -9 -5000x 766 ρBMP(x) = 0.57 x 10 x e (accounting for the inhomogenous ventrally peaking distribution of 767 bmp2b mRNA in zebrafish embryos) 768 769 Initial conditions 770 BMP initial concentration: 2.85 x 10-8 mol/m3 everywhere (one-twentieth of the concentration 771 used for Xenopus frogs in (Inomata et al. 2013)) 772 773 Chordin initial concentration: 0 everywhere 774 Chordin-BMP complex initial concentration: 0 everywhere 775 776 Model 3: Long-range accumulation and feedback 777 The model was developed for frog embryogenesis. For the simulations in the present study the 778 equations, geometry, initial conditions, and parameters used were exactly as described in 779 (Inomata et al. 2013):

19

10 [BMP] v ([ADMP] [BMP]) D 2[BMP] BMP  [BMP]  t 10 10 BMP kBMP ([ADMP] [BMP])  [ChdBMP] Chd  k[Chd][BMP] [Szl] [Chd] [ChdBMP] [ChdADMP] 1 ki km

10 [Chd] vk  [Chd] D 2[Chd] Chd Chd  Chd  t 10 10 [Szl] [Chd] [ChdBMP] [ChdADMP] kChd ([ADMP] [BMP]) 1  ki km kk[Chd][BMP] [Chd][ADMP]

10 [ADMP] vk D 2[ADMP] ADMP ADMP  [ADMP]  t 10 10 BMP kADMP ([ADMP] [BMP])  [ChdADMP] Chd  k[Chd][ADMP] [Szl] [Chd] [ChdBMP] [ChdADMP] 1 ki km

20 [Szl] v ([ADMP] [BMP]) D 2[Szl]Szl  [Szl] t 20 20 Szl kSzl ([ADMP] [BMP])

[ChdBMP]  [ChdBMP] Dk 2[ChdBMP] Chd  [Chd][BMP] t [Szl] [Chd] [ChdBMP] [ChdADMP] 1 ki km

[ChdADMP]  [ChdADMP] 780 D 2[ChdADMP]  Chd  k[Chd][ADMP] t [Szl] [Chd] [ChdBMP] [ChdADMP] 1 ki km 781 782 Embryo geometry and boundary conditions 783 Embryo length: 1000 x 10-6 m (1000 µm, the typical length of a frog embryo) 784 Constant Chordin flux from the dorsal boundary: 4.8 x 10-12 mol/(m2s) 785 No-flux boundary condition for all other species on both ventral and dorsal boundaries 786 787 Parameter values 788 km = 25 x 10-6 mol/m3 789 ki = 25 x 10-6 mol/m3 -10 3 790 vChd = 5 x 10 mol/(m s) -8 3 791 kChd = 7 x 10 mol/m -10 3 792 vBMP = 1.4 x 10 mol/(m s) 20

-7 3 793 kBMP = 3.5 x 10 mol/m -6 3 794 vSzl = 100 x 10 mol/(m s) -6 3 795 kSzl = 1 x 10 mol/m -9 3 796 vADMP = 3.2 x 10 mol/(m s) -8 3 797 kADMP = 3 x 10 mol/m -3 798 Chd = 1 x 10 /s -4 799 BMP = 2 x 10 /s -5 800 Szl = 3.8 x 10 /s 801 D = 15 µm2/s 802 k = 280 m3/(mol s) 803 804 Initial conditions 805 BMP initial concentration: 0.57 x 10-6 x e-1000x mol/m3 throughout the embryo (the amplitude of 806 this distribution is the same as in (Inomata et al. 2013), but the initial BMP profile was modeled 807 as a gradient instead of uniform) 808 Chordin initial concentration: 0 everywhere 809 ADMP initial concentration: 0 everywhere 810 Sizzled initial concentration: 0 everywhere 811 Chordin-BMP complex initial concentration: 0 everywhere 812 Chordin-AMP complex initial concentration: 0 everywhere 813 814 For the simulations in Figure 4 - figure supplement 1E-J, all parameters were identical to the 815 parameter values listed above except for D(BMP) = 3 µm2/s, D(Chd) = 6 µm2/s, D(ChdADMP) = 816 10 µm2/s, and D(ChdBMP) = 10 µm2/s. D(Sizzled) was set to 150 µm2/s in Figure 4 - figure 817 supplement 1E, and to 10 µm2/s in Figure 4 - figure supplement 1F-J. D(ADMP) was varied from 818 0.1 µm2/s to 150 µm2/s as indicated in Figure 4 - figure supplement 1E-J. 819 820 Model 4: Self-regulating reaction-diffusion system 821 The non-dimensional model, geometry, initial conditions, and parameters used for the 822 simulations were similar to the ones described in (Francois et al. 2009):

[BMP] [BMP]2 D 2[BMP]   [BMP]  t BMP(1 [Chd])[Szl] BMP BMP 2 [Chd]2 [Chd] DChd [Chd]   Chd [Chd]  Chd 823 t [ADMP] [ADMP] D 22[ADMP]  [Chd]   [ADMP] t ADMP ADMP [Szl] D 22[Szl]  [BMP]   [Szl] t Szl Szl 824 825 Embryo geometry and boundary conditions 826 Embryo length: 25 827 No-flux boundary conditions on the ventral and dorsal boundaries 828 829 Parameter values 21

830 DChd = DBMP = 6 831 µChd = µBMP = 1.2 832 ρChd = ρBMP = 0.1 833 µADMP = µSzl = 1.5 834 DADMP = DSzl = 150 835 836 Initial conditions -0.1x 837 BMP initial concentration: ρBMP = e 838 Chordin initial concentration of 1 from position 0 to 24 and Chordin initial concentration of 10 839 from 24 to 25 (i.e., the dorsal organizer) in the simulated embryo 840 ADMP initial concentration: 1 everywhere 841 Sizzled initial concentration: 1 everywhere 842 843 For the simulations in Figure 4 - figure supplement 1K-P, all parameters were identical to the 844 parameter values listed above except for D(BMP) = 3 and D(Chd) = 6. D(Sizzled) was set to 150 845 in Figure 4 - figure supplement 1K, and to 10 in Figure 4 - figure supplement 1L-P. D(ADMP) 846 was varied from 0.1 to 150 as indicated in Figure 4 - figure supplement 1K-P. 847 848 Model 5: Shuttling 849 For Model 5, a minimal transport model that excludes the effects of downstream patterning 850 circuits was used to illustrate the biophysical aspects of shuttling (Ben-Zvi et al. 2008): 851 BMP D 2[BMP] Chd BMP   Xlr ChdBMP  BMP  (x ) t BMP BMP BMP Chd 852 D 2[Chd] Chd BMP  Chd t Chd Chd ChdBMP D 2[ChdBMP] Chd BMP   Xlr ChdBMP   ChdBMP t ChdBMP Chd 853 854 Embryo geometry and boundary conditions 855 Embryo length: 300 x 10-6 m (300 µm) 856 Constant Chordin flux from the dorsal boundary: 3 x 10-14 mol/(m2s) 857 No-flux boundary condition for all other species on both ventral and dorsal boundaries 858 859 Parameter values 2 860 DBMP = 0.1 µm /s 2 861 DChd = 10 µm /s 2 862 DChdBMP = 10 µm /s -5 863 BMP = 8.9 x 10 /s (measured in the present study) -5 864 Chd = 9.6 x 10 /s (measured in the present study) 865  = 100 x 103 m3/(mol s) 866  =  867 [Xlr] = 2 x 10-8 mol/m3 -10 -5000x 868 ρBMP(x) = 0.57 x 10 x e (accounting for the inhomogeneous ventrally peaking distribution 869 of bmp2b mRNA in zebrafish embryos) 22

870 871 Initial conditions 872 BMP initial concentration: 0.57 x 10-7 x e-5000x mol/m3 throughout the embryo 873 Chordin initial concentration: 0 everywhere 874 Chordin-BMP complex initial concentration: 0 everywhere 875 876 Shuttling simulations of adjacent BMP and Chordin clones shown in Figure 5 877 The one-dimensional simulations in Figure 5 were executed similarly to the ones described above 878 and solved at 15 and 75 min for comparison to the zebrafish embryo double transplantation 879 experiments. The solutions in Figure 5A and Figure 5E were normalized to the highest free BMP 880 concentration in the simulation without the Chordin source, and the solutions in Figure 5B and 881 Figure 5F were normalized to the free BMP concentration at the BMP source boundary (at 100 882 μm) for each condition to facilitate comparison between the gradient ranges. 883 The double transplantation experiments were modeled using the following equations: BMP D 2[BMP] BMP   Chd BMP   Xlr ChdBMP    t BMP BMP BMP BMP Chd 884 D 2[Chd] Chd BMP    t Chd Chd Chd ChdBMP D 2[ChdBMP] Chd BMP   Xlr ChdBMP t ChdBMP 885 886 with 887 1 in the BMP source 888 훿 = { BMP 0 otherwise 889 890 and 891 1 in the Chordin source 892 훿 = { Chd 0 otherwise 893 894 Embryo geometry and boundary conditions 895 Embryo length: 300 x 10-6 m (300 µm) 896 BMP source: between 50 and 100 µm from the left boundary 897 Chordin source: between 200 and 250 µm from the left boundary 898 No-flux boundary conditions on the left and right boundaries 899 900 Parameter values for simulations of shuttling predictions (Figure 5A+B) 2 901 DBMP = 2 µm /s (measured in the present study) 902 BMP = 0.0001/s (similar to measurements in the present study) -5 3 903 ηBMP = 5 x 10 mol/(m s) -5 3 904 ηChd = 5 x 10 mol/(m s) 2 905 DChd = 100 µm /s 906 DChdBMP = DChd 907  = 10 x 103 m3/(mol s) 23

908  =  909 [Xlr] = 2 x 10-7 mol/m3 910 911 Parameter values for simulations with experimentally measured diffusivities (Figure 5E+F) 2 912 DBMP = 2 µm /s (measured in the present study) 913 BMP = 0.0001/s (similar to measurements in the present study) -5 3 914 ηBMP = 5 x 10 mol/(m s) -5 3 915 ηChd = 5 x 10 mol/(m s) 2 916 DChd = 6 µm /s (measured in the present study) 2 917 DChdBMP = 2.2 µm /s (measured in the present study) 918  = 10 x 103 m3/(mol s) 919  =  920 [Xlr] = 2 x 10-7 mol/m3 921 922 Initial conditions 923 BMP initial concentration: 0 everywhere 924 Chordin initial concentration: 0 everywhere 925 Chordin-BMP complex initial concentration: 0 everywhere

24

926 References 927 Alexandre, C., A. Baena-Lopez, J. P. Vincent. 2014. Patterning and growth control by 928 membrane-tethered Wingless. Nature 505(7482): 180-5. doi: 10.1038/nature12879. 929 Barkai, N., D. Ben-Zvi. 2009. 'Big frog, small frog'--maintaining proportions in embryonic 930 development: delivered on 2 July 2008 at the 33rd FEBS Congress in Athens, Greece. FEBS J 931 276(5): 1196-207. doi: EJB6854 [pii]10.1111/j.1742-4658.2008.06854.x. 932 Ben-Zvi, D., N. Barkai. 2010. Scaling of morphogen gradients by an expansion-repression 933 integral feedback control. Proc Natl Acad Sci U S A 107(15): 6924-9. doi: 934 10.1073/pnas.0912734107. 935 Ben-Zvi, D., A. Fainsod, B. Z. Shilo, N. Barkai. 2014. Scaling of dorsal-ventral patterning in the 936 Xenopus laevis embryo. Bioessays 36(2): 151-6. doi: 10.1002/bies.201300136. 937 Ben-Zvi, D., G. Pyrowolakis, N. Barkai, B. Z. Shilo. 2011a. Expansion-repression mechanism for 938 scaling the Dpp activation gradient in Drosophila wing imaginal discs. Curr Biol 21(16): 1391-6. 939 doi: 10.1016/j.cub.2011.07.015. 940 Ben-Zvi, D., B. Z. Shilo, N. Barkai. 2011b. Scaling of morphogen gradients. Curr Opin Genet 941 Dev. doi: 10.1016/j.gde.2011.07.011. 942 Ben-Zvi, D., B. Z. Shilo, A. Fainsod, N. Barkai. 2008. Scaling of the BMP activation gradient in 943 Xenopus embryos. Nature 453(7199): 1205-11. doi: nature07059 [pii]10.1038/nature07059. 944 Bläßle, A., P. Müller. 2015. PyFDAP: automated analysis of fluorescence decay after 945 photoconversion (FDAP) experiments. Bioinformatics 31(6): 972-4. doi: 946 10.1093/bioinformatics/btu735. 947 Brankatschk, M., B. J. Dickson. 2006. Netrins guide Drosophila commissural axons at short 948 range. Nat Neurosci 9(2): 188-94. doi: 10.1038/nn1625. 949 Connors, S. A., J. Trout, M. Ekker, M. C. Mullins. 1999. The role of tolloid/mini fin in 950 dorsoventral pattern formation of the zebrafish embryo. Development 126(14): 3119-30. 951 Cui, Y., F. Jean, G. Thomas, J. L. Christian. 1998. BMP-4 is proteolytically activated by furin 952 and/or PC6 during vertebrate embryonic development. EMBO J 17(16): 4735-43. doi: 953 10.1093/emboj/17.16.4735. 954 Degnin, C., F. Jean, G. Thomas, J. L. Christian. 2004. Cleavages within the prodomain direct 955 intracellular trafficking and degradation of mature bone morphogenetic protein-4. Mol Biol Cell 956 15(11): 5012-20. doi: 10.1091/mbc.E04-08-0673. 957 Dickmeis, T., S. Rastegar, P. Aanstad, M. Clark, N. Fischer, V. Korzh, U. Strähle. 2001. 958 Expression of the anti-dorsalizing morphogenetic protein gene in the zebrafish embryo. Dev 959 Genes Evol 211(11): 568-72. doi: 10.1007/s00427-001-0190-3. 960 Dominici, C., J. A. Moreno-Bravo, S. R. Puiggros, Q. Rappeneau, N. Rama, P. Vieugue, A. 961 Bernet, P. Mehlen, A. Chedotal. 2017. Floor-plate-derived netrin-1 is dispensable for 962 commissural axon guidance. Nature 545(7654): 350-4. doi: 10.1038/nature22331. 963 Fisher, S., M. E. Halpern. 1999. Patterning the zebrafish axial skeleton requires early chordin 964 function. Nat Genet 23(4): 442-6. doi: 10.1038/70557.

25

965 Francois, P., A. Vonica, A. H. Brivanlou, E. D. Siggia. 2009. Scaling of BMP gradients in 966 Xenopus embryos. Nature 461(7260): E1; discussion E2. 967 Gurskaya, N. G., V. V. Verkhusha, A. S. Shcheglov, D. B. Staroverov, T. V. Chepurnykh, A. F. 968 Fradkov, S. Lukyanov, K. A. Lukyanov. 2006. Engineering of a monomeric green-to-red 969 photoactivatable fluorescent protein induced by blue light. Nat Biotechnol 24(4): 461-5. doi: 970 nbt1191 [pii] 10.1038/nbt1191. 971 Hammerschmidt, M., F. Pelegri, M. C. Mullins, D. A. Kane, F. J. van Eeden, M. Granato, M. 972 Brand, M. Furutani-Seiki, P. Haffter, C. P. Heisenberg, Y. J. Jiang, R. N. Kelsh, J. Odenthal, R. 973 M. Warga, C. Nüsslein-Volhard. 1996. dino and mercedes, two genes regulating dorsal 974 development in the zebrafish embryo. Development 123: 95-102. 975 Harmansa, S., F. Hamaratoglu, M. Affolter, E. Caussinus. 2015. Dpp spreading is required for 976 medial but not for lateral wing disc growth. Nature 527(7578): 317-22. doi: 977 10.1038/nature15712. 978 Haskel-Ittah, M., D. Ben-Zvi, M. Branski-Arieli, E. D. Schejter, B. Z. Shilo, N. Barkai. 2012. 979 Self-organized shuttling: generating sharp dorsoventral polarity in the early Drosophila embryo. 980 Cell 150(5): 1016-28. doi: 10.1016/j.cell.2012.06.044. 981 Horton, R. M., Z. L. Cai, S. N. Ho, L. R. Pease. 1990. Gene splicing by overlap extension: tailor- 982 made genes using the polymerase chain reaction. Biotechniques 8(5): 528-35. 983 Inomata, H., T. Shibata, T. Haraguchi, Y. Sasai. 2013. Scaling of dorsal-ventral patterning by 984 embryo size-dependent degradation of Spemann's organizer signals. Cell 153(6): 1296-311. doi: 985 10.1016/j.cell.2013.05.004. 986 Jones, C. M., N. Armes, J. C. Smith. 1996. Signalling by TGF-beta family members: short-range 987 effects of Xnr-2 and BMP-4 contrast with the long-range effects of activin. Curr Biol 6(11): 988 1468-75. 989 Kicheva, A., P. Pantazis, T. Bollenbach, Y. Kalaidzidis, T. Bittig, F. Jülicher, M. González- 990 Gaitán. 2007. Kinetics of morphogen gradient formation. Science 315(5811): 521-5. doi: 991 315/5811/521 [pii] 10.1126/science.1135774. 992 Kimmel, C. B., W. W. Ballard, S. R. Kimmel, B. Ullmann, T. F. Schilling. 1995. Stages of 993 embryonic development of the zebrafish. Dev Dyn 203(3): 253-310. 994 Kishimoto, Y., K. H. Lee, L. Zon, M. Hammerschmidt, S. Schulte-Merker. 1997. The molecular 995 nature of zebrafish swirl: BMP2 function is essential during early dorsoventral patterning. 996 Development 124(22): 4457-66. 997 Koos, D. S., R. K. Ho. 1999. The nieuwkoid/dharma homeobox gene is essential for bmp2b 998 repression in the zebrafish pregastrula. Dev Biol 215(2): 190-207. doi: 10.1006/dbio.1999.9479. 999 Lele, Z., M. Nowak, M. Hammerschmidt. 2001. Zebrafish admp is required to restrict the size of 1000 the organizer and to promote posterior and ventral development. Dev Dyn 222(4): 681-7. doi: 1001 10.1002/dvdy.1222. 1002 Leung, T., J. Bischof, I. Soll, D. Niessing, D. Zhang, J. Ma, H. Jackle, W. Driever. 2003. 1003 bozozok directly represses bmp2b transcription and mediates the earliest dorsoventral asymmetry 1004 of bmp2b expression in zebrafish. Development 130(16): 3639-49.

26

1005 Meeker, N. D., S. A. Hutchinson, L. Ho, N. S. Trede. 2007. Method for isolation of PCR-ready 1006 genomic DNA from zebrafish tissues. Biotechniques 43(5): 610-4. 1007 Miller-Bertoglio, V. E., S. Fisher, A. Sanchez, M. C. Mullins, M. E. Halpern. 1997. Differential 1008 regulation of chordin expression domains in mutant zebrafish. Dev Biol 192(2): 537-50. doi: 1009 10.1006/dbio.1997.8788. 1010 Müller, P., K. W. Rogers, B. M. Jordan, J. S. Lee, D. Robson, S. Ramanathan, A. F. Schier. 2012. 1011 Differential diffusivity of Nodal and Lefty underlies a reaction-diffusion patterning system. 1012 Science 336(6082): 721-4. doi: 10.1126/science.1221920. 1013 Müller, P., K. W. Rogers, S. R. Yu, M. Brand, A. F. Schier. 2013. Morphogen transport. 1014 Development 140(8): 1621-38. doi: 10.1242/dev.083519. 1015 Müller, P., A. F. Schier. 2011. Extracellular movement of signaling molecules. Dev Cell 21(1): 1016 145-58. doi: 10.1016/j.devcel.2011.06.001. 1017 Mullins, M. C., M. Hammerschmidt, D. A. Kane, J. Odenthal, M. Brand, F. J. van Eeden, M. 1018 Furutani-Seiki, M. Granato, P. Haffter, C. P. Heisenberg, Y. J. Jiang, R. N. Kelsh, C. Nüsslein- 1019 Volhard. 1996. Genes establishing dorsoventral pattern formation in the zebrafish embryo: the 1020 ventral specifying genes. Development 123: 81-93. 1021 Pedelacq, J. D., S. Cabantous, T. Tran, T. C. Terwilliger, G. S. Waldo. 2006. Engineering and 1022 characterization of a superfolder green fluorescent protein. Nat Biotechnol 24(1): 79-88. doi: 1023 nbt1172 [pii]10.1038/nbt1172. 1024 Petrasek, Z., P. Schwille. 2008. Precise measurement of diffusion coefficients using scanning 1025 fluorescence correlation spectroscopy. Biophys J 94(4): 1437-48. doi: 1026 10.1529/biophysj.107.108811. 1027 Plouhinec, J. L., E. M. De Robertis. 2009. Systems biology of the self-regulating morphogenetic 1028 gradient of the Xenopus gastrula. Cold Spring Harb Perspect Biol 1(2): a001701. doi: 1029 10.1101/cshperspect.a001701. 1030 Plouhinec, J. L., L. Zakin, Y. Moriyama, E. M. De Robertis. 2013. Chordin forms a self- 1031 organizing morphogen gradient in the extracellular space between ectoderm and mesoderm in the 1032 Xenopus embryo. Proc Natl Acad Sci U S A 110(51): 20372-9. doi: 10.1073/pnas.1319745110. 1033 Preibisch, S., S. Saalfeld, J. Schindelin, P. Tomancak. 2010. Software for bead-based registration 1034 of selective plane illumination microscopy data. Nat Methods 7(6): 418-9. doi: 1035 10.1038/nmeth0610-418. 1036 Ramel, M. C., C. S. Hill. 2013. The ventral to dorsal BMP activity gradient in the early zebrafish 1037 embryo is determined by graded expression of BMP ligands. Dev Biol 378(2): 170-82. doi: 1038 10.1016/j.ydbio.2013.03.003. 1039 Rogers, K. W., A. Bläßle, A. F. Schier, P. Müller. 2015. Measuring protein stability in living 1040 zebrafish embryos using fluorescence decay after photoconversion (FDAP). J Vis Exp 95: 52266. 1041 doi: 10.3791/52266. 1042 Roy, S., T. B. Kornberg. 2011. Direct delivery mechanisms of morphogen dispersion. Sci Signal 1043 4(200): pt8. doi: 10.1126/scisignal.2002434. 1044 Sako, K., S. J. Pradhan, V. Barone, A. Ingles-Prieto, P. Müller, V. Ruprecht, D. Capek, S. 1045 Galande, H. Janovjak, C. P. Heisenberg. 2016. Optogenetic Control of Nodal Signaling Reveals a 27

1046 Temporal Pattern of Nodal Signaling Regulating Cell Fate Specification during Gastrulation. Cell 1047 Rep 16(3): 866-77. doi: 10.1016/j.celrep.2016.06.036. 1048 Schier, A. F., W. S. Talbot. 2005. Molecular genetics of axis formation in zebrafish. Annu Rev 1049 Genet 39: 561-613. 1050 Schindelin, J., I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. 1051 Rueden, S. Saalfeld, B. Schmid, J. Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. 1052 Tomancak, A. Cardona. 2012. Fiji: an open-source platform for biological-image analysis. Nat 1053 Methods 9(7): 676-82. doi: 10.1038/nmeth.2019. 1054 Schmid, B., G. Shah, N. Scherf, M. Weber, K. Thierbach, C. P. Campos, I. Roeder, P. Aanstad, J. 1055 Huisken. 2013. High-speed panoramic light-sheet microscopy reveals global endodermal cell 1056 dynamics. Nat Commun 4: 2207. doi: 10.1038/ncomms3207. 1057 Sopory, S., S. M. Nelsen, C. Degnin, C. Wong, J. L. Christian. 2006. Regulation of bone 1058 morphogenetic protein-4 activity by sequence elements within the prodomain. J Biol Chem 1059 281(45): 34021-31. doi: 10.1074/jbc.M605330200. 1060 Tucker, J. A., K. A. Mintzer, M. C. Mullins. 2008. The BMP signaling gradient patterns 1061 dorsoventral tissues in a temporally progressive manner along the anteroposterior axis. Dev Cell 1062 14(1): 108-19. doi: 10.1016/j.devcel.2007.11.004. 1063 Umulis, D., M. B. O'Connor, S. S. Blair. 2009. The extracellular regulation of bone 1064 morphogenetic protein signaling. Development 136(22): 3715-28. doi: 136/22/3715 1065 [pii]10.1242/dev.031534. 1066 Varadarajan, S. G., J. H. Kong, K. D. Phan, T. J. Kao, S. C. Panaitof, J. Cardin, H. Eltzschig, A. 1067 Kania, B. G. Novitch, S. J. Butler. 2017. Netrin1 Produced by Neural Progenitors, Not Floor 1068 Plate Cells, Is Required for Axon Guidance in the Spinal Cord. Neuron 94(4): 790-9 e3. doi: 1069 10.1016/j.neuron.2017.03.007. 1070 Xu, P. F., N. Houssin, K. F. Ferri-Lagneau, B. Thisse, C. Thisse. 2014. Construction of a 1071 vertebrate embryo from two opposing morphogen gradients. Science 344(6179): 87-9. doi: 1072 10.1126/science.1248252. 1073 Yu, S. R., M. Burkhardt, M. Nowak, J. Ries, Z. Petrasek, S. Scholpp, P. Schwille, M. Brand. 1074 2009. Fgf8 morphogen gradient forms by a source-sink mechanism with freely diffusing 1075 molecules. Nature 461(7263): 533-6. doi: nature08391 [pii]10.1038/nature08391. 1076 Zinski, J., Y. Bu, X. Wang, W. Dou, D. Umulis, M. Mullins. 2017. Systems biology derived 1077 source-sink mechanism of BMP gradient formation. eLife 6: e22199. doi: 10.7554/eLife.22199.

1078

28

1079 Figure Legends 1080 1081 Figure 1. BMP signaling (pSmad1/5/9) gradient formation and simulations of five major 1082 dorsal-ventral patterning models over relevant zebrafish developmental stages (3 h). A) 1083 Two-dimensional Hammer-Aitoff projections (2D maps) of pSmad1/5/9-immunostained 1084 individual wild type zebrafish embryos at different developmental stages. Embryos were imaged 1085 using light sheet microscopy (see Materials and Methods for details). B) Quantification of 1086 ventral-to-dorsal average pSmad1/5/9 distributions in one-dimensional projections of 2D maps 1087 generated for embryos at different developmental stages (n = 3 for each stage) as in (A). Error 1088 bars denote standard error. C-G) Gradient formation kinetics simulated for Models 1-5 at relevant 1089 zebrafish developmental stages. 1090 1091 Figure 1 - figure supplement 1. Mathematical formulation of five major models of 1092 BMP/Chordin-mediated dorsal-ventral patterning. See Materials and Methods for details. 1093 Selected essential features of the models are illustrated on the right. A) Model 1: Graded source- 1094 sink (mobile BMP). In this model, BMP diffuses from a ventrally biased, graded source, and 1095 Chordin produced from the dorsal side inhibits BMP by irreversible binding. B) Model 2: Graded 1096 source-sink (immobile BMP). In this model, BMP diffusion is negligible (D = 0 μm2/s). The 1097 mechanism of restricting BMP signaling by Chordin irreversibly binding to BMP is the same as 1098 in Model 1, but with weaker binding kinetics. C) Model 3: Long-range accumulation and 1099 feedback. Model and parameters were adapted from (Inomata et al. 2013). D) Model 4: Self- 1100 regulating reaction diffusion system. Model and parameters were adapted from (Francois et al. 1101 2009). E) Model 5: Shuttling. A simplified model without feedback to purely illustrate the 1102 biophysical aspects of shuttling was adapted from (Ben-Zvi et al. 2008). 1103 1104 Figure 2. Theoretical predictions for the influence of the inhibitor Chordin on the BMP 1105 signaling gradient and experimental test. A-E) Simulations of BMP distributions in five major 1106 models of dorsal-ventral patterning in the presence (black) or absence (red) of Chordin. The BMP 1107 and Chordin sources are indicated below each graph in green and blue, respectively. Note that the 1108 spatial production rates in Models 3 and 4 are modulated over time by feedback. F-G) 1109 Quantification of average pSmad1/5/9 distributions in wild type (black) and chordin-/- (red) 1110 embryos using one-dimensional projections of 2D maps. Wild type n = 7, chordin-/- mutants n = 1111 10. Error bars denote standard error. H) p-values (unpaired two-tailed t-test assuming equal 1112 variance) calculated as a function of space between pSmad1/5/9 distributions in wild type and 1113 chordin-/- embryos shown in (F) indicate no significant difference of pSmad1/5/9 on the ventral 1114 side but a dramatic expansion into dorsal-lateral domains. 1115 1116 Figure 3. Gradient formation kinetics of fluorescently tagged BMP and Chordin. A) 1117 Schematic of BMP2b-sfGFP and -Dendra2 fusion constructs. B) Fluorescent BMP2b fusion 1118 constructs can induce ventralization, a BMP-overexpression phenotype (Kishimoto et al. 1997). 1119 mRNA amounts equimolar to 2 pg of BMP2b mRNA were injected at the one-cell stage, and 1120 images were taken 30 hours post-fertilization (hpf). C) Rescue of a BMP2b mutant (swr-/-) with 1121 BMP2b-Dendra2. 2.74 pg of BMP2b-Dendra2-encoding mRNA were injected at the one-cell 1122 stage, and images were taken at 30 hpf. In a separate experiment with 1 pg of BMP2b-sfGFP- 1123 encoding mRNA, 20% (9/44) of all injected swr-/- mutants were rescued, 16% (7/44) were 1124 ventralized, and 64% (28/44) were dorsalized. D) Schematic of Chordin-sfGFP and -Dendra2 1125 fusion constructs. E) Fluorescent Chordin constructs can induce dorsalization, a Chordin- 29

1126 overexpression phenotype. mRNA amounts equimolar to 30 pg of Chordin mRNA were injected 1127 at the one-cell stage, and images were taken at 30 hpf. F+G) Light sheet microscopy images of 1128 BMP- and Chordin-sfGFP gradients forming from a local source in live zebrafish embryos. 1129 Approximately 50-75 cells expressing BMP2b-sfGFP (F) or Chordin-sfGFP (G) were 1130 transplanted into host embryos at sphere stage (see Materials and Methods for details). The 1131 images show gradient formation in single optical slices approximately 20 min after 1132 transplantation. H+I) Quantification of BMP2b-sfGFP (H) and Chordin-sfGFP (I) gradient 1133 formation kinetics from a local source (BMP2b-sfGFP: n = 8; Chordin-sfGFP: n = 5). Dashed 1134 lines indicate the distance at which the protein distributions drop to 50% of their maximal 1135 concentration 60 min post-transplantation. 1136 1137 Figure 3 - figure supplement 1. Detailed characterization of fluorescently tagged BMP2b 1138 and Chordin. A) Ventralized and dorsalized phenotypes at 24 hours post-fertilization (hpf) were 1139 categorized using established classification schemes (Mullins et al. 1996, Kishimoto et al. 1997). 1140 B) Embryos were injected with equimolar amounts of mRNA encoding BMP2b (1 pg, n = 102), 1141 BMP2b-sfGFP (1.49 pg, n = 101), and BMP2b-Dendra2 (1.47 pg, n = 107) at the one-cell stage. 1142 BMP2b-sfGFP induced stronger ventralization, and BMP2b-Dendra2 induced weaker 1143 ventralization compared to untagged BMP2b. C) To determine whether the differences in the 1144 degree of ventralization (B) are due to changes in protein activity or protein levels, extracellularly 1145 enriched extracts were obtained from zebrafish embryos injected with mRNA amounts equimolar 1146 to 444 pg BMP2b-FLAG-encoding mRNA. Levels and processing of FLAG-tagged BMP ligands 1147 were assessed using anti-FLAG western blots. Green asterisks to the left of a band indicate 1148 properly processed mature BMP2b ligand; blue asterisks indicate unprocessed full-length pro- 1149 protein. Similar to FLAG-tagged BMP2b, FLAG-tagged BMP2b-sfGFP and -Dendra2 are 1150 properly processed and mostly secreted as mature ligands into the extracellular space. BMP2b- 1151 sfGFP-FLAG protein levels are higher compared to FLAG-tagged BMP2b, possibly owing to the 1152 rapid folding kinetics of sfGFP (Pedelacq et al. 2006); in contrast, BMP2b-Dendra2-FLAG levels 1153 are lower. The correlation between protein levels and activity (B) suggests that the fluorescent 1154 BMP2b constructs are equivalent to untagged BMP2b in inducing downstream signaling 1155 responses. D) Phenotype distributions at 24 hpf. Zebrafish embryos were injected at the one-cell 1156 stage with equimolar amounts of mRNA encoding Chordin (30 pg, n = 41), Chordin-sfGFP (37 1157 pg, n = 39), Chordin-Dendra2 (37 pg, n = 39), and Chordin-FLAG (30 pg, n = 33) (uninjected: n 1158 = 49). E) Extracellularly enriched fractions were obtained from zebrafish embryos injected with 1159 mRNA equimolar to 500 pg of Chordin-FLAG. Levels and processing of FLAG-tagged Chordin 1160 constructs were assessed using anti-FLAG western blots. Green asterisks indicate properly 1161 processed mature Chordin; blue asterisks indicate unprocessed full-length protein. Similar to the 1162 correlation between BMP2b construct levels and ventralization activity, the dorsalization activity 1163 of Chordin constructs (D) is correlated with protein levels. F-H) Distribution of BMP2b/Chordin- 1164 sfGFP in transplantation donors similar to those used in experiments shown in Figures 3 and 5 1165 Embryos were injected at the one-cell stage with 500 pg BMP2b-sfGFP- (G) or 1000 pg Chordin- 1166 sfGFP- (H) encoding mRNA (compare to uninjected embryo (F)). Embryos were imaged using 1167 light sheet microscopy at sphere stage (5 - 5.5 hpf), when transplantations were carried out in the 1168 experiments shown in Figures 3 and 5. Maximum intensity projections are shown. 1169 1170 Figure 3 - figure supplement 2. Modeling of BMP and Chordin gradient formation kinetics 1171 and comparison to measured gradients. Gradient simulations were executed in a three- 1172 dimensional embryo-like geometry with a local production source and uniform diffusion and

30

1173 clearance as in (Müller et al. 2012). Gradient formation was simulated for 70 min and compared 1174 to gradients measured in vivo ≈70-75 min post-transplantation. A 50 by 50 logarithmically spaced 1175 parameter grid was simulated for diffusion coefficients (D) ranging from 0.1 to 50 µm2/s and -5 -4 1176 clearance rate constants (k1) ranging from to 1 x 10 /s to 5 x 10 /s. The fits in (A) and (B) were 1177 constrained with the measured clearance rate constants of BMP2b-Dendra2 and Chordin-Dendra2 1178 and fitted with D as the free parameter. The fits in (C) and (D) were constrained with the 1179 measured diffusion coefficients of fluorescent BMP2b and Chordin constructs and fitted with k1 1180 as the free parameter. The data in (E) and (F) was overlaid with simulations using the measured 1181 D and k1 values. G-H) Sensitivity analysis of gradient simulations with all combinations of 1182 measured D and k1 values as well as D and k1 values three standard deviations above and below 1183 the measured averages (rainbow colors) overlaid with the experimental data (black). R2 values 1184 indicate the goodness of the fit. Error bars denote standard deviation. 1185 1186 Figure 4. Biophysical measurements of BMP and Chordin protein stability and diffusivity. 1187 A+B) FDAP protein stability measurements for BMP2b-Dendra2 (A) and Chordin-Dendra2 (B). 1188 Error bars denote standard deviation. BMP2b-Dendra2: n = 22; Chordin-Dendra2: n = 6. C+D) 1189 FRAP effective protein diffusivity measurements for BMP2b-Dendra2 (C) and Chordin-Dendra2 1190 (D). Data and fits from single experiments are shown. E) Bar chart of the average effective 1191 diffusion coefficients from FRAP experiments. Error bars denote standard error. BMP2b- 1192 Dendra2: n = 6; BMP2b-sfGFP: n = 8; Chordin-Dendra2: n = 8; Chordin-sfGFP: n = 6; Sizzled- 1193 sfGFP: n = 12. F) Free diffusion coefficients of BMP2b-sfGFP and Chordin-sfGFP measured in a 1194 diffraction-limited spot within the zebrafish embryonic extracellular space far away from cell 1195 membranes (see Materials and Methods for details). Error bars denote standard error. BMP2b- 1196 sfGFP: n = 17 measurements from 4 embryos; Chordin-sfGFP: n = 19 measurements from 5 1197 embryos. G) Negligible influence of Chordin on BMP2b effective diffusion. Untagged Chordin 1198 was co-expressed with BMP2b-Dendra2 (n = 8) or BMP2b-sfGFP (n = 9) in zebrafish embryos 1199 subjected to FRAP measurements at blastula stages. The data shown for BMP2b-Dendra2 and 1200 BMP2b-sfGFP FRAP experiments without co-expressed Chordin is identical to the data shown in 1201 (E). p-values (unpaired two-tailed t-test assuming equal variance) are shown for statistically 1202 significant (p < 0.05) data sets. 1203 1204 Figure 4 - figure supplement 1. Characterization of Sizzled diffusion and its role in gradient 1205 formation. A) Schematic of the Sizzled-sfGFP fusion protein. B) Anti-FLAG western blot 1206 analysis of Sizzled-sfGFP. Green asterisks indicate full-length Sizzled fusions. C) 1207 Characterization of phenotypes after overexpression of Sizzled fusion proteins (mRNA injections 1208 at the one-cell stage equivalent to 1 pg sizzled mRNA; uninjected n = 45, Sizzled n = 49, Sizzled- 1209 FLAG n = 46, Sizzled-sfGFP n = 51). D) FRAP analysis of Sizzled-sfGFP (D = 9.7 ± 3.2 µm2/s, 1210 n = 12) effective diffusion. Data and fit from a single experiment is shown. E-J) Simulations of 1211 Model 3 using the effective diffusion coefficients of BMP2b and Chordin measured here instead 1212 of the previously assumed value D = 15 µm2/s (Inomata et al. 2013). The diffusion coefficient of 1213 Sizzled was set to 150 µm2/s in (E) and to the measured value of 10 µm2/s in (F-J). ADMP 1214 diffusivity was varied from 0.1 µm2/s to 150 µm2/s as indicated in (E-J). Gradients form over 1215 time, but the gradient evolution profiles are not consistent with the pSmad1/5/9 distribution 1216 measurements in Figure 1B. K-P) Simulations of Model 4 using the ratio of effective 1217 BMP/Chordin diffusion coefficients (i.e. Chordin is approximately two to three times more 1218 diffusive than BMP; D(BMP) = 3, D(Chordin) = 6) measured here. The diffusion coefficient of 1219 Sizzled was set to 150 in (K) as in (Francois et al. 2009) and to 10 in (L-P), reflecting the ~3-fold

31

1220 higher measured diffusivity of Sizzled compared to BMP2b. ADMP diffusivity was varied from 1221 0.1 to 150 (Francois et al. 2009) as indicated in (K-P). With 50-fold higher diffusion coefficients 1222 for ADMP and Sizzled compared to BMP (K) gradients peaking on the ventral side form over 1223 time, but with realistic diffusion ratios relevant gradients do not form (L-P). 1224 1225 Figure 5. Testing shuttling of BMP2b predicted by Model 5. A) One-dimensional model of 2 2 1226 two clones expressing BMP (green) or Chordin (blue) with DBMP = 2 μm /s, DChd = 100 μm /s, 2 1227 and DChdBMP = 100 μm /s. BMP levels increase over time due to constant production. In the 1228 presence of Chordin, the BMP gradient is deflected away from the Chordin source indicative of 1229 shuttling (compare black and red lines). Solid lines show total BMP levels (i.e., BMP + ChdBMP 1230 in the presence of Chordin), and dashed line shows free BMP levels. B) BMP gradients to the 1231 right of the BMP-expressing clone re-normalized to the BMP concentration at the boundary to 1232 show that the range of BMP is decreased between the two clones in the presence of Chordin. The 1233 main panel shows total BMP levels (i.e., BMP + ChdBMP in the presence of Chordin), and the 1234 inset shows free BMP levels (dashed lines). C) Experimental test of the predictions in (A) and 1235 (B). Clones of cells expressing BMP2b-sfGFP (green) were generated by transplanting 1236 approximately 50-75 cells from a donor embryo into wild type hosts at sphere stage (see 1237 Materials and Methods for details). Another clone of cells (red) was transplanted next to the 1238 BMP2b-sfGFP-expressing clone shortly after. The red clone is marked by the presence of 1239 fluorescent Alexa 546-coupled dextran. Cells from red-labeled clones either contained only 1240 Alexa 546-coupled dextran (Movie 9) or Alexa-546-coupled dextran and ectopic chordin mRNA 1241 (Movie 10). 15-20 min after transplantation of the clones, embryos were imaged using light sheet 1242 microscopy. The image shows gradient formation in a single optical slice approximately 20 min 1243 after transplantation. D) Quantification of average BMP2b-sfGFP gradients at ~15 min or ~75 1244 min after transplantation in embryos generated as in (C) with (red/brown) or without (black/gray) 1245 ectopic Chordin sources. Error bars denote standard error. n = 8 for each condition. E) One- 1246 dimensional simulation of two clones expressing BMP (green) or Chordin (blue) with the 2 2 1247 experimentally measured diffusion coefficients DBMP = 2 μm /s, DChd = 6 μm /s, and DChdBMP = 1248 2.2 μm2/s. BMP levels increase over time due to constant production. Solid lines show total BMP 1249 levels (i.e., BMP + ChdBMP in the presence of Chordin), and the dashed line shows free BMP 1250 levels. Only the distribution of free BMP is affected as a consequence of Chordin binding, and 1251 the gradient of total BMP is not deflected away from the Chordin source (compare solid black 1252 and red lines). F) Gradients of total BMP levels to the right of the BMP expressing clone 2 1253 simulated with the experimentally measured diffusion coefficients (DBMP = 2 μm /s, DChd = 6 2 2 1254 μm /s, and DChdBMP = 2.2 μm /s) and renormalized to the concentration at the boundary show that 1255 the range of BMP is not decreased between the two clones in the presence of Chordin.

32

1256 Movie Legends 1257 1258 Movie 1. 3D reconstruction of pSmad1/5/9 localization in a wild type sphere stage zebrafish 1259 embryo imaged by light sheet microscopy. 1260 1261 Movie 2. 3D reconstruction of pSmad1/5/9 localization in a wild type 30% epiboly stage 1262 zebrafish embryo imaged by light sheet microscopy. 1263 1264 Movie 3. 3D reconstruction of pSmad1/5/9 localization in a wild type 50% epiboly stage 1265 zebrafish embryo imaged by light sheet microscopy. 1266 1267 Movie 4. 3D reconstruction of pSmad1/5/9 localization in a wild type shield stage zebrafish 1268 embryo imaged by light sheet microscopy. 1269 1270 Movie 5. 3D reconstruction of pSmad1/5/9 localization in a wild type 60% epiboly stage 1271 zebrafish embryo imaged by light sheet microscopy. 1272 1273 Movie 6. 3D reconstruction of pSmad1/5/9 localization in a chordin-/- shield stage zebrafish 1274 embryo imaged by light sheet microscopy. 1275 1276 Movie 7. Gradient formation in a dome stage wild type embryo with a BMP2b-sfGFP clone. 1277 Imaging started approximately 15 min post-transplantation. Interval between frames: 5 min. 1278 1279 Movie 8. Gradient formation in a dome stage wild type embryo with a Chordin-sfGFP clone. 1280 Imaging started approximately 15 min post-transplantation. Interval between frames: 5 min. 1281 1282 Movie 9. Gradient formation in three representative dome stage wild type embryos with BMP2b- 1283 sfGFP clones (green) next to clones labeled with Alexa 546-coupled dextran (red). Imaging 1284 started approximately 15 min post-transplantation. Interval between frames: 5 min. Images were 1285 normalized to the mean intensity of a region close to the BMP2b-sfGFP source boundary in each 1286 embryo at the first time point, and normalized images are shown with identical 1287 minimum/maximum display settings. 1288 1289 Movie 10. Gradient formation in three representative dome stage wild type embryos with 1290 BMP2b-sfGFP clones (green) next to chordin-expressing clones labeled with Alexa 546-coupled 1291 dextran (red). Imaging started approximately 15 min post-transplantation. Interval between 1292 frames: 5 min. Images were normalized to the mean intensity of a region close to the BMP2b- 1293 sfGFP source boundary in each embryo at the first time point, and normalized images are shown 1294 with identical minimum/maximum display settings.

33

1295 Table 1. Summary of model assumptions, predictions, and experimental findings.

Model 1 Model 2 Model 3 Model 4 Model 5 Experimental Graded source- Graded source- Long-range Self-regulating Shuttling findings sink (mobile sink (immobile accumulation reaction- BMP) BMP) and feedback diffusion system

Diffusivity of D(BMP) > 0 D(BMP) ≈ 0 D(BMP) ≈ D(Chd) D(BMP) ≈ D(Chd) D(BMP) << D(BMP)  D(Chd) BMP and D(Chd) high High Low D(Chd) (≈2 and 6 µm2/s) Chordin D(BMP) < D(Chd)

Effect of Chordin Chd enhances on BMP No effect No effect No effect No effect No effect BMP diffusion diffusivity

(BMP) ≈ (Chd) Half-life of BMP (BMP) ≈ (Chd) Unconstrained (BMP) >> (Chd) (BMP) ≈ (Chd) (BMP) > (Chd)* (130 and 120 and Chordin min)

pSmad gradient Progressive rise Progressive rise Initially high Progressive rise Progressive rise Progressive rise formation ventrally, always ventrally, always dorsally and ventrally, always ventrally, always ventrally, always kinetics low dorsally low dorsally ventrally low dorsally low dorsally low dorsally

Ventral pSmad peak decreased No No No No Yes No in the absence of Chordin?

Dorso-lateral pSmad expansion in the Yes Yes Yes No Yes Yes absence of Chordin?

D(Szl) ≈ D(BMP) Diffusivity of D(ADMP) & D(ADMP) & & D(Chd) Sizzled relative NA NA D(Szl) ≈ D(BMP) D(Szl) >> D(BMP) NA (≈10, 2, and 6 to BMP/Chordin & D(Chd) & D(Chd) µm2/s)

1296 *the simplified shuttling model without ADMP presented here is based on the experimentally measured clearance rate constants of BMP and 1297 Chordin; the full model for scale-invariant patterning including ADMP (Ben-Zvi et al. 2008) assumes a lower stability of Chordin due to Xlr- 1298 mediated degradation

34

A Developmental stage sphere stage 30% epiboly 50% epiboly shield stage 60% epiboly

high

pSmad1/5/9

low

B C Model 1: Graded source-sink (mobile BMP) 1.2 1.2 sphere stage 30% epiboly 1 50% epiboly 1 shield stage 0.8 60% epiboly 0.8

0.6 0.6

0.4 0.4

0.2 0.2 Normalized pSmad intensity 0 0

0 20 40 60 80 100 Normalized free BMP concentration 0 20 40 60 80 100 ventral Embryo length (%) dorsal Embryo length (%)

D Model 2: Graded source-sink (immobile BMP) E Model 3: Long-range accumulation and feedback 1.2 1.2

1 1

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0 0 Normalized free BMP concentration Normalized free BMP concentration 0 20 40 60 80 100 0 20 40 60 80 100 Embryo length (%) Embryo length (%)

F Model 4: Self-regulating reaction-diffusion system G Model 5: Shuttling 1.2 1.2

1 1

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0 0 Normalized free BMP concentration Normalized free BMP concentration 0 20 40 60 80 100 0 20 40 60 80 100 Embryo length (%) Embryo length (%)

Figure 1 little to no diffusion moderate diffusion high diffusion

A Model 1: Graded source-sink (mobile BMP) ∂[BMP] = D ∇2[BMP] −κ [Chd][BMP]− λ [BMP]+ ρ (x) ∂t BMP BMP BMP ∂[Chd] Chd = D ∇2[Chd] −κ [Chd][BMP]− λ [Chd] BMP ChdBMP ∂t Chd Chd ∂[ChdBMP] = D ∇2[ChdBMP] + κ [Chd][BMP]− λ [ChdBMP] ∂t ChdBMP Chd

B Model 2: Graded source-sink (immobile BMP) ∂[BMP] = −κ [Chd][BMP]− λ [BMP]+ ρ (x) ∂t BMP BMP ∂[Chd] Chd = D ∇2[Chd] −κ [Chd][BMP]− λ [Chd] BMP ChdBMP ∂t Chd Chd ∂[ChdBMP] = D ∇2[ChdBMP] + κ [Chd][BMP]− λ [ChdBMP] ∂t ChdBMP Chd

C Model 3: Long-range accumulation and feedback 10 ∂[BMP] v ([ADMP] +[BMP]) λ [ChdBMP] = D∇2[BMP] + BMP − λ [BMP] + Chd − k[Chd][BMP] ∂t 10 + + 10 BMP [Szl] [Chd] +[ChdBMP] +[ChdADMP] kBMP ([ADMP] [BMP]) 1+ + ki km 10 ∂[Chd] v k λ [Chd] = D∇2[Chd] + Chd Chd − Chd − k[Chd][BMP] − k[Chd][ADMP] ∂t 10 + + 10 [Szl] [Chd] +[ChdBMP] +[ChdADMP] kChd ([ADMP] [BMP]) 1+ + ki km BMP ChdBMP 10 ∂[ADMP] v k λ [ChdADMP] Chd = D∇2[ADMP] + ADMP ADMP − λ [ADMP] + Chd − k[Chd][ADMP] ∂t 10 + + 10 BMP [Szl] [Chd] +[ChdBMP] +[ChdADMP] kADMP ([ADMP] [BMP]) 1+ + ki km 20 Szl Xlr ∂[Szl] v ([ADMP] +[BMP]) = ∇2 + Szl − λ D [Szl] Szl[Szl] ∂t k 20 + ([ADMP] +[BMP])20 Szl Chd ∂[ChdBMP] λ [ChdBMP] = D∇2[ChdBMP] − Chd + k[Chd][BMP] ADMP ChdADMP ∂t [Szl] [Chd] +[ChdBMP] +[ChdADMP] 1+ + ki km ∂[ChdADMP] λ [ChdADMP] = D∇2[ChdADMP] − Chd + k[Chd][ADMP] ∂t [Szl] [Chd] +[ChdBMP] +[ChdADMP] 1+ + ki km

D Model 4: Self-regulating reaction-diffusion system ∂[BMP] [BMP]2 = D ∇2[BMP] + − µ [BMP] + ρ ∂t BMP (1+[Chd])[Szl] BMP BMP BMP Szl ∂[Chd] [Chd]2 = D ∇2[Chd] + − µ [Chd] + ρ ∂t Chd [ADMP] Chd Chd ∂[ADMP] = D ∇2[ADMP] +[Chd]2 − µ [ADMP] ∂t ADMP ADMP Chd ADMP ∂[Szl] = D ∇2[Szl] +[BMP]2 − µ [Szl] ∂t Szl Szl

E Model 5: Shuttling ∂[BMP] = D ∇2[BMP] −κ [Chd][BMP] + λ [Xlr][ChdBMP]− λ [BMP]+ ρ (x) ∂t BMP BMP BMP ∂[Chd] = D ∇2[Chd] −κ [Chd][BMP]− λ [Chd] Chd Xlr ∂t Chd Chd BMP ChdBMP BMP ∂[ChdBMP] = D ∇2[ChdBMP] + κ [Chd][BMP] − λ [Xlr][ChdBMP]− λ [ChdBMP] ∂t ChdBMP Chd

Figure 1 - figure supplement 1 A Model 1: Graded source-sink (mobile BMP) B Model 2: Graded source-sink (immobile BMP) 1.2 1.2

1 1

0.8 0.8 wild type without Chordin 0.6 0.6

0.4 0.4

0.2 graded localized 0.2 graded localized BMP source Chordin source BMP source Chordin source 0 0

Normalized free BMP concentration 0 20 40 60 80 100 Normalized free BMP concentration 0 20 40 60 80 100 Embryo length (%) Embryo length (%)

C Model 3: Long-range accumulation and feedback D Model 4: Self-regulating reaction-diffusion system 1.2 1.2

1 1

0.8 wild type 0.8 wild type without Chordin without Chordin 0.6 0.6

0.4 0.4

0.2 uniform BMP 0.2 uniform BMP localized self-regulating production competence production competence Chordin source Chordin source with initial bias (BMP initially graded) (BMP initially graded) 0 0

Normalized free BMP concentration 0 20 40 60 80 100 Normalized free BMP concentration 0 20 40 60 80 100 Embryo length (%) Embryo length (%)

E Model 5: Shuttling F 1.2 wild type -/- 1 chordin mutant 1

0.8 0.8 wild type without Chordin 0.6 0.6

0.4 0.4

0.2 0.2 graded localized BMP source Chordin source

0 Normalized pSmad1/5/9 intensity 0

Normalized free BMP concentration 0 20 40 60 80 100 0 20 40 60 80 100 Embryo length (%) Embryo length (%) G H 1 high 0.8

0.6 pSmad1/5/9

p−value 0.4

0.2 low

-/- Wild type chordin mutant 0 0 20 40 60 80 100 Embryo length (%)

Figure 2 A B Uninjected +BMP2b +BMP2b- +BMP2b- C Uninjected +BMP2b- sfGFP Dendra2 Dendra2 BMP2b signal sequence linker 1 linker 2 BMP2b pro-domain sfGFP/Dendra2 mature domain

Furin cleavage site

Wild type BMP2b-/- mutants D E +Chordin +Chordin- +Chordin- Chordin sfGFP Dendra2 signal sequence linker 1 linker 2 Chordin NTD Chordinmature internal domain domain sfGFP/Dendra2 Chordin CTD

Tolloid cleavage site 1 Tolloid cleavage site 2

F high G high

BMP2b-sfGFP Chordin-sfGFP

H low I low 1 70 min 1 70 min 65 min 65 min 60 min 60 min 0.8 55 min 0.8 55 min 50 min 50 min 45 min 45 min 0.6 40 min 0.6 40 min 35 min 35 min 30 min 30 min 0.4 25 min 0.4 25 min 20 min 20 min

0.2 0.2

0 0 Normalized BMP2b-sfGFP intensity 0 50 100 150 200 Normalized Chordin-sfGFP intensity 0 50 100 150 200 Distance from source boundary (µm) Distance from source boundary (µm)

Figure 3 A Wild type B 100% D 100%

90% 90%

WT C1 80% 80%

70% 70%

V1 C2 60% 60%

50% 50%

V2 C3 40% 40% Percent of total Percent of total

30% 30%

C5 V3 C4 20% V4 20% C4 V3 C3 10% V2 10% C2 V1 C1 WT WT V4 C5 0% 0% Ventralized Dorsalized BMP2b BMP2b- BMP2b- Un- Chd Chd- Chd- Chd- sfGFP Dendra2 injected sfGFP Dendra2 FLAG

C BMP2b fusion constructs, anti-FLAG E Chordin fusion constructs, anti-FLAG

kDa kDa 250 Uninjected Chd-FLAG Chd-FLAG-sfGFP Chd-FLAG-Dendra2 Uninjected Chd-FLAG Chd-FLAG-sfGFP Chd-FLAG-Dendra2 Uninjected BMP2b-FLAG BMP2b-FLAG-sfGFP BMP2b-FLAG-Dendra2 Uninjected BMP2b-FLAG BMP2b-FLAG-sfGFP BMP2b-FLAG-Dendra2 * * * 100 150 * * * background * * * * 75 * * * * bands 50 * * * * * * 100 * *

37 75 25 background bands * * 50 20

10-37 extracellularly enriched fraction cellular fraction extracellularly enriched fraction cellular fraction

F G H

Uninjected BMP2b-sfGFP Chordin-sfGFP

Figure 3 - figure supplement 1 BMP2b-sfGFP gradients Chordin-sfGFP gradients

2 -5 2 2 -5 2 A R =0.88, k1=8.6 x 10 /s, D=4.0 µm /s B R =0.87, k1=9.4 x 10 /s, D=5.8 µm /s Fit with xed and free Fit with xed and free 1 k1 D 1 k1 D

0.8 0.8

0.6 0.6

0.4 0.4 Normalized intensity 0.2 Normalized intensity 0.2

0 0 0 50 100 150 0 50 100 150 Distance from source boundary (µm) Distance from source boundary (µm)

2 -5 2 2 -5 2 C R =0.83, k1=1.0 x 10 /s, D=2.7 µm /s D R =0.87, k1=12.9 x 10 /s, D=5.8 µm /s Fit with free and xed Fit with free and xed 1 k1 D 1 k1 D

0.8 0.8

0.6 0.6

0.4 0.4 Normalized intensity Normalized intensity 0.2 0.2

0 0 0 50 100 150 0 50 100 150 Distance from source boundary (µm) Distance from source boundary (µm)

2 -5 2 2 -5 2 E R =0.80, k1=8.6 x 10 /s, D=2.7 µm /s F R =0.87, k1=9.4 x 10 /s, D=5.8 µm /s Overlay with xed and xed Overlay with xed and xed 1 k1 D 1 k1 D

0.8 0.8

0.6 0.6

0.4 0.4

Normalized intensity 0.2 Normalized intensity 0.2

0 0 0 50 100 150 0 50 100 150 Distance from source boundary (µm) Distance from source boundary (µm)

2 -5 2 2 -5 2 R =−1.866, k1=7.4 x 10 /s, D=0.1 µm /s R =−3.022, k1=7.4 x 10 /s, D=0.1 µm /s G 2 -5 2 H 2 -5 2 R =−1.888, k1=11.0 x 10 /s, D=0.1 µm /s R =−3.051, k1=11.9 x 10 /s, D=0.1 µm /s 2 -5 2 2 -5 2 R =−1.873, k1=8.6 x 10 /s, D=0.1 µm /s R =−3.035, k1=9.4 x 10 /s, D=0.1 µm /s 1 2 -5 2 1 2 -5 2 R =0.807, k1=7.4 x 10 /s, D=2.7 µm /s R =0.868, k1=7.4 x 10 /s, D=5.8 µm /s 2 -5 2 2 -5 2 R =0.790, k1=11.0 x 10 /s, D=2.7 µm /s R =0.873, k1=11.9 x 10 /s, D=5.8 µm /s 2 -5 2 2 -5 2 R =0.801, k1=8.6 x 10 /s, D=2.7 µm /s R =0.872, k1=9.4 x 10 /s, D=5.8 µm /s 0.8 2 -5 2 0.8 2 -5 2 R =0.467, k1=7.4 x 10 /s, D=8.5 µm /s R =0.315, k1=7.4 x 10 /s, D=12.4 µm /s 2 -5 2 2 -5 2 R =0.541, k1=11.0 x 10 /s, D=8.5 µm /s R =0.425, k1=11.9 x 10 /s, D=12.4 µm /s 2 -5 µ 2 2 -5 µ 2 0.6 R =0.495, k1=8.6 x 10 /s, D=8.5 m /s 0.6 R =0.365, k1=9.4 x 10 /s, D=12.4 m /s

0.4 0.4 Normalized intensity 0.2 Normalized intensity 0.2

0 0 0 50 100 150 0 50 100 150 Distance from source boundary (µm) Distance from source boundary (µm)

Figure 3 - figure supplement 2 A BMP2b-Dendra2 B Chordin-Dendra2 Pre- Time post photoconversion (min) Pre- Time post photoconversion (min) photoconversion 7 107 207 photoconversion 21 121 221

1 1 Data Data Model Model

0.8 -5 0.8 -5 k1 = 8.9 x 10 /s k1 = 9.6 x 10 /s τ = 130 min τ = 120 min 0.6 0.6

0.4 0.4

0.2 0.2

0 0 Normalized extracellular intensity Normalized extracellular intensity 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Time post photoconversion (min) Time post photoconversion (min)

C BMP2b-Dendra2 D Chordin-Dendra2 Time post bleach (s) Time post bleach (s) Pre-bleach 10 300 3000 Pre-bleach 10 300 3000

1 1

0.8 0.8

0.6 0.6

0.4 0.4 D = 2.0 µm2/s D = 6.0 µm2/s Normalized intensity 0.2 Normalized intensity 0.2 Data Data Model Model 0 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time (s) Time (s)

E F p = 7 x 10-6 G /s) /s)

2 12.5 60 4 2 /s) 2

10.0 p = 6 x 10-4 45 3

p = 6 x 10-3 7.5 30 2 5.0

15 1 2.5

0 Free di usion coecient ( µ m 0 0 E ective di usion coecient ( µ m BMP2b- BMP2b- Chordin- Chordin- Sizzled- 0 BMP2b- Chordin- E ective di usion coecient ( µ m 0 BMP2b- BMP2b- BMP2b- BMP2b- Dendra2 sfGFP Dendra2 sfGFP sfGFP sfGFP sfGFP Dendra2 Dendra2 sfGFP sfGFP +Chordin +Chordin

Figure 4 Time post bleach (s) A C D Pre-bleach 10 300 3000 signal sequence linker 100% Sizzled sfGFP 90%

80%

B 70% 1 Sizzled-sfGFP

60% Dead

Uninjected Sizzled-FLAG Sizzled-FLAG- sfGFP Uninjected Sizzled-FLAG Sizzled-FLAG- sfGFP 0.8 kDa C5 100 back- 50% C4 70 C3 55 * * ground C2 0.6 40% C1

bands Percent of total WT 35 30% 0.4 25 * * = 9.8 µm2/s 20% D

Normalized intensity 0.2 15 10% Data Model extracellularly cellular fraction 0% 0 enriched fraction Un- Sizzled Sizzled- Sizzled- 0 500 1000 1500 2000 2500 3000 injected Flag sfGFP Time (s)

E Model 3 with measured D(BMP) and D(Chd) F Model 3 with measured D(BMP), D(Chd), and D(Szl) G Model 3 with measured D(BMP), D(Chd), and D(Szl) 1.2 1.2 1.2

1 1 1 D(Szl) = 150 µm2/s D(ADMP) = 150 µm2/s D(ADMP) = 150 µm2/s D(ADMP) = 100 µm2/s 0.8 0.8 0.8

0.6 0.6 0.6

0.4 sphere stage 0.4 0.4 30% epiboly 0.2 50% epiboly 0.2 0.2 shield stage 60% epiboly 0 0 0 Normalized free BMP concentration 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Embryo length (%) Embryo length (%) Embryo length (%) H Model 3 with measured D(BMP), D(Chd), and D(Szl) I Model 3 with measured D(BMP), D(Chd), and D(Szl) J Model 3 with measured D(BMP), D(Chd), and D(Szl) 1.2 1.2 1.2

1 1 1

D(ADMP) = 10 µm2/s D(ADMP) = 1 µm2/s D(ADMP) = 0.1 µm2/s 0.8 0.8 0.8

0.6 0.6 0.6

0.4 0.4 0.4

0.2 0.2 0.2

0 0 0

Normalized free BMP concentration 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Embryo length (%) Embryo length (%) Embryo length (%)

K Model 4 with measured D(BMP)/D(Chd) ratios L Model 4 with measured D(BMP)/D(Chd)/D(Szl) ratios M Model 4 with measured D(BMP)/D(Chd)/D(Szl) ratios 3.5 3.5 3.5

3 D(Szl) = 150 3 3 D(ADMP) = 150 D(ADMP) = 150 D(ADMP) = 100 2.5 2.5 2.5

2 2 2

1.5 1.5 1.5

1 1 1

0.5 0.5 0.5

0 0 0 Normalized free BMP concentration 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Embryo length (%) Embryo length (%) Embryo length (%)

N Model 4 with measured D(BMP)/D(Chd)/D(Szl) ratios O Model 4 with measured D(BMP)/D(Chd)/D(Szl) ratios P Model 4 with measured D(BMP)/D(Chd)/D(Szl) ratios 3.5 3.5 3.5

3 3 3 D(ADMP) = 10 D(ADMP) = 1 D(ADMP) = 0.1 2.5 2.5 2.5

2 2 2

1.5 1.5 1.5

1 1 1

0.5 0.5 0.5

0 0 0 Normalized free BMP concentration 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Embryo length (%) Embryo length (%) Embryo length (%)

Figure 4 - figure supplement 1 A Double clone simulations, shuttling prediction B Double clone simulations, shuttling prediction 1 1 Free BMP 1.2 with Chordin source, 75 min (total BMP) 0.8 with Chordin source, 75 min 0.6 1 0.8 (free BMP) 0.4

without Chordin source, 75 min 0.2

0.8 0

0.6 Normalized free BMP concentration 0 50 100 150 200 Distance from BMP source boundary (µm) 0.6 0.4 - Chordin source, 15 min + Chordin source, 15 min Chordin source 0.4 - Chordin source, 75 min BMP source + Chordin source, 75 min 0.2 0.2 D(BMP) = 2 µm2/s D(BMP) = 2 µm2/s D(Chordin) = 100 µm2/s D(Chordin) = 100 µm2/s

Normalized BMP concentration µ 2 µ 2 0 D(ChordinBMP) = 100 m /s 0 D(ChordinBMP) = 100 m /s 0 50 100 150 200 250 300 Normalized total BMP concentration 0 50 100 150 200 Embryo length (µm) Distance from BMP source boundary (µm)

C Double clone experiment D Double clone experiment 1 with wild type clone, ≈15 min with Chordin clone, ≈15 min with wild type clone, ≈75 min 0.8 with Chordin clone, ≈75 min

0.6

0.4

0.2

Normalized BMP2-sfGFP intensity 0 0 50 100 150 200 BMP2b-sfGFP source Chordin source Distance from BMP2-sfGFP source boundary (µm)

E Double clone simulations, measured diffusivities F Double clone simulations, measured diffusivities 1 1.2 with Chordin source, 75 min - Chordin source, 15 min (total BMP) + Chordin source, 15 min - Chordin source, 75 min 1 with Chordin source, 75 min 0.8 (free BMP) + Chordin source, 75 min without Chordin source, 75 min 0.8 0.6

0.6 0.4 0.4 Chordin source BMP source 0.2 0.2 D(BMP) = 2 µm2/s D(BMP) = 2 µm2/s D(Chordin) = 6 µm2/s D(Chordin) = 6 µm2/s

Normalized BMP concentration D(ChordinBMP) = 2.2 µm2/s D(ChordinBMP) = 2.2 µm2/s 0 0 0 50 100 150 200 250 300 Normalized total BMP concentration 0 50 100 150 200 Embryo length (µm) Distance from BMP source boundary (µm)

Figure 5