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Biophys J
Biophys J
Biophysical Journal
0006-3495
1542-0086
The Biophysical Society

S0006-3495(23)00159-5
10.1016/j.bpj.2023.03.006
Articles
Surfactants or scaffolds? RNAs of varying lengths control the thermodynamic stability of condensates differently
Sanchez-Burgos Ignacio 1
Herriott Lara 1
Collepardo-Guevara Rosana rc597@cam.ac.uk
23∗
Espinosa Jorge R. jr752@cam.ac.uk
14∗∗
1 Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, United Kingdom
2 Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
3 Department of Genetics, University of Cambridge, Cambridge, United Kingdom
4 Departament of Chemical Physics, Faculty of Chemical Sciences, Universidad Complutense de Madrid, Madrid, Spain
∗ Corresponding author rc597@cam.ac.uk
∗∗ Corresponding author jr752@cam.ac.uk
25 7 2023
06 3 2023
122 14 29732987
9 11 2022
2 3 2023
© 2023 Biophysical Society.
2023
Biophysical Society
https://creativecommons.org/licenses/by/4.0/ This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Biomolecular condensates, thought to form via liquid-liquid phase separation of intracellular mixtures, are multicomponent systems that can include diverse types of proteins and RNAs. RNA is a critical modulator of RNA–protein condensate stability, as it induces an RNA concentration-dependent reentrant phase transition—increasing stability at low RNA concentrations and decreasing it at high concentrations. Beyond concentration, RNAs inside condensates can be heterogeneous in length, sequence, and structure. Here, we use multiscale simulations to understand how different RNA parameters interact with one another to modulate the properties of RNA–protein condensates. To do so, we perform residue/nucleotide resolution coarse-grained molecular dynamics simulations of multicomponent RNA–protein condensates containing RNAs of different lengths and concentrations, and either FUS or PR25 proteins. Our simulations reveal that RNA length regulates the reentrant phase behavior of RNA–protein condensates: increasing RNA length sensitively rises the maximum value that the critical temperature of the mixture reaches, and the maximum concentration of RNA that the condensate can incorporate before beginning to become unstable. Strikingly, RNAs of different lengths are organized heterogeneously inside condensates, which allows them to enhance condensate stability via two distinct mechanisms: shorter RNA chains accumulate at the condensate’s surface acting as natural biomolecular surfactants, while longer RNA chains concentrate inside the core to saturate their bonds and enhance the density of molecular connections in the condensate. Using a patchy particle model, we additionally demonstrate that the combined impact of RNA length and concentration on condensate properties is dictated by the valency, binding affinity, and polymer length of the various biomolecules involved. Our results postulate that diversity on RNA parameters within condensates allows RNAs to increase condensate stability by fulfilling two different criteria: maximizing enthalpic gain and minimizing interfacial free energy; hence, RNA diversity should be considered when assessing the impact of RNA on biomolecular condensates regulation.

Editor: Alberto Perez.
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pmcSignificance

RNA is a critical modulator of the biophysical properties of biomolecular condensates, such as their stability and viscosity. Inside cells, a single condensate can contain RNAs of multiple different lengths at varying concentrations. Here, we take advantage of multiscale simulations to investigate the intramolecular organization and biophysical properties of RNA–protein condensates that contain RNAs of different lengths. Our simulations reveal that RNAs of different lengths are distributed heterogeneously inside condensates. Short RNAs accumulate preferentially at the condensate’s interface, acting as natural surfactants, whereas long RNAs concentrate deep within the core, strengthening the overall connectivity of the condensed liquid network. Furthermore, we demonstrate that RNA length and concentration cooperate to fine-tune the RNA-driven reentrant phase behavior of RNA–protein condensates: long RNAs increase both the maximum concentration of RNA that condensates can incorporate before dissolving, and their range of stability.

Introduction

Intracellular organization represents a fundamental aspect of regulation with respect to both structure and function. While membrane-bound organelles are responsible for forming large, often permanent compartments within the cell, a more dynamic compartmentalization can be also achieved through membraneless organelles (1). Membraneless organelles, also referred to as biomolecular condensates, possess the two key properties of intracellular compartments: the existence of a defined boundary between the compartment and its surroundings, and the ability of components to diffuse freely within the compartment (2,3). Biomolecular condensates are thought to form via liquid–liquid phase separation (LLPS) of intracellular mixtures (e.g., proteins, RNA, DNA, and chromatin). Thus, the boundary of condensates is not a traditional lipid membrane, but rather the liquid–liquid interface separating a condensed liquid from its surrounding cytoplasm or nucleoplasm. Since the discovery of P-granule condensates in 2009 (4), important examples of biomolecular condensates including the nucleolus (5,6), Cajal bodies (7,8), paraspeckles (9,10), stress granules (11,12), and chromatin (13,14) (a finding that drove the paradigm shift away from the once prominent theory of the 30-nm fiber (15,16,17)) have been exhaustively investigated.

RNA-binding proteins are common components of intracellular biomolecular condensates (18,19,20,21,22). Several features of RNA-binding proteins underpin their ability to form condensates that are sensitively regulated by RNA. For instance, RNA-binding proteins are multidomain multivalent molecules, many of which can establish sufficiently strong homotypic interactions to act as scaffolds in biomolecular condensates—e.g., the heterogeneous nuclear ribonucleoprotein 1 (hnRNPA1) (12,23), fused in sarcoma (FUS) (24,25,26), the GTPase-activating protein SH3 domain-binding protein 1 (G3BP1) (27,28,29,30) and the transactivation response DNA-binding protein 43 (TDP-43) (31,32,33). In addition, RNA-binding proteins can bind to RNA both specifically and promiscuously via their RNA recognition motifs (RRMs), positively charged domains, and intrinsically disordered regions (IDRs) with low-complexity amino acid sequences (34,35,36). Both in vitro and, more recently, in silico experiments have demonstrated the role of RNA as a critical regulator of RNA-protein condensates (37,38,39,40,41,42,43,44). The RNA–binding protein Whi3 has been shown to partition into different condensates depending on the secondary structure of the RNA to which it is bound (45). Proteins such as FUS remain soluble in the nucleus, where RNA concentration is high, but form aggregates in the cytoplasm where RNA concentration is lower (46). Such impact of RNA concentration on protein aggregation may be relevant to rationalize the presence of pathological FUS aggregates (characteristic of amyotrophic lateral sclerosis) in the cytoplasm of postmortem tissues (47) versus their absence from the nuclei (48). The pattern of low levels of RNA promoting condensation versus higher concentrations promoting dissolution is described as RNA-driven reentrant phase behavior (37,43,46) and is particularly important when considering the role of RNA in complex coacervation (44,49,50,51). Complex coacervation frequently enables the phase separation of so-called cognate proteins, which, unlike FUS, cannot sustain LLPS through protein–protein interactions alone, but instead rely on interactions with a partner biomolecule such as RNA (52). The 25-repeat proline-arginine peptide (PR25) is a representative example of a protein that undergoes complex coacervation at physiological conditions driven mostly by electrostatic interactions with RNA (44,51).

RNA length has been shown to mediate condensate reentrant phase behavior (53). Specifically, transcriptional condensate formation and dissolution was shown to be regulated by both RNA length and concentration: short, nascent RNAs present at transcription initiation stimulate condensation, while longer nucleic acids resulting from transcriptional bursts promote dissolution (53). The nature of transcriptional bursting, with the total number of RNA molecules as well as their lengths increasing (54), means it is unclear whether the reentrant phase behavior of transcriptional condensates is a function of RNA length, concentration, or a combination of both. In vitro experimentation has proved valuable in demonstrating the various ways in which RNA regulates LLPS of RNA-binding proteins (18,19,20,21,22,37,38,39,40,41,46). Complementary, computational modeling and simulations can provide mechanistic insight into the experimental observations, and molecular detail regarding the condensate’s thermodynamic, kinetic, and structural properties (55). Computer simulations can also elucidate condensate properties such as droplet surface tension, protein molecular contact maps, or protein/RNA/DNA conformational ensembles (56,57,58,59,60,61). Moreover, key features of LLPS, such as valency (62,63), topology (64,65), or binding affinity (66,67,68), can be precisely controlled in simulations. In that sense, simulations have proved useful for the study of biomolecular condensates at various levels of resolution: ranging from atomistic force fields to lattice-based physical models (16,51,69,70,71,72).

Here, we use molecular dynamics (MD) simulations, taking advantage of the benefits of computational modeling (56,57,58,59,60,61), to investigate in molecular detail the role of RNA length and concentration in the regulation of biomolecular condensates. Specifically, we aim to determine how RNA concentration and length cooperate or compete to affect the RNA-dependent reentrant phase behavior of RNA-binding proteins (18,19,20,37,38,44,46). We use our sequence-dependent Mpipi model (73), which predicts protein phase diagrams in quantitative agreement with experiments, to study the reentrant phase behavior of two archetypal proteins, FUS and PR25, known to undergo LLPS either by homotypic interactions or complex coacervation, respectively (74). Furthermore, we investigate the effect of RNA length on condensate organization by simulating proteins with mixtures of RNA of different lengths. In particular, we aim to identify whether patterns similar to those previously described with colloidal scaffold–surfactant models (63) can also exist in RNA-protein systems. Finally, we show that, even when we model biomolecules as simple patchy colloids (64), the strong influence of RNA length and concentration on the phase behavior of RNA–protein condensates can be captured, suggesting that such behavior is dictated by general physical parameters like the molecular valency, binding affinity, and polymer length.

Materials and methods

Since the formation of phase-separated condensates entails the collective interactions among thousands of different proteins and other biomolecules, the study of LLPS has benefited from the development and application of coarse-grained approaches, including mean field simulations (75,76,77,78,79), lattice-based models (80,81,82,83), minimal models (65,66), and residue-resolution simulations (57,58,67,84,85,86,87,88). In this work, we employ two protein/RNA coarse-grained models of different resolutions previously developed by us: 1) the residue/nucleotide resolution Mpipi force field for proteins and RNA (73) and 2) the MD-Patchy model in which whole proteins are represented as patchy particles, and RNA as self-avoiding flexible polymers (44,64,89).

Within the Mpipi force field (73), amino acids and RNA bases are represented by single beads with unique chemical identities (Fig. 1 a) in which hydrophobic, π–π, and cation–π interactions are modeled through a Wang-Frenkel (mid-range) potential (90), and electrostatic interactions via Yukawa/Debye–Hückel (long-range) potentials (84). Bonded interactions between consecutive residues within the same protein (or nucleotides within the same RNA strand) are described with a harmonic potential. Furthermore, within this model, intrinsically disordered regions of proteins and RNA strands are treated as fully flexible polymers, while globular domains are described as rigid bodies based on their corresponding crystal structures taken from the Protein Data Bank and adapted to the model resolution. The interactions between “buried” amino acids within globular domains are scaled down by 70% as done previously in (73,74). The solvent is modeled implicitly, and the screening effects of monovalent ions in solution at physiological concentrations (i.e., ∼150 mM NaCl) are approximated by the Debye length of the Yukawa/Debye–Hückel potential. Because the Debye–Hückel potential invokes a mean field theory approximation, important effects such as ion condensation, ion correlations, ion heterogeneity, and specific ion binding are ignored. Additional effects that are not accounted for are the identity of the ions (e.g., Na+, K+ versus Mg2+), and the entropic contributions of water (57,91). Thus, by using the Debye–Hückel potential, we assume that the effects of ions in solution can be approximated by the simple reduction of charge–charge interactions. Nonetheless, the approximation is exact in the low salt limit, and previous residue-resolution coarse-grained models invoking this approximation have been successfully employed to predict the phase diagrams and the single-molecule radii of gyration of proteins in quantitative agreement with experiments within the range of 100–150 mM NaCl (73,84,87). Regarding RNA–protein condensates, such implicit solvent coarse-grained models have been able to uncover molecular and thermodynamic mechanisms explaining their regulation (44,84,89,92). Like other molecular models with reduced physical details, these residue-resolution coarse-grained models are able to compensate for the innacuracies of the Debye–Hückel by using experimental and/or atomistic data in their parameterizations. Details on the force field parameters and simulation setups are provided in the supporting material.Figure 1 Reentrant phase behavior driven by RNA is regulated by both concentration and length. (a) Residue resolution coarse-grained simulations with the Mpipi model (73) to investigate phase separation of RNA–protein mixtures. Coarse-grained representation of (full sequence) FUS, PR25, and a 400-nt polyU RNA strand using the Mpipi model (73) in which each amino acid or nucleotide is represented by a single bead. Please note that the size of the beads depicted in this panel has been conveniently rescaled for visualization purposes. In FUS protein, beads of different colors indicate different protein domains. Direct coexistence simulations of polyU-PR25 (top) and FUS-polyU (bottom) are also included. (b) Comparison of the predicted condensate densities as a function of temperature (renormalized by the highest critical temperature) for polyU–PR25 mixtures composed by polyU strands of 400 nt (black symbols) and 20 nt (blue symbols) using direct coexistence simulations (solid circles) and bulk NpT simulations (solid squares). The estimated critical temperature of each system by both ensembles is depicted by empty symbols of the corresponding shape and color. Snapshots of a direct coexistence simulation and a bulk NpT simulation are included to illustrate the analogy between both ensembles when describing the system condensed phase. Continuous lines represent the phase diagram coexistence lines. (c) Normalized critical temperature of polyU-PR25 mixtures as a function of the U/PR25 mass ratio for different polyU strand lengths as indicated in the legend. (d) Normalized critical temperature of FUS-polyU mixtures as a function of the U/FUS mass ratio for different polyU strand lengths as indicated in the legend. Dashed lines connecting the critical temperatures as a function of concentration are included as a visual guide. While in (c) all temperatures have been normalized by the highest T at which phase separation was observed (T = 435 K), in (d) all temperatures have been normalized by the critical temperature of pure FUS (Tc,FUS = 365 K). Please note that higher critical temperatures in our model correspond to higher driving forces to undergo LLPS (i.e., lower saturation concentration). To see this figure in color, go online.

In addition to the residue-resolution Mpipi model, we employ a minimal coarse-grained patchy model (MD-Patchy (64)) to elucidate whether the role of RNA length and concentration in RNA–protein condensates is determined by general molecular features such as valency, binding affinity, or the relative RNA/protein length. Within our patchy particle simulations, proteins are described as pseudo hard sphere (93) particles decorated with sticky patches, which account for the protein binding sites (modeled through square-well-like potentials (94)), and RNA strands are modeled as fully flexible self-avoiding polymers that can interact attractively with RNA-binding proteins via midrange nonspecific interactions (89). Each RNA bead accounts for several nucleotides and has the same size as those of the proteins (89). Regarding the nonbonded potential, RNA–RNA interactions are described by a pseudo hard sphere potential in combination with a Yukawa/Debye–Hückel screened potential (for further details on the model potential and parameters see self-avoiding polymers trigger concentration-dependent reentrant phase behavior of colloidal patchy-particle condensates modulated by polymer length and supporting material) and an implicit solvent model. Accordingly, the diluted phase (i.e., the protein-poor liquid phase) and the condensed phase (i.e., the protein-rich liquid phase) are effectively a vapor and a liquid phase, respectively. Overall, the combination of both Mpipi and MD-Patchy models represents a multiscale approach for studying RNA–protein condensates given that the scale resolution of the patchy particles is approximately 2 orders of magnitude lower than that of the Mpipi residue-resolution model. Specifically, within the Mpipi model, FUS and PR25 are represented by ∼500 and 50 amino acids, respectively. In comparison, only one bead is use for the whole proteins in the MD-Patchy simulations.

To determine the stability of RNA–protein condensates, we evaluate the phase diagrams (in the temperature-density plane) of the different systems by means of direct coexistence simulations (95,96). Within the direct coexistence approach (Fig. 1 a), the two coexisting phases of a given system are placed in the same simulation box. The simulation box used is rectangular, with an elongated side perpendicular to the interfaces—long enough to capture the bulk density of each phase—while the parallel sides are chosen such that proteins and RNA cannot interact with themselves across the periodic boundary conditions (43). We employ the canonical ensemble (constant number of molecules [N], system volume [(V)], and temperature [T], or NVT)). Once direct coexistence simulations reach equilibrium, we measure the coexisting densities of both the diluted and condensed phases along the long axis of the box, excluding the fluctuations at the interfaces and keeping the center of mass of the system fixed. By repeating this procedure at different temperatures—until we reach supercritical temperatures, i.e., where phase separation is no longer observed—we can evaluate phase diagrams (Fig. 1 b). Finally, to avoid finite system-size effects close to the critical point, we estimate the critical temperature (Tc) and density (ρc) using the law of critical exponents and rectilinear diameters (97) (as shown in (64,89)). Fig 1 a shows a direct coexistence simulation with a system composed of PR25 and poly-uridine (polyU) RNA strands of 400 nucleotides (nt) and FUS with polyU strands of the same length at conditions in which both systems undergo LLPS.

To evaluate condensate densities while controlling accurately the concentration of individual components inside them, we perform additional simulations in the isothermal-isobaric ensemble (NpT). These NpT simulations allow us to fix the desired composition of a multicomponent condensate with ease, e.g., the RNA/protein proportion, which is difficult to do in the direct coexistence method. As shown in Fig. 1 b, NpT simulations provide a similar representation of the condensed phase as direct coexistence simulations—although avoiding the effects of interfaces. By fixing the system pressure to zero, and enabling the volume of the simulation box to isotropically fluctuate, we allow the condensed phase to equilibrate. Stable phase-separated condensates exhibit an equivalent coexistence density as that obtained from direct coexistence simulations, whereas unstable systems cannot sustain the condensed phase and tend toward infinitely dilute densities. Within the NpT ensemble, condensates are only stable at temperatures where the interactions between biomolecules are sufficiently strong to overcome the entropic cost of forming a percolating liquid network, without the need for pressure to be exerted on the simulation box. Finally, once the system densities are equilibrated, the critical temperature of each condensate can be estimated within the interval between the highest temperature at which the system is stable and the lowest temperature at which it is not. We note that the coexistence pressure from direct coexistence simulations deviates slightly from that imposed in NpT simulations (0 bar) at temperatures close to the critical one. However, to test the validity of determining critical temperatures through NpT simulations, we compare the condensate coexistence densities and critical temperatures obtained via NpT versus direct coexistence simulations for mixtures of polyU-PR25 with different strand lengths (Fig. 1 b). Based on a systematic difference of less than 2% in the predicted Tc, we conclude that the NpT approach to estimate critical temperatures is a reasonable method that allows us to have a better control of the RNA/protein ratio within condensates at all conditions.

Results and discussion

RNA length modulates the RNA concentration-dependent reentrant phase behavior of RNA–protein condensates

We first investigate how the RNA concentration-dependent reentrant phase behavior of RNA–protein condensates is influenced by the length of single-stranded RNA. For this, we perform direct coexistence and bulk NpT simulations to evaluate the critical temperature of each system (as detailed in materials and methods) using the residue/nucleotide resolution Mpipi force field (73), which has been shown to achieve quantitative agreement with experimental phase diagrams of RNA-binding proteins. We compare the behavior of two phase-separating RNA-binding proteins, FUS (526 residues, sequence in supporting material) and PR25, for which phase behavior is modulated differently by RNA (44). FUS can form single-component condensates via homotypic interactions, which increase in stability at moderate RNA concentrations (37,43,46). PR25 is an arginine-rich peptide, which requires RNA to phase separate via heterotypic RNA–protein interactions at physiological conditions (44,51). For each case, we simulate solutions containing tens to hundreds of individual proteins in the presence of disordered single-stranded polyU RNA molecules with five different lengths: 20, 50, 100, 200, and 400 nt. For all RNA lengths, we test different polyU concentrations defined through the U/protein mass ratio, which allows us to quantify the total number of U nucleotides in the mixtures, regardless of whether they are assembled in longer or shorter polyU chains. Importantly, it has been shown that combining RNA-binding proteins and RNA at ratios resulting in electroneutral mixtures enhances the stability of RNA–protein condensates (42,43). Thus, here we explore a range of U/protein mass ratios that lie around the electroneutral point. We focus on single-stranded polyU RNA for simplicity and to follow previous studies on RNA-protein phase separation (18,37,74).

For the polyU-PR25 mixtures, the electroneutral point lies at the 1.21 U/protein mass ratio. Thus, we perform simulations for polyU-PR25 mixtures spanning the range between 0.78 and 2.24 U/PR25 mass ratios. For the electroneutral polyU-PR25 system, we first demonstrate that NpT simulations quantitatively reproduce the condensed phase coexistence densities found in phase diagrams constructed using standard NVT direct coexistence simulations (64,84). From a set of direct coexistence simulations at varying temperatures, we extract the phase diagrams for two polyU-PR25 mixtures containing RNA strands of varying lengths (20 and 400 nt) but keeping a constant U concentration (mass ratio of 1.21) regardless of RNA length (Fig. 1 b). Then, we simulate these systems in the NpT ensemble at zero pressure (using a cubic box). As shown in Fig. 1 b, this approach provides consistent condensate densities to those obtained via direct coexistence simulations (as long as the density of the dilute phase is very low). As our direct coexistence simulations indicate, approximating coexistence densities from NpT simulations is reasonable for most of the temperatures with densities of the dilute phase being of the order 1 × 10−3 g/cm3 (please note that the solvent is implicitly considered within the force field). Since with NpT simulations the density of the dilute phase cannot be measured, the value for the critical temperature cannot be calculated using the law of critical exponents and rectilinear diameters (97), as is the case in the direct coexistence simulations. However, an interval at which the critical temperature falls can be estimated. Fig. 1 b shows that the values of the critical temperatures estimated from bulk NpT simulations (as the mid temperature of the computed interval; described in materials and methods) lie within the uncertainty of the critical temperatures evaluated from direct coexistence simulations and the law of critical exponents and rectilinear diameters.

Having established that NpT simulations can provide robust estimates of the critical temperature, we move forward with the NpT ensemble to investigate the interplay between RNA concentration and the effects of RNA length on condensate stability. To consider the effect of RNA length independently, we keep the total amount of U nucleotides in the mixtures fixed, and assemble them in polyU chains of different lengths. When the U/PR25 mass ratio is kept constant, we observe a monotonic increase in the critical temperature of the condensates as the RNA length increases. For example, for polyU-PR25 mixtures at ratios satisfying the electroneutral point (i.e., 1.21 polyU/PR25 mass ratio), there is a 20% enhancement in the critical temperature when the RNA chain length increases from 20 to 400 nt (Fig. 1 c). Such behavior can be ascribed to the density of protein–RNA intermolecular contacts increasing significantly as the RNA lengthens, especially at strand lengths of tens to hundreds of nucleotides, as discussed in (44). Because PR25 must bind to RNA to form a condensed liquid network, adding covalent bonds within the RNA chains—for instance, by replacing many short strands with a longer one—increases the PR25–RNA critical temperature by zipping together large chunks of RNA, which would otherwise be driven away by the dominant RNA–RNA electrostatic repulsion. When we next fix the RNA chain length, and investigate the impact of RNA concentration on the stability of polyU-PR25 condensates, for all the RNA lengths we study, we confirm that PR25 exhibits the well-known RNA concentration-dependent reentrant behavior of RNA-binding proteins discovered experimentally (22,37,46). That is, the stability of polyU-PR25 condensates—quantified by the values of the critical temperature—gradually increases as the RNA concentration goes from low to moderate (up to approximately the electroneutral point), then it reaches a maximum value, and finally decreases as the RNA concentration increases even further. Remarkably, looking at the combined effects of RNA length and concentration reveals that RNA length significantly modulates such reentrant behavior. Specifically, increasing RNA length sensitively raises the maximum value that the critical temperature of the mixture reaches (i.e., how much the condensate stability can be boosted by RNA), and the maximum concentration of U nucleotides that the condensate can incorporate before beginning to become unstable (i.e., when the RNA chains are longer, more nucleotides can form part of the condensate before it begins to dissolve). Thus, the most stable polyU-PR25 condensates are formed by the longest RNA chains we study, and, unexpectedly, contain U/PR25 concentrations above the electroneutral point (Fig. 1 c).

We next investigate whether such behavior also holds for proteins that are able to undergo phase separation on their own, i.e., via homotypic protein–protein interactions (65,98). For this, we focus on the protein FUS and test the impact of adding polyU of varying lengths and at different concentrations. Our simulations contain 48 replicas of FUS (full sequence, see supporting material) and polyU chains of 20, 50, 100, 200, or 400 nt in length. For all the different polyU lengths, we prepare mixtures at concentrations spanning the range of U/FUS mass ratio from 0 to 0.19. First, we calculate the critical temperature of pure FUS condensates, obtaining a value of Tc,FUS = 365 K. This temperature is in reasonable agreement (considering the coarse-grained nature of the model) with the experimental protein thermostability of FUS (∼355 K (99)). Next, we look at mixtures containing RNA at the concentration corresponding to the electroneutral point (mass ratio of 0.049), and we confirm that performing NpT bulk simulations reproduces the length-dependent increase in critical temperature identified previously via direct coexistence simulations (44). Specifically, when we mix FUS with RNA of 100, 200, or 400 nt at the electroneutral ratio (0.049 U/FUS mass ratio), we see a marginal increase in critical temperature—3% with respect to the value for pure FUS system (Fig. 1 d)—in agreement with our previous direct coexistence results (44). Adding 20-nt polyU to FUS, the shortest polyU molecules we study, hinders phase separation, with the effect being amplified at higher polyU concentrations. This occurs because 20-nt polyU is too short to bridge FUS molecules and enhance the connectivity of the condensed liquid, as shown previously (43,44). For RNA lengths of 50, 100, 200, and 400 nt, the RNA concentration-dependent reentrant phase behavior of FUS is observed. That is, gradually increasing the concentration of polyU up to a given threshold (in our case a U/FUS mass ratio of around ∼0.1) increases the critical temperature, while adding polyU at concentrations beyond such threshold reduces the critical temperature. The observation of peak critical temperatures for FUS condensates containing 50-nt polyU at polyU concentrations surpassing the electroneutral point (i.e., ∼0.1), is consistent with in vitro studies (20). As in polyU–PR25 mixtures, we find that the maximum enhancement in phase separation occurs at higher polyU/protein mass ratios for longer-chain polyU systems. Overall, when polyU length is increased from 20 to 400 nucleotides, the mass ratio at which the system displays the highest critical temperature increases from 0 (no RNA) to 0.12 (Fig. 1 d). Nevertheless, we observe that the RNA length-dependent effects for polyU–FUS mixtures are significantly smaller than for polyU–PR25 mixtures (see Fig. 1, c and d).

Our results for FUS are consistent with a number of in vitro studies characterizing its RNA concentration-dependent reentrant phase behavior (41,46). However, that low levels of RNA promote phase separation, while higher RNA levels promote dissolution contrasts with the observation that some condensates are able to form in regions of the cell with very high levels of RNA (up to RNA/protein mass ratios of ∼40) (100). Moreover, despite RNA being at high concentrations, it has been shown to play a key role in initiating phase separation of FUS by nucleating protein condensates (20,46,100). For example, RNA plays a prominent role in triggering P-body formation, which occurs as a result of a strong increase in mRNA concentration (100,101). Also, FUS-containing paraspeckles in the nucleus are thought to be nucleated by the long noncoding RNA Neat1, despite the high background RNA concentration (20,46). Even though in vitro studies have not explicitly revealed how the length of RNA defines the maximum RNA concentration that a condensate rich in RNA-binding proteins can take before its stability begins to decrease, there is evidence that indirectly supports this theory: a number of in vitro and in silico studies have identified that minimum RNA lengths are needed to promote phase separation of RNA-binding proteins (43,102) and others have found that shorter RNA molecules are more potent promoters of condensate dissolution (46), in agreement with our results from Fig. 1 d. Here, we show directly that increasing the length of the nucleic acid chain increases the capacity of the RNA to promote phase separation and to be incorporated into the condensate at higher RNA concentrations than their shorter counterparts. This result is also supported by in vitro observations of the linker histone H1 having a greater tendency to phase separate with longer RNA molecules compared with shorter ones (103). Therefore, previous findings which have shown that high concentrations of RNA promote condensate dissolution ought to be contextualized with information on the length of the studied nucleic acids. As demonstrated here, it is possible for phase separation to be favored at high RNA concentrations if the RNA chains are long enough to bind multiple proteins simultaneously. Assembling nucleotides in longer RNA chains has the additional advantage of decreasing the electrostatic repulsion among phosphates of separate nucleotides due to the presence of more covalent bonds.

Since our results support the hypothesis that longer RNA molecules are more powerful enhancers of phase separation due to their ability to increase the connectivity of the condensed liquid (66,98), we next investigate this behavior by examining the stability of condensates containing both long and short polyU chains (Fig. 2 a). To do so, we simulate mixtures of PR25 in the presence of polyU strands of two different lengths, 50 and 400 nt, such that each length represents half of the total polyU mass ratio concentration in each system. For these mixed RNA length systems, we explore polyU/PR25 mass ratios ranging from 0.76 to 2.1. We find that mixed RNA length systems display critical temperatures in between those of the pure short and long RNA chain systems, and with the maximum enhancement of critical temperature also occurring at intermediate polyU/PR25 mass ratios between that of the pure short and pure long RNA systems (Fig. 2 b). We also study FUS-polyU mixtures of 50- and 400-nt polyU strands (such that each length represents half of the total polyU mass ratio concentration) spanning mass ratios from 0 to 0.196. Similar to the results for PR25, the mixed length systems in FUS present intermediate critical temperatures compared with the pure long-chain and short-chain RNA systems, as well as patterns of reentrant phase behavior in which the maximum critical temperature peaks at an intermediate polyU/FUS mass ratio between that of the pure long-chain and short-chain RNA systems (Fig. 2 c).Figure 2 RNA-driven reentrant phase behavior of FUS and PR25 polyU systems including mixtures with different RNA strand lengths. (a) Representation of PR25, FUS, and two RNA strands of 50 and 400 nt each following the same color code and considerations discussed in Fig. 1a. Please note that the size of the beads depicted in this panel has been conveniently rescaled for visualization purposes. (b) Normalized critical temperature of polyU-PR25 mixtures as a function of the U/PR25 mass ratio for different polyU strand lengths as indicated in the legend. (c) Normalized critical temperature of FUS-polyU mixtures as a function of the U/FUS mass ratio for different polyU strand lengths as indicated in the legend. For the systems with mixed polyU lengths, each length represents half of the total polyU concentration. While in (b) all temperatures have been normalized by the highest T at which phase separation was observed (T = 425 K), in (c) all temperatures have been normalized by the critical temperature of pure FUS (Tc,FUS). To see this figure in color, go online.

Our findings reveal that mixed length polyU systems are generally more stable than short-chain polyU systems; further emphasizing the ability of long polyU strands to show a stabilizing effect on condensates up to higher concentrations, given that we observe this behavior even when shorter polyU molecules are present. Our observations are consistent with in vitro RNA–FUS phase separation assays reporting that the lncRNA Neat1 (short isoform, length = 3.7 kb) was able to drive reappearance of FUS droplets that had previously been solubilized with tRNA (70–100 nt (104)) (46).

RNA length and concentration determine the internal organization of molecules in RNA–protein condensates and the properties of their interfaces

To rationalize the interaction of RNA length and concentration in modulating the stability of RNA–protein condensates, we now characterize the organization of the different molecules inside the RNA–protein condensates by quantifying the densities of polyU versus proteins across the condensate. These density profiles reveal that there are considerable differences in the distribution of proteins versus polyU depending on the concentration of RNA. Protein-rich systems (i.e., low polyU/PR25 mass ratios) form condensates with a surface coated by PR25 peptides (Fig. 3, a and b), whereas the surfaces of polyU-rich droplets (i.e., high polyU/PR25 mass ratios) are mostly coated by polyU chains (Fig. 3, c and d).Fgure 3 Structural condensate organization of RNA-binding proteins in the presence of long and short RNA strands. (a) PolyU–PR25 mixture with a 0.8 U/PR25 mass ratio where polyU strands are 50 and 400 nt long (each length contributing half to the total polyU concentration). Top: representative snapshot of a direct coexistence simulation of the system, where PR25 molecules are colored in red and long and short RNAs are depicted in blue and cyan, respectively. Middle: density profile of PR25 (red) and polyU RNA (black) along the long axis of the simulation box. Bottom: RNA density profile decomposed in 400-nt (blue) and 50-nt (cyan) polyU chains. (b) The same as in (a), but for a polyU–PR25 mixture with a U/PR25 mass ratio of 0.8 and polyU strands of 400 nt only. Note that we only show one density profile since here all RNAs are of equal length. (c) The same as in (a), but for a polyU–PR25 mixture with a U/PR25 mass ratio of 1.6, where polyU strands are also 50 and 400 nt long. (d) The same as in (b), but for a polyU-PR25 mixture with a U/PR25 mass ratio of 1.6 and polyU strands of 400 nt only. The temperature of systems shown in (a–d) was 0.9 with respect to their corresponding critical temperature. (e) RNA–FUS mixture at T/Tc,FUS = 0.98 and with a U/FUS mass ratio of 0.14, where polyU RNA strands are 50 and 400 nt long (each length contributing half to the total polyU concentration). Top: representative snapshot of a direct coexistence simulation. Middle: density profile of FUS (green) and RNA (black) along the long axis of the simulation box. Bottom: RNA density profile decomposed in 400-nt (blue) and 50-nt (cyan) polyU chains. (f) Surface tension for different polyU–PR25 mixtures, all of them at a temperature of 0.85 with respect to its corresponding critical temperature for the system indicated in the legend. The high RNA concentration corresponds to a U/PR25 mass ratio of 1.6, while the low RNA concentration corresponds to a U/PR25 mass ratio of 0.8. To see this figure in color, go online.

In polyU–PR25 condensates combining RNAs of different lengths, we find that the RNAs exhibit a striking spatially heterogeneous distribution. The longer 400-nt polyU molecules accumulate in the condensate core, while the shorter 50-nt polyU molecules concentrate preferentially toward the condensate surface (Fig. 3, a and c). Simulations approximating proteins as patchy colloids have revealed the same heterogeneous organization of high- and low-valency proteins within multicomponent condensates. By looking at the problem from a condensed matter perspective, the simulations revealed that burying high-valency proteins in the center, and exposing low-valency species to the interface, maximizes the enthalpic gain for condensate formation (most bonds of the higher-valency molecules are satisfied at the condensate core) and reduces the interfacial free energy at the droplet interface because the lower-valency molecules act as surfactants (63,66,105). In addition, longer RNAs occupy a smaller excluded volume if they are in the core of the condensate versus if they are localized toward the interface or within the diluted phase. The excluded volume associated with a single 400-nt RNA strand in the condensed phase is expected to be lower than that of eight 50-nt RNA chains. This effect results in a maximization of the system entropy when long RNA strands (compared with short ones) are recruited to the condensate core. Similarly, by preferentially positioning short RNA strands at the interface, the overall RNA excluded volume can be reduced. Hence, both enthalpic and entropic factors likely contribute to explain the heterogeneous arrangement of short and long RNAs within phase-separated condensates shown in Fig. 3, a and c. In Fig. 3 e, we also show that polyU-FUS condensates of mixed RNA length (with equal concentration of 50- and 400-nt strands) display multilayered RNA organization, preferentially locating short polyU chains at the interface and long RNA strands in the core. Such structural organization maximizes at the same time the condensate liquid network connectivity and minimizes the interfacial penalty. We have corroborated that the observed condensate architecture is robust against changes in temperature, which is the variable that globally controls the molecular interaction strength (106) in our simulations. To do so, we computed the same density profiles as in Fig. 3, a–e at moderately lower and higher temperatures (i.e., 0.85 and 0.95 T/Tc) and found remarkably similar protein and RNA structural arrangements within the condensates (Fig. S1).

Since distinct molecules at the condensate interface can translate into significantly different interfacial properties, such as interfacial free energies (22,43), coalescence fusion rates (107), size-conservation (6,63), or uneven molecule exchange rates (66), we now calculate the interfacial free energy (γ; see supporting material for further details on these calculations). We focus on PR25 condensates because converging the value of γ for FUS-based droplets is computationally unfeasible due to the size of FUS (526 amino acids). We start by computing the interfacial free energy for two types of 400-nt polyU–PR25 condensates: with a PR25-rich interface (i.e., low U/PR25 mass ratio of 0.8) and with a polyU-rich interface (i.e., high U/PR25 mass ratio of 1.6), as shown in Fig. 3 f. To facilitate the comparison, in both cases we simulate the systems at the same relative temperature (T/Tc = 0.85). Strikingly, we find that the condensate with a polyU-rich interface presents a much lower interfacial free energy (almost half) than that with a PR25-rich interface. Such an unexpected finding explains how a high concentration of polyU, beyond the electroneutral point, can boost the stability of condensates: by incorporating a large concentration of RNA, condensates experience a trade-off between the destabilizing effect of a decreased enthalpic gain due to the larger electrostatic repulsion among equally charged nucleotides, and the stabilizing effect of the decrease in the condensate energetic penalty of forming an interface when it is coated with polyU. Our results, therefore, reveal that, in condensates with an excess of polyU, polyU behaves like a surfactant.

To analyze the impact of RNA length, we now calculate the interfacial free energy of two different condensates containing the shorter 50-nt polyU RNA: a PR25, 50- and 400-nt polyU condensate, and a PR25 and 50-nt polyU condensate. We estimate the interfacial free energy at the same temperature used above (T/Tc = 0.85) and at the lower U/PR25 mass ratio of 0.8 (T/Tc = 0.85), since imposing a high RNA concentration with short polyU molecules within the condensed phase in a direct coexistence simulation is not feasible. We observe that increasingly adding 50-nt polyU molecules progressively decreases the interfacial free energy of the condensate, with respect to the value of the 400-nt polyU-PR25 condensate (Fig. 3 f). This observation reinforces the idea that, in RNA-protein condensates that contain RNAs of different lengths, positioning the shorter RNA species at the interface reduces the surface tension as such shorter RNAs act as better surfactants than longer ones (108). Hence, the advantage of mixed length RNA condensates exhibiting multilayered organization results from them presenting similar low surface tensions as those only formed by short RNA strands, while showing considerably higher stability due to long RNA strands increasing the enthalpic gain for condensate formation by contributing more connections to the liquid network connectivity together with PR25.

In addition to the interfacial free energy, we also investigate the molecular contacts that distinct protein domains establish with RNA in RNA–FUS and RNA–PR25 droplets. Following the methodology described in (43,71,109), we estimate the frequency of heterotypic polyU–protein interactions at residue-resolution level (Fig. S2). This calculation is performed at T = 0.95 Tc, and in the presence of both long (400-nt) and short (50-nt) RNA strands for both RNA–PR25 and RNA–FUS systems (further details of these simulations are provided in the supporting material). While in RNA–PR25 droplets RNA–protein interactions are homogeneously distributed across the PR25 sequence, in RNA–FUS condensates only specific regions preferentially interact with polyU, such as the RNA-recognition motifs (from the 282nd to the 371st residue), and the three arginine-glycine-rich regions (RGG1: 163 to 267; RGG2: 371 to 422; RGG3: 453 to 526; Fig. S2), in qualitative agreement with experimental observations (34,46,47). These results demonstrate how coarse-grained models, such as the Mpipi, can recapitulate the preferential binding of RNA to certain amino acid motifs within proteins.

Multilayered condensates such as those found in Fig. 3, a, c, and e for polyU–PR25 and polyU–FUS mixtures, respectively, can be found across the cell and include FUS-containing paraspeckles (9), stress granules (30), and the nucleolus (6). Indeed, condensate structure and organization has important implications for the behavior of the various components, with those located in the core exhibiting slower exchange rates compared with molecules in the outer shell (66,98). Experiments and simulations reveal that longer RNA strands lead to higher viscosities in RNA–protein condensates (18,19,20,43,110). Thus, in mixed RNA condensates, a stable core containing long polyU strands is expected to have a higher viscosity, while an outer shell with short polyU strands a lower viscosity (43). Gelification of RNA–protein condensates via fibrillation, with potential pathological implications (21,47,111), has been shown to be seeded at the interface due to a local increase of protein density at the surface (112); hence, incorporating short RNAs into RNA–protein condensates might contribute to preventing their maturation because it decreases the probability of high density fluctuations at the interface.

Self-avoiding polymers trigger concentration-dependent reentrant phase behavior of colloidal patchy-particle condensates modulated by polymer length

To investigate whether the observed impact of RNA length and concentration on the phase behavior of RNA-protein condensates rely on general molecular features such as protein valency, binding affinity, or the relative polymer size/length between proteins and RNA, we employ a minimal coarse-grained model of colloidal patchy particles with self-avoiding polymer chains to mimic proteins and RNA, respectively (89). Iterations of this minimal coarse-grained model have been previously used to investigate critical factors in LLPS such as surface tension, droplet size conservation, or condensate substructure (44,66). The aim of our minimal simulations here is to assess, beyond protein sequence and specific molecular features, the thermodynamic parameters that explain the general differences between the impact of RNA length and concentration on homotypic phase separation versus RNA–protein heterotypic complex coacervation.

We start by computing the phase diagrams of two different types of colloidal patchy particles in the presence of different concentrations and lengths of a self-avoiding polymer that mimics RNA. The first type are patchy particles decorated with three binding sites in a planar arrangement separated by 120° angles (Fig. 4 a; see supporting material for further details on the model). Like FUS, these colloidal particles—referred to henceforth as scaffold proteins—are able to phase separate on their own via homotypic interactions below a reduced temperature of T∗ = 0.09 (89) (see details on reduced units in the supporting material). On the other hand, the second type of patchy colloids possess two binding sites in a polar arrangement, which by construction can only form linear chains and not three-dimensional percolated networks that sustain phase separation (62,64,65) (Fig. 4 a). Like PR25, two binding site colloidal particles—referred to henceforth as cognate proteins—cannot phase separate on their own (44). We perform direct coexistence simulations of both scaffold and cognate proteins for different polymer bead/protein ratios using polymer chains of 10, 20, 50, and 100 beads such that the polymer bead/protein ratio is defined in terms of the number of polymer and protein beads, ranging from 0.2 to 1.Figure 4 Minimal coarse-grained model for protein LLPS. (a) Green and red spheres represent the excluded volume of scaffold and cognate proteins, respectively, while gray patches represent the binding sites of the proteins. Two different proteins are modeled: scaffold proteins, with three binding sites in a planar equidistant arrangement, and cognate proteins, with two binding sites in a polar arrangement. Blue spherical beads account for ∼5 nt each in the RNA model. Please note that, for visualization purposes, the size of the RNA beads has been scaled down. For further technical details on the model, please see the supporting material. (b) Normalized critical temperature of RNA–cognate protein mixtures as a function of the RNA/cognate protein ratio for different RNA strand lengths as indicated in the legend. (c) Normalized critical temperature of RNA–scaffold protein mixtures as a function of the RNA/scaffold protein ratio for different RNA strand lengths as indicated in the legend. While in (b) all temperatures have been normalized by the highest T (T∗ = 0.11) at which phase separation was observed, in (c) all temperatures have been normalized by the critical temperature of the scaffold protein in the absence of RNA (Tc∗ = 0.09). To see this figure in color, go online.

First, by focusing on a given polymer bead/protein ratio (i.e., 0.4), we capture the RNA length-dependent enhancement of LLPS reported in our sequence-dependent coarse-grained simulations of PR25 and FUS (Fig. 1) where systems containing longer RNA strands can phase separate up to higher critical temperatures (Fig. 4, b and c). For cognate colloidal particles, increasing the “RNA” chain length from 10 to 100 beads at an RNA/protein ratio of 0.4 leads to a 50% increase in the critical temperature (Fig. 4 b). In contrast, the enhancement in critical temperature for the same polymer/protein concentration with scaffold proteins is just 8% (Fig. 4 c). Clearly, scaffolds show much more subtle dependency on RNA length compared with cognate proteins, in full agreement with our previous sequence-dependent simulations shown in Figs. 1 and 2.

Secondly, by gradually varying the polymer bead/protein ratio (from 0.2 to 1; Fig. 4, b and c), patterns of concentration-dependent reentrant phase behavior for both types of proteins and distinct RNA polymer lengths can be observed. A moderate increase in the polymer bead/protein ratio leads to an enhancement in the critical temperature, while any further increase in self-avoiding polymer levels results in LLPS inhibition (i.e., lower critical temperatures). For the cognate protein mixtures, we find a significant shift in the ratio that gives the highest critical temperature as a function of polymer length; consistent with our results for PR25 with polyU (Fig. 1 c). On the other hand, for the scaffold protein mixtures, the shift in the maximum critical temperature toward higher polymer/protein ratios with length is more modest; also in qualitative agreement with our polyU–FUS simulations shown in Fig. 1 d. Remarkably, by means of the colloidal patchy particle model, we can explore mixtures with polymer RNA chains much longer than the size of the proteins. We discover that, while condensates with RNA lengths of 50 or 100 beads are stable up to higher critical temperatures compared with those of shorter lengths (i.e., 20 beads), for all polymer bead/protein ratios and for both scaffold and cognate proteins, beyond a certain length at which RNA greatly exceeds the size of the proteins (e.g., 50 times longer than the protein size), the effect of RNA length on LLPS becomes extremely mild (Fig. 4, b and c); red and black curves). These results also support the notion that the longer RNA strands promote condensate stability by increasing the connectivity among proteins within the condensate network (43,44). Moreover, since even the shortest polymer length added to the scaffold–cognate mixtures meets this criterion, we do not observe the disruptive influence on LLPS of extremely short RNA chains (i.e., 20 nt) with FUS (526 amino acids) observed in Fig. 1 d.

Our results are consistent with the experimental observation that longer RNA strands present weaker dissociation constants with the N-RRM1-2 domains of TDP-43 (which, like PR25, cannot phase separate on their own at physiological conditions) than threefold shorter RNA strands (33). Furthermore, it has been shown that length and charge segregation in the IDR domain of VRN1-like proteins has a critical impact on modulating the DNA-induced VRN1 phase separation—where liquid-like, gel-like, or no phase separation behavior can be switched depending on the IDR length and the presence of neutral versus highly charged domains (113). Overall, our patchy particle results presented here highlight that the the impact of RNA length and concentration on the reentrant phase behavior observed for both homotypic and heterotypic phase-separating proteins is a general property of soft-matter systems, such as biomolecules. Therefore, general features of biomolecules, such as their valency, topology, binding affinity, and relative length or size, is what ultimately dictates the intricate phase behavior of multicomponent biomolecular condensates. Such conclusions are supported by our findings using patchy particle simulations, which highlight the capacity of the minimal model to capture specific RNA-protein condensate behaviors observed with the Mpipi sequence-dependent force field (Fig. 1). For instance, the two approaches consistently predict a much more significant increase in the critical temperature of RNA–PR25 condensates with RNA length than that found in RNA–FUS condensates. Such agreement highlights the key role of fundamental physical parameters, such as molecular valency, binding affinity, and polymer length, in the regulation of RNA–protein condensates.

Conclusions

In this study, using a multiscale modeling approach we reveal how RNA length can tune the concentration-dependent reentrant phase behavior of RNA-protein condensates. Drawing together the results from our sequence-dependent model and patchy particle simulations, we demonstrate that long RNA polymers act as enhancers of phase separation. Not only do longer RNA strands enable phase separation up to higher critical temperatures, they also facilitate phase separation up to higher RNA/protein ratios. We show that this is a physical feature of long polymers, since consistent mass ratios and net charges are used for all our RNA/polymer systems with different lengths. Our finding that longer chain RNA molecules increase the capacity of RNA to raise the critical solution temperature to higher values and that the corresponding condensates can incorporate a higher proportion of RNA nucleotides are consistent with the wide body of work demonstrating the stabilizing role of molecules with an increasing number of repeating chemical building blocks, or higher valencies, on biomolecular condensates (e.g., longer RNAs (44), DNAs (114, 16), or polySUMO/polySIM (98), and IDPs with more stickers (35,56,115).

In addition, our finding that long RNA tends to localize to the condensate’s core, whereas shorter strands accumulate at the droplet surface, provides further support for the theory that the stabilizing and enabling effects of long RNA chains comes, in part, from their ability to act as nucleators (46) and scaffolds (44) in phase-separated condensates. While long RNA stabilize condensates by increasing the density of molecular connections of the liquid network, short RNAs act as better surfactants that increase condensate stability by reducing their interfacial free energy (63). Moreover, the influence of RNA length on condensate organization and viscoelastic properties has important implications on the dynamics of the different components and the mechanisms explaining liquid-to-solid transitions, with potential implications in neurodegenerative disorders (18,19,21,47,107).

Considering the significant interplay between RNA length and concentration might be relevant to rationalize why some biomolecular condensates, such as stress granules or paraspeckles, can be nucleated by long RNA strands (20,46,100) despite being in RNA-rich environments. According to our results, such behavior might be facilitated by RNAs serving as scaffolds and surfactants of RNA-protein condensates at high concentration. In particular, while high RNA concentrations are expected to inhibit phase separation (53), a diverse population of shorter and longer RNAs can yield stable condensates by incorporating the longer RNAs at concentrations beyond the electroneutral point at the condensate core—to enhance condensate connectivity—and the shorter RNAs at the condensate interface—to reduce the interfacial free energy. The observation that RNA length has a similar impact on the concentration-dependent reentrant phase behavior for both FUS and PR25 condensates, although quantitatively shifting the maximum critical temperature by substantially different extents, is also significant and further emphasizes that this observation results from the physical properties of long RNA chains rather than merely on the type of interaction driving phase separation.

Our results also provide thermodynamic and molecular evidence for the hypothesis by Henninger et al. (53) that RNA length and concentration may act in concert to regulate the formation of intranuclear condensates. Specifically, the hypothesis that formation and dissolution of transcriptional condensates is regulated by RNA through a negative feedback loop (53) could be explained by RNA concentration-dependent reentrant phase behavior alone. However, our findings suggesting that longer-chain RNAs, which are produced during a transcriptional burst, stabilize condensates up to higher RNA concentrations may provide robustness to the feedback loop. As higher nucleotide concentrations would need to be reached for condensate dissolution, the transcriptional condensates would remain intact until sufficient levels of longer-chain mRNA have been synthesized.

Taken together, our results provide a thermodynamic view into some of the many ways in which RNA may act as a key regulator of phase separation in the cell and add to the growing consensus considering its role as essential for developing a robust understanding of the regulation and dysregulation of biomolecular condensates (21,116). Several causes of condensate damage in neurodegenerative disorders, such as disease-associated mutations (117,118), do not alter the fundamental changes in phase behavior that differentiate liquid-like condensates from solid-like aggregates (107), but act to increase the likelihood of these changes occurring (111). In other words, the properties of condensates containing mutated proteins might not be discernibly different from those containing wild-type proteins other than in terms of the timescale of their maturation to solid-like aggregates. This suggests that research into potential treatments for condensate-associated diseases may benefit from fundamental biophysical mechanisms of biomolecular condensate regulation (119,120,121,122).

Author contributions

R.C.-G. and J.R.E. designed the research. I.S.-B. and L.H. performed the research. I.S.-B. and L.H. analyzed the data. I.S.-B., L.H., R.C.-G., and J.R.E. developed new methods. J.R.E. supervised the research. R.C.-G. and J.R.E. wrote the original draft. All authors edited the paper.

Supporting material

Document S1. Figures S1 and S2

Document S2. Article plus supporting material

Acknowledgments

This project has received funding from the Oppenheimer Research Fellowship of the University of Cambridge. I.S.-B. acknowledges funding from the Oppenheimer Fellowship, a Derek Brewer scholarship of Emmanuel College, and 10.13039/501100000266 EPSRC Doctoral Training Program studentship, number EP/T517847/1. J.R.E. also acknowledges funding from the Roger Ekins Research Fellowship of Emmanuel College and the Ramon y Cajal fellowship (RYC2021-030937-I). R.C.-G. acknowledges funding from the 10.13039/501100000781 European Research Council (ERC) under the European Union 10.13039/501100007601 Horizon 2020 research and innovation program (grant agreement 803326). This work has been performed using resources provided by the Cambridge Tier-2 system operated by the University of Cambridge Research Computing Service (http://www.hpc.cam.ac.uk) funded by EPSRC Tier-2 capital grant EP/P020259/1.

Declaration of interests

The authors declare no competing interests.

Ignacio Sanchez-Burgos and Lara Herriott contributed equally to this work.

Supporting material can be found online at https://doi.org/10.1016/j.bpj.2023.03.006.
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