Phase-separating RNA-binding proteins form heterogeneous distributions of clusters in subsaturated solutions.

Macromolecular phase separation is thought to be one of the processes that drives the formation of membraneless biomolecular condensates in cells. The dynamics of phase separation are thought to follow the tenets of classical nucleation theory, and, therefore, subsaturated solutions should be devoid of clusters with more than a few molecules. We tested this prediction using in vitro biophysical studies to characterize subsaturated solutions of phase-separating RNA-binding proteins with intrinsically disordered prion-like domains and RNA-binding domains. Surprisingly, and in direct contradiction to expectations from classical nucleation theory, we find that subsaturated solutions are characterized by the presence of heterogeneous distributions of clusters. The distributions of cluster sizes, which are dominated by small species, shift continuously toward larger sizes as protein concentrations increase and approach the saturation concentration. As a result, many of the clusters encompass tens to hundreds of molecules, while less than 1% of the solutions are mesoscale species that are several hundred nanometers in diameter. We find that cluster formation in subsaturated solutions and phase separation in supersaturated solutions are strongly coupled via sequence-encoded interactions. We also find that cluster formation and phase separation can be decoupled using solutes as well as specific sets of mutations. Our findings, which are concordant with predictions for associative polymers, implicate an interplay between networks of sequence-specific and solubility-determining interactions that, respectively, govern cluster formation in subsaturated solutions and the saturation concentrations above which phase separation occurs.

Phase separation of RNA-binding proteins with disordered prion-like domains (PLDs) and RNA-binding domains (RBDs) is implicated in the formation and dissolution of membraneless biomolecular condensates such as RNA–protein (RNP) granules (1–9). Macroscopic phase separation is a process whereby a macromolecule in a solvent separates into a dilute, macromolecule-deficient phase that coexists with a dense, macromolecule-rich phase (10, 11). In a binary mixture, the soluble phase, comprising dispersed macromolecules that are well mixed with the solvent, becomes saturated at a concentration designated as csat. Above csat, for total macromolecular concentrations ctot that are between the binodal and spinodal, phase separation of full-length RNA-binding proteins and PLDs is thought to follow classical nucleation theory (12–15).

In classical nucleation theories, clusters representing incipient forms of the new dense phase form within dispersed phases of supersaturated solutions defined by ctot > csat (16, 17). In the simplest formulation of classical nucleation theory (16–18), the free energy of forming a cluster of radius a is . Here, Δµ is the difference in the chemical potential between the one-phase and two-phase regimes (see discussion in ), which is negative in supersaturated solutions and positive in subsaturated solutions; ρ is the number of molecules per unit volume, and γ is the interfacial tension between dense and dilute phases. At temperature T, in a seed-free solution, the degree of supersaturation s is defined as , where R is the ideal gas constant. Here, s is positive for ctot > csat, and, as s increases, cluster formation becomes more favorable. Above a critical radius a*, the free energy of cluster formation can overcome the interfacial penalty, and the new dense phase grows in a thermodynamically downhill fashion. Ideas from classical nucleation theory have been applied to analyze and interpret the dynamics of phase separation in supersaturated solutions (12, 13, 15). Classical nucleation theories stand in contrast to two-step nucleation theories that predict the existence of prenucleation clusters in supersaturated solutions (19–22). These newer theories hint at the prospect of there being interesting features in subsaturated solutions, where ctot < csat and s < 0.

The subsaturated regime, where s is negative, corresponds to the one-phase regime. Ignoring the interfacial tension, the free energy of realizing clusters with n molecules in subsaturated solutions is: ΔF = –nΔµ. Therefore, the probability P(n) of forming a cluster of n molecules in a subsaturated solution is proportional to exp(sn). Accordingly, the relative probability P(n)/P(1) of forming clusters with n molecules will be exp(s(n – 1)). This quantity, which may be thought of as the concentration of clusters with n molecules, is negligibly small for clusters with more than a few molecules. This is true irrespective of the degree of subsaturation, s. Is this expectation from classical nucleation theories valid? We show here that subsaturated solutions feature a rich distribution of species not anticipated by classical nucleation theories. We report results from measurements of cluster size distributions in subsaturated solutions of phase-separating RNA-binding proteins from the FUS-EWSR1-TAF15 (FET) family. We find that these systems form clusters in subsaturated solutions, and that the cluster sizes follow heavy-tailed distributions. The abundant species are always small clusters. However, as total macromolecular concentration (ctot) increases, the distributions of cluster sizes shift continuously toward larger values. We discuss these findings in the context of theories for associative polymers (9, 23–30).

Results

Macroscopic Phase Separation Is Not Observed in Subsaturated Solutions.

We quantified csat using a spin-down-based absorbance assay. At low concentrations, any prior aggregates that are present in solution are removed upon centrifugation at 20,000 relative centrifugal force (RCF) units. Results from this assay are summarized in Fig. 1 for FUS-SNAP. At low ctot, the concentration in the supernatant increases monotonically with the bulk concentration of SNAP-tagged FUS. However, above a threshold concentration, which we designate as csat, the concentration in the supernatant remains fixed at a plateau value. This is consistent with the establishment of phase equilibrium between dilute and dense phases (Fig. 1).

Fig. 1.

FUS-SNAP has a quantifiable csat whereby condensates form only in supersaturated solutions. (A) Sample data for absorbance-based spin-down assays. Data shown here are for FUS-SNAP in 20 mM Tris, pH 7.4, and 100 mM KCl at ∼25 °C. The red dashed line intersects the abscissa at 3 µM, which is the inferred csat for this construct. (B–F) Microscopy images collected at the 18-h time point for solutions containing different concentrations of FUS-SNAP in 20 mM Tris, pH 7.4, and 100 mM KCl at ∼25 °C. For imaging purposes, 5% of the total mixture in each sample is made up of FUS-eGFP. (Scale bar, 10 µm.) The data show the presence of micron-scale condensates at or above csat of ∼3 µM. The FUS constructs used were expressed and purified using method A ().

To test whether csat is a true saturation concentration, we performed microscopy-based measurements for solutions containing different amounts of FUS-SNAP and untagged FUS (). The concentrations investigated range from 0.25 µM to 4 µM. Data were collected ∼30 min after sample preparation, and, for each sample, a series of images were collected at different time points over an 18-h period. Results at the 18-h time point are shown in Fig. 1 for different concentrations of FUS-SNAP. Irrespective of the time point of interrogation, condensate formation of FUS-SNAP is only detectable at or above csat ≈ 3 µM. Similar data were obtained for untagged FUS (). Based on these results, we conclude that macroscopic phase separation is not realized in subsaturated solutions and that the FUS molecules are defined by construct- and solution condition–specific saturation concentrations.

Clusters Spanning a Range of Sizes Form in Subsaturated Solutions of FUS.

First, we used dynamic light scattering (DLS) to characterize subsaturated solutions of untagged FUS (Fig. 2 and ) and FUS-SNAP (Fig. 2 and ). Unless otherwise specified, all measurements were performed in 20 mM Tris, pH 7.4, and 100 mM KCl at ∼25 °C. The DLS results we obtain are robust to the protocols used to express and purify FUS and FUS-SNAP molecules ().

Fig. 2.

DLS data show that clusters spanning a range of sizes form in subsaturated solutions. (A) Measurements were performed at different bulk concentrations of untagged FUS (see legend) that represent different degrees of subsaturation −2 ≤ s ≤ 0. Scattering intensities, measured 8 min after sample preparation, shift toward larger values as the total macromolecular concentration ctot approaches the csat of ∼2 µM. (B and C) Scattering intensity was measured at 0.5 µM (B) and 1 µM (C) of FUS-SNAP at 8 min after sample preparation and before centrifugation (brown curves). The solutions were centrifuged at 20,000 RCF for 5 min at room temperature. Then, scattering intensities of the supernatant were measured at the 8-min time point. These data are shown in blue curves in B and C. They show the presence of species of sizes ranging between 7 and 100 nm. The FUS constructs were expressed and purified using method A ().

The DLS data are shown as scattering intensities plotted against the apparent hydrodynamic diameter (dh). For calibration, the dh of untagged FUS monomers is ∼7 nm. The intensity profiles for untagged FUS collected at 0.25 µM show two peaks (Fig. 2). The peak at ∼8 nm corresponds to monomers and oligomers. The second peak at ∼200 nm corresponds to mesoscale clusters. The observed bimodality could imply clusters of fixed size forming via either microphase separation (31) or micellization (32). To test for this possibility, we investigated how the DLS signals change with increasing protein concentrations (Fig. 2). For microphase separation or micellization, the locations of the peaks should stay in place while the intensities of the peaks change with respect to one another. We do not observe this behavior. Instead, the location of the peak corresponding to larger dh values shifts to the right. At higher concentrations, DLS becomes blind to the presence of smaller species. As a result, the peak at lower values of dh vanishes above a concentration of 0.7 µM.

The apparent bimodality seen in intensity profiles can also arise from a heavy-tailed distribution of cluster sizes, whereby the most abundant species are monomers and oligomers. In this scenario, bimodality at low concentrations below 0.7 µM can result from smaller species being the most abundant, and the largest, mesoscale species having the highest scattering cross-sections (33). This would mask the presence of species of intermediate sizes. To test for the presence of species of intermediate sizes, we subjected subsaturated solutions of FUS-SNAP molecules to centrifugation at 20,000 RCF. This removes species larger than 100 nm in diameter. Although the bulk concentrations prior to centrifugation were 0.5 and 1 µM , the centrifugation step lowers the total macromolecular concentration. The top of the centrifuged solution was then collected for DLS measurements. The DLS data, collected after centrifugation, are shown in Fig. 2 for FUS-SNAP. The scattering intensity profiles, measured after centrifugation, show the presence of species in the size range of 7 nm to 100 nm for the apparent dh. These species include monomers and an assortment of higher-order species. The upper limit on the number of FUS molecules per cluster (nmol) is estimated as the ratio of the hydrodynamic volume of a cluster of size dh to that of the monomer. This yields upper bounds on estimates of nmol of 10, 102, and 103 for dh values of ∼15, ∼30, and ∼70 nm, respectively.

Taken together with data obtained prior to centrifugation, the parsimonious interpretation of the data is that the distributions of cluster sizes are likely to be exponentials with heavy tails, such as Weibull distributions (34). This would be concordant with reversible processes such as isodesmic associations that lack a threshold concentration, with average sizes evolving continuously as concentrations increase (35, 36).

Morphologies of the Largest Clusters That Form in Subsaturated Solutions.

We used negative stain transmission electron microscopy (TEM) to characterize morphologies of the largest clusters that form in subsaturated solutions of FUS-SNAP. Given their sizes, we refer to these species as mesoscale clusters. These clusters have roughly spherical morphologies (Fig. 3 and ). This was further confirmed using DLS data collected for untagged FUS at two different angles (Fig. 3). Based on their quasi-spherical morphologies and plausible densities within clusters, we estimate that mesoscale clusters with diameters of ∼150 nm encompass roughly 102 to 103 molecules.

Fig. 3.

Mesoscale clusters that form in subsaturated solutions have quasi-spherical morphologies. (A) Representative TEM image of 2 µM FUS-SNAP. The collections of TEM images were used to quantify the distribution of sizes (Inset and ). (B) DLS data collected at two different angles corroborate the spherical morphologies of clusters observed in subsaturated solutions. Samples used here were prepared using method A ().

Mesoscale Clusters Are of Low Overall Abundance.

We quantified the abundance of mesoscale clusters using nanoparticle tracking analysis (NTA) (37). In these measurements, we track the Brownian motion of scatterers using dark-field microscopy (Movies S1 and S2). We collected NTA data for untagged FUS (Fig. 4) and FUS-SNAP (Fig. 4). The distributions of mesoscale cluster sizes shift toward larger values with increasing protein concentrations. NTA also enables quantification of the percentage of molecules in solution that make up mesoscale clusters (). In a 250-nM solution of FUS-SNAP, the total volume fraction of proteins is ϕ ≈ 1.4 × 10−5, and the fraction of the solution volume taken up by mesoscale clusters is ϕmeso ∼4 × 10−8. This translates to 0.15% of the protein molecules in solution being a part of mesoscale clusters (Fig. 4). For a concentration just below csat, the relative abundance of mesoscale clusters increases to ∼1%. Similar results, highlighting the low abundance of mesoscale clusters,were obtained for untagged FUS ().

Fig. 4.

Mesoscale clusters have low overall abundance. (A) NTA data for untagged FUS (csat ≈ 2 µM) were collected at different concentrations that represent different degrees of subsaturation. (B) NTA data for FUS-SNAP (csat ≈ 3 µM) at different degrees of subsaturation. (C) Relative abundance of mesoscale clusters, quantified at different degrees of subsaturation for FUS-SNAP. The constructs used were expressed and purified using method A ().

Clusters Increase in Size with Increasing Concentrations, and the Size Distributions Have Heavy Tails.

Are non-mesoscale clusters monomers? To answer this question, we probed the distributions across a broader range of sizes using orthogonal, fluorescence-based approaches to characterize subsaturated solutions and access length scales that are distinct from those accessed using DLS and NTA measurements. Fluorescence anisotropy can be applied for detecting the presence of clusters with different numbers of molecules. These experiments use a small fraction of fluorescently labeled molecules (tracers) and a majority fraction of molecules that lack a fluorescent label. We used confocal multiparameter detection (MFD), which measures the fluorescence anisotropies of diffusing particles (38). This allows us to monitor the size-dependent rotational diffusion of molecules. We performed experiments with a fixed concentration (100 nM) of FUS-eGFP and added FUS-SNAP as a titrant with the concentration of FUS-SNAP ranging from 0 µM to 5 µM. The anisotropy increases monotonically at low concentrations of FUS-SNAP (Fig. 5). This indicates the presence of smaller clusters such as dimers, trimers, tetramers, etc. each with increased volumes that result in longer times for molecular rotational diffusion. The anisotropy of eGFP is especially sensitive to the presence of small clusters. However, this signal saturates for larger clusters. This is because the measured apparent volume has a nonlinear scaling due to the inverse relationship between anisotropy and volume. Further, the flexible FUS backbone and long eGFP linker may diminish the actual change in anisotropy. To test for the presence of clusters larger than oligomers, we used the environmentally sensitive dye Nile Red, which offers a higher dynamic range in anisotropy. With Nile Red, we see a strong continuous increase in anisotropy as the concentration of FUS-SNAP is increased (Fig. 5). The signal does not saturate as the concentrations of FUS-SNAP increase. That this lack of saturation emanates from large bright clusters is confirmed in the binned histogram of fluorescence intensity of the photon trace (Fig. 5). These data show that the size distributions of clusters that form in subsaturated solutions have heavy tails, andthe distributions shift continually toward larger cluster sizes as concentrations increase.

Fig. 5.

Fluorescence anisotropy and brightness-based measurements show the presence of clusters in subsaturated solutions. (A) Normalized fluorescence anisotropy from confocal MFD plotted against the concentration FUS-SNAP, which is the titrant. Data were collected at 50 mM KCl. The sample was prepared using method B. We also titrated FUS-SNAP from 0 µM to 3 µM in the presence of 20 nM Nile Red. Unlike the anisotropy measured using eGFP fluorescence (green), the measurements based on Nile Red (red) do not show saturation behavior, implying a continuous growth of cluster sizes with the concentration of FUS-SNAP. (B) With increasing FUS-SNAP concentrations in the presence of 20 nM Nile Red, we observe bright particles, with apparent heavy-tailed distributions. (C) MCS data showing the formation of clusters in subsaturated solutions comprising FUS-GFP, prepared using method A. The apparent sizes of clusters, quantified in terms of photon intensity per cluster where 1 Mcnt = 1 million photons per millisecond, increase with increasing protein concentration. The FUS-GFP constructs used in the MCS experiments were expressed and purified using method A ().

Next, we turned to confocal detection under flow by using microfluidic confocal spectroscopy (MCS). This is a brightness-based method that combines microfluidic mixing and flow with confocal detection (39–41). MCS measurements are sensitive to the presence of species that span a broad size range, from tens to hundreds of nanometers. Due to convective flow, the measurement is not reliant on diffusion alone for sampling species of different sizes in solution (). We used FUS-eGFP (csat ≈ 4 µM; ) for the MCS measurements. Data obtained at concentrations of 0.25, 0.5, and 1 µM were plotted as the brightness per event. These data clearly show the formation of clusters in subsaturated solutions whose average sizes evolve continuously with concentration (Fig. 5).

Other FET Family Proteins Also Form Clusters in Subsaturated Solutions.

Next, we asked whether the formation of clusters in subsaturated solutions is unique to FUS or whether this is a feature that is shared by other members of the FET family of RNA-binding proteins. We collected DLS data in subsaturated solutions for untagged hnRNP-A3 (csat ≈ 6 µM; and Fig. 6), EWSR1-SNAP (csat ≈ 2 µM; and Fig. 6), and TAF15-SNAP (csat ≈ 2 µM; and Fig. 6). These data show that other FET family proteins also form clusters in subsaturated solutions. The average sizes of these clusters increase with protein concentration. Raw DLS data in the form of autocorrelation functions are shown in .

Fig. 6.

Clusters also form in subsaturated solutions of FET family proteins. DLS data show evidence for mesoscale clusters in subsaturated solutions for (A) hnRNP-A3 (csat ≈ 6 µM), (B) SNAP-tagged TAF15 (csat ≈ 2 µM), and (C) SNAP-tagged EWSR1 (csat ≈ 2 µM).

Clusters Are Reversible, and Molecules Exchange between Clusters.

Using DLS, we find that the sizes of clusters decrease upon dilution and increase with increased concentration in the subsaturated regime (Fig. 7 and ). This observation points to the reversibility of cluster formation in subsaturated solutions whereby they shrink upon dilution and grow when concentrations increase. For cluster formation to be reversible, the molecules must exchange between clusters or between clusters and the bulk solution. To test for this, we used Förster resonance energy transfer (FRET) experiments (setup shown in Fig. 7). These experiments show that FUS molecules readily exchange across clusters (Fig. 7 and ).

Fig. 7.

Clusters in subsaturated solution form via reversible associations, and molecules readily exchange between clusters. (A) DLS data were collected at different time points for SNAP-tagged FUS at 3 µM. (B) Upon dilution to 1 µM, the DLS data show changes to the intensity profiles, with the appearance of smaller species. (C) Increasing the concentration from 1 µM to 2.5 µM leads to an increased preference for larger species. (D) Schematic showing the design of the FRET assay. Here, two sets of clusters are formed, each using a total concentration of 1 µM SNAP-tagged FUS molecules. In each set, 5% of the molecules carry a fluorescent label (Alexa Fluor 488 [green] or Alexa Fluor 46 [red]). The clusters are mixed to achieve a total concentration of 1 µM. The mixture is excited using a 488-nm laser, and the emission spectrum is measured from 520 nm to 600 nm. If molecules exchange between the clusters, then we expect to see a peak at the excitation maximum of 573 nm. (E) Fluorescence emission spectra show the decay of fluorescence for molecules with the Alexa 488 label and for the mixture. The latter shows a maximum at 573 nm, which is indicative of the exchange of molecules between the clusters. The FUS constructs used in this experiment were expressed and purified using method A.

The data presented in Figs. 2–7 show the presence of clusters in subsaturated solutions. The average cluster sizes increase as concentrations increase and approach csat. The clusters are equilibrium species that form and dissolve via reversible associations. The low abundance of mesoscale clusters quantified using NTA, the presence of smaller species, readily detected using fluorescence anisotropy, and the presence of a broad spectrum of species indicated by MFD, fluorescence intensity distribution analysis, and MCS suggest that the distributions of cluster sizes are concentration dependent and heavy tailed.

Growth of Macroscopic Phases above csat.

In the physics of stochastic processes, it is known that random variables with broad distributions, specifically, heavy-tailed distributions, can be generators of condensation phenomena (42). Therefore, guided by precedents in the literature (43, 44), we used DLS to ask whether the heavy-tailed distributions of cluster sizes generate discernible signatures of transitions from finite-sized clusters to condensates just above csat. Specifically, we used DLS to probe the presence of slow modes (44) in the temporal evolution of autocorrelation functions for concentrations of untagged FUS that are below and above csat. Below csat, the autocorrelation functions reach a steady state and do not change with time after a few minutes (Fig. 8). The timescales interrogated here are roughly seven orders of magnitude longer than the time it takes for individual FUS molecules to diffuse across 10 nm. Just above csat (Fig. 8), the autocorrelation functions show the presence of slow modes. Such modes have been observed for polymers in dense phases, and have been attributed to reptation (44). However, we interpret our observation of slow modes to imply that clusters grow into micron-scale condensates above csat. The relevant data are shown for hnRNPA3, EWSR1-SNAP, and TAF15-SNAP (Fig. 8 and ). That the slow modes in autocorrelation functions point to the onset of condensation processes was independently verified using microscopy. These data show that condensation as a function of time leads to the formation of dense phases (Figs. 8-8G). The observed temporal evolution is consistent with a coarsening process whereby larger condensates grow at the expense of smaller ones (45, 46). Our analysis also shows that the lowest concentration at which one observes the onset of slow modes in autocorrelation functions measured using DLS can be used as an efficient, centrifugation-free protocol for estimating csat. Further, these data suggest that csat in systems that feature heavy-tailed distributions of clusters in subsaturated solution may be viewed as the threshold concentration for the onset of coarsening through coalescence, a key signature of macroscopic phase separation (47).

Fig. 8.

Clusters grow into micron-scale bodies above csat. (A) Temporal evolution of autocorrelation functions from DLS measurements for untagged FUS. Below csat, the sizes of mesoscale clusters reach a steady state. (B) Above csat, we observe increased amplitudes of the autocorrelation function at longer times, (annotated using a gray arrow). (C) DLS data for hnRNPA3, EWSR1-SNAP, and TAF15-SNAP. Below csat, the cluster sizes reach a steady state. (D–G) Evidence of the growth into micrometer-scale condensates, displaying coarsening whereby fewer condensates grow by absorbing smaller species. This is made clear by the long-time evolution of micrometer-scale condensates formed by 3 µM untagged FUS containing 5% FUS-eGFP.

Cluster Formation and Macroscopic Phase Separation Can Be Decoupled.

Solutes such as 1,6-hexanediol (HD) can suppress phase separation and dissolve micron-scale condensates (30, 48). We used DLS to measure the impact of increased HD concentration on low-abundance mesoscale clusters vs. macroscopic phase separation. We observe a dose-dependent response of macroscopic phase separation on HD. Specifically, the presence of a dense phase, characterized by the appearance of slow modes in the autocorrelation functions, is weakened and abrogated at increased concentrations of HD (Fig. 9 ). However, profiles of autocorrelation functions, namely, the presence of fast modes that are consistent with the presence of clusters, persist even upon the addition of up to 1% wt/vol of HD. Similar results were obtained when we queried the effects of adenosine 5′-triphosphate (ATP), which is thought to be a condensate dissolving hydrotrope at the concentrations used here (49). Further, the distributions of clusters formed at csat (∼2 µM) show minimal changes in the presence of HD and/or ATP (Fig. 9).

Fig. 9.

Solutes dissolve condensates while having a minimal effect on clusters. For untagged FUS, above csat, there are slow modes in the autocorrelation functions; see B. (A–C) This feature is weakened in (A) 0.25% and (B) 0.5% and lost in (C) 1% 1,6 hexanediol (HD), which dissolves condensates for concentrations above csat. However, clusters that form via fast modes persist upon the addition of HD. (D) Similar observations were obtained in the presence of 3 mM ATP-Mg. (E) NTA data, collected at a concentration of 2 µM for untagged FUS, show that the solutes have discernible effects on the distribution of cluster sizes. Within statistical error of the measurements, the effects of solutes on clusters in subsaturated solutions are small when compared with the impact of solutes on the loss of slow modes above csat.

We interpret the results of solute titrations to mean that there are at least two separable energy scales that contribute to condensate formation. Solutes such as HD and ATP primarily affect solvent quality, whereby the Flory χ parameter is altered to impact the overall solubility profiles of FUS molecules. This is consistent with the observations that polyols such as HD lower the macroscopic surface tension of water (50). Accordingly, we reason that cluster formation is likely to be influenced by distinct, sequence- or chemistry-specific interactions, that can be separable using solutes but are generally strongly coupled to driving forces for macroscopic phase separation.

Impacts of Mutagenesis on Cluster Formation and Phase Separation.

We used a combination of mutagenesis experiments and experiments based on changes to solution conditions to query the extent of coupling between interactions that drive cluster formation vs. macroscopic phase separation. We measured the sensitivity of cluster formation and phase separation of full-length, untagged FUS to changes in pH (). These experiments show that increasing the net charge weakens cluster formation in subsaturated solutions (). This leads to a clear upshift of the csat for phase separation (). Likewise, increasing the concentration of monovalent salts also weakens cluster formation (). Therefore, increasing the net charge above a system-specific threshold or screening of electrostatic interactions weakens cluster formation and macroscopic phase separation.

To test the contributions of sequence-specific interactions to the coupling between cluster formation and macroscopic phase separation, we replaced 24 Arg residues in the RBD of full-length FUS with Gly residues. These mutations shift csat up by at least an order of magnitude (9) and concomitantly lower the abundance of mesoscale clusters by over an order of magnitude (Fig. 10 and ). Likewise, substitution of aromatic Tyr residues with Ser in the PLD of full-length FUS abrogates phase separation in the low micromolar range while also lowering the abundance of mesoscale clusters by over an order of magnitude (Fig. 10 and ). These results highlight a strong coupling between clustering and macroscopic phase separation when Arg or aromatic residues are removed (). In contrast, we find that substitution of 10 Asp and 4 Glu residues with Gly within the RBD of full-length FUS stabilizes cluster formation (Fig. 11 and ). Specifically, at a concentration of 2 µM, the abundance of clusters increases by a factor of 1.8 when compared with wild-type FUS. However, the increase in abundance of clusters is not accompanied by evidence of condensate formation, even at a bulk concentration of 4 µM ().

Fig. 10.

Mutagenesis experiments reveal chemistry-specific effects of different residue types on the formation of mesoscale clusters in subsaturated solutions of FUS. (A) NTA data show that substituting 24 Arg residues with Gly within the RBD reduces the abundance of mesoscale clusters. (B) Replacing aromatic residues within the PLD of full-length FUS shows a valence-dependent reduction in the abundance of mesoscale clusters. (C) Replacing Asp/Glu with Gly in the RBD of full-length FUS enhances chemistry-specific interactions that stabilize clusters. (D) Substitution of six Phe residues with Gly in the RBD of full-length FUS lowers the abundance of clusters. (E) Likewise, substitution of six Tyr with Ser in the RBD of full-length FUS also lowers the abundance of clusters.

Fig. 11.

Alterations to chemistry-specific interactions impact the abundance of clusters. (A) RBDs and PLDs of FUS feature differences in amino acid compositions. (B) NTA data show that the lower valence and absence of Arg-π interactions reduces the abundance of mesoscale clusters for the PLD of FUS by roughly two orders of magnitude when compared with full-length FUS. (C) In contrast, the RBD of FUS forms mesoscale clusters that are an order of magnitude more abundant than the PLD.

Next, we queried the impact of replacing six of the Phe residues within the RBD of full-length FUS with Gly (Fig. 10 and ) vs. replacing six of the Tyr residues in the RBD with Ser (Fig. 10 and ). Although both Phe and Tyr are aromatic residues, the effects of replacing these moieties are quantitatively different. At equivalent concentrations, the abundance of mesoscale clusters, detected using NTA, is at least threefold lower when Tyr residues are substituted with Ser when compared with substituting Phe residues with Gly. In both cases, macroscopic phase separation is also not observed for bulk concentrations up to 10 µM (). The differences between Phe and Tyr are reminiscent of recent results for the PLD of hnRNP-A1 (51).

Impact of the Diversity of Chemistry-Specific Interactions on Cluster Formation and Phase Separation.

The distribution of residue types is different across full-length FUS compared with the PLD and RBD alone (Fig. 11). The measured csat values of PLDs are at least two orders of magnitude higher than those of full-length proteins (9, 52). We asked whether this change in csat was accompanied by changes in cluster formation. NTA measurements show that, at equivalent molar concentrations, the abundance of mesoscale clusters formed by the PLD of FUS is lower by a factor of 60 when compared with the abundance of such clusters formed by full-length FUS (Fig. 11 and ). The DLS measurements show that macroscopic phase separation of the PLD was not observed for concentrations up to 150 µM (). The sequence of the RBD features a significant number of aromatic and anionic residues, and its measured csat is ∼20 µM (). This is an order of magnitude lower than that of the PLD. NTA data show that, at a molar concentration of 1 µM, mesoscale clusters formed by the RBD (Fig. 11 and ) are at least 10 times more abundant than clusters formed by the PLD. This highlights the contributions of sequence- or chemistry-specific interactions to cluster formation and phase separation.

Simulations Show That Systems Featuring At Least Two Energy Scales Behave Very Differently from Those with a Single Energy Scale.

One way to introduce distinct energy scales into a polymeric system is via the framework of associative polymers (9, 23, 26–29, 53–57). These are macromolecules with attractive groups known as “stickers” that are interspersed by “spacers” (23, 25, 26, 55, 58). Stickers can form noncovalent reversible cross-links with one another (30, 51, 59, 60). The strengths of intersticker interactions are governed by the functional groups that define stickers. Therefore, in a stickers-and-spacers framework, intersticker interactions are specific interactions, whereas spacers define the intrinsic χ and contribute to the overall solubility profile of the polymer (30, 51, 59, 60). In recent computational work, FUS molecules were modeled as diblock polymers (61). Note that associative polymers represent a superset that encompasses specific instantiations such as diblock systems.

We used the LaSSI (Lattice Simulation Engine for Sticker and Spacer Interactions) engine (27), to model lattice polymers featuring a single energy scale vs. models for associative polymers with at least two energy scales. Our phenomenological models are intended to uncover possibilities that come from competing energy scales. First, we considered a model homopolymer where all units are identical (Fig. 12, Left). Here, all interactions are uniform and isotropic, and they are described by a single energy scale, ε. For the finite-sized homopolymer considered here, phase separation requires that ε be negative (χ must be positive), and the magnitude of ε must be greater than 0.1 k Results for ε values of −0.15 k and −0.2 k are shown in Fig. 12, Left. Making ε stronger by a factor of 4/3, realized by lowering ε from −0.15 k and −0.2 k, decreases ϕsat by three orders of magnitude (Fig. 12, Left). This is because phase separation is a highly cooperative process when it is governed by a single energy scale (62). Above a threshold value, small changes to the energy scale ε will dramatically alter the overall solubility, and this is manifest as large changes to csat. The dense phases formed by homopolymers are essentially polymer melts with volume fractions of ϕden ≈ 1 ().

Fig. 12.

Results from LaSSI simulations highlight the distinctions between homopolymers governed by a single energy scale vs. associative polymers with two energy scales. Each polymer has 12 beads. For homopolymers (results shown in Left), all beads are the same. For associative polymers, the red beads are stickers, and the blue beads are spacers. We quantify the probability P(n) of observing clusters comprising n molecules. The data are presented in two rows (A) and (B), with four panels per row. In each panel, the dashed lines represent distributions computed from LaSSI simulations that were performed above the model-specific csat, and the solid lines represent distributions computed in subsaturated solutions. The colors of the dashed and solid lines represent the extent of supersaturation (s > 0 for ϕ > ϕsat) or subsaturation (s < 0 for ϕ < ϕsat), respectively. Results in Left are for the homopolymer described by a single energy scale ε, whereas results in Left Center, Right Center, and Right are for associative polymers featuring two energy scales, namely, the excluded volumes of spacers and the specific sticker–sticker interactions with anisotropic interactions worth gε, where g = 30, 45, and 60, respectively.

The introduction of distinct energy scales alters the overall phase behavior. In our model for associative polymers, each bead is designated as being a sticker or a spacer (red vs. blue beads in Fig. 12). Stickers form specific anisotropic interactions with one another. For a given value of ε, the strengths of anisotropic intersticker interactions are set to be gε, where g equals 30, 45, or 60 (Fig. 12, Left Center, Right Center, and Right). The spacers do not engage in attractive spacer–spacer or spacer–sticker interactions. Their only contribution is to the generic excluded volume. For values of ε where the homopolymers undergo phase sepa ration, we observe three distinct effects of introducing two different energy scales. First, the value of the saturation concentration ϕsat is renormalized to be larger than that of the equivalent homopolymer. Although ϕsat decreases with increasing g, the decrease is considerably smaller when compared with what is observed for the homopolymer when the magnitude of ε is increased by similar extents. Second, clusters form in subsaturated solutions. The size distributions of clusters are heavy tailed, and their quantitative features are sensitive to both g and ε. This highlights the coupling between the effects of specific sticker–sticker interactions and generic, solubility-determining interactions. Third, the interplay between stickers and spacers causes a dilution of polymer concentrations in the dense phase (). Instead of a polymer melt, the dense phases are condensate-spanning networks defined by intersticker cross-links that are diluted by spacers. The overall thrust of our simulation results is concordant with results from simulations performed by Ranganathan and Shakhnovich (63) of systems with similar architectures.

Discussion

A simple way to describe the driving forces for phase separation is using the mean field Flory–Huggins formalism (10, 11). These simple theories have been the mainstay for quantitative descriptions and analysis of phase transitions driven by multivalent proteins and nucleic acids in vitro and in cells (12–15, 45, 47, 62, 64–68). In this formalism, there is only one effective energy scale as captured by the parameter χ (10). For a purely phase separation–based process (10, 11), subsaturated solutions should feature dispersed monomers and very few small clusters, if any, at any given time. In this work, we report results from our investigations of the types of species that form in subsaturated solutions of phase-separating RNA-binding proteins with disordered PLDs and RBDs. We find that subsaturated solutions do not conform to expectations based on systems that are characterized by a single energy scale such as the Flory χ-parameter. Therefore, the biophysical principles underlying biomolecular condensate formation and dissolution should not be described using simple, Flory-Huggins-stylemodels for macroscopic phase separation.

The presence of different energy scales is best illustrated by the response to solutes, in which clusters and condensates respond differently to HD and ATP. Phase separation is likely driven mainly by composition-specific interactions that determine the solubility profiles of FUS and FUS-like molecules. However, our data also show that the sequence features of FUS and FUS-like molecules can engender a strong coupling between the driving forces for cluster formation and phase separation. Mutations to stickers weaken cluster formation and increase csat. This indicates that the mechanism of phase separation is intimately tied to the structure of the underlying size distribution of clusters that form in subsaturated solutions. The picture that emerges is of networks of chemistry-specific, interresidue interactions (7, 9, 51, 52, 69) driving cluster formation and determining the extent of coupling between cluster formation and phase separation. It is important to emphasize that the clusters that we report here are not the prenucleation clusters that have been reported for various systems in supersaturated solutions (19–22). Nor are they micellar species or facsimiles of microphase separation. Instead, they are distinct species that appear to form via mechanisms that are paralogous to isodesmic reversible associations (36) that generate heavy-tailed distributions of cluster sizes.

Recently, Zhao et al. (70) showed that the N protein of the severe acute respiratory syndrome coronavirus 2 virus, which has been studied for its macroscopic phase separation (71, 72), also forms an assortment of clusters in subsaturated solutions. Likewise, Seim et al. (73) discovered that the interplay between specific homotypic and heterotypic interactions of the fungal protein Whi3 influences the distribution of protein cluster sizes that forms in dilute phases that coexist with Whi3-RNA granules. Mutations to the specific interactions that generate clusters through homotypic interactions can either enhance or diminish clustering, and this has a concomitant effect on the concentrations of Whi3 proteins in the dense phase (73). Both reports highlight the importance of dilute phase clusters that are either modulated by heterotypic interactions or influence phase behavior driven by heterotypic interactions.

Mesoscale clusters of low overall abundance have been reported for subsaturated solutions of folded proteins that form crystalline solids (74, 75). These clusters were found to have fixed size, irrespective of protein concentration (74), and are likely to be manifestations of microphase separation (31). In contrast, we observe continuous growth in the sizes and abundance of clusters with concentration. As discussed below, the framework of associative polymers provides a plausible explanation for our observations.

Associative polymers undergo two types of transitions namely, percolation without phase separation—also known as sol–gel transitions—or phase separation coupled to percolation (25–28, 56, 57). Above a system-specific threshold concentration known as the percolation threshold, or cperc (27–29, 57), nonstoichiometric clusters become connected into a percolated or system-spanning network (27–29, 57). Quantitatively, cperc is determined by the numbers (valence) of stickers, diversity of sticker types (29), and strengths of intersticker interactions (28, 29). If cperc < csat, then associative polymers undergo percolation without phase separation. Alternatively, if csat < cperc < cden, where cden is the concentration of the dense phase formed via phase separation (57, 76), then phase separation and percolation are coupled . In this scenario, the condensates form via PSCP and are akin to spherical microgels (77), whereby the percolated network is condensate spanning. The prepercolation clusters that form in subsaturated solutions are direct manifestations of clusters predicted to define sols formed by associative polymers undergoing either percolation without phase separation or phase separation coupled to percolation.

Precedents for Clusters in Subsaturated Solutions.

The multivalent domain linker systems studied by Rosen and coworkers (57, 76, 78–81) are exemplars of associative polymers featuring an interplay between site-specific domain–motif interactions and linker-mediated solubility profiles. Li et al. (76) investigated the phase behaviors of systems where phase transitions are driven by multivalent interactions among poly-SH3 and poly-PRM (proline-rich module) molecules. Existence of a threshold concentration for phase transitions requires that there be at least three SH3 domains and three PRMs within the associating molecules. This is consistent with the presence of a valence-dependent percolation threshold (82, 83). Li et al. (76) showed that, as the valence (numbers) of SH3 domains and PRMs increases, the threshold concentration for phase transitions decreases. Importantly, Li et al. (76) also reported the presence of clusters in subsaturated solutions. These were detectable using DLS and small-angle X-ray scattering. The phase transitions were referred to by Li et al. as macroscopic liquid–liquid phase separation that is thermodynamically coupled to sol–gel transitions. This phrasing is synonymous with the process we describe here as phase separation coupled to percolation or PSCP.

Biological Relevance of Clusters That Form in Subsaturated Solutions.

Our results lead us to propose that intrinsically disordered RNA-binding proteins from the FET family belong to the class of polymers known as associative polymers. Our findings show that chemistry- or site-specific sticker-mediated interactions and solubility-determining spacer-mediated interactions are separable in systems with sticker and spacer architectures (28, 30, 51, 52, 56, 57, 84–90). Prepercolation clusters, with size distributions featuring heavy tails, are likely to be present at endogenous concentrations that tend to be in the nanomolar to low micromolar range in live cells (91). The clusters we observe are likely to be the bridge that connects to recent findings regarding dynamic clusters comprising multivalent molecules (92, 93). Importantly, the recent work of Cho et al. (94) identified cytoplasmic clusters formed by several RNA-binding proteins under endogeneous, unstressed conditions. These clusters are distinct from cytoplasmic stress granules, which are bona fide condensates that form in response to stress through the process of phase separation coupled to percolation (5–7). Now that we know what to look for, we expect there to be many more accounts of clusters, precursors of condensates, forming at endogenous levels in live cells. The clusters of interest will lack a phase boundary and will form via reversible associations, and the distributions of their sizes and shapes will be determined by a complex network of homotypic and heterotypic interactions.

What are the potential consequences of clusters defined by heavy-tailed size distributions forming in subsaturated solutions in cells? Process control via biomolecular condensates requires that phase separation be robust and reproducible (3). In a classical phase separation system, the barrier to nucleation will determine the response time. Clusters in subsaturated solutions will likely speed up the response time by lowering the barrier for phase separation. Accordingly, we postulate that clusters poise RNA-binding proteins for robust condensate formation in response to stimuli. Our discovery of the presence of clusters following heavy-tailed size distributions in subsaturated solutions suggests that regulation can also occur at the level of shaping the distribution of cluster sizes. This can happen through a variety of heterotypic interactions, specifically with RNA molecules. Additionally, chaperones are known to modulate size distributions of self-associating molecules (12), and one could imagine chaperones acting to reshape the size distributions of clusters that form in subsaturated solution and in dilute phases that coexist with condensates. Additionally, deleterious interactions with cellular components that lead to disease (95), and the dynamical arrest of condensate growth (63), could also occur at the level of clusters in dilute phases and / or subsaturated solutions.

Materials and Methods

All proteins were first expressed in 1 L SF9 (1 million/mL) insect cells with 5 mL of P2 virus and harvested 72 h postinfection. We used a centrifugation approach to determine saturation concentrations. The samples at the indicated protein concentration were incubated for 30 min, the solutions were spun down at 20,000 RCF on a benchtop centrifuge unit, and the concentration was measured in the clarified supernatant by using a Bradford assay. Details of all the constructs used in the experiments, the protein expression and purification protocols that distinguish methods A and B, the setup and analysis of DLS, NTA, MFD, MCS, and TEM experiments, raw data from DLS measurements, and the LaSSI simulations are described in .