Patterning precision under non-linear morphogen decay and molecular noise
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eLife assessment
The authors use analytic calculations and numerical simulations to convincingly show that the purported benefits of nonlinear decay in morphogen gradients may be marginal in some cases and completely reversed in others (far from the concentration source). This is a valuable contribution to the field, as it questions common assumptions about the biological function of non-linear morphogen decays during development.
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Abstract
Morphogen gradients can instruct cells about their position in a patterned tissue. Non-linear morphogen decay has been suggested to increase gradient precision by reducing the sensitivity to variability in the morphogen source. Here, we use cell-based simulations to quantitatively compare the positional error of gradients for linear and non-linear morphogen decay. While we confirm that non-linear decay reduces the positional error close to the source, the reduction is very small for physiological noise levels. Far from the source, the positional error is much larger for non-linear decay in tissues that pose a flux barrier to the morphogen at the boundary. In light of this new data, a physiological role of morphogen decay dynamics in patterning precision appears unlikely.
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eLife assessment
The authors use analytic calculations and numerical simulations to convincingly show that the purported benefits of nonlinear decay in morphogen gradients may be marginal in some cases and completely reversed in others (far from the concentration source). This is a valuable contribution to the field, as it questions common assumptions about the biological function of non-linear morphogen decays during development.
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Reviewer #1 (Public Review):
This article is somewhat far afield from my typical line of research, but, to not bury the lede, I thought that this article makes an important point and is rigorously argued but could use some space to breathe in order to increase its impact.
More precisely, the authors perform a set of detailed calculations and simulations to show that the purported benefits of having non-linear morphogen decays are small near the source and decidedly reversed near the far end. I didn't have any specific concerns with these calculations, but one question I did have was if the typical context of morphogen gradients needs to be taken into account a little more (the paper doesn't really discuss how downstream morphogen gradients' noise might be affected by the structure of noise discussed here).
That said, I think that this …
Reviewer #1 (Public Review):
This article is somewhat far afield from my typical line of research, but, to not bury the lede, I thought that this article makes an important point and is rigorously argued but could use some space to breathe in order to increase its impact.
More precisely, the authors perform a set of detailed calculations and simulations to show that the purported benefits of having non-linear morphogen decays are small near the source and decidedly reversed near the far end. I didn't have any specific concerns with these calculations, but one question I did have was if the typical context of morphogen gradients needs to be taken into account a little more (the paper doesn't really discuss how downstream morphogen gradients' noise might be affected by the structure of noise discussed here).
That said, I think that this is a rigorous submission.
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Reviewer #2 (Public Review):
In this work, the authors tackle the question of how a non-linear decay in a morphogen gradient might affect downstream patterning specificity. In the first section of the paper, they address this theoretically, by examining the nature of morphogen gradients assuming either linear or non-linear degradation of the morphogen, using previously-established equations. Assuming variation in the concentration of morphogen at the source, they show that a linear decay model results in uniform shifts in the location of a threshold concentration of morphogen that only depend on the relative concentration changes, while a non-linear decay model yield shifts with more complex dependencies on concentration.
The next section of the paper addresses gradient patterning precision by accounting for not only variation in the …
Reviewer #2 (Public Review):
In this work, the authors tackle the question of how a non-linear decay in a morphogen gradient might affect downstream patterning specificity. In the first section of the paper, they address this theoretically, by examining the nature of morphogen gradients assuming either linear or non-linear degradation of the morphogen, using previously-established equations. Assuming variation in the concentration of morphogen at the source, they show that a linear decay model results in uniform shifts in the location of a threshold concentration of morphogen that only depend on the relative concentration changes, while a non-linear decay model yield shifts with more complex dependencies on concentration.
The next section of the paper addresses gradient patterning precision by accounting for not only variation in the source concentration of morphogen, but also in the parameters that describe the production, degradation, diffusion, and cell size, for both a linear and non-linear decay model. The key finding from this section is that, while non-linear decay can produce some improvements in patterning reliability near the morphogen source, it fares far worse than linear decay in regions far from the morphogen gradient. Simulations that include explicit morphogen-producing cells demonstrate that simpler models that exclude this detail may have overestimated the benefits of a non-linear morphogen decay.
The strength of this work is tackling head-on the question of how a non-linear decay of morphogen affects patterning precision using both theory and simulations. Non-linear decays have been observed in nature, and therefore this question is one of interest. The methods used by the authors provide convincing evidence for their claims, and the results, particularly the importance of simulating morphogen-producing cells, are likely to be of interest to the community interested in the design principles of morphogens and developmental patterning.
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Reviewer #3 (Public Review):
This paper addresses the impact of non-linear protein degradation on the precision of morphogen gradients. Since the predominant model for the formation of morphogen gradients is a production/diffusion/degradation model understanding the contribution of degradation is an important question. This paper investigates the properties of the simplest and most general mathematical model for gradient formation. As such, this work is of interest. The main conclusion of the paper is that non-linear protein degradation has little impact on the precision of the morphogen gradient near the source of production of the morphogen and it reduces precision far away from the source. These conclusions are supported by the mathematical analysis presented. The paper is a difficult read for people unfamiliar with the current …
Reviewer #3 (Public Review):
This paper addresses the impact of non-linear protein degradation on the precision of morphogen gradients. Since the predominant model for the formation of morphogen gradients is a production/diffusion/degradation model understanding the contribution of degradation is an important question. This paper investigates the properties of the simplest and most general mathematical model for gradient formation. As such, this work is of interest. The main conclusion of the paper is that non-linear protein degradation has little impact on the precision of the morphogen gradient near the source of production of the morphogen and it reduces precision far away from the source. These conclusions are supported by the mathematical analysis presented. The paper is a difficult read for people unfamiliar with the current literature.
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