Emergence of planar cell polarity from the interplay of local interactions and global gradients
Curation statements for this article:-
Curated by eLife
eLife assessment
This study presents a valuable model for the emergence of planar cell polarity from the interplay of local interactions and global gradient. The framework of this model is solid, although the appreciation of its result should in places be more quantitative. A quality of this model is its simplicity and its convenience for experimental testing.
This article has been Reviewed by the following groups
Listed in
- Evaluated articles (eLife)
- Computational and Systems Biology (eLife)
Abstract
Planar cell polarity (PCP) – tissue-scale alignment of the direction of asymmetric localization of proteins at cell-cell interface – is essential for embryonic development and physiological functions. Abnormalities in PCP can lead to neural tube closure defects and misaligned hair follicles. Decoding the mechanism responsible for PCP establishment and maintenance remains a fundamental open question. While the roles of various molecules – broadly classified into “global” and “local” modules – have been well-studied, their necessity and sufficiency in explaining PCP and connecting their perturbations to experimentally observed patterns has not been examined. Here, we develop a minimal model that captures the proposed features of these modules – a global tissue-level gradient and local asymmetric distribution of protein complexes. Our model suggests that while polarity can emerge without a gradient, the gradient can provide the direction of polarity and maintain PCP robustly in presence of stochastic perturbations. We also recapitulated swirling patterns seen experimentally and features of domineering non-autonomy, using only three free model parameters - protein binding rate, concentration of proteins forming heterodimer across cell boundaries and gradient steepness. We explain how self-stabilizing asymmetric localizations in presence of tissue-level gradient can lead to robust PCP patterns and reveal minimal design principles for a polarized system.
Article activity feed
-
Author Response
Reviewer #1 (Public Review)
The manuscript by Singh et al proposes a new theoretical model for the phenomenon of planar cell polarity (PCP). The new model is simulating the emergence of the subcellular polarity of the Fat-Ds pathway, based on the interactions of the protocadherins Fat and Ds at the boundary between cells and in response to external gradients. Several mathematical models for PCP have been previously developed focusing on different aspects of PCP, including non-autonomy domineering (Amonlirdviman et al.), the effect of stochasticity on polarity (Burak et al.), gradient sensing (Mani et al), formation of molecular bridges (Fisher et al.) to name a few. The current modeling approach suggests a new model, based on a relatively simple set of equations for membrane Fat and Ds and their interactions, both in …
Author Response
Reviewer #1 (Public Review)
The manuscript by Singh et al proposes a new theoretical model for the phenomenon of planar cell polarity (PCP). The new model is simulating the emergence of the subcellular polarity of the Fat-Ds pathway, based on the interactions of the protocadherins Fat and Ds at the boundary between cells and in response to external gradients. Several mathematical models for PCP have been previously developed focusing on different aspects of PCP, including non-autonomy domineering (Amonlirdviman et al.), the effect of stochasticity on polarity (Burak et al.), gradient sensing (Mani et al), formation of molecular bridges (Fisher et al.) to name a few. The current modeling approach suggests a new model, based on a relatively simple set of equations for membrane Fat and Ds and their interactions, both in 1D (line of cells) and in 2D (hexagonal array). The equations are relatively simple on one hand, allowing performing tractable computational analysis as well as analytical approximations, while on the other hand allowing tracking membrane protein levels, which is what is measured experimentally. It has been previously shown that achieving polarity requires local feedback that amplify complexes in one orientation at the expense of complexes in the opposite orientation (e.g. Mani et al.). Interestingly, the current manuscript shows that a simple assumption, that Fat-DS complexes are stabilized when bound is sufficient to induce PCP when concentrations are high enough. The authors use the model to show how it captures several experimental observations, as well as to analyze the sensitivity to noise, the response to gradients, and the response to local perturbations (mutant clones). The manuscript is clear and the analysis is mostly coherent and sensible (although some parts need to be clarified, see below). The main issue I have with the manuscript is that it mostly describes how it captures different features that were mostly explained in previous models. I do think the authors should do more with their model to explain features that were not explained by other models, and/or generate non-trivial predictions that can be tested experimentally.
We thank the reviewer for the positive feedback and valuable comments We have comprehensively modified the manuscript by including new results and detailing the specific model prediction and their potential experimental tests to address the concerns.
Reviewer #2 (Public Review):
The setting of planar cell polarity in epithelial tissues involves a complex interplay of chemical interactions. While local interactions can spontaneously give rise to cell polarity, planar cell polarity also involves tissue scale gradients whose effects are not clear. To understand their role, the authors built a minimal mechanistic model in considering two atypical cadherins, Fat (Ft) and Dachsous (Ds) which can associate at cell-cell interfaces to form hetero-dimers in which monomers belong to adjacent cells. This association can be seen as a local interaction between cells and is also sensitive to overall concentration gradients. From their model which appears to capture diverse experimental observations, the authors conclude that tissue-scale gradients provide to planar cell polarity a directional cue and some robustness to cellular stochasticity. While this model comes after similar works reaching similar predictions, the quality of this model is in its simplicity, its convenience for experimental testing, and the diversity of experimental observations it recapitulates.
A strength of this work is to recapitulate many experimental observations made on planar cell polarity. It, for example, seems to capture the response of tissues to perturbations such as local downregulation of some important proteins, and the polarity patterns observed in the presence of noise in synthesis or cell-to-cell heterogeneity. It also gives a mechanistic description of planar cell polarity, making its experimental interpretation simple. Finally, the simplicity of the model facilitates its exploration and makes it easily testable because of the reduced amount of free model parameters.
A weakness of this work is that it comes after several models with similar hypotheses and similar predictions.
Another weakness is that some conclusions of this work rely on visual appreciation rather than quantification. This is particularly true for what concerns 2D patterns. An argument of the authors is for example that their model reproduces a variety of known spatial patterns, but the comparison with experiments is only visual and would be more convincing in being more quantitative.
We are grateful to the reviewer for a critical evaluation of the manuscript and for giving important suggestions. We have incorporated all the comments and revised the manuscript accordingly by including quantitative analysis of all the results presented.
Reviewer #3 (Public Review):
Using theory, the authors study mechanisms for establishing planar cell polarity (PCP) through local and global modules. These modules refer to the interaction between neighbouring cells and tissue-wide gradients, respectively. Whereas local interactions alone can lead to tissue-wide alignment PCP, a global gradient can set the direction of PCP and maintain the pattern in presence of noise. In contrast, the authors argue that a global gradient can only generate PCP to an extent that is proportional to the gradient magnitude.
The authors formulate a discrete model in one and two spatial dimensions that describe the assembly dynamics of PCP proteins on membranes. The number of proteins per cell remains constant. Additive noise is introduced to account for stochasticity in the attachment/detachment kinetics of proteins. Furthermore, ’quenched’ noise is introduced to account for variations of protein numbers between cells. The authors perform simulations of the stochastic discrete model in various situations. In addition, they derive a continuum description to perform some analytical computations.
The strength of this analysis relies clearly on showing that simple dynamics can lead to tissue-wide PCP even in absence of a gradient in protein expression. A number of phenomena observed in tissues are qualitatively reproduced. In two spatial dimensions, they find swirling patterns that resemble patterns found in tissues when a global gradient is absent. The model also captures qualitative effects due to the down-regulation of one of the PCP proteins in a certain region of the tissue.
The main weak point is that, from a physical point of view, the findings are not particularly surprising. Furthermore, some assumptions underlying the model, need some more justification. This holds notably for the question, of why additive noise is appropriate to account for the effect of stochasticity in the attachment-detachment dynamics of the proteins. Finally, the authors consider a situation that they consider to be one of the most interesting features of PCP, namely, the formation of PCP in the presence of a region with a down-regulated PCP protein and in presence of a gradient. Unfortunately, the effect is not very clear and the data provided remains limited.
We thank the reviewer for the valuable comments are critique of the work. We have considered all the concerns and revised the manuscript comprehensively. In particular, we have elaborated the sections on model assumptions and added new figures/figure-panels to quantitatively present the model predictions. We have also revised the details of the one-dimensional continuum theory for PCP which, we feel, presents a detailed quantitative picture of PCP and its dependence on model parameters.
-
eLife assessment
This study presents a valuable model for the emergence of planar cell polarity from the interplay of local interactions and global gradient. The framework of this model is solid, although the appreciation of its result should in places be more quantitative. A quality of this model is its simplicity and its convenience for experimental testing.
-
Reviewer #1 (Public Review):
The manuscript by Singh et al proposes a new theoretical model for the phenomenon of planar cell polarity (PCP). The new model is simulating the emergence of the subcellular polarity of the Fat-Ds pathway, based on the interactions of the protocadherins Fat and Ds at the boundary between cells and in response to external gradients. Several mathematical models for PCP have been previously developed focusing on different aspects of PCP, including non-autonomy domineering (Amonlirdviman et al.), the effect of stochasticity on polarity (Burak et al.), gradient sensing (Mani et al), formation of molecular bridges (Fisher et al.) to name a few. The current modeling approach suggests a new model, based on a relatively simple set of equations for membrane Fat and Ds and their interactions, both in 1D (line of cells) …
Reviewer #1 (Public Review):
The manuscript by Singh et al proposes a new theoretical model for the phenomenon of planar cell polarity (PCP). The new model is simulating the emergence of the subcellular polarity of the Fat-Ds pathway, based on the interactions of the protocadherins Fat and Ds at the boundary between cells and in response to external gradients. Several mathematical models for PCP have been previously developed focusing on different aspects of PCP, including non-autonomy domineering (Amonlirdviman et al.), the effect of stochasticity on polarity (Burak et al.), gradient sensing (Mani et al), formation of molecular bridges (Fisher et al.) to name a few. The current modeling approach suggests a new model, based on a relatively simple set of equations for membrane Fat and Ds and their interactions, both in 1D (line of cells) and in 2D (hexagonal array). The equations are relatively simple on one hand, allowing performing tractable computational analysis as well as analytical approximations, while on the other hand allowing tracking membrane protein levels, which is what is measured experimentally. It has been previously shown that achieving polarity requires local feedback that amplify complexes in one orientation at the expense of complexes in the opposite orientation (e.g. Mani et al.). Interestingly, the current manuscript shows that a simple assumption, that Fat-DS complexes are stabilized when bound is sufficient to induce PCP when concentrations are high enough. The authors use the model to show how it captures several experimental observations, as well as to analyze the sensitivity to noise, the response to gradients, and the response to local perturbations (mutant clones). The manuscript is clear and the analysis is mostly coherent and sensible (although some parts need to be clarified, see below). The main issue I have with the manuscript is that it mostly describes how it captures different features that were mostly explained in previous models. I do think the authors should do more with their model to explain features that were not explained by other models, and/or generate non-trivial predictions that can be tested experimentally.
-
Reviewer #2 (Public Review):
The setting of planar cell polarity in epithelial tissues involves a complex interplay of chemical interactions. While local interactions can spontaneously give rise to cell polarity, planar cell polarity also involves tissue scale gradients whose effects are not clear. To understand their role, the authors built a minimal mechanistic model in considering two atypical cadherins, Fat (Ft) and Dachsous (Ds) which can associate at cell-cell interfaces to form hetero-dimers in which monomers belong to adjacent cells. This association can be seen as a local interaction between cells and is also sensitive to overall concentration gradients. From their model which appears to capture diverse experimental observations, the authors conclude that tissue-scale gradients provide to planar cell polarity a directional cue …
Reviewer #2 (Public Review):
The setting of planar cell polarity in epithelial tissues involves a complex interplay of chemical interactions. While local interactions can spontaneously give rise to cell polarity, planar cell polarity also involves tissue scale gradients whose effects are not clear. To understand their role, the authors built a minimal mechanistic model in considering two atypical cadherins, Fat (Ft) and Dachsous (Ds) which can associate at cell-cell interfaces to form hetero-dimers in which monomers belong to adjacent cells. This association can be seen as a local interaction between cells and is also sensitive to overall concentration gradients. From their model which appears to capture diverse experimental observations, the authors conclude that tissue-scale gradients provide to planar cell polarity a directional cue and some robustness to cellular stochasticity. While this model comes after similar works reaching similar predictions, the quality of this model is in its simplicity, its convenience for experimental testing, and the diversity of experimental observations it recapitulates.
A strength of this work is to recapitulate many experimental observations made on planar cell polarity. It, for example, seems to capture the response of tissues to perturbations such as local downregulation of some important proteins, and the polarity patterns observed in the presence of noise in synthesis or cell-to-cell heterogeneity. It also gives a mechanistic description of planar cell polarity, making its experimental interpretation simple. Finally, the simplicity of the model facilitates its exploration and makes it easily testable because of the reduced amount of free model parameters.
A weakness of this work is that it comes after several models with similar hypotheses and similar predictions. Another weakness is that some conclusions of this work rely on visual appreciation rather than quantification. This is particularly true for what concerns 2D patterns. An argument of the authors is for example that their model reproduces a variety of known spatial patterns, but the comparison with experiments is only visual and would be more convincing in being more quantitative.
-
Reviewer #3 (Public Review):
Using theory, the authors study mechanisms for establishing planar cell polarity (PCP) through local and global modules. These modules refer to the interaction between neighbouring cells and tissue-wide gradients, respectively. Whereas local interactions alone can lead to tissue-wide alignment PCP, a global gradient can set the direction of PCP and maintain the pattern in presence of noise. In contrast, the authors argue that a global gradient can only generate PCP to an extent that is proportional to the gradient magnitude.
The authors formulate a discrete model in one and two spatial dimensions that describe the assembly dynamics of PCP proteins on membranes. The number of proteins per cell remains constant. Additive noise is introduced to account for stochasticity in the attachment/detachment kinetics of …
Reviewer #3 (Public Review):
Using theory, the authors study mechanisms for establishing planar cell polarity (PCP) through local and global modules. These modules refer to the interaction between neighbouring cells and tissue-wide gradients, respectively. Whereas local interactions alone can lead to tissue-wide alignment PCP, a global gradient can set the direction of PCP and maintain the pattern in presence of noise. In contrast, the authors argue that a global gradient can only generate PCP to an extent that is proportional to the gradient magnitude.
The authors formulate a discrete model in one and two spatial dimensions that describe the assembly dynamics of PCP proteins on membranes. The number of proteins per cell remains constant. Additive noise is introduced to account for stochasticity in the attachment/detachment kinetics of proteins. Furthermore, 'quenched' noise is introduced to account for variations of protein numbers between cells. The authors perform simulations of the stochastic discrete model in various situations. In addition, they derive a continuum description to perform some analytical computations.
The strength of this analysis relies clearly on showing that simple dynamics can lead to tissue-wide PCP even in absence of a gradient in protein expression. A number of phenomena observed in tissues are qualitatively reproduced. In two spatial dimensions, they find swirling patterns that resemble patterns found in tissues when a global gradient is absent. The model also captures qualitative effects due to the down-regulation of one of the PCP proteins in a certain region of the tissue.
The main weak point is that, from a physical point of view, the findings are not particularly surprising. Furthermore, some assumptions underlying the model, need some more justification. This holds notably for the question, of why additive noise is appropriate to account for the effect of stochasticity in the attachment-detachment dynamics of the proteins. Finally, the authors consider a situation that they consider to be one of the most interesting features of PCP, namely, the formation of PCP in presence of a region with a down-regulated PCP protein and in presence of a gradient. Unfortunately, the effect is not very clear and the data provided remains limited.
-
-