Thermodynamics and kinetics of phase separation of protein-RNA mixtures by a minimal model

Abstract

Intracellular liquid-liquid phase separation enables the formation of biomolecular condensates, such as ribonucleoprotein granules, which play a crucial role in the spatiotemporal organization of biomolecules (e.g., proteins and RNAs). Here, we introduce a patchy-particle polymer model to investigate liquid-liquid phase separation of protein-RNA mixtures. We demonstrate that at low to moderate concentrations, RNA enhances the stability of RNA-binding protein condensates because it increases the molecular connectivity of the condensed-liquid phase. Importantly, we find that RNA can also accelerate the nucleation stage of phase separation. Additionally, we assess how the capacity of RNA to increase the stability of condensates is modulated by the relative protein-protein/protein-RNA binding strengths. We find that phase separation and multiphase organization of multicomponent condensates is favored when the RNA binds with higher affinity to the lower-valency proteins in the mixture than to the cognate higher-valency proteins. Collectively, our results shed light on the roles of RNA in ribonucleoprotein granule formation and the internal structuring of stress granules.

Significance

The interior of cells contains several membraneless compartments that are composed of proteins and RNA. These compartments are formed and sustained by liquid-liquid phase separation (LLPS). Here, we introduce a minimal coarse-grained model to study LLPS of protein-RNA mixtures. We find that RNA can increase the stability of phase-separated compartments by enhancing the molecular connectivity of proteins. Additionally, our results show that RNA actively recruits proteins, accelerating the nucleation and fusion stages of LLPS. Interestingly, we find that spatial segregation within protein-RNA compartments is controlled by fine-tuning the interaction strengths and stoichiometries of components. Our model, therefore, provides a useful tool for building a comprehensive mechanistic and thermodynamic view of protein-RNA LLPS.

Introduction

In recent years, it has become clear that liquid-liquid phase separation (LLPS) is responsible for the formation of membraneless organelles, including P granules and nuclear bodies (1, 2, 3, 4). These cellular bodies, often referred to as biomolecular condensates, display liquid-like properties such as the ability to flow, coalesce, and drip (5, 6, 7, 8, 9) and are thought to self-assemble via condensation of proteins and other macromolecules in the cytoplasm and nucleoplasm. Specifically, multidomain proteins (5,8,10) and those comprising intrinsically disordered regions (11, 12, 13, 14) have been shown to undergo LLPS, both in vitro and in cells. LLPS is mainly driven by multivalent protein-protein interactions (15,16); for example, several phase-separating proteins possess low-complexity domains that foster protein-protein condensation (2,17,18). Interactions with RNA (19, 20, 21, 22, 23) have been shown to strongly mediate LLPS; indeed, the vast majority of membraneless organelles (including nucleoli (19,24,25), stress granules (26,27), P granules (13,20,28), and processing bodies (29,30)) are ribonucleoprotein (RNP) granules (31, 32, 33, 34, 35,36), consisting of RNA and RNA-binding proteins (RBPs) (37). A central goal of this work is to further elucidate one of the potential mechanisms by which RNA can enhance (or inhibit) LLPS and obtain predictive rules governing the composition of protein-RNA condensates.

In vitro experiments reveal that although condensates are multicomponent systems, only a small subset of components may be required for LLPS (24,38). For example, P granules are made up of several RNA and protein molecules; however, LAF-1 (a protein found in P granules) can self-associate into droplets that resemble P granules in vitro (13). In some cases, macromolecules that undergo LLPS may bind to and recruit other molecules to phase-separated droplets. Landmark work by Banani and collaborators (39) showed that polySUMO and polySIM proteins assembled into droplets when mixed and subsequently recruited fluorescently labeled SIM and SUMO monomers, respectively, to the condensates. Components such as polySUMO and polySIM that drive LLPS are often classified as “scaffolds” and molecules that partition into droplets formed by scaffolds (e.g., SIM and SUMO monomers) are termed “clients” (39). Scaffold and client stoichiometric ratios, valencies, and binding affinities have been postulated as crucial in compositional control of membraneless organelles (39).

Importantly, RNA molecules can be selectively recruited to condensates, and this recruitment is tuned by several factors including RNA length, flexibility, and shape (12,22,40,41). For instance, some RNA-binding proteins contain structured RNA-binding regions—including certain RNA recognition motifs and zinc fingers—that bind to specific RNA sequences and drive phase separation (22,42). In other cases, RBPs recruit RNA in a nonspecific manner (e.g., via intrinsically disordered regions and arginine-rich regions) (20,37,43), thereby partitioning RNA molecules into phase-separated droplets. Still, several RBPs may contain sites for both specific and nonspecific RNA binding (37,42,44,45). Accordingly, RNA polymers tend to mimic low-complexity domains, exhibiting multivalence character and high propensity for adopting numerous conformations that promote condensation (23). In general, RNA valence increases with length, and longer RNAs have been found to drive stress granule formation (26). Additionally, the RBP/RNA ratio is also very important, with high RNA ratios suppressing LLPS and lower RNA concentrations promoting LLPS of several proteins (21,37,42,44,46). In the latter case, RNA molecules may essentially act as scaffolds for LLPS. To better understand the interplay between these and other factors, we therefore require biophysical models that can investigate the phase behavior of RBP-RNA mixtures.

Polymer physics provides key rules for predicting phase behavior of polymeric systems (47). For a given homopolymer-solvent mixture, the system produces two phases (i.e., a dense, polymer-rich phase and a dilute, solvent-rich phase) when the enthalpy of mixing exceeds the entropy of mixing. Flory-Huggins Theory quantifies the entropic and enthalpic terms of such systems and estimates the critical condition for phase separation (48,49). Subsequent to these works, analytical (14,50, 51, 52, 53, 54, 55, 56, 57) and mean-field theoretical approaches (58, 59, 60, 61) have been developed to study phase behavior of charged polymers and intrinsically disordered proteins (IDPs). Additionally, sequence-dependent continuum models (62, 63, 64, 65, 66) have been designed for probing biomolecular phase behavior. These models have proved extremely useful in identifying correlations between protein sequence and LLPS. Minimal continuum models (67, 68, 69, 70, 71, 72, 73, 74, 75) (including patchy-particle models) (69, 70, 71, 72, 73, 74,76) and lattice-based approaches (16,77, 78, 79, 80, 81) (notably “stickers-and-spacers” representations) (16,77,79) have significantly complemented and augmented these studies, revealing concentration-dependent features of multicomponent protein systems, aiding in the design of experimental studies on phase behavior, and accessing complete phase diagrams. The study of phase diagrams of biopolymer systems provides valuable insight in the various factors that influence phase separation. However, measuring complete phase diagrams is time consuming, and the study of biomolecular phase behavior at atomic resolution is computationally expensive. Hence, approaches that simultaneously preserve important molecular and physicochemical details of LLPS and capture observable phase behavior in an efficient manner are appealing because they can be implemented at moderate computational cost.

Here, we develop a simple coarse-grained approach that approximates key features of phase-separating RBPs and their RNA counterparts. The model is simple enough to permit simulation of phase transitions in mixtures containing thousands of proteins at low computational cost, it can be conveniently implemented, and it does not require extensive optimization of parameter sets. Using this minimal model, we investigate the effect of adding an RNA-like polymer to a pure RBP system. We find that the RNA polymer enhances the connectivity of RBPs and increases the critical temperature for phase separation. These results are consistent with experiments, in which RNA was found to decrease the critical concentration for LLPS in RBP-RNA mixtures (21,37,42,44). Additionally, we demonstrate that RNA-like polymers accelerate the nucleation stage of protein condensate formation. We then study competition and cooperative effects in multicomponent protein-RNA mixtures and demonstrate how the droplet composition is tuned by the valencies, stoichiometries, and relative interaction strengths of the molecular components. Taken together, our work demonstrates the usefulness of minimal coarse-grained models in obtaining general rules governing RNA-driven LLPS and suggests possible molecular mechanisms involved in intracellular phase separation.

Methods

Minimal coarse-grained model

We have developed a minimal coarse-grained model for RBPs that captures their multivalency (82) and RNA-binding ability—the two essential characteristics for LLPS of RBP-RNA mixtures—and can probe condensed-matter properties of biomolecular phase separation in an efficient manner. A key advantage of our approach is that all the potentials in our minimal protein model are continuous and can be conveniently implemented in parallelized molecular dynamics software, which allows us to investigate systems of up to 10 thousand proteins. Additionally, the design of the model eliminates the need for optimizing and storing extensive parameter sets, which ensures its utility and portability.

Our minimal model represents RBPs as hard spheres (of molecular diameter σ = 3.405 Å) decorated with attractive patches or “stickers” on their surface (Fig. 1 A). We model two types of RBPs: 1) those that can drive phase separation via homotypic RBP-RBP interactions and hence act as scaffolds and 2) those whose homotypic interactions are insufficient to drive phase separation and hence act as clients that are recruited into condensates via their interactions with the scaffolds. Based on our previous work exploring the role of valency in protein LLPS (82), we set three attractive LLPS-binding sites per scaffold RBP (three-valency RBPs), and two per client RBP (two-valency RBPs); this simple distinction allows us to capture the essential difference in the phase behavior between scaffolds and clients. Although many proteins, including RBPs, that undergo LLPS possess intrinsically disordered regions (11, 12, 13, 14,16,84), our model captures the effects of protein multivalency and, therefore, approximates the way in which intrinsically disordered proteins interact with each other (73) and with RNA.

Figure 1.

Obtaining phase diagrams of RBP-RNA mixtures. (A) Patchy-particle polymer model for simulating interactions between proteins and RNAs is shown. RNA is modeled as a (hard-sphere) self-avoiding polymer. RBPs are represented by hard spheres decorated with attractive patches. (B) Phase diagrams computed in terms of inverse interprotein interaction strength ($E_{RBP}^c$/E_prot-prot; $E_{RBP}^c$ is the critical inverse protein-protein interaction strength of the pure RBP) and volume fraction of the RBP (i.e., ϕ_RBP) are given. In each system, 1000 RBPs were used, along with n (n = 0, 1, 2, 3) chains of a 40-mer RNA. The densities of the dilute and condense phases are estimated from the density profiles, as described in the main text and Fig. S1. Horizontal error bars represent the standard deviations in the coexisting volume fractions. (C) Snapshots of direct coexistence simulations of RBP (top) and RBP$+$RNA (3 × 40-mer) mixture (bottom) at $E_{RBP}^c$/E_prot-prot ≈ 1.05 are shown. (D) Residue-level coarse-grained representations of PolyU RNA and RBP FUS are given. In the model, each protein residue or nucleic acid is represented as a single bead (see text and Supporting materials and methods for details). (E) Phase diagrams computed in terms of temperature (T/$T_{FUS}^c$; $T_{FUS}^c$ is the critical temperature of pure FUS) and density of FUS (ρ_FUS) are given. In each system, 24 chains of FUS were used, along with n (n = 0, 1, 2, 3) chains of PolyU 175 nt long. The densities of the dilute and condense phases are estimated from the density profiles, as described in the Supporting materials and methods. Horizontal error bars represent standard deviations in the coexisting densities. (F) Snapshots of direct coexistence simulations of pure FUS (top) and FUS$+$PolyU (3 × 175 nt) mixture (bottom) at T/$T_{FUS}^c$ ≈ 1.00 are shown. In phase diagrams, individual critical values of the inverse E_prot-prot (E^c) or T (T^c) are estimated by fitting the differences in ϕ_RBP or ρ_FUS (as described in (82)), and corresponding critical ϕ_RBP or ρ_FUS are derived by assuming that the law of rectilinear diameters and critical exponents (83) holds in the vicinity of E^c or T^c. Uncertainties in the estimation of critical values (error bars) are obtained by performing the fitting procedure on three independent data sets. To see this figure in color, go online.

RNA molecules contain negatively charged sugar-phosphate backbones, and therefore tend to behave as self-avoiding polymers. Hence, as an extension to our previous work (82), we represent single-stranded unstructured RNAs (i.e., A or U rich with negligible basepairing probability) as flexible self-avoiding polymers (i.e., chains of hard spheres (85)) that interact with the minimal RBPs via attractive interactions (Fig. 1 A). The weak attractive interactions between patchy “RBP” particles and polymers typify RBP-RNA interactions observed in biomolecular condensates (20,21,37,42, 43, 44).

Direct coexistence simulations

We employ direct coexistence simulations (86, 87, 88) to compute the phase diagrams of the protein-RNA mixtures, i.e., both liquid phases are simulated via molecular dynamics in the same simulation box (82). Specifically, we measure the volume fraction of the protein (Fig. 1 B) in each phase as a function of the protein-protein interaction strength. The volume fraction of the RBP (ϕ_RBP) in a phase is defined as ϕ_RBP = NV_RBP/V ∝ C_RBP, where N is the total number of RBPs, V_RBP is the molecular volume of an RBP (i.e., 4/3 π(σ/2)³], V is the total system volume, and C_RBP is the concentration). LLPS in cells occurs over narrow temperature ranges; therefore, we assess the phase behavior of our mixtures by varying the interprotein interaction strengths (E_prot-prot) at a fixed temperature.

At a given value of the interprotein interaction strength, the system is simulated until the potential energy and the density profile along the box long axis have converged (Fig. S1 A). LLPS is then marked by the presence of sharp interfaces (Fig. S1 B). The volume fractions of the protein-rich and protein-poor phases are then computed by averaging the volume fractions (i.e., from the density profile) for the respective phases, excluding regions near the interfaces (Fig. S1 B). Hence, for a particular protein, the compositions of the coexisting protein-rich and protein-poor phases define the range of volume fractions (or concentrations) for which LLPS takes place (Fig. 1 B). Having established this reference phase diagram, we then assess the effect of adding an RNA-like polymer or different proteins on the location of the phase boundaries (Fig. 1, B and C). This approach allows us to obtain general rules for how proteins and RNA molecules may partition into two-liquid phases. Further details of our patchy-particle model (82) and the simulation parameters used are found in Supporting materials and methods, Sections SI and SII.

Results and Discussion

Minimal model validation

Many proteins that undergo homotypic LLPS have been shown to participate in multivalent heterotypic interactions with RNA that also facilitate LLPS (37,42,44). For example, Molliex and co-workers (44) showed that although RBP hnRNPA1 was able to phase separate on its own, LLPS of hnRNPA1 was significantly enhanced in the presence of RNA. This effect was marked by a dramatic decrease in the concentration of hnRNPA1 required for phase separation (44). Similar results were also reported by Lin and colleagues (37). RNA has also been shown to drive droplet formation of RBP Whi3 (22,42) and PGL-3 protein (20) at physiological protein concentrations.

We first employ our minimal model to probe the effects of adding RNA at low to moderate concentrations (i.e., ϕ_RNA/ϕ_RBP < 15%) on the phase boundary of a single type of RNA-binding protein (i.e., a trivalent RBP). The protein can self-associate via three binding sites on its surface and, as such, serves as a prototype for proteins that exhibit homotypically driven LLPS. At different interprotein interaction strengths (i.e., 11.5 ≤ E_prot-prot ≤ 14 k_BT), we compute the phase boundaries of the pure protein system (Fig. 1 B). We then calculate the coexistence curve and the minimal interaction strength needed for phase separation (i.e., the critical point; at E_prot-prot ∼10.786 k_BT). Above the critical point, the pure protein system forms a single well-mixed phase (Fig. 1 C, top panel). At larger interaction strengths (i.e., below the critical point), the system separates into protein-rich and protein-poor phases (Fig. 1 B).

We then add a polymer that mimics an intrinsically disordered RNA chain (i.e., a self-avoiding (85) fully flexible polymer made up of 40 monomeric units; 1 × 40-mer) that interacts with the RBPs via moderately weak attractive interactions (E_prot-RNA ∼3 k_BT). We choose this polymer length because it allows us to achieve a low RNA/protein concentration (i.e., ∼4–12% RNA) that is consistent with experiments (20,37,44) while obtaining marked trends for how RNA affects protein LLPS. We then simulate the new RBP-RNA mixture above the critical point of the pure system (Fig. 1 B), at which the RBP can no longer sustain LLPS on its own. Note that to assess directly how effectively the RBP condenses in the presence of the RNA-like polymer, we compute our phase diagrams in terms of the volume fraction of the RBP, as opposed to assessing the combined volume fraction of the RBP and RNA. Consistent with experimental studies of RBP-RNA mixtures (20,22,37,42,44), the RNA-like polymer promotes phase separation of the trivalent RBP, i.e., a higher critical inverse interaction strength and a broader coexistence region are obtained for the mixture versus the pure protein system (red curve in Fig. 1 B).

As in the case of the Whi3-RNA mixture (22,42), the trivalent RBPs interact with the RNA polymer via different sites than those used for protein-protein association. This suggests that the RNA polymer acts as a high-valency molecule that effectively enhances the connectivity of the protein liquid network. Indeed, the average number of protein-protein bonds in the RBP condensate increases fourfold when three 40-mer RNA-like polymers are added to the RBP system at an interprotein interaction strength of 11 k_BT (Fig. 2). Experiments and simulations have recently demonstrated that increasing the protein valency raises the critical temperature for phase separation (16,73). These findings are consistent with earlier predictions by Bianchi et al. (90). Li et al. (5) also obtained a strong correlation between the phase boundary and the valency of interacting molecules for engineered SH3m-PRMn protein mixtures. Importantly, Rao and Parker (91) demonstrated that messenger RNA enhanced P-body assembly by providing multiple interaction sites for certain P-body proteins. Moreover, mutations that hindered RNA binding suppressed P-body formation (91). Ries et al. (92) recently showed that polymethylated messenger RNAs can act as multivalent scaffolds for binding certain proteins and driving LLPS.

Figure 2.

RNA enhances the average valency of RNA-binding proteins. Systems in (A) and (B) are identical, in terms of composition, to those in Fig. 1, B and E. (A) Average protein valency (bonds/σ³) as a function of number of RNA chains (n), computed via the patchy-particle polymer model at an interprotein interaction strength (i.e., E_prot-prot) of 11 k_BT (E_c^RBP/E_prot-prot = 0.98), is given. The density of each system was first equilibrated to the coexisting density of the condensed-liquid branch of their respective phase diagram (i.e., without interfaces). The systems were then simulated in the NVT ensemble to determine the average protein valency in the droplet. (Right panel) Zoomed-in snapshots of some RBPs within the simulation box showing differences in interprotein connectivity are given. For clarity, the RNA-like polymers are not depicted in the uppermost snapshot. (B) Interprotein connectivity (bonds/nm³) is shown; bonds correspond to interprotein or protein-RNA contacts, as described in the Supporting materials and methods), versus number of PolyU chains (n), computed via the reparameterized residue-level coarse-grained model (62,66,89) at 395 K (T/T_c = 0.96). The systems were prepared as in (A), i.e., isotropic NpT simulations, followed by NVT ensemble computations to measure the droplet interprotein connectivity. (Right panel) Zoomed-in snapshots of some FUS proteins within the simulation box showing differences in interprotein connectivity are given. For clarity, the PolyU chains are not depicted in the uppermost snapshot. In (A) and (B), error bars (i.e., standard error) are of the same size or smaller than the symbols. To see this figure in color, go online.

We also test whether multiple RNA-like polymers can also enhance LLPS. Thus, in addition to the original RBP-RNA mixture, we study the phase behavior for systems containing two (2 × 40-mer) and three (3 × 40-mer) RNA-like chains. Within our model, we obtain a monotonic increase in the critical point for LLPS and a widening of the coexistence region (Fig. 1 B). Thus, in all cases tested, the RNA-like polymer enhances LLPS of our patchy RBPs. We note that, by construction, our model is only valid at low to moderate RNA concentrations, at which our approximation that RNA behaves as a self-avoiding polymer (rather than exhibiting long-range repulsion) and the assumption that RNA does not compete for RBP-RBP binding sites are reasonable. In other words, the monotonic LLPS enhancement we observe is not expected to hold at high RNA concentrations.

To verify the preceding predictions obtained via the minimal model, we investigated the effects of PolyU RNA on the phase behavior of the ALS-associated RBP fused in sarcoma (FUS). FUS is an ideal example of an RBP that can both undergo LLPS on its own via homotypic interactions (17,93,94,95) and exhibit phase-separation enhancement (i.e., undergo LLPS at low protein concentrations) in the presence of low to moderate concentrations of RNA (96, 97, 98). Using a reparameterization (66) of the residue-level coarse-grained model of Dignon et al. (62) (Fig. 1 D), we compute the phase diagram of the pure FUS system (Fig. 1 E) and then probe the impact of adding moderate concentrations of PolyU (modeled using the parameters proposed in (89)). For the high-resolution simulations, each residue or nucleic acid is represented by a single bead (with associated hydrophobicity, mass, and charge); therefore, we are able to delineate which protein and RNA regions drive LLPS.

Consistent with experiments (17,93,94), we observe that FUS phase separates because of homotypic interactions, mainly via hydrophobic prion-like domain (PLD)-PLD interactions and cation-π interactions between Tyr residues in the PLD and Arg residues in Arg-Gly-Gly-rich region domains (see Fig. S2 B). Importantly, when we add increasing amounts of PolyU, we observe that the critical temperature of the mixture also exhibits a monotonic increase, by 0.8–2.4% for one to three chains of 175 nucleotides (nt) (Fig. 1 E), which implies that addition of RNA permits phase separation of FUS at higher temperatures, at which the phase separation of FUS alone is unfavorable. Because temperature in the coarse-grained model directly impacts the relative strength of protein-protein interactions, this result also suggests that the addition of RNA would permit the formation of FUS condensates under other unfavorable LLPS conditions (e.g., salt, pH, etc.). Unlike our minimal model, the residue-level coarse-grained model explicitly considers the electrostatic repulsion among RNA chains and the competition of RNA for specific scaffold-scaffold binding sites—e.g., it accounts for arginine-rich regions being utilized for FUS-FUS interactions as well as for FUS-RNA interactions. Therefore, it can be used to investigate the role of higher concentrations of RNA in FUS condensates. These analyses reveal that higher RNA concentrations dissolves the FUS condensates (Fig. S3), as observed experimentally (21).

If we compare the phase diagrams computed with both models at low to moderate concentrations of RNA, we observe that both predict an increase in the size of the coexistence region upon insertion of RNA (Fig. 1, B and E). However, the condensed-branch of the residue-level coarse-grained phase diagrams (Fig. 1 E) do not exhibit the marked increase in density upon insertion of the PolyU chains predicted by our minimal model (Fig. 1 B). Although both models predict an enhancement in the connectivity of FUS proteins due to addition of PolyU (see Fig. 2 B), our minimal model overestimates such enhancement. We note that the residue-level model likely describes the experimental phase behavior of FUS-RNA mixtures better because it accounts more adequately for the actual size, shape, flexibility, and chemical identity of the different molecular species involved in LLPS.

However, although our minimal model was designed to study general features of RBP-RNA LLPS, it can be conveniently parameterized to study specific protein-RNA systems (such as FUS-RNA mixtures) more intimately. For example, whereas in our study, the RNA-like polymer interacts with RBPs in a nonspecific manner, selective binding can be introduced in the model via simple pairwise definitions. Despite the limitations of a minimal approximation, the preceding residue-level study demonstrates the usefulness of a minimal model in capturing qualitative trends of RNA-driven LLPS at low to moderate RNA concentrations. Therefore, in what follows, we exploit the advantage of the minimal model to access the sufficiently large system sizes and long timescales needed to elucidate the thermodynamic and kinetic mechanism of RNA-driven RBP LLPS. We then present a comprehensive look at the regulation of condensate stability by RNA and how this is modulated by the addition of different types of proteins to the RBP-RNA condensates.

Moderate RNA concentrations accelerate the nucleation and growth of RBP condensates

Beyond increasing the size of the coexistence region by connectivity enhancement, the question is how is the thermodynamic and kinetic mechanism of RBP LLPS impacted by RNA? To investigate this, we define a “protein cluster size” order parameter Q that measures the average number of proteins in a given protein cluster (i.e., Q loosely describes the size of the emerging protein condensates) throughout our simulations. We first determine whether a protein is in a diluted or condensed region by employing a nearest neighbor criterion (99), wherein proteins are assigned to condensed regions if, within a cutoff distance of 1.26 σ, they have at least three neighbors. Once all proteins are assigned, two proteins are considered to be part of the same condensed region (i.e., protein cluster) if they are separated by less than 1.26 σ from each other. The size of the largest protein cluster (Q₁), therefore, probes the nucleation potential of the system. We first computed Q₁ at different interprotein interaction strengths for the pure protein system and in the presence of one to three 40-mer RNA-like polymers (Fig. 3 A). The critical protein-protein interaction strength (10.786 k_BT) for the pure protein system is indicated on the figure (i.e., vertical dashed line). Below this threshold (i.e., left of the vertical line), the largest cluster in the pure RBP system contains ∼50 proteins. At a given interprotein interaction strength, the size of the largest protein cluster increases monotonically as more RNA-like polymers are added. Strikingly, there is a 10-fold increase in the size of the largest protein cluster (∼600 proteins) upon adding three 40-mer RNA-like polymers at interprotein interaction strengths at which the pure RBP does not phase separate (i.e., below 10.786 k_BT). Additionally, when RNA is added, we obtain a gain (of ∼1 k_BT) in the stability of protein clusters. It follows that RNA effectively recruits numerous protein molecules and increases the thermodynamic stability of protein clusters.

Figure 3.

Thermodynamics and kinetics of protein cluster formation. (A) For a system containing 1000 RBPs, we measure the number of RBPs in the largest equilibrium cluster (Q₁) versus the protein-protein interaction strength (E_prot-prot). We then add n (n = 1, 2, 3) chains of a 40-mer RNA-like polymer and again measure the size of the largest protein cluster. The horizontal axis is scaled based on the critical inverse protein-protein interaction strength for LLPS of the pure RBP (1/$E_{RBP}^c$; vertical dashed line). At a protein-protein interaction strength of 10.5 k_BT (or $E_{RBP}^c$/E_prot-prot ≈ 1.05) snapshots of the RBP + RNA (3 × 40-mer) mixture (top) and the pure RBP (bottom) are shown in the leftmost panel. A large distinct protein cluster forms in the RBP-RNA mixture versus smaller dispersed clusters in pure protein system. (B) For the pure RBP (black curve) and the RBP + RNA (3 × 40-mer) mixture (blue curve), we evaluate the number of RBPs in the two largest clusters (Q₁ + Q₂) as a function of time (t^∗; as defined in the Supporting materials and methods) at an interprotein bond strength of 12 k_BT (or $E_{RBP}^c$/E_prot-prot ≈ 0.90). Left of the vertical dashed line, both systems exist as well-mixed fluids. Both systems equilibrate to form phase-separated condensates (i.e., LLPS). To see this figure in color, go online.

We then probe the evolution of the two largest protein clusters (denoted Q₁ + Q₂) as a function of time (Fig. 3 B). In the early stages of condensation, protein clusters have a tendency to fuse and segregate often, and so the number of proteins in the two largest clusters is a more robust condensation parameter than just Q₁. To obtain a homogeneous distribution of proteins in the simulation box, we initially zeroed all attractive interactions in each system. We then activate all attractive interactions, setting the protein-protein interaction strength to a value where both systems undergo LLPS (i.e., 12 k_BT). Therefore, Q₁ + Q₂ vs. time directly measures the speed of condensate formation. We find that the two largest condensates form approximately four times faster in the presence of the polymer (i.e., 3 × 40-mer RNAs) than in the pure system. Furthermore, whereas the condensate grows in a roughly monotonic fashion in the RBP-RNA mixture (blue curve in Fig. 3 B), condensate sizes fluctuate to a greater extent (black curve in Fig. 3 B) in the absence of the RNA.

Our simulations explain the origin of these important differences in the kinetic mechanism of condensate formation in the absence and presence of RNA. In the absence of RNA, RBPs initially form many small protein-rich nuclei. The growth of these small nuclei is dependent on their capacity to outcompete one another for binding to the free RBPs that remain in the diluted phase and/or are undergoing fusion among themselves. This competition, along with time needed for fusion of many clusters, effectively slows down the condensation process and results in the initial lag time we observe before the exponential growth rate begins (black curve in Fig. 3 B). In contrast, when RNA is present, we observe formation of only a few dominant nuclei (i.e., as many clusters as there are RNA strands), which reduces competition and facilitates their growth and dominance. This results in RNA considerably accelerating the formation rate of the equilibrium condensate and a negligible lag time (blue curve in Fig. 3 B).

Therefore, in addition to increasing the stability of condensates, RNA promotes LLPS by accelerating the nucleation and growth of condensates. In the literature, Falahati et al. (25) proposed a seeding mechanism for the formation of the nucleolus. Specifically, they reported that rRNA transcription precedes nucleolus assembly (25), which subsequently recruits and localizes nucleolar proteins-fostering protein cross-linking and eventual condensation. Our results are consistent with these findings, demonstrating that RNA may drive RBP condensation by facilitating the formation of the first condensate nuclei (even in conditions in which RBPs alone cannot nucleate) and also by accelerating the growth of such nuclei once formed (with respect to the rate of growth of RBPs alone).

Ability of RNA to increase condensate stability depends on the composition of the system

Banani and co-workers (39) provided an initial framework to explain compositional control of membraneless organelles. Specifically, they demonstrated how low-valency molecules (termed clients) can be recruited to condensates by binding to scaffolds (molecules that can phase separate on their own). They also highlighted that the valencies and relative concentrations of scaffolds and clients played significant roles in dictating the final droplet composition. In another study, Saha et al. (20) found that competition among certain proteins for RNA binding sites altered P-granule-like droplet composition.

Here, we investigate how RNA may affect condensate stability in systems containing different types of proteins. In particular, we examine cooperation and competition effects in multicomponent mixtures comprising scaffolds, clients, and low concentrations of RNA. First, we consider the case of an intracellular mixture containing scaffolds and clients. Clients are defined as low-valency proteins that cannot phase separate on their own (i.e., via homotypic client-client interactions); importantly, clients can be trafficked into the condensates by binding with high affinity at the same sites used for homotypic scaffold-scaffold interactions. The protein composition of this mixture is 64% scaffolds (trivalent proteins; Fig. 4 A) and 36% clients (divalent proteins; Fig. 4 A)—i.e., the mixture contains a scaffold/client ratio of 1.78—and all interprotein interaction strengths are equivalent. Notably, in comparison with the pure RBP (in Fig. 1 B), this mixture shows a reduced propensity to phase separate (i.e., a drop in the critical inverse protein-protein interaction strength by ∼7%; see Fig. S3). This result agrees well with the original scaffold-client model (39) predictions and is further supported by previous computational (69) and experimental work (70). For example, Nguemaha and Zhou (69) demonstrated that regulators of LLPS (analogous to clients in this case) may lead to suppression of driver (i.e., scaffolds) phase separation if regulator-driver binding affinities are comparable with driver-driver ones. In this scenario, regulators or clients displace drivers or scaffolds from the condensate at the expense of weakening the strength and connectivity of the percolated network (69,73).

Figure 4.

Composition of biomolecular condensates is regulated by the relative interaction strengths of molecular components. (A) Depiction of clients (divalent proteins), scaffolds (trivalent proteins), and a 40-mer RNA is given. (B) Reference client-scaffold mixture composed of 36% divalent proteins (clients) and 64% trivalent proteins (scaffolds) at an interprotein interaction strength of 11.75 k_BT is shown. (C–E) Phase behavior of client-scaffold-RNA mixtures (i.e., mixtures I–III) described in Table 1 is shown. To see this figure in color, go online.

We then add RNA to the reference scaffold-client mixture and investigate whether RNA enhances LLPS of this system. In particular, we consider the case in which, in addition to scaffolds, clients bind to RNA with high affinity. To probe the effects of RNA, we simulate the mixture very close to the critical protein-protein interaction strength of the reference client-scaffold mixture (i.e., 11.75 k_BT; see Fig. 4 B; Fig. S4). Upon equilibration, no LLPS is observed (mixture I in Table 1; Fig. 4 C), i.e., an absence of sharp and well-defined interfaces. Interestingly, the RNA-like polymer is almost entirely coated by scaffolds (∼84%), despite the binding strength of both client and scaffold proteins with the RNA being equal (Table 1). This disparity in the type of proteins coating the polymer strongly suggests that the dissociation constants for the higher-valency scaffolds (which can form more bonds with surrounding molecules) are smaller. Thus, higher-valency RBPs have a greater probability of remaining bound to RNA (and bound in the percolating network).

Table 1.

Investigating how RNA tunes the stability of client--scaffold protein condensates

Mixture	I	II	III
Client-scaffold interaction?	yes	yes	yes
Client-RNA interaction?	yes	no	yes
Scaffold-RNA interaction?	yes	yes	no
Proteins coating RNA	84 ± 0.5% scaffolds	99 ± 0.5% scaffolds	1 ± 0.5% scaffolds
Scaffold/client ratio after RNA coating	1.65 ± 0.01	1.55 ± 0.01	2.27 ± 0.01
Change in scaffold/client ratio	−7 ± 0.5%	−13 ± 0.5%	+28 ± 0.5%
Variation in size of largest protein cluster (ΔQ1)	−3 ± 1%	−7 ± 1%	+7 ± 1%
RNA enhances LLPS?	no	no	yes

We start with a reference mixture containing 64% (768 trivalent proteins) scaffolds and 36% (432 divalent proteins) clients (i.e., a reference scaffold/client ratio of 1.78) that can undergo LLPS. We then add a 40-mer RNA at an interprotein interaction strength of 11.75 k_BT (i.e., close to the critical protein-protein interaction strength of the original scaffold-client mixture), modulate the cross interactions between the mixture components, and analyze whether the RNA polymer enhances LLPS reference of the mixture. To assess the ratio of scaffolds/clients remaining after coating the RNA, we consider all scaffolds and clients that are not directly bound to the RNA polymer. The change in this ratio is computed with respect to the 1.78 reference value. We also assess the change in Q₁ (number of scaffolds and clients in the largest cluster) to quantify the enhancement or inhibition of LLPS of the mixture upon adding RNA. Snapshots of observed phase behaviors are given in Fig. 4.

Consequently, in a mixture containing both RNA-binding scaffolds and RNA-binding clients, RNA shows a preference for interacting with the scaffolds (even though in our model, both scaffold-RNA and client-RNA bonds have the same interaction strength by construction). On similar grounds, scaffolds preferentially associate with adjacent scaffolds, creating a higher concentration of clients in the remaining mixture. We quantify the scaffold/client ratio in the remaining mixture (i.e., the effective ratio) by considering all proteins in the system, except those that are directly coating the RNA polymer. This quantity allows us to estimate the number of scaffolds that are available for binding to (and recruiting) clients. In mixture I, we find that the effective scaffold/client ratio decreases by ∼7% with respect to the reference mixture. Our recent work (73) demonstrates that the addition of low-valency clients that are strong competitors for scaffold-scaffold interactions (like the ones in mixture I) decreases the stability of condensates by diminishing the connectivity of the liquid network and that this effect is amplified as the scaffold/client ratio decreases. Therefore, in the presence of strong-competing clients and with a limited number of scaffolds, RNA indirectly decreases the connectivity of the condensed liquid by essentially reducing the effective scaffold/client ratio. Hence, the net effect is that droplet formation is not enhanced in the presence of RNA; indeed, the size of the largest protein cluster (Q₁) decreases by ∼3% when the RNA-like polymer is added to the mixture. Conversely, we find that when clients do not compete for scaffold binding sites, a reduction in the effective scaffold/client ratio does not inhibit LLPS (Fig. S5) because clients cannot replace LLPS-stabilizing scaffold-scaffold connections with LLPS-inhibiting scaffold-client ones.

Next, we test the effect of the RNA-like polymer on the phase behavior of a mixture of RNA-binding scaffolds and non-RNA-binding clients (i.e., the interaction strength between the client proteins and the RNA is set to zero; mixture II in Table 1 and Fig. 4 D). Clients compete with the RNA polymer (and with the scaffolds themselves) for binding to the scaffold proteins. However, clients are now unable to bind directly to the RNA polymer; hence, upon equilibration, ∼99% of the molecules coating the RNA polymer are scaffolds. The interaction of scaffolds with RNA and adjacent scaffolds effectively decreases the ratio of available scaffolds/clients by ∼13$\text{\%}$ with respect to the reference mixing ratio. There are effectively more clients in the remaining mixture that compete strongly with scaffolds for scaffold-scaffold binding sites; hence, the more LLPS-stabilizing scaffold-scaffold connections are replaced by connectivity-diminishing scaffold-client ones. Thus, the size of the largest protein cluster diminishes (i.e., ΔQ₁ ≈ −7%), and droplet formation is not enhanced (mixture II in Table 1). In fact, the reduction in the size of the largest protein clusters (i.e., nucleation is suppressed) in mixtures I and II suggests that the RNA inhibits phase separation in these systems.

Finally, we assess the effects of RNA on the phase boundaries of a mixture of non-RNA-binding scaffolds and RNA-binding clients (i.e., we switch off the attractive interaction between the scaffolds and the RNA; mixture III in Table 1). Addition of the RNA-like polymer increases the size of the largest protein cluster by ∼7%. RNA enhances LLPS of this system (Fig. 4 E) because it exclusively recruits clients and effectively sequestrates them away from scaffolds. Accordingly, RNA decreases the availability of clients that would otherwise compete with scaffold self-assembly. Hence, droplet formation is promoted when RNA shows a preference for clients; in this final mixture, clients constitute ∼99% of the molecules coating the RNA polymer. Ergo, the effective ratio of scaffolds/clients increases, ensuring that there are sufficient free-binding sites on the scaffolds to foster scaffold-scaffold interactions and phase separation.

Mixing non-RNA-binding scaffolds and RNA-binding clients with RNA yields multiphase condensates with a marked spatial segregation of the RNA and associated clients in the condensate (Fig. 4 E); in contrast to the binary RNA-binding scaffold-RNA mixture (i.e., without clients), in which the RNA is embedded within the liquid drop (bottom panel in Fig. 1 C), the client-coated RNA is now located near the droplet interface. Even in the other mixtures (Fig. 4, C and D), where no marked protein phase separation is observed, the RNA is, in general, uniformly coated by the surrounding proteins. This spatial segregation can be rationalized from the smaller contribution that low-valency proteins are expected to have to the interfacial free energy and the melting enthalpy of condensates (38,100,101,76). Consequently, the client-coated RNA migrates to the edge of the condensate to minimize both the interfacial free energy of the system and the chemical potential of the droplet.

Overall, we find that spatial segregation of species within condensates leading to multiphase condensates can be achieved in multicomponent mixtures and is controlled by fine-tuning the effective scaffold/client ratio and interaction strengths among species. Our results agree well with recent experiments in which it is reported that different polymers partition into multiphase droplets depending on the relative interactions between mixture components (102,103). Such multiphase segregation within condensates has also been reported for mixtures of model IDPs and RNA (100), as well as the nucleolus (38) and stress granules (104), where internal structuring into various subcompartments (e.g., a core-shell) may arise. Hence, this model may prove useful in advancing our understanding of LLPS into multiphase biomolecular condensates.

Data availability statement

The source code for the patchy-particle model can be accessed here: https://github.com/CollepardoLab/md_patchy_model.

Conclusions

In this work, we have introduced a patchy-particle polymer model capable of probing LLPS in protein-RNA mixtures from a mechanistic and thermodynamic point of view. Specifically, we have studied the effects of RNA 1) on phase separation of model RBPs, 2) on the thermodynamics and kinetics of condensate formation, and 3) in the stability of multicomponent phase-separated protein-RNA mixtures. From our simulations, fundamental rules and features relating to LLPS in these systems emerge at low to moderate RNA concentrations: 1) RNAs can act as high-valency molecules that promote phase separation by increasing the effective valency (i.e., connectivity) of RBPs (scaffolds), 2) RNA molecules increase the stability of condensates and accelerate the nucleation process, 3) addition of RNA to phase-separated scaffold-client (low-valency proteins) mixtures can lead to suppression of LLPS because of competition between RNA and clients for scaffold binding sites, and 4) spatial segregation of components within phase-separated protein-RNA droplets is controlled by fine-tuning the effective ratio of scaffold/client proteins and interaction strengths of components. In particular, our work suggests that inhomogeneous cellular bodies may form at low RNA concentrations, when the RNA polymer exhibits a higher affinity for client proteins than for scaffolds.

Our findings provide an account of how low to moderate concentrations of RNA can significantly enhance phase separation of RNA-binding proteins, enabling LLPS even under unfavorable conditions (e.g., supercritical temperatures, extreme pH values, and subsaturation protein concentrations), and postulates the high valency of RNAs as the molecular origin of such enhancement. The high valency of RNA is a critical modulator of RBP LLPS because it augments the molecular connectivity of condensates (thereby increasing their stability) and increases the enthalpic gain of bringing many RBPs in close contact to form the first nuclei. The mechanisms proposed here to explain how the influence of RNA on the phase behavior of RNA-binding proteins can be used to guide the design of in vitro experiments. Together, our work provides a useful tool for interrogating protein-RNA systems and for elucidating mechanisms of intracellular LLPS.

Editor: Rohit Pappu.

Author contributions

J.A.J., J.R.E., D.F., and R.C.-G. designed the research. J.A.J., J.R.E., I.S.-B., and A.G. performed the simulations. J.A.J., J.R.E., I.S.-B., and A.G. analyzed the data. J.A.J., J.R.E., D.F., and R.C.-G. wrote the manuscript, and R.C.-G. supervised the research.