Theory of non-dilute binding and surface phase separation applied to membrane-binding proteins
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eLife Assessment
This important study presents a compelling theoretical framework for understanding condensation or phase separation of membrane-bound proteins, with a focus on the organization of tight junction components. By incorporating non-dilute binding effects into thermodynamic models and validating the model's predictions with in vitro experiments on the tight junction protein ZO-1, the authors provide a quantitative tool that combines theory and experiments and will help researchers in the field quantitatively interpret their findings. Given that phase separation of membrane bound molecules is becoming key in signaling, spanning from immune signaling to cell-cell adhesion, this work will be of broad interest for cell biologists and biophysicists.
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Abstract
Surface binding and surface phase separation of cytosolic scaffold proteins on lipid membranes are involved in many cellular processes, such as cell signaling, cell adhesion, and cortex regulation. However, the interplay between surface binding and surface phase separation is poorly understood. In this work, we study this interplay by deriving a general thermodynamic model and applying it to in vitro reconstitution experiments of membrane-binding proteins involved in tight junction initiation. Our theory extends the classical surface binding isotherm to account for non-dilute and heterogeneous conditions where components can phase separate. We use our theory to demonstrate how surface phase separation is governed by the interaction strength among membrane-bound scaffold proteins and their binding affinity to the membrane surface. Comparing the theory to reconstitution experiments, we show that tuning the oligomerization state of the adhesion receptors in the membrane controls surface phase transition and patterning of the scaffold protein ZO1. These findings suggest a fundamental role of the interplay between non-dilute surface binding and surface phase separation in forming the tight junction. More broadly, our work highlights non-dilute surface binding and surface phase separation as a common organizational principle for membrane-associated structures in living cells.
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eLife Assessment
This important study presents a compelling theoretical framework for understanding condensation or phase separation of membrane-bound proteins, with a focus on the organization of tight junction components. By incorporating non-dilute binding effects into thermodynamic models and validating the model's predictions with in vitro experiments on the tight junction protein ZO-1, the authors provide a quantitative tool that combines theory and experiments and will help researchers in the field quantitatively interpret their findings. Given that phase separation of membrane bound molecules is becoming key in signaling, spanning from immune signaling to cell-cell adhesion, this work will be of broad interest for cell biologists and biophysicists.
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Reviewer #1 (Public review):
Summary:
Biomolecular condensates are essential part of cellular homeostatic regulation. In this manuscript, authors develop a theoretical framework for phase separation of membrane bound proteins. They show the effect of non-dilute surface binding and phase separation on tight junction protein organization.
Strengths:
It is an important study considering the phase separation of membrane bound molecules are taking the center stage of signaling, spanning from immune signaling to cell-cell adhesion. A theoretical framework will help biologists to quantitatively interpret their findings.
Weaknesses:
Understandably, authors used one system to test their theory (ZO-1). However, to establish a theoretical framework, this is sufficient.
Comments on revisions:
I do not recommend new experiments. The manuscript is …
Reviewer #1 (Public review):
Summary:
Biomolecular condensates are essential part of cellular homeostatic regulation. In this manuscript, authors develop a theoretical framework for phase separation of membrane bound proteins. They show the effect of non-dilute surface binding and phase separation on tight junction protein organization.
Strengths:
It is an important study considering the phase separation of membrane bound molecules are taking the center stage of signaling, spanning from immune signaling to cell-cell adhesion. A theoretical framework will help biologists to quantitatively interpret their findings.
Weaknesses:
Understandably, authors used one system to test their theory (ZO-1). However, to establish a theoretical framework, this is sufficient.
Comments on revisions:
I do not recommend new experiments. The manuscript is clear and establishes a new step in understanding the physical chemistry of biomolecular condensates.
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Author response:
The following is the authors’ response to the original reviews.
Reviewer #1 (Public review):
Summary:
Biomolecular condensates are an essential part of cellular homeostatic regulation. In this manuscript, the authors develop a theoretical framework for the phase separation of membrane-bound proteins. They show the effect of non-dilute surface binding and phase separation on tight junction protein organization.
Strengths:
It is an important study, considering that the phase separation of membrane-bound molecules is taking the center stage of signaling, spanning from immune signaling to cell-cell adhesion. A theoretical framework will help biologists to quantitatively interpret their findings.
Weaknesses:
Understandably, the authors used one system to test their theory (ZO-1). However, to establish a theoretical …
Author response:
The following is the authors’ response to the original reviews.
Reviewer #1 (Public review):
Summary:
Biomolecular condensates are an essential part of cellular homeostatic regulation. In this manuscript, the authors develop a theoretical framework for the phase separation of membrane-bound proteins. They show the effect of non-dilute surface binding and phase separation on tight junction protein organization.
Strengths:
It is an important study, considering that the phase separation of membrane-bound molecules is taking the center stage of signaling, spanning from immune signaling to cell-cell adhesion. A theoretical framework will help biologists to quantitatively interpret their findings.
Weaknesses:
Understandably, the authors used one system to test their theory (ZO-1). However, to establish a theoretical framework, this is sufficient.
We acknowledge this limitation. While we agree that additional systems would strengthen the generality of our theory, we note that the focus of this work is to introduce and validate a theoretical framework. As the reviewer notes, this is sufficient for establishing the framework. Nonetheless, we are open to further collaborations or future studies to test the model with other systems.
Reviewer #2 (Public review):
Summary:
The authors present a clear expansion of biophysical (thermodynamic) theory regarding the binding of proteins to membrane-bound receptors, accounting for higher local concentration effects of the protein. To partially test the expanded theory, the authors perform in vitro experiments on the binding of ZO1 proteins to Claudin2 C-terminal receptors anchored to a supported lipid bilayer, and capture the effects that surface phase separation of ZO1 has on its adsorption to the membrane.
Strengths:
(1) The derived theoretical framework is consistent and largely well-explained.
(2) The experimental and numerical methodologies are transparent.
(3) The comparison between the best parameterized non-dilute theory is in reasonable agreement with experiments.
Weaknesses:
(1) In the theoretical section, what has previously been known, compared to which equations are new, should be made more clear.
We have revised the theory section to clearly distinguish previously established formulations from novel contributions following equation (4), which is .
(2) Some assumptions in the model are made purely for convenience and without sufficient accompanying physical justification. E.g., the authors should justify, on physical grounds, why binding rate effects are/could be larger than the other fluxes.
For our problem, binding is relevant together with diffusive transport in each phase. Each process is accompanied by kinetic coefficients that we estimate for the experimental system. For the considered biological systems (and related ones), it is difficult to determine whether other fluxes (see, e.g., Eq. 8(e)) have relaxed or not. We note that their effects are, of course, included in the kinetic model applied to the coarsening of ZO1 surface condensates as boundary conditions. But we cannot exclude that the corresponding kinetic coefficient in the actual biological system is large enough such that, e.g., Eq. (9e) does not vanish to zero “quasi-statically”. We have now added a sentence to the outlook highlighting the relevance of testing those flux-force relationships in biological systems.
(3) I feel that further mechanistic explanation as to why bulk phase separation widens the regime of surface phase separation is warranted.
We have discussed the mechanistic explanation related to bulk protein interaction strength in the manuscript in the section: “Effects of binding affinity and interactions on surface phase separation”. We explained how the bulk interaction parameter affects the binding equilibrium.
(4) The major advantage of the non-dilute theory as compared with a best parameterized dilute (or homogenous) theory requires further clarification/evidence with respect to capturing the experimental data.
We thank reviewer for this helpful question. To address this point, we have added new paragraphs in the conclusion section, which explicitly discuss the necessity of employing the non-dilute theory for interpreting the experimental data.
(5) Discrete (particle-based) molecular modelling could help to delineate the quantitative improvements that the non-dilute theory has over the previous state-of-the-art. Also, this could help test theoretical statements regarding the roles of bulk-phase separation, which were not explored experimentally.
We appreciate the suggestion and agree that such modeling would be valuable. However, this is beyond the scope of the current study.
(6) Discussion of the caveats and limitations of the theory and modelling is missing from the text.
We sincerely appreciate the reviewer’s helpful comment. We have added a discussion in the conclusion section outlining the caveats and limitations of our modeling approach.
Reviewing Editor Comments:
Upon discussing with the reviewers, we feel that this manuscript could significantly be improved if testing the model with a different model system (beyond ZO1/tight junctions), in which case we foresee that we could enhance the strength of evidence from "compelling" to "exceptional". But of course, this is up to the authors to go for it or not, the paper is already very good.
Reviewer #2 (Recommendations for the authors):
(1) Lines 132-134: Re-word, the use of "complex" is confusing.
We have rephrased the sentence for clarity. The revised version reads: ṽ𝑃𝑅 are the molecular volume and area of the protein-receptor complex ѵ𝑃𝑅, respectively”, and the changes have been in the revised manuscript.
(2) Line 154 use of ""\nu"" for volume and area could be avoided for better clarity.
We thank the reviewer for this helpful suggestion. We have removed the statement involving ""\nu"" as these quantities have already been defined in the preceding context.
(3) Line 158 the total "Helmholtz" free energy F...
We have added the word "Helmholtz" to the sentence.
(4) Line 160 typo "In specific,..."
We carefully checked this sentence but could not identify a typo.
(5) For equation 5 explain the physical origins of each term, or provide a reference if this equation is explained elsewhere.
Thank you very much for your valuable suggestions. We have carefully rephrased Equation (5) and added a paragraph immediately afterward to provide a detailed explanation of its physical meaning.
(6) Derivation on lines 163-174 is poorly written. Make the logical flow between the equations clearer.
We greatly appreciate your insightful suggestions. Equation (6) has been carefully revised for clarity, and the explanation has been rewritten to ensure better readability. All modifications are Done.
(7) Define bold "t" in Equation 6.
The variable “t” has been explicitly defined in the context for clarity.
(8) In equations. 7b-7c the nablas (gradients) should be the 2D versions.
We have updated the gradient operators in Equations (7b) and (7c) [Eq. (9) in revised manuscript] to their 2D forms for consistency.
(9) Line 190, avoid referring to the future Equation 14, and state in words what is meant by "thermodynamic equilibrium".
We have added the explanation of “thermodynamic equilibrium” and remove the reference to equation accordingly.
(10) In Equation 11 you don't explain what you are doing ( which is a perturbation around the minimum of the free energy).
We have revised the paragraph before equation (11) [Eq. (13) in revised manuscript] to clarify that the expression represents a perturbation around the minimum of the free energy.
(11) In Equation 12, doesn't this also depend on how you have written equation 6 (not just equation 5).
Eq. (12) [Eq. (14) in revised manuscript] is derived directly from the variation of the total free energy F. In contrast, Eq. (6) contains the time derivative of free energies that were not written in their final form. In the revised version, we have now given the conjugate forces and fluxes in Eqs. (7) and (8) for clarity.
(12) Line 206 specify the threshold of local concentration (or provide a reference).
We have specified the threshold of local concentration in the revised text, and the corresponding statement has been highlighted.
(13) Line 223 is the deviation from ideality captured in a pair-wise fashion? I presume it does not account for N many-body interactions?
Yes, our model is formulated within a mean-field framework that incorporates pairwise (second order) interaction coefficients. For example, 𝜒𝑃𝑅 -𝑅 characterizes the interaction between the complex 𝑃𝑅 and the free receptor 𝑅, 𝜒𝑅 -L the interaction between free receptor 𝑅 and free lipid 𝐿, 𝜒𝑃𝑅-𝐿 the interaction between complex 𝑃𝑅and free lipid 𝐿. We have stressed this choice of free energy in the revised manuscript.
(14) Line 274, how do the authors know the secondary effects (of which they should mention a few) do not significantly impact the observed behaviour?
We sincerely thank the reviewer for the helpful comment. First, the parameters 𝜒𝑅 -L and 𝜒𝑃𝑅 -𝑅 are not essential based on the experimental observations. For more information, please see our revised paragraph on the choice of the specific parameter values, which has been in the following Eq. (21).
(15) It's not clear how Figures 3 b and c are generated with reference to which parameters are changed to investigate with/without bulk phase separation.
To improve clarity, we have revised Figure 3 to display the corresponding parameter values directly in each panel. Figures 3b and 3c were generated by computing the surface binding curves (as shown in Fig. 2) for each binding affinity 𝜔𝑃𝑅 and membrane-complex interaction strength 𝜒𝑃𝑅-𝐿, under different bulk interaction strengths chi, to compare the cases with and without bulk phase separation.
(16) The jump between theory and the "Mechanism in ..." section is too much. The authors should include the biological context of tight junctions and ZO1 in the main introduction.
We appreciate the reviewer’s suggestion. Following this comment, we have added an extended discussion in the main introduction to provide the necessary biological context of tight junctions and ZO1. In addition, we inserted new bridging paragraphs between the theoretical section and the section “Mechanism in tight junction formation” to create a smoother transition from theory to experiments. These revisions help to better connect the theoretical framework with the biological phenomena discussed in the later section.
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Author Response:
We sincerely thank the reviewers and the editorial team for their thoughtful and constructive evaluation of our manuscript. We are very pleased that both reviewers and the Reviewing Editor found the work to be compelling and of interest to the community studying membrane-associated condensates. Below we outline our planned revisions in response to the public reviews.
Reviewer #1
We appreciate Reviewer #1’s positive evaluation of the study’s significance and the utility of our theoretical framework.
- Understandably, the authors used one system to test their theory (ZO-1). However, to establish a theoretical framework, this is sufficient.
Response: We acknowledge this limitation. While we agree that additional systems would strengthen the generality of our theory, we note that the focus of this work is to introduce and …
Author Response:
We sincerely thank the reviewers and the editorial team for their thoughtful and constructive evaluation of our manuscript. We are very pleased that both reviewers and the Reviewing Editor found the work to be compelling and of interest to the community studying membrane-associated condensates. Below we outline our planned revisions in response to the public reviews.
Reviewer #1
We appreciate Reviewer #1’s positive evaluation of the study’s significance and the utility of our theoretical framework.
- Understandably, the authors used one system to test their theory (ZO-1). However, to establish a theoretical framework, this is sufficient.
Response: We acknowledge this limitation. While we agree that additional systems would strengthen the generality of our theory, we note that the focus of this work is to introduce and validate a theoretical framework. As the reviewer notes, this is sufficient for establishing the framework. Nonetheless, we are open to further collaborations or future studies to test the model with other systems.
Reviewer #2
We are grateful for Reviewer #2’s detailed comments and will address each of the points as follows:
- In the theoretical section, what has previously been known, compared to which equations are new, should be made more clear.
Response: We will revise the theory section to clearly distinguish previously established formulations from novel contributions.
- Some assumptions in the model are made purely for convenience and without sufficient accompanying physical justification. E.g., the authors should justify, on physical grounds, why binding rate effects are/could be larger than the other fluxes.
Response: We will expand the discussion to provide key physical justification, especially to explain why binding rate effects are/could be larger than the other fluxes.
- I feel that further mechanistic explanation as to why bulk phase separation widens the regime of surface phase separation is warranted.
Response: We will elaborate on the mechanism underlying this coupling.
- The major advantage of the non-dilute theory as compared with a best parameterized dilute (or homogenous) theory requires further clarification/evidence with respect to capturing the experimental data.
Response: We will clarify this comparison more explicitly and highlight how the non-dilute model captures key nonlinear behaviors and concentration-dependent adsorption phenomena that the dilute model fails to reproduce.
- Discrete (particle-based) molecular modelling could help to delineate the quantitative improvements that the non-dilute theory has over the previous state-of-the-art. Also, this could help test theoretical statements regarding the roles of bulk-phase separation, which were not explored experimentally.
Response: We appreciate the suggestion and agree that such modeling would be valuable. However, this is beyond the scope of the current study. We will add a discussion on how discrete simulations could be used to further test our theory in future work.
- Discussion of the caveats and limitations of the theory and modelling is missing from the text.
Response: We will add a paragraph outlining caveats and limitations of the modelling.
We believe these changes will significantly improve the clarity and impact of our manuscript, and we thank the reviewers again for their valuable input.
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eLife Assessment
This important study presents a compelling theoretical framework for understanding phase separation of membrane-bound proteins, with a focus on the organization of tight junction components. By incorporating non-dilute binding effects into thermodynamic models and validating the model's predictions with in vitro experiments on the tight junction protein ZO-1, the authors provide a quantitative tool that will be of interest for biologists interested in membrane-associated condensates. While further clarification of model assumptions and broader mechanistic context would strengthen the work even further, the combination of theory and experiment here is robust and a key advancement in the field.
-
Reviewer #1 (Public review):
Summary:
Biomolecular condensates are an essential part of cellular homeostatic regulation. In this manuscript, the authors develop a theoretical framework for the phase separation of membrane-bound proteins. They show the effect of non-dilute surface binding and phase separation on tight junction protein organization.
Strengths:
It is an important study, considering that the phase separation of membrane-bound molecules is taking the center stage of signaling, spanning from immune signaling to cell-cell adhesion. A theoretical framework will help biologists to quantitatively interpret their findings.
Weaknesses:
Understandably, the authors used one system to test their theory (ZO-1). However, to establish a theoretical framework, this is sufficient.
-
Reviewer #2 (Public review):
Summary:
The authors present a clear expansion of biophysical (thermodynamic) theory regarding the binding of proteins to membrane-bound receptors, accounting for higher local concentration effects of the protein. To partially test the expanded theory, the authors perform in vitro experiments on the binding of ZO1 proteins to Claudin2 C-terminal receptors anchored to a supported lipid bilayer, and capture the effects that surface phase separation of ZO1 has on its adsorption to the membrane.
Strengths:
(1) The derived theoretical framework is consistent and largely well-explained.
(2) The experimental and numerical methodologies are transparent.
(3) The comparison between the best parameterized non-dilute theory is in reasonable agreement with experiments.
Weaknesses:
(1) In the theoretical section, what has …
Reviewer #2 (Public review):
Summary:
The authors present a clear expansion of biophysical (thermodynamic) theory regarding the binding of proteins to membrane-bound receptors, accounting for higher local concentration effects of the protein. To partially test the expanded theory, the authors perform in vitro experiments on the binding of ZO1 proteins to Claudin2 C-terminal receptors anchored to a supported lipid bilayer, and capture the effects that surface phase separation of ZO1 has on its adsorption to the membrane.
Strengths:
(1) The derived theoretical framework is consistent and largely well-explained.
(2) The experimental and numerical methodologies are transparent.
(3) The comparison between the best parameterized non-dilute theory is in reasonable agreement with experiments.
Weaknesses:
(1) In the theoretical section, what has previously been known, compared to which equations are new, should be made more clear.
(2) Some assumptions in the model are made purely for convenience and without sufficient accompanying physical justification. E.g., the authors should justify, on physical grounds, why binding rate effects are/could be larger than the other fluxes.
(3) I feel that further mechanistic explanation as to why bulk phase separation widens the regime of surface phase separation is warranted.
(4) The major advantage of the non-dilute theory as compared with a best parameterized dilute (or homogenous) theory requires further clarification/evidence with respect to capturing the experimental data.
(5) Discrete (particle-based) molecular modelling could help to delineate the quantitative improvements that the non-dilute theory has over the previous state-of-the-art. Also, this could help test theoretical statements regarding the roles of bulk-phase separation, which were not explored experimentally.
(6) Discussion of the caveats and limitations of the theory and modelling is missing from the text.
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