Cellular compartmentalisation and receptor promiscuity as a strategy for accurate and robust inference of position during morphogenesis
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eLife assessment
This work is of high relevance to developmental and quantitative biologists with an interest in morphogen-mediated position decoding. A general mathematical model formulation is presented that is nevertheless accessible to a broad audience. Model tests via perturbation experiments in the Drosophila wing disc look promising and inspire a new round of data generation.
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Abstract
Precise spatial patterning of cell fate during morphogenesis requires accurate inference of cellular position. In making such inferences from morphogen profiles, cells must contend with inherent stochasticity in morphogen production, transport, sensing and signalling. Motivated by the multitude of signalling mechanisms in various developmental contexts, we show how cells may utilise multiple tiers of processing (compartmentalisation) and parallel branches (multiple receptor types), together with feedback control, to bring about fidelity in morphogenetic decoding of their positions within a developing tissue. By simultaneously deploying specific and nonspecific receptors, cells achieve a more accurate and robust inference. We explore these ideas in the patterning of Drosophila melanogaster wing imaginal disc by Wingless morphogen signalling, where multiple endocytic pathways participate in decoding the morphogen gradient. The geometry of the inference landscape in the high dimensional space of parameters provides a measure for robustness and delineates stiff and sloppy directions. This distributed information processing at the scale of the cell highlights how local cell autonomous control facilitates global tissue scale design.
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Author Response
Reviewer #1 (Public Review):
Iyer et al. address the problem of how cells exposed to a graded but noisy morphogen concentration are able to infer their position reliably, in other words how the positional information of a realistic morphogen gradient is decoded through cell-autonomous ligand processing. The authors introduce a model of a ligand processing network involving multiple ”branches” (receptor types) and ”tiers” (compartments where ligand-bound receptors can be located). Receptor levels are allowed to vary with distance from the source independently of the morphogen concentration. All rates, except for the ligand binding and unbinding rates, are potentially under feedback control. The authors assume that the cells can infer their position from the output of the signalling network in an optimal way. The …
Author Response
Reviewer #1 (Public Review):
Iyer et al. address the problem of how cells exposed to a graded but noisy morphogen concentration are able to infer their position reliably, in other words how the positional information of a realistic morphogen gradient is decoded through cell-autonomous ligand processing. The authors introduce a model of a ligand processing network involving multiple ”branches” (receptor types) and ”tiers” (compartments where ligand-bound receptors can be located). Receptor levels are allowed to vary with distance from the source independently of the morphogen concentration. All rates, except for the ligand binding and unbinding rates, are potentially under feedback control. The authors assume that the cells can infer their position from the output of the signalling network in an optimal way. The resulting parameter space is then explored to identify optimal ”network architectures” and parameters, i.e. those that maximise the fidelity of the positional inference. The analysis shows how the presence of both specific and non-specific receptors, graded receptor expression and feedback loops can contribute to improving positional inference. These results are compared with known features of the Wnt signalling system in Drosophila wing imaginal disc.
The authors are doing an interesting study of how feedback control of the signalling network reading a morphogen gradient can influence the precision of the read-out. The main strength of this work is the attention to the development of the mathematical framework. While the family of network architectures introduced here is not completely generic, there is enough flexibility to explore various features of realistic signalling systems. It is exciting to find that some network topologies are particularly efficient at reducing the noise in the morphogen gradient. The comparison with the Wnt system in Drosophila is also promising.
Major comments:
- The authors assume that the cell estimates its position through the maximum a posteriori estimate, Eq.(5), which is a well-defined mathematical object; it seems to us however that whether the cell is actually capable of performing this measurement is uncertain (it is an optimal measurement in some sense, but there is no guarantee that the cell is optimal in that respect). Notably, this entails evaluating p(theta), which is a probability distribution over the entire tissue, so this estimate can not be done with purely local measurements. Can the authors comment on this and how the conclusions would change if a different position measurement was performed?
This is indeed an important question. Our viewpoint is that if the cells were to use a maximum a posteriori (MAP) estimate (Eq. 5) to decode their positions, then what features of the channel architecture would lead to small errors in positional inference. Whether the maximum a posteriori estimate is employed by the cell, or some other estimate, is an important but difficult question to address. Our choice has been motivated by how this estimate has allowed the precise determination of developmental fates in the context of gap gene expression in Drosophila embryo [1, 2, 3]. We had earlier computed the inference error with a different estimate i.e.
which computes the mean squared deviations of the inferred positions from the true position for each x, taking into account the entire distribution p(x∗|x). While the qualitative results are the same, the inference errors showed spurious jitters from outliers in sampling the noisy morphogen input distribution. This consistency might suggest that our qualitative results are insensitive to the choice of the estimate.
Further, when evaluating the MAP estimate, the term p(θ) in the denominator serves as a normalisation factor to ensure p(x|θ) is a probability density. This is not strictly necessary for MAP estimation. Since p(θ) does not depend on x, the MAP estimate can be written as follows
without the need for evaluating p(θ). In the case of a uniform prior, it would be equivalent to maximum likelihood estimate (MLE) i.e.
- One of the features of the signalling networks studied in the manuscript is the ability of the system to form a complex (termed a conjugated state, Q) made of two ligands L, one receptor and one nonsignalling receptor. While there are clear examples of a single ligand binding to two signalling receptors (e.g. Bmps), are there also known situations where such a complex with two ligands, one receptor, and one non-signalling receptor can form? In the Wnt example (Fig. 10a), it is not clear what this complex would be? In general, it would be great to have a more extended discussion of how the model hypothesis for the signalling networks could relate to real systems.
This is a good suggestion. We have now added a discussion on the various possible realisations of the “conjugate state” Q in Section 3.6. We have also explored the various states in the context of different signalling contexts such as Dpp, Hh, Fgf in the Discussion section.
The conjugated state ‘Q’ represents a combination of the readings from the two branches i.e. receptor types. This could be realised through processes like ligand exchange or complex formation, both in a shared spatial location such as a compartment. As discussed in the original manuscript (Section 3.6 of the revised manuscript), the ligand Wg in the Wg signalling pathway is internalised through two separate endocytic pathways associated with the receptor types - signalling receptor Frizzled (via Clathrin-mediated endocytosis (CME)) and non-signalling receptor HSPGs (via the CLIC/GEEC pathway (CLIC - (clathrin-independent carriers, GEEC - GPI-anchored protein-enriched early endosomal compartments)). Both pathways meet in a common early endosomal compartment where the ligands may be exchanged between the two receptors [4]. In a previous work by Hemalatha et al [4], we had shown that there are more Wg-DFz2 interactions in the endosomal compartment (measured through FRET) than on the cell surface. Therefore, the non-signalling receptors directing Wg through the CLIC/GEEC pathway titrate the amount of Wg interaction with the signalling receptor, DFz2.
As mentioned in the original manuscript (Section 3.3 and subsection 4.2 of the Discussion in the revised manuscript), apart from Wg signalling, non-signalling receptors such as the HSPGs have also been proposed to act as co-receptors for Dpp, Hh, FGF (reviewed in [5, 6]). Although some ligands bind to the core protein of HSPG, the majority of the ligands bind to the negatively charged HS chains [7, 8]. Here, the coreceptors HSPGs aid in capturing diffusible ligands and presenting the same to signalling receptors (either on the cell surface or within endosomes).
- The authors consider feedback on reaction rates - it would seem natural to also consider feedback on the total number of receptors; notably, since there are known examples of receptors transcriptionally down-regulated by their ligands (e.g. Dpp/Tkv)? Also it is not clear in insets such as in Fig. 7b, if the concentration plotted corresponds to the concentration of receptors bound to ligands?
As mentioned in the original manuscript (Section 2.2 of the revised manuscript), we have indeed considered control on reaction rates and receptors, although the control on the latter is done with the constraint of receptor profiles being monotonic. Further, while the control on reaction rates is considered via feedbacks explicitly, the control on receptors is done via an approach akin to the openloop control used in control theory. In reality, cellular control on receptors will involve transcriptional up- or down-regulation of receptor and thus warrant a feedback control approach – however, the timescales involved in such a control are different from the binding-unbinding and signalling timescales.
Therefore, in the current work, we take the morphogen profile to be given i.e. independent of receptor concentrations, and we ask for the receptor concentrations that would help reduce the inference errors.
Our predictions of increasing signalling receptor and decreasing non-signalling receptors in a twobranch channel architecture are consistent with the known transcriptional up-regulation of Dally/Dlp and down-regulation of Fz by Wg signalling [9].
In a future work, we will extend the control on receptors to include feedbacks explicitly. Furthermore, the explicit feedback control on receptors may need to be considered concomitantly with the effect of receptors on morphogen dynamics (i.e. morphogen sculpting by receptors) along with the possibility of spatial correlations in receptor concentrations through neighbouring cell-cell interactions.
As mentioned in the original manuscript (Section 2.2 of the revised manuscript), the variables ψ and φ stand for the total (bound + unbound) surface receptor concentrations of the signalling and the non-signalling receptors respectively. Therefore, the insets showing receptor profiles such as in Fig. 6b, 7b, and Appendix H Fig.8b,e correspond to the total surface receptor concentrations.
- The authors are clear about the fact that they consider the morphogen gradient to be fixed independently of the reaction network; however, that seems like a very strong assumption; in the Dpp morphogen gradient for instance over expression of the Tkv receptor leads to gradient shortening. Can the authors comment on this?
This point is related to the earlier question 4. As discussed in the Discussion of the original manuscript (subsection 4.3 of the revised manuscript), we focus on finding the optimal receptor concentration profiles and reaction networks that enable precision and robustness in positional information from a given noisy morphogen profile. The framework and the optimisation scheme within it will prescribe different receptor profiles and reaction networks for different monotonically behaving, noisy morphogen profiles. It is possible that cells may achieve the optimal receptor concentrations via feedback control on production of the receptors.
Broadly, morphogen dynamics depends on cell surface receptors, which could participate in both the inference and the sculpting of the morphogen profile, and factors independent of them such as extracellular degradation, transport and production, etc. In our present work, we have taken the receptors involved in sculpting and inference as being independent.
In a more general case, feedback control on receptors will change the receptor concentrations as well as the morphogen profile. We are currently working on realising such a feedback control on receptors within the same broader information theoretic framework proposed in the current work.
- Fig. 10f is showing an exciting result on the change in endocytic gradient CV in the WT and in DN mutant of Garz. Can the authors check that the Wg morphogen gradient is not changing in these two conditions? And can they also show the original gradient, and not only its CV?
The reviewer raises a legitimate concern – could the observed changes in CV upon perturbation of endocytic machinery be attributed to a systematic change in the mean levels of the endocytosed Wg alone? In the original manuscript (Appendix O Fig.17b,c of the revised manuscript), we show the normalised profiles of endocytic Wg in control and myr-Garz-DN cases. Here, in Fig.1 below, we show a comparison between the mean Wg concentrations (measured as fluorescence intensity) in control wing discs and discs wherein CLIC/GEEC endocytic pathway is removed using UAS-myr-Garz-DN. For clarity, we show the discs with largest and smallest fluorescence intensities from the control and myr-Garz-DN discs. It is hard to conclude that the mean concentrations are significantly different in the two cases.
Reviewer #2 (Public Review):
The work of Iyer et al. uses a computational approach to investigate how cells using multiple tiers of processing and multiple parallel receptor types allow more accurate reading of position from a noisy signal. Authors find that combining signaling and non-signaling types of receptors together with additional feedback increases the accuracy of positional readout against extrinsic noise that is conveyed in the morphogen signal. Further, extending the number of layers of signal processing counteracts the intrinsic stochasticity of the signal reading and processing steps. The mathematical formulation of the model is general but comprehensive in the way it handles the difference between branches and tiers for the processing of channels with feedbacks. The results of the model are presented from simple one-branch and one-tier architecture to two-branch and two-tier architecture with feedbacks. Interestingly authors find that adding more tiers results in only very small improvements in the accuracy of positional readout. The model is tested against a perturbation experiment that impairs one of the signaling branches in the Drosophila wing disc, but the comparison is only qualitative as further experiment-oriented work is planned in a separate paper.
Strengths
There is a clear statement of objectives, model, and how the model is evaluated. In particular, the objective is to find what number of receptor types and their concentrations for a given number of tiers and feedback types is resulting in the most accurate positional readout. The employed optimization procedure is capable to find signalling architectures that result in one cell diameter positional precision for most of the tissue with 3-4 cells at the tissue end that is most distant to the morphogen source. This demonstrates that employing additional complexity in signal processing results in a very accurate positional readout, which is comparable with estimates of positional precision obtained in other developmental systems (Petkova et al., Cell 2019, Zagorski et al., Science 2017).
The optimal signalling architectures indicate that both signalling (specific) and non-signalling (nonspecific) receptors affect the precision of positional readout, but the contributions of each type of these receptors are qualitatively different. Even slight perturbation of signalling receptors drives the system out of optimum, resulting in a decrease in positional precision. In contrast, the non-signalling receptors could accommodate much larger perturbations. This observation could provide a biophysical explanation for how cross-talk between different morphogen species could be realized in a way that positional precision is kept at the optimum when morphogen signaling undergoes extrinsic and intrinsic perturbations.
Last, the model formulation allows to specifically address perturbations of signalling and feedbacks, that could be explored to validate model predictions experimentally in Drosophila wing disc, but also in other developmental tissues. The authors present a proof-of-concept by obtaining consistent results of variation of output profiles in two-tier two-branch architectures with non-signaling branch removed and intensity profiles of Wg in wing disc where the CLIC/GEEC endocytic pathway was perturbed.
Weaknesses
The list of model parameters is long including more than 20 entries for two-tier two-branch architectures. This is expected, as the aim of the model is to describe the sophisticated signalling architecture mimicking the biological system. However, this also makes it very challenging or impossible to provide guiding principles or understanding of the system behaviour for the complete space of signalling architectures that optimize positional readout. Although, the employed optimization procedure finds solutions that exhibit very high positional accuracy, there is only very limited notion how these solutions depend on variation of different parameters. The authors do not address the following question, whether these solutions correspond to broad global optima in the space of all solutions, or were rather fine-tuned by the optimization procedure and are quite rare.
It is unclear how contributions from the intrinsic noise affect the system behaviour compared to contributions from extrinsic noise. In principle, the two-branch one-tier architecture results in an already very accurate positional readout across the tissue. The adding of another tier seems to provide only a very weak improvement over a one-tier solution. It is possible that contributions from intrinsic noise for the investigated signalling architectures are only mildly affecting the system compared with contributions from extrinsic noise. Hence, it is difficult to assess whether the claim of reducing intrinsic noise by adding another tier is supported by the presented data, as the contributions from intrinsic noise could overall very weakly affect the positional readout.
The optimal response of the channel to extrinsic and intrinsic noises is very distinct. As noted correctly by the reviewer, an additional tier provides only a marginal improvement in inference error due extrinsic noise (compare Fig.7 and Fig.8 in the revised manuscript). However, as shown in Fig.9c of the revised manuscript (same as in the original manuscript), adding an extra tier provides a substantial improvement in inference errors due to intrinsic noise.
References
[1] Gasper Tkacik, Julien O Dubuis, Mariela D Petkova, and Thomas Gregor. Positional information, positional error, and readout precision in morphogenesis: a mathematical framework. Genetics, 199:39– 59, 2015.
[2] Mariela D Petkova, Gasper Tkacik, William Bialek, Eric F Wieschaus, and Thomas Gregor. Optimal decoding of cellular identities in a genetic network. Cell, 176:844–855, 2019.
[3] Julien O Dubuis, Gaˇsper Tkaˇcik, Eric F Wieschaus, Thomas Gregor, and William Bialek. Positional information, in bits. Proceedings of the National Academy of Sciences, 110:16301–16308, 2013.
[4] Anupama Hemalatha, Chaitra Prabhakara, and Satyajit Mayor. Endocytosis of wingless via a dynaminindependent pathway is necessary for signaling in drosophila wing discs. Proceedings of the National Academy of Sciences, 113:E6993–E7002, 2016.
[5] Xinhua Lin. Functions of heparan sulfate proteoglycans in cell signaling during development. Development, 131:6009–6021, 2004.
[6] Stephane Sarrazin, William C Lamanna, and Jeffrey D Esko. Heparan sulfate proteoglycans. Cold Spring Harbor perspectives in biology, 3(7):a004952, 2011.
[7] Catherine A Kirkpatrick, Sarah M Knox, William D Staatz, Bethany Fox, Daniel M Lercher, and Scott B Selleck. The function of a drosophila glypican does not depend entirely on heparan sulfate modification. Developmental biology, 300(2):570–582, 2006.
[8] Mariana I Capurro, Ping Xu, Wen Shi, Fuchuan Li, Angela Jia, and Jorge Filmus. Glypican-3 inhibits hedgehog signaling during development by competing with patched for hedgehog binding. Developmental cell, 14(5):700–711, 2008.
[9] Kenneth M Cadigan, Matthew P Fish, Eric J Rulifson, and Roel Nusse. Wingless repression of drosophila frizzled 2 expression shapes the wingless morphogen gradient in the wing. Cell, 93(5):767–777, 1998.
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eLife assessment
This work is of high relevance to developmental and quantitative biologists with an interest in morphogen-mediated position decoding. A general mathematical model formulation is presented that is nevertheless accessible to a broad audience. Model tests via perturbation experiments in the Drosophila wing disc look promising and inspire a new round of data generation.
-
Reviewer #1 (Public Review):
Iyer et al. address the problem of how cells exposed to a graded but noisy morphogen concentration are able to infer their position reliably, in other words how the positional information of a realistic morphogen gradient is decoded through cell-autonomous ligand processing. The authors introduce a model of a ligand processing network involving multiple "branches" (receptor types) and "tiers" (compartments where ligand-bound receptors can be located). Receptor levels are allowed to vary with distance from the source independently of the morphogen concentration. All rates, except for the ligand binding and unbinding rates, are potentially under feedback control. The authors assume that the cells can infer their position from the output of the signalling network in an optimal way. The resulting parameter space …
Reviewer #1 (Public Review):
Iyer et al. address the problem of how cells exposed to a graded but noisy morphogen concentration are able to infer their position reliably, in other words how the positional information of a realistic morphogen gradient is decoded through cell-autonomous ligand processing. The authors introduce a model of a ligand processing network involving multiple "branches" (receptor types) and "tiers" (compartments where ligand-bound receptors can be located). Receptor levels are allowed to vary with distance from the source independently of the morphogen concentration. All rates, except for the ligand binding and unbinding rates, are potentially under feedback control. The authors assume that the cells can infer their position from the output of the signalling network in an optimal way. The resulting parameter space is then explored to identify optimal "network architectures" and parameters, i.e. those that maximise the fidelity of the positional inference. The analysis shows how the presence of both specific and non-specific receptors, graded receptor expression and feedback loops can contribute to improving positional inference. These results are compared with known features of the Wnt signalling system in Drosophila wing imaginal disc.
The authors are doing an interesting study of how feedback control of the signalling network reading a morphogen gradient can influence the precision of the read-out. The main strength of this work is the attention to the development of the mathematical framework. While the family of network architectures introduced here is not completely generic, there is enough flexibility to explore various features of realistic signalling systems. It is exciting to find that some network topologies are particularly efficient at reducing the noise in the morphogen gradient. The comparison with the Wnt system in Drosophila is also promising.
Major comments:
- The authors assume that the cell estimates its position through the maximum a posteriori estimate, Eq.(5), which is a well-defined mathematical object; it seems to us however that whether the cell is actually capable of performing this measurement is uncertain (it is an optimal measurement in some sense, but there is no guarantee that the cell is optimal in that respect). Notably, this entails evaluating p(theta), which is a probability distribution over the entire tissue, so this estimate can not be done with purely local measurements. Can the authors comment on this and how the conclusions would change if a different position measurement was performed?
- One of the features of the signalling networks studied in the manuscript is the ability of the system to form a complex (termed a conjugated state, Q) made of two ligands L, one receptor and one non-signalling receptor. While there are clear examples of a single ligand binding to two signalling receptors (e.g. Bmps), are there also known situations where such a complex with two ligands, one receptor, and one non-signalling receptor can form? In the Wnt example (Fig. 10a), it is not clear what this complex would be? In general, it would be great to have a more extended discussion of how the model hypothesis for the signalling networks could relate to real systems.
- The authors consider feedback on reaction rates - it would seem natural to also consider feedback on the total number of receptors; notably, since there are known examples of receptors transcriptionally down-regulated by their ligands (e.g. Dpp/Tkv)? Also it is not clear in insets such as in Fig. 7b, if the concentration plotted corresponds to the concentration of receptors bound to ligands?
- The authors are clear about the fact that they consider the morphogen gradient to be fixed independently of the reaction network; however, that seems like a very strong assumption; in the Dpp morphogen gradient for instance over expression of the Tkv receptor leads to gradient shortening. Can the authors comment on this?
- Fig. 10f is showing an exciting result on the change in endocytic gradient CV in the WT and in DN mutant of Garz. Can the authors check that the Wg morphogen gradient is not changing in these two conditions? And can they also show the original gradient, and not only its CV?
-
Reviewer #2 (Public Review):
The work of Iyer et al. uses a computational approach to investigate how cells using multiple tiers of processing and multiple parallel receptor types allow more accurate reading of position from a noisy signal. Authors find that combining signaling and non-signaling types of receptors together with additional feedback increases the accuracy of positional readout against extrinsic noise that is conveyed in the morphogen signal. Further, extending the number of layers of signal processing counteracts the intrinsic stochasticity of the signal reading and processing steps. The mathematical formulation of the model is general but comprehensive in the way it handles the difference between branches and tiers for the processing of channels with feedbacks. The results of the model are presented from simple …
Reviewer #2 (Public Review):
The work of Iyer et al. uses a computational approach to investigate how cells using multiple tiers of processing and multiple parallel receptor types allow more accurate reading of position from a noisy signal. Authors find that combining signaling and non-signaling types of receptors together with additional feedback increases the accuracy of positional readout against extrinsic noise that is conveyed in the morphogen signal. Further, extending the number of layers of signal processing counteracts the intrinsic stochasticity of the signal reading and processing steps. The mathematical formulation of the model is general but comprehensive in the way it handles the difference between branches and tiers for the processing of channels with feedbacks. The results of the model are presented from simple one-branch and one-tier architecture to two-branch and two-tier architecture with feedbacks. Interestingly authors find that adding more tiers results in only very small improvements in the accuracy of positional readout. The model is tested against a perturbation experiment that impairs one of the signaling branches in the Drosophila wing disc, but the comparison is only qualitative as further experiment-oriented work is planned in a separate paper.
Strengths
There is a clear statement of objectives, model, and how the model is evaluated. In particular, the objective is to find what number of receptor types and their concentrations for a given number of tiers and feedback types is resulting in the most accurate positional readout. The employed optimization procedure is capable to find signalling architectures that result in one cell diameter positional precision for most of the tissue with 3-4 cells at the tissue end that is most distant to the morphogen source. This demonstrates that employing additional complexity in signal processing results in a very accurate positional readout, which is comparable with estimates of positional precision obtained in other developmental systems (Petkova et al., Cell 2019, Zagorski et al., Science 2017).
The optimal signalling architectures indicate that both signalling (specific) and non-signalling (non-specific) receptors affect the precision of positional readout, but the contributions of each type of these receptors are qualitatively different. Even slight perturbation of signalling receptors drives the system out of optimum, resulting in a decrease in positional precision. In contrast, the non-signalling receptors could accommodate much larger perturbations. This observation could provide a biophysical explanation for how cross-talk between different morphogen species could be realized in a way that positional precision is kept at the optimum when morphogen signaling undergoes extrinsic and intrinsic perturbations.
Last, the model formulation allows to specifically address perturbations of signalling and feedbacks, that could be explored to validate model predictions experimentally in Drosophila wing disc, but also in other developmental tissues. The authors present a proof-of-concept by obtaining consistent results of variation of output profiles in two-tier two-branch architectures with non-signaling branch removed and intensity profiles of Wg in wing disc where the CLIC/GEEC endocytic pathway was perturbed.
Weaknesses
The list of model parameters is long including more than 20 entries for two-tier two-branch architectures. This is expected, as the aim of the model is to describe the sophisticated signalling architecture mimicking the biological system. However, this also makes it very challenging or impossible to provide guiding principles or understanding of the system behaviour for the complete space of signalling architectures that optimize positional readout. Although, the employed optimization procedure finds solutions that exhibit very high positional accuracy, there is only very limited notion how these solutions depend on variation of different parameters. The authors do not address the following question, whether these solutions correspond to broad global optima in the space of all solutions, or were rather fine-tuned by the optimization procedure and are quite rare.
It is unclear how contributions from the intrinsic noise affect the system behaviour compared to contributions from extrinsic noise. In principle, the two-branch one-tier architecture results in an already very accurate positional readout across the tissue. The adding of another tier seems to provide only a very weak improvement over a one-tier solution. It is possible that contributions from intrinsic noise for the investigated signalling architectures are only mildly affecting the system compared with contributions from extrinsic noise. Hence, it is difficult to assess whether the claim of reducing intrinsic noise by adding another tier is supported by the presented data, as the contributions from intrinsic noise could overall very weakly affect the positional readout.
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