Interplay of condensate material properties and chromatin heterogeneity governs nuclear condensate ripening

Reviewer #1 (Public review):

Summary:

The manuscript "Interplay of condensate material properties and chromatin heterogeneity governs nuclear condensate ripening" presents experiments and theory to explain the dynamic behavior of nuclear condensates. The authors present experimental data that shows the size of multiple artificially induced condensates as a function of time for various conditions. They identify different dynamic regimes, which all differ from traditional Ostwald ripening. By careful analysis and comparison with a quantitative model, the authors conclude that the elastic effects of the chromatin are relevant and the interplay between (heterogeneous) elasticity and surface tension governs the droplets' behavior. However, since they apply a simple model to a complex system, I think that the work is sometimes prone to over-interpretation, which I detail below. In summary, since droplet growth in a heterogeneous, elastic environment is unavoidable for condensates, this work achieves an important step toward understanding this complex setting. The work will likely stimulate more experiments (using different methods or alternative settings) as well as theory (accounting for additional effects, like spatial correlations).

Strengths:

A particularly strong point of the work is the tight integration between experiment and theory. Both parts are explained well at an appropriate level with more details in the methods section and the supplementary information. I cannot comment much on the experiments, but they seem convincing to me and the authors quantify the relevant parameters. Concerning the theory, they derive a model at the appropriate level of description. The analysis of the model is performed and explained well. Even though spatial correlations are not taken into account, the model will serve as a useful basis for developing more complicated models in the future. It is also worth mentioning that the clear classification into different growth regimes is helpful since such results, with qualitative predictions for parameter dependencies, likely also hold in more complex scenarios.

Weaknesses:

I think that the manuscript would profit from more precise definitions and explanations in multiple points, as detailed below. Clearly, not all these points can be fully incorporated in a model at this point, but I think it would be helpful to mention weaknesses in the manuscript and to discuss the results a bit more carefully.

(1) The viscosity analysis likely over-interprets the data. First, the FRAP curves do not show clear exponential behavior. For Figure 1C, there are at least two time scales and it is not clear to me why the shorter time scale right after bleaching is not analyzed. If the measured time scale were based on the early recovery, the differences between the two cases would likely be very small. For Figure 1D, the recovery is marginal, so it is not clear how reliable the measurements are. More generally, the analysis was performed on condensates of very different sizes, which can surely affect the measurements; see https://doi.org/10.7554/eLife.68620 for many details on using FRAP to analyze condensate dynamics. Second, the relaxation dynamics are likely not purely diffusive in a viscous environment since many condensates show elastic properties (https://doi.org/10.1126/science.aaw4951). I could very well imagine that the measured recovery time is related to the viscoelastic time scale. Third, the assumption of the Stokes-Einstein-Sutherland equation to relate diffusivity and viscosity is questionable because of viscoelasticity and the fact that the material is clearly interacting, so free diffusion is probably not expected.

(2) A large part of the paper is spent on the difference between different dynamic regimes, which are called "fusion", "ripening", and "diffusion-based" (with slightly different wording in different parts). First, I would welcome consistent language, e.g., using either fusion or coalescence. Second, I would welcome an early, unambiguous definition of the regimes. A definition is given at the end of page 2, but this definition is not clear to me: Does the definition pertain to entire experiments (e.g., is something called "fusion" if any condensates fuse at any time in the experiment?), or are these labels used for different parts of the experiment (e.g., would the data in Figure 1H first be classified as "ripening" and then "diffusion-based")? More generally, the categorization seems to depend on the observed system size (or condensate count) and time scale. Third, I find the definition of the ripening time a bit strange since it is clearly correlated with droplet size. Is this dependency carefully analyzed in the subsequent parts?

(3) The effect of the elastic properties of the chromatin is described by a Neo-Hookean model, but the strains R/\xi used in the theory are of the order of 100, which is huge. At such high strains, the Neo-Hookean model essentially has a constant pressure 5E/6, so the mesh size \xi does not matter. It is not clear to me whether chromatin actually exhibits such behavior, and I find it curious that the authors varied the stiffness E but not the mesh size \xi when explaining the experiments in the last section although likely both parameters are affected by the experimental perturbations. In any case, https://doi.org/10.1073/pnas.2102014118 shows that non-linear elastic effects related to breakage and cavitation could set in, which might also be relevant to the problem described here. In particular, the nucleation barrier discussed in the later part of the present manuscript might actually be a cavitation barrier due to elastic confinement. In any case, I would welcome a more thorough discussion of these aspects (in particular the large strains).

(4) The description of nucleation on page 7 is sloppy and might be misleading. First, at first reading I understood the text as if droplets of any radius could nucleate with probability p_nuc related to Eq. 7. This must be wrong since large droplets have ΔG<0 implying p_nuc > 1. Most likely, the nucleation rate only pertains to the critical radius (which is what might be meant by R_0, but it is unclear from the description). In this case, the critical radius and its dependence on parameters should probably be discussed. It might also help to give the value of the supersaturation S in terms of the involved concentrations, and it should be clarified whether P_E depends on R_0 or not (this might also relate to the cavitation barrier raised in point 3 above). Secondly, it is a bit problematic that E is sampled from a normal distribution, which allows for negative stiffnesses! More importantly, the exact sampling protocol is important since sampling more frequently (in the simulations) leads to a larger chance of hitting a soft surrounding, which facilitates nucleation. I could not find any details on the sampling in the numerical simulations, but I am convinced that it is a crucial aspect. I did find a graphical representation of the situation in Figure S4A, but I think it is misleading since there is no explicit space in the model and stiffnesses are not correlated.

Reviewer #2 (Public review):

Summary:

The authors used a chemical linker to induce phase separation in U2OS cell nuclei with two different proteins, a coiled-coil protein (Mad1) and a disordered domain (from LAF-1), whose condensates were purported to have different material properties. First, they performed Fluorescence Recovery After Photobleaching (FRAP) and estimated the viscosity via the Stokes-Einstein equation. Combined with droplet fusion assays, this yielded an estimate of the surface tension, wherein the disordered condensates were found to have 130 times higher surface tension than the coiled-coil condensates. Confocal fluorescence microscopy was used to follow condensates over time, enabling classification of growth events as either fusion-, ripening-, or diffusion-based, and subsequent comparison of the relative abundances of these growth events between the two condensate types. Coiled-coil condensates grew primarily by diffusive processes, whereas disordered condensates grew primarily by ripening processes. The coarsening rates were described by growth exponents extracted from power-law fits of average normalized condensate radius over time. In both cases, these growth exponents were smaller than those predicted by theory, leading the authors to propose that nuclear condensate growth is generally suppressed by chromatin mechanics, as found in previous studies albeit with different exponents. The authors developed a theory to understand how the extent of this effect may depend on condensate material properties like surface tension. Treating chromatin as a neo-Hookean elastic solid, the authors assume a form of mechanical pressure that plateaus with increasing condensate size, and the resulting theory is used to analyze the observed condensate growth dynamics. A linearized extension of the theory is used to distinguish between suppressed, elastic, and Ostwald ripening. Finally, the authors consider the impact of different chromatin environments on condensate growth patterns and dynamics, which is achieved experimentally with another cell type (HeLa) and with a drug that decondenses chromatin (TSA). They find that condensate growth patterns are not significantly changed in either condensate type, but that the number of condensates nucleated and their related growth exponent are more sensitive to variations in chromatin stiffness in the coiled-coil system due to its low surface tension.

Strengths:

This work provides evidence that nuclear condensates can coarsen not only by fusion but also by continuous diffusive growth processes, predominant in coiled-coil condensates, and ripening, predominant in disordered condensates. Across these different condensate types and coarsening mechanisms, the authors find growth exponents lower than theoretical expectations, reinforcing the notion that elastic media can suppress condensate growth in the nucleus. Combined with theory, these observed differences in growth patterns and rates are argued to originate from differences in material properties, namely, surface tension relative to local chromatin stiffness. The authors further suggest that the few ripening events that are seen in coiled-coil condensates may be elastic in nature due to gradients in chromatin stiffness as opposed to Ostwald ripening. If this assertion proves to be robust, it would mark an early observation of elastic ripening in living cells.

Weaknesses:

(1) The assertion that nuclear condensates experience an external pressure from the chromatin network implies that chromatin should be excluded from the condensates (Nott et al., Molecular Cell (2015); Shin et al., Cell (2018)). This has not been shown or discussed here. While Movie 1 suggests the coiled-coil condensates may exclude chromatin, Movie 2 suggests the disordered condensates do not. LAF-1, as an RNA helicase, interacts with RNA, and RNA can be associated with chromatin in the nucleus. RNA can also modulate droplet viscosity. The authors' analysis of the disordered condensate data only makes sense if these condensates exclude chromatin, which they have not demonstrated, and which appears not to be the case.

(2) Critical physical parameters like viscosity and surface tension have not been directly measured but rather are estimated indirectly using FRAP and the Stokes-Einstein equation. While not uncommon in the field, this approach is flawed as droplet viscosity is not simply determined by the size of the composing particles. Rather, in polymeric systems, viscosity strongly depends on the local protein concentration and intermolecular interactions (Rubinstein & Semenov Macromolecules (2001)). This unjustified approach propagates to the surface tension estimate since only the ratio of viscosity to surface tension is explicitly measured. Since the paper's conclusions strongly hinge on the magnitude of the surface tension, a more accurate estimate or direct measurement of this salient material property is called for.

(3) The phase diagram of growth modes very much depends on the assumption of neo-Hookean elasticity of the chromatin network. This assumption is poorly justified and calls into question the general conclusions about possible growth phases. The authors need to either provide evidence for neo-Hookean elasticity, or, alternatively, consider a model in which strain stiffening or thinning continues as droplets grow, which would likely lead to very different conclusions, and acknowledge this uncertainty.

(4) There is limited data for the elastic ripening claim. In Figure 3E, only one data point resides in the elastic ripening (δ < 0) range, with a few data points very close to zero.

(5) The authors claim that "our work shows that the elastic chromatin network can stabilize condensates against Ostwald ripening but only when condensate surface tension is low." This claim also depends on the details of the chosen neo-Hookean model of chromatic elasticity, and it is not studied here whether these results are robust to other models.

(6) It is also not clear how the total number of Mad1 proteins and LAF-1 disordered regions change while the condensates evolve with time. As the experiments span longer than 6 hours, continued protein production could lead to altered condensate coarsening dynamics. For example, continued production of Mad1 can lead to the growth of all Mad1 condensates, mimicking the diffusive growth process.

Author response:

We appreciate the reviewer’s recognition of the strengths of our work as well as their constructive critiques and insightful suggestions for improvement. In this provisional response, we outline how we plan to address the reviewer’s comments in the revised manuscript.

(1) Viscosity and surface tension are not accurately measured.

We thank the reviewers for bringing up this important point. We are aware that FRAP is not the best method to accurately measure condensate viscoelasticity due to the problems the reviewers and others in the field have pointed out. More accurate methods of measuring fluorescent protein mobility, such as single-molecule tracking or fluorescence correlation spectroscopy, can be used; however, they cannot accurately reflect the time scale dependence of viscoelasticity in the condensate either. Other methods such as rheology and micropipette aspiration that have been used to measure condensate viscoelasticity in vitro are not accessible in living cells yet. Similarly, there is no readily available method to directly measure the surface tension of condensates in live cells. Therefore, we used FRAP and fusion assays to estimate the ratio of surface tension between the two condensates. This ratio was then used to determine the surface tension of the coiled coil condensates in the model after estimating the surface tension for disordered condensate from in vitro measurements (https://doi.org/10.1016/j.bpr.2021.100011). In the revision, we will adjust our FRAP fitting and use condensates with similar sizes to make our FRAP data more accurate. However, based on the large difference we observed for these two condensates, we do not believe these FRAP improvements would change the conclusions.

We are also aware that the stokes-einstein relation strictly applies to purely viscous systems. One can apply the generalized Stokes-Einstein relation, which links the diffusion coefficient to the complex viscoelastic modulus of the medium. However, the complex modulus is difficult to determine in cells through live imaging. We thus used the Stokes-Einstein relation to estimate the ratio of effective viscosities, assuming elastic deformations relax faster. In the revision, we will add these assumptions to our discussion.

(2) Justification of a Neo-Hookean elasticity model for chromatin.

We thank the reviewer for highlighting this important aspect of our work. The observation that the strains R/ξ in our initial model are of the order of 100 is valid and raises questions about the applicability of the Neo-Hookean model. While it is true that at such high strains, the pressure becomes nearly constant (5E/6), our model remains applicable within the range of strains relevant to chromatin, particularly for small droplets where R/ξ values are more moderate. This is explicitly considered in the section “Effect of mechanical heterogeneity on condensate nucleation and growth,” where we also account for heterogeneous mesh sizes correlated with local stiffness. While these points are discussed in the supplementary material, we acknowledge that these details are not clearly presented in the main text, and we will revise the manuscript to explicitly discuss the strain regime and model applicability.

We agree that varying both the stiffness E and mesh size ξ would provide a more comprehensive understanding of the system, as both parameters are likely affected by experimental perturbations. We will revisit our analysis to incorporate variations in ξ alongside E and discuss the potential effects on our results.

Furthermore, the stabilization of condensate size by chromatin elasticity arises from the size-dependent pressure exerted by the elastic network, which is a feature of strain-stiffening elastic media rather than a specific property of the Neo-Hookean model. However, we agree that exploring the robustness of our results under alternative elasticity models would strengthen the manuscript. In the revised version, we will analyze additional elasticity models, including strain stiffening and thinning, to evaluate how these might influence our conclusions and to provide a broader context for the predicted growth phases.

The connection between the nucleation barrier and the cavitation barrier is particularly intriguing. The referenced study (https://doi.org/10.1073/pnas.2102014118) highlights non-linear elastic effects, including breakage and cavitation, which may be relevant in our system. We will explore whether cavitation effects due to elastic confinement play a role in the nucleation dynamics observed here and include a discussion of these mechanisms in the revised manuscript.

(3) Unclear description of nucleation in the model.

We thank the reviewer for pointing out the lack of clarity in our description of nucleation. R_0​ represents the critical radius for nucleation, beyond which droplets grow spontaneously. The nucleation probability p_nuc​ is evaluated at R_0​, which depends on the free energy barrier ΔG, supersaturation S, and the elastic properties of the surrounding medium. We will include a clearer explanation of R_0​, its dependence on parameters, and its role in nucleation in the revised manuscript.

We ensure that the stiffness is sampled from a truncated normal distribution, preventing negative stiffness values. Sampling is performed at fixed intervals, and we will clarify the protocol to avoid bias and ensure consistency in the simulations.

Supersaturation S will be defined regarding solute and solvent concentrations, and we will discuss its influence on ΔG and R_0​.

The dependence of the elastic pressure P_E​ on R_0​, with stiffer surroundings leading to smaller nucleated droplets, will be explicitly clarified. We also agree that Figure S4A may be misleading, as it suggests spatial correlations in stiffness. We will revise the figure and caption to better represent the model assumptions.

(4) Limited data for the elastic ripening claim.

We acknowledge the reviewer’s concern regarding the limitation of support for the claim in the current manuscript. We believe our data do indicate elastic ripening. Particularly, the data points very close to zero are not necessarily artifacts of the fitting, as the elastic ripening can be very slow due to small differences in the local stiffness values around the droplets. We have mentioned this at the end of the section “Condensate material properties and chromatin heterogeneity determine the modes of ripening”. We shall revisit these results and remedy this concern with more data and analysis in the revised manuscript.

(5) Confusion for dynamic regimes such as "fusion", "ripening", and "diffusion-based" and the problem with using “ripening time” to compare ripening speed.

We will clear up our definitions of the dynamic regimes and ensure consistent language use. The ripening time was defined as the time it takes per length of droplets to shrink. This way, the size dependence of the absolute ripening time is decoupled and thus can be used to compare the speed of ripening between two condensates. This is not well-explained in our current version. In the revision, we will redefine the normalized ripening time to avoid this confusion.

(6) Chromatin should be excluded from the condensates

We have data to support that chromatin is excluded from the condensates. We will add the data in the revision.

(7) Effect of protein production on the diffusive growth process.

From the experiment, we do not believe that protein production is a significant source of the diffusive growth because for coiled-coil condensates nucleated with Hotag3 there was little diffusive growth. In the model also, condensates can grow for hours in the absence of protein production, depending on chromatin stiffness and surface tension. We aim to address the effect of protein production on growth in the revised manuscript.