Positive feedback regulation of frizzled-7 expression robustly shapes a steep Wnt gradient in Xenopus heart development, together with sFRP1 and heparan sulfate

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    Evaluation Summary:

    Regulation of morphogen diffusion that controls tissue patterning is an important issue in developmental biology. The study deals with the mechanisms that establishes the Wnt gradient combining a mathematical model and experiments considering multiple extracellular components such as receptor and diffusible antagonist. The study revealed that the ligand/receptor feedback enables robust and quick formation of the morphogen gradient and that the diffusible antagonist also plays a role in this process. With some strengthening of experimental data and better explanation of the modeling, this study will be a useful contribution to the field.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)

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Abstract

Secreted molecules called morphogens govern tissue patterning in a concentration-dependent manner. However, it is still unclear how reproducible patterning can be achieved with diffusing molecules, especially when that patterning concerns differentiation of thin tissues. Wnt is a morphogen that organizes cardiac development. Wnt6 patterns cardiogenic mesoderm to induce differentiation of a thin tissue, the pericardium, in Xenopus . In this study, we revealed that a Wnt receptor, frizzled-7 , is expressed in a Wnt-dependent manner. With a combination of experiments and mathematical modeling, this receptor-feedback appears essential to shape a steep gradient of Wnt signaling. In addition, computer simulation revealed that this feedback imparts robustness against variations of Wnt ligand production and allows the system to reach a steady state quickly. We also found that a Wnt antagonist sFRP1, which is expressed on the opposite side of the Wnt source, accumulates on N-acetyl-rich heparan sulfate (HS). N-acetyl-rich HS concentration is high between the sources of Wnt and sFRP1, achieving local inhibition of Wnt signaling via restriction of sFRP1 spreading. These integrated regulatory systems restrict the Wnt signaling range and ensure reproducible patterning of the thin pericardium.

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  1. Author Response:

    Reviewer #1:

    The aim of this paper to reveal the mechanisms that establish the Wnt gradient combining a mathematical model and experiments is of general importance. The results of computer simulations and biological experiments are interesting because they consider multiple extracellular components. They successfully demonstrated that the ligand/receptor feedback and the other extracellular components shape the morphogen gradient of Wnt ligand so that the fine patterning found in heart development can be explained. However, I feel that quantification of the experimental data, explanation of the mathematical model and discussion of the results are not sufficient in the current manuscript.

    Major points:

    1. Experimental validation of the results of computer simulations is very important in this study. However, many of experimental data were not properly quantified or statistically tested. The authors would need to quantify the experimental results when appropriate and perform statistical tests (e.g. Figs. 1E, 2A, 4A-B, Supplemental Figs. 6, 7).

    We are sorry for the lack of quantitative and statistical analyses in many experiments. We revised all the points (graphs and statistical analyses in Figs 1, 2, 4; Figure 1-figure supplement 1; Figure 3-figure supplement 7; Figure 4-figure supplement 1, 2).

    1. Design of the mathematical model is not sufficiently explained in the main text. Besides details in the method section, the basic design of the model and simulation should be briefly explained. For example, initial distribution of Fzd7, regions that produce Wnt6 and sFRP1, and interpretation of the simulation results should be added for Fig. 3 (page 10, line 11-16).

    We are sorry for the inconvenience. In this revision, we wrote the basic design of the model and simulation in the main text.

    As an interpretation of the simulation results, we added an explanation as follows:

    The Wnt signaling gradient became steeper with increased feedback strength. Considering a threshold of signal activation (Fig. 3A, dashed line), feedback results in restriction of the Wnt-activated region.

    1. The authors demonstrated the roles of Wnt6/Fzd7 feedback and sFRP/Heparan sulfate binding. A typical simulation data showing the roles of sFRP and Heparan sulfate would need to be shown in the main figure.

    Thank you for your suggestions. We moved a typical result of sFRP/HS simulation from the original supplemental figure to a main figure (Fig. 4G).

    Unfortunately, they did not sufficiently discuss their actions using the mathematical model. They would need to at least qualitatively discuss these points. How do they control Wnt gradient? What are the roles of these two mechanisms? What are the difference? How do they influence with each other? Simplified models may be necessary to reveal the relationship between these two mechanisms and to gain mechanistic insights.

    Thank you for pointing out these critical points.

    For Wnt gradients, receptor feedback, sFRP, and HS are synergistically acting for the restriction of signal activated region (steep gradient).

    However, there are some differences. The receptor-feedback can overcome the variation of Wnt production but sFRP1 and HS cannot because sFPR1 expression is inhibited by Wnt, which forms a positive feedback loop for Wnt signaling (Gibb et al., 2013). Thus, sFRP1/HS cannot buffer the variation of Wnt production.

    In this revision, we added these explanations.

    [They will influence each other] Because sFRP1 inhibits Wnt signaling, sFRP1 reduces fzd7 expression. This occurs mainly in the right side (because sFRP1 is expressed in the right side), resulting in a short-range activation of Wnt signaling.

    Deeply considering your comments, we recognized that we did not describe sFRP1/HS function in the title of the previous version. We revised it as follows:

    Previous) Positive Feedback Regulation of fzd7 Expression Robustly Shapes Wnt Signaling Range in Early Heart Development

    Current) Positive feedback regulation of fzd7 expression robustly shapes a steep Wnt gradient in early heart development, together with sFRP1 and heparan sulfate

    Additionally, the situation studied in this paper would need to be compared with the other examples of ligand/receptor feedback, and the similarity and difference should also be discussed (e.g. Hedgehog/Patched and Wingless/Frizzled2 in the fly wing).

    Thank you for your helpful comments.

    As you mentioned, the gene regulatory circuit of our Wnt6/Fzd7 is similar to that of Hedgehog (Hh)/Patched (Ptc): both of the morphogens commit self-enhanced degradation via induction of receptor expression (Eldar et al., 2003; Hh induces Ptc expression, and this increases Hh degradation). In the case of Wingless/Frizzled2, the gene regulatory circuit is different from that of Wnt6/Fzd7: Wingless commits self-enhanced degradation via repression of receptor expression. Wingless inhibits Fzd2 expression, and Fzd2 inhibits Wingless degradation. Both gene regulatory circuits function as a robust system for morphogen variations (Alon, 2006).

    There is also a little difference between Wnt6/Fzd7 and Hh/Ptc. In the Hh, the receptor Ptc inhibits downstream signaling. Thus, the network of Hh restricts the ligand distribution as is the case with Wnt, but the signal activity is not as steep as Wnt (highly Ptc expression inhibits the signaling).

    We added these explanations.

    Reviewer #2:

    In this work, the authors tried to understand the effect of receptor and diffusible inhibitors on the Wnt morphogen gradient during heart development by combining experiment and computational modeling. The experimental part seems to be a solid contribution to this academic field, and I appreciate the interdisciplinary attempt to combine the results with the computational model. However, their results may be interpreted more clearly using classical mathematical models.

    First of all, we greatly thank you for evaluating our manuscript. And thank you very much for explaining classical models in detail.

    1. Classical models may be enough.

    Previous mathematical models provided stronger predictions than numerical simulations, and I am not sure numerical results provided by the authors give us new insights. For example, Eldar et al. (2003) have provided analytical results on why the concentration becomes robust. In normal SDD model

    u'(x,t) = -d_1 u(x,t) + d_u \Delta u(x,t),

    the steady-state solution is exponential function,

    u_s(x) = u_0 exp(- \sqrt (d_1/d_u)x)

    , and the amount of morphogen production at the boundary critically affects the result (If the production becomes 1/2, the concentration becomes 1/2 everywhere). On the other hand, if the degradation is promoted by the morphogen itself (in this case, by the upregulation of the receptor expression), the governing equation becomes

    u'(x,t) = -d_2 u(x,t)^2 + d_u \Delta u(x,t),

    the solution is

    u_s(x) =A/(x+x_b)^2

    ($A$ and $x_b$ are constants determined by $d_u$ and $d_2$). It converges to

    u_s(x) =A/x^2

    and the morphogen gradient profile does not change much when the morphogen production is relatively high (that means there is a condition to be robust).

    Similarly, a linear approximation is enough to understand the diffusion length change - diffusion length of the morphogen gradient (the length necessary to become morphogen concentration 1/e) is in general $\sqrt{D_u /d_1}$, and feedback mechanism should increase d_1 in first-order estimation, hence decreasing the diffusion length. Binding to HSPG may have a similar effect (in the case of FGF, HSPG is necessary to the binding of FGFR, and the situation is very different).

    Thank you again for your explanations. Our explanations in the previous manuscript were not enough.

    –Difference of our computational simulation and the classical analysis:

    We think we need numerical simulation to consider points not addressed with previous analytical methods. The following two points are the new points that are too complicated to handle with analytical methods.

    1. Transient state is considered, which is hard to analyze without computer simulation.

    Considering the in vivo situation, we cannot determine whether the fate determination takes place at a transient or steady state (as described in page 7, line 14). So, we analyzed it not limited to a steady state but including transient state in our simulation.

    1. Receptor has multiple functions in interaction with multiple molecule species: (i) binds to the ligand and restricts the ligand spreading, (ii) activates the intracellular signaling, and (iii) degrade the ligand (new Supplementary Fig. 1A). We would like to include these different functions separately in the simulation. In addition, we considered sFRP1 and N-acetyl-rich HS. Thus, we need a multivariate nonlinear reaction-diffusion equation, which is hard to handle without computer simulation.

    To clarify these points, we added an explanation of the multiple receptor functions with a schematic figure (Supplementary Fig. 1A).

    –Importance/significance of our simulation:

    We first confirmed that our simulation reached a similar conclusion as the classical simulation at a certain time point (~ 1 day after the onset of simulation): the network was robust against variation of Wnt production. In addition, examining the time change of activation level, we have found that this network is robust against changes in speed of the differentiation. We added these explanations.

    1. Biological example of Wnt fluctuation

    The authors examine the effect of Wnt production fluctuation, but their motivation is not clear. Eldar et al. (2003) is motivated by the fact that the Shh heterozygote knockout has no phenotype, although the amount of mRNA is halved. Theoretically, it should have a major effect on the organs utilizing the Shh morphogen gradient (actually, haploinsufficiency is observed, but the phenotype is mild). The authors would need to provide some argument why they are interested in the robustness to the Wnt expression fluctuation.

    We all agree with your opinion. Compared with Eldar et al. (2003), our motivation is not clear to set 50% for the variance of ligand production.

    It is generally accepted that gene expression is different between individuals. In contrast, the proportions of the patterned tissues are almost the same among individuals.

    We examine this general question in our specific example of Wnt production. Here we focused on an extreme example (50% increase) among various sizes of gene expression.

    We added a phrase “as an extreme case” to clarify that it is an example in the revised manuscript.

    1. Wnt signal distribution

    It is difficult for general readers to understand why the Wnt signal distribution in the simulations (0 around 0-10 µm, Sudden disappearance at 40 µm) is appropriate. The authors can provide the profile plot of the actual measurement, which corresponds to the modeling result.

    Sorry for this inconvenience. As indicated in Figure 1—figure supplement 1B, Fzd7 shows a limited expression in pericardium. Fzd7 expression was not detected in epidermis (Figure 1—figure supplement 1B), which is the Wnt source (Lavery et al., 2008), indicating that the sudden increase of Fzd7 expression near Wnt source (at x = 10 μm) is reasonable (because the amount of Wnt at x = 10 μm is considered to be above the threshold for Fzd7 expression). In the prospective myocardium region, Fzd7 expression was also disappeared suddenly (Figure 1—figure supplement 1B), suggesting that the activity of Wnt signaling is also disappeared suddenly in the region. We added the explanations.

    In addition to the indirect estimation of Wnt signaling from Fzd7 expression, to directly confirm the “sudden disappearance” of Wnt signaling, we tried following three ways, but they failed. We examined (i) a transgenic reporter line of Wnt signaling (TCF-promoter-driven GFP) and (ii) immunohistochemistry (IHC) of beta-catenin (nucleus localization of beta-catenin is an indicator of the activation of Wnt signaling) and (iii) IHC of active beta-catenin (which only detect the active form of beta-catenin), expecting more gradual signal distribution, compared to the readout of Fzd7 expression which may have a threshold to express. But (i) the background signal was high in the transgenic. (ii) The background signal was also high with IHC maybe because beta-catenin is abundant also in the cytoplasm in heart region. (iii) The signal of active beta-catenin was not changed by Wnt addition in Xenopus.

    In addition, about the width of wnt6 and fzd7 expression, we measured the actual size of the fzd7-expressed region (Figure 1—figure supplement 1B), which was around 32 μm. It was almost the same as that in the model (30 μm). The width of Wnt6-expressed region was set to be 10 μm following a previous report (Lavery et al., 2008). We added explanations for the width of the expressions.

    1. Variable "Wnt signal"

    It is not clear what the variable "Wnt signal" means. As far as I understand, the signal inside the cell changes quickly (in the case of FGF, the ERK phosphorylation state changes within a minute). The author should provide a concrete example of this "Wnt signal" (maybe mRNA expression of some marker gene?).

    We agree with your opinion. As an indicator of Wnt signal activation, we think of the translocation of β-catenin (a transcriptional regulator) into the nucleus. Indeed, the translocation is observed at least in a 15 min and concurrently the transcription of the target gene is observed (Kafri et al., 2016), suggesting this translocation (the activation of the signal in the cells) is recognized enough by the cells within a minute. We added this explanation.

    1. Use of BMP measurement values.

    In addition, I am not sure whether using BMP values for the estimate of Wnt dynamics is appropriate. I have an impression that BMP is a fast-diffusing molecule that has a less binding affinity to ECM compared to FGFs. Although I have not dealt with Wnts, they are reported to bind strongly to ECM.

    Thank you for the comments. In this revision, we used all of the reported Wnt values. According to this parameter change, we performed computer simulation again. All the conclusions were not changed.

    Reviewer #3:

    A summary of the study and the strengths of this manuscript: The authors found several new molecular interactions that may be essential for understanding the mechanism of steep gradient formation of Wnt ligands in the prospective cardiac field.

    One of the new findings is that expression of a Wnt receptor, Frizzled7, in the prospective heart field is activated by Wnt/b-catenin signaling, as well as by Wnt6 ligands, which is involved in the patterning of this field. They also found that the diffusing Wnt6 ligand is trapped at the surface of cells in which Frizzled7 is ectopically expressed. It seems reasonable that the combination of signal-dependent receptor expression and receptor-dependent ligand capture would result in a steep gradient of morphogen molecules. In fact, this idea is supported by mathematical modeling. In addition, this modeling suggests that the receptor feedback mechanism provides robustness to morphogen-mediated patterning against fluctuations in morphogen production.

    Another highlight of their study is that the soluble Wnt antagonist, sFRP1, specifically binds to N-acetyl HS, and this modification of HS is specifically detected in the outer of the cardiogenic field. The localized N-acetyl HS may also be involved in Wnt gradient formation by inhibiting Wnt signaling around myocardium region.

    The weaknesses of this manuscript: Although the issue they address in this manuscript is very important for understanding the mechanism of morphogen-based tissue patterning, most of the experimental data presented in this manuscript are preliminary.

    We added and revised many experiments (including computational analysis) in this revision. In particular, in Figs 1, 2, 4; Figure 1-figure supplement 1; Figure 3-figure supplement 7; Figure 4-figure supplement 1, 2.

    Therefore, interpretations other than the ones they have argued for in this manuscript are quite possible. any other interpretations except those they claimed in this manuscript are still possible.

    For example, the authors argue that receptor feedback is essential for the formation of steep Wnt gradients (lines 8-9 in the abstract), but their model does not rule out an alternative possibility that high levels of receptor expression in the cardiogenic field form steep gradients.

    We agree.

    As you mentioned, high levels of receptor expression can form steep gradients. In a case distributions are similar with and without feedback, the changes in the boundary position in response to Wnt production change seemed smaller with feedback than without (Fig. 3B), providing a possibility that feedback has higher robustness to the variation.

    These explanations were poor in the previous version. We added explanation.

    In addition, it would be a waste of energy because too much receptor expression is needed. If the initial expression of receptor is critical for the patterning (not the receptor feedback), the amount and the area should be tightly controlled by an additional mechanism.

    We added these explanations to the result and discussion sections.

    Furthermore, they have not succeeded in directly examining the effect of receptor feedback on Wnt6 gradient formation. Although the data shown in Supplementary Figure 6E appear to support the contribution of feedback mechanisms to patterning, the results do not exclude another interpretation that an increase in Wnt trapper molecules simply inhibits the receptor-mediated clearance of Wnt ligands from the extracellular space in the pericardial region, resulting in an increase of extracellular Wnt ligands and their long-range transport.

    Thank you for your comment. As you mentioned, the Wnt trapper inhibits clearance. However, at the same time as it inhibits clearance, it also inhibits diffusion of Wnt. These two inhibitions happen simultaneously for the same duration. Thus, the trapper will not promote long-range transport via competitive inhibition of the Wnt clearance.

    Thus, from the results using the trapper, we can conclude that the receptor expressed after the activation of Wnt signal (not the initial amount of receptor) is critical for determining the range of Wnt signaling (e.g. the width of the resulting pericardium).

    We added these explanations in the new text.

    With regard to the restriction of sFRP1 diffusion, no evidence has been presented to show that N-acetyl modification of HS is actually involved in the restriction of sFRP1 diffusion, the formation of Wnt gradient, and the patterning of prospective cardiac fields. This lack of data significantly undermines the credibility of the conclusions presented in this paper.

    We performed a new experiment.

    We overexpressed Ndst1 enzyme that modifies N-acetyl to N-sulfo HS to eliminate N-acetyl HS, and analyzed if heart patterning is changed. We revealed that Ndst1 expression results in a reduced pericardium but an increased myocardium region, suggesting that N-acetyl HS promotes pericardium differentiation and inhibits myocardium differentiation.

    We added these explanations and figures (Fig. 4F; Figure 4-figure supplement 2A-C).

  2. Evaluation Summary:

    Regulation of morphogen diffusion that controls tissue patterning is an important issue in developmental biology. The study deals with the mechanisms that establishes the Wnt gradient combining a mathematical model and experiments considering multiple extracellular components such as receptor and diffusible antagonist. The study revealed that the ligand/receptor feedback enables robust and quick formation of the morphogen gradient and that the diffusible antagonist also plays a role in this process. With some strengthening of experimental data and better explanation of the modeling, this study will be a useful contribution to the field.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)

  3. Reviewer #1 (Public Review):

    The aim of this paper to reveal the mechanisms that establish the Wnt gradient combining a mathematical model and experiments is of general importance. The results of computer simulations and biological experiments are interesting because they consider multiple extracellular components. They successfully demonstrated that the ligand/receptor feedback and the other extracellular components shape the morphogen gradient of Wnt ligand so that the fine patterning found in heart development can be explained. However, I feel that quantification of the experimental data, explanation of the mathematical model and discussion of the results are not sufficient in the current manuscript.

    Major points
    1. Experimental validation of the results of computer simulations is very important in this study. However, many of experimental data were not properly quantified or statistically tested. The authors would need to quantify the experimental results when appropriate and perform statistical tests (e.g. Figs. 1E, 2A, 4A-B, Supplemental Figs. 6, 7).

    2. Design of the mathematical model is not sufficiently explained in the main text. Besides details in the method section, the basic design of the model and simulation should be briefly explained. For example, initial distribution of Fzd7, regions that produce Wnt6 and sFRP1, and interpretation of the simulation results should be added for Fig. 3 (page 10, line 11-16).

    3. The authors demonstrated the roles of Wnt6/Fzd7 feedback and sFRP/Heparan sulfate binding. A typical simulation data showing the roles of sFRP and Heparan sulfate would need to be shown in the main figure. Unfortunately, they did not sufficiently discuss their actions using the mathematical model. They would need to at least qualitatively discuss these points. How do they control Wnt gradient? What are the roles of these two mechanisms? What are the difference? How do they influence with each other? Simplified models may be necessary to reveal the relationship between these two mechanisms and to gain mechanistic insights.

    Additionally, the situation studied in this paper would need to be compared with the other examples of ligand/receptor feedback, and the similarity and difference should also be discussed (e.g. Hedgehog/Patched and Wingless/Frizzled2 in the fly wing).

  4. Reviewer #2 (Public Review):

    In this work, the authors tried to understand the effect of receptor and diffusible inhibitors on the Wnt morphogen gradient during heart development by combining experiment and computational modeling. The experimental part seems to be a solid contribution to this academic field, and I appreciate the interdisciplinary attempt to combine the results with the computational model. However, their results may be interpreted more clearly using classical mathematical models.

    1. Classical models may be enough.

    Previous *mathematical* models provided stronger predictions than numerical simulations, and I am not sure numerical results provided by the authors give us new insights. For example, Eldar et al. (2003) have provided analytical results on why the concentration becomes robust. In normal SDD model

    u'(x,t) = -d_1 u(x,t) + d_u \Delta u(x,t),

    the steady-state solution is exponential function,

    u_s(x) = u_0 exp(- \sqrt (d_1/d_u)x)

    , and the amount of morphogen production at the boundary critically affects the result (If the production becomes 1/2, the concentration becomes 1/2 everywhere). On the other hand, if the degradation is promoted by the morphogen itself (in this case, by the upregulation of the receptor expression), the governing equation becomes

    u'(x,t) = -d_2 u(x,t)^2 + d_u \Delta u(x,t),

    the solution is

    u_s(x) =A/(x+x_b)^2

    ($A$ and $x_b$ are constants determined by $d_u$ and $d_2$). It converges to

    u_s(x) =A/x^2

    and the morphogen gradient profile does not change much *when the morphogen production is relatively high* (that means there is a condition to be robust).

    Similarly, a linear approximation is enough to understand the diffusion length change -
    diffusion length of the morphogen gradient (the length necessary to become morphogen concentration 1/e) is in general $\sqrt{D_u /d_1}$, and feedback mechanism should increase d_1 in first-order estimation, hence decreasing the diffusion length. Binding to HSPG may have a similar effect (in the case of FGF, HSPG is necessary to the binding of FGFR, and the situation is very different).

    2. Biological example of Wnt fluctuation

    The authors examine the effect of Wnt production fluctuation, but their motivation is not clear. Eldar et al. (2003) is motivated by the fact that the Shh heterozygote knockout has no phenotype, although the amount of mRNA is halved. Theoretically, it should have a major effect on the organs utilizing the Shh morphogen gradient (actually, haploinsufficiency is observed, but the phenotype is mild). The authors would need to provide some argument why they are interested in the robustness to the Wnt expression fluctuation.

    3. Wnt signal distribution

    It is difficult for general readers to understand why the Wnt signal distribution in the simulations (0 around 0-10 µm, Sudden disappearance at 40 µm) is appropriate. The authors can provide the profile plot of the actual measurement, which corresponds to the modeling result.

    4. Variable "Wnt signal"

    It is not clear what the variable "Wnt signal" means. As far as I understand, the signal inside the cell changes quickly (in the case of FGF, the ERK phosphorylation state changes within a minute). The author should provide a concrete example of this "Wnt signal" (maybe mRNA expression of some marker gene?).

    5. Use of BMP measurement values.

    In addition, I am not sure whether using BMP values for the estimate of Wnt dynamics is appropriate. I have an impression that BMP is a fast-diffusing molecule that has a less binding affinity to ECM compared to FGFs. Although I have not dealt with Wnts, they are reported to bind strongly to ECM.

  5. Reviewer #3 (Public Review):

    A summary of the study and the strengths of this manuscript:
    The authors found several new molecular interactions that may be essential for understanding the mechanism of steep gradient formation of Wnt ligands in the prospective cardiac field.

    One of the new findings is that expression of a Wnt receptor, Frizzled7, in the prospective heart field is activated by Wnt/b-catenin signaling, as well as by Wnt6 ligands, which is involved in the patterning of this field. They also found that the diffusing Wnt6 ligand is trapped at the surface of cells in which Frizzled7 is ectopically expressed. It seems reasonable that the combination of signal-dependent receptor expression and receptor-dependent ligand capture would result in a steep gradient of morphogen molecules. In fact, this idea is supported by mathematical modeling. In addition, this modeling suggests that the receptor feedback mechanism provides robustness to morphogen-mediated patterning against fluctuations in morphogen production.

    Another highlight of their study is that the soluble Wnt antagonist, sFRP1, specifically binds to N-acetyl HS, and this modification of HS is specifically detected in the outer of the cardiogenic field. The localized N-acetyl HS may also be involved in Wnt gradient formation by inhibiting Wnt signaling around myocardium region.

    The weaknesses of this manuscript:
    Although the issue they address in this manuscript is very important for understanding the mechanism of morphogen-based tissue patterning, most of the experimental data presented in this manuscript are preliminary. Therefore, interpretations other than the ones they have argued for in this manuscript are quite possible. any other interpretations except those they claimed in this manuscript are still possible.

    For example, the authors argue that receptor feedback is essential for the formation of steep Wnt gradients (lines 8-9 in the abstract), but their model does not rule out an alternative possibility that high levels of receptor expression in the cardiogenic field form steep gradients. Furthermore, they have not succeeded in directly examining the effect of receptor feedback on Wnt6 gradient formation. Although the data shown in Supplementary Figure 6E appear to support the contribution of feedback mechanisms to patterning, the results do not exclude another interpretation that an increase in Wnt trapper molecules simply inhibits the receptor-mediated clearance of Wnt ligands from the extracellular space in the pericardial region, resulting in an increase of extracellular Wnt ligands and their long-range transport.

    With regard to the restriction of sFRP1 diffusion, no evidence has been presented to show that N-acetyl modification of HS is actually involved in the restriction of sFRP1 diffusion, the formation of Wnt gradient, and the patterning of prospective cardiac fields. This lack of data significantly undermines the credibility of the conclusions presented in this paper.