RNA length has a non-trivial effect in the stability of biomolecular condensates formed by RNA-binding proteins.

Biomolecular condensates formed via liquid-liquid phase separation (LLPS) play a crucial role in the spatiotemporal organization of the cell material. Nucleic acids can act as critical modulators in the stability of these protein condensates. To unveil the role of RNA length in regulating the stability of RNA binding protein (RBP) condensates, we present a multiscale computational strategy that exploits the advantages of a sequence-dependent coarse-grained representation of proteins and a minimal coarse-grained model wherein proteins are described as patchy colloids. We find that for a constant nucleotide/protein ratio, the protein fused in sarcoma (FUS), which can phase separate on its own-i.e., via homotypic interactions-only exhibits a mild dependency on the RNA strand length. In contrast, the 25-repeat proline-arginine peptide (PR25), which does not undergo LLPS on its own at physiological conditions but instead exhibits complex coacervation with RNA-i.e., via heterotypic interactions-shows a strong dependence on the length of the RNA strands. Our minimal patchy particle simulations suggest that the strikingly different effect of RNA length on homotypic LLPS versus RBP-RNA complex coacervation is general. Phase separation is RNA-length dependent whenever the relative contribution of heterotypic interactions sustaining LLPS is comparable or higher than those stemming from protein homotypic interactions. Taken together, our results contribute to illuminate the intricate physicochemical mechanisms that influence the stability of RBP condensates through RNA inclusion.

Introduction

Cells require precise compartmentalization of their material into different organelles in order to function. While some of these organelles and compartments are shaped by physical membranes, many others are thought to be sustained by liquid–liquid phase separation (LLPS) [1-4]. Like oil and water, biomolecules including multivalent proteins and, in some cases, nucleic acids, can spontaneously demix into phase-separated droplets known as biomolecular condensates [5, 6]. Beyond compartmentalization, numerous vital roles have been recently associated with biomolecular condensates, including cell signaling [2, 7], formation of super-enhancers [8], genome organization [9-12], and aiding cells to sense and react to environmental changes [13], among many others [14-17]. Within the extensive class of biomolecules that can undergo phase separation at physiological conditions, RNA-binding proteins (RBPs), such as FUS [18-20], hnRNPA1 [21, 22], TDP-43 [23-25], TAF-15 [26, 27], G3BP1 [28-31] or EWSR1 [26, 27, 32], have been widely investigated due to their implications in the stability of stress granules [33, 34], P granules [1, 35, 36] and other RNA granules/bodies [37-39].

Phase-separation of RBPs can be both promoted or inhibited by the presence of RNA in an RNA-concentration, and sometimes RNA-structure, dependent manner [27, 32, 40–50]. From the physicochemcial point of view, RBPs possess key features that explain their highly RNA–sensitive phase behaviour. RBPs are multidomain proteins that combine aromatic-rich and arginine-rich intrinsically disordered regions (IDRs) [26, 51]—boosting the RBP’s multivalency needed for LLPS—with globular domains that exhibit high affinity for RNA (termed RNA recognition motifs (RRMs)) [52]. Hence, RBPs and RNA can establish both specific RNA--RRM interactions and non-specific electrostatic, cation–π and π–π interactions. To gain a mechanistic understanding of the intricate modulation of RBP condensate stability by RNA, experiments where single amino acids are mutated and/or post-translationally modified (e.g. phosphorylated [10, 11, 53] or methylated [18, 54, 55]) are of great value. Alongside, sequence-dependent molecular simulations can help uncover how specific protein regions, amino acid-RNA interactions, or RNA properties influence the experimentally observed behavior [49, 50, 56–58].

Computer simulations have been instrumental in advancing the characterization of biomolecular condensates from a thermodynamic, molecular and mechanistic perspective [6, 59–61]. Many approaches, such as atomistic Molecular Dynamics (MD) simulations [61-63], sequence-dependent coarse-grained models [56, 64–67] or minimal representations of proteins [68-73], as well as lattice-based simulations [74-77] and mean field models [78-82] have been developed and exploited to interrogate biomolecular LLPS. These approaches have shed light on the effects of key parameters in LLPS, encompassing protein length [83, 84], amino acid sequence [56, 64, 65, 85, 86], multivalency [74, 87–93], conformational flexibility [94, 95], and multicomponent composition [49, 69, 96–100]. Moreover, computer simulations have uncovered links between chemical modifications, sequence mutations, and protein–protein or protein–DNA interactions [101-106]. Coarse-grained models have also been employed to investigate the RNA-induced reentrant LLPS behaviour of RBPs [49, 50], the effect of RNA on phase separation of small prion-like domains such as those of FUS, [69, 107], protamine [108] and LAF-1 [49], and the emergence of multiphasic protein–RNA condensates [109].

In this work, we focus on single-stranded disordered RNA and ask: What is the function of RNA strand length in biomolecular LLPS? For this, we use our recently developed residue/nucleotide-resolution coarse-grained protein/RNA model [57], which predicts biomolecular phase diagrams in quantitative agreement with experiments. We demonstrate striking and contrasting effects of RNA length on the phase behaviour of RBPs. For RBPs like FUS, which can undergo LLPS via homotypic protein–protein interactions, low-to-moderate RNA concentrations invariably lead to moderate enhancement of condensate stability, irrespective of the RNA length (for a fixed total nucleotide/protein concentration). In contrast, for RBPs like PR25 that undergo RNA-dependent complex coacervation (i.e., LLPS driven by heterotypic protein–RNA interactions), increasing RNA length at constant total nucleotide concentration significantly promotes condensate stability. Next, we use minimal coarse-grained simulations to look at the problem from a soft condensed matter perspective. Our minimal simulations reveal that the striking differences in the impact of RNA length on complex coacervation versus homotypic LLPS originates in the diversity of intermolecular connections that biomolecules employ in the different scenarios to sustain the liquid network of the condensates.

Materials and methods

Multiscale modelling approach for RBP–RNA phase separation

Biomolecular LLPS entails the self-assembly of thousands of different proteins and other biomolecules into liquid-like condensates. Although experiments and simulations have begun to approach condensates at the atomistic level [19,61,110], the study of LLPS is often not amenable to atomistic-level simulations. Instead, coarse-grained models including mean field simulations [78–82, 111], lattice-based models [74-77], and high-resolution sequence-dependent approaches [56, 64–67, 112], are becoming the go-to simulation methods for characterizing the mechanistic and molecular details of biomolecular condensates. Here, we employ two protein/RNA coarse-grained models of different resolutions, previously developed by us, to elucidate the role of RNA length in modulating LLPS of RBPs: (1) the Mpipi sequence-dependent residue-resolution coarse-grained model for proteins and RNA [57], and (2) a minimal model in which proteins are represented as patchy particles, and RNA as self-repulsive flexible polymers [69, 91] (Fig 1).

Fig 1

Coarse-grained models used to investigate phase separation of RBP–RNA mixtures.

Left: Residue-resolution sequence-dependent coarse-grained representation of full FUS, PR25, and a 400-mer polyU RNA strand, using the Mpipi model [57]. The Mpipi model represents each amino acid and nucleotide by a single bead and describes the solvent implicitly. Please note that the size of the beads represented in this panel have been conviniently rescaled for visualization purposes. Globular protein domains are modelled as rigid bodies based on the crystal structure of the folded domains, whereas disordered protein regions and RNA are treated as fully flexible polymers. Coloured beads indicate distinct types of residues/nucleotides. Right: Minimal model for scaffold proteins, cognate proteins, and RNA, as done previously [69, 91, 120]. White patches represent protein binding sites, while green and red spheres account for the excluded volume of the scaffold and cognate proteins, respectively [91]. RNA is modelled as a self-repulsive flexible polymer of (pseudo) hard-spheres [69]. Please note that the real size of the RNA beads has been intentionally reduced in this image to facilitate its visualization; in the simulations, the size of each RNA bead is the same as the central pseudo hard-sphere of the proteins.

Within the Mpipi model, protein residues and RNA bases are represented by single beads with unique chemical identities (Fig 1 Left) in which hydrophobic, π–π and cation–π interactions are modelled through a mid-range pairwise potential (Wang–Frenkel potential [113]), and electrostatic interactions via Yukawa long-range potentials [56]. Bonded interactions between sequential amino acids within the same protein, or nucleotides within the same RNA strand, are described with a harmonic potential. Additionally, within Mpipi, the intrinsically disordered regions of the proteins and RNA strands are treated as fully flexible polymers. Globular domains are described as rigid bodies based on their corresponding experimental atomistic structures taken from the Protein Data Bank (PDB) and adapted to the model resolution. In the Mpipi model, the interactions between ‘buried’ amino acids within globular domains are scaled down. The physiological concentration of monovalent ions in solution (i.e., ∼150 mM NaCl), within the implicit solvent model, is approximated by the screening length of the Yukawa/Debye-Hückel potential. Further details on the model parameters, protein sequences and simulation setups are provided in the S1 Text.

Complementary to the residue-resolution sequence-dependent model, we employ a minimal coarse-grained model [69, 91] to investigate the role of RNA length in RBPs LLPS. Within this model, proteins are described by pseudo hard-sphere (PHS) [115] particles decorated with sticky patches that represent the protein binding sites (modelled through square-well-like potentials [116]); these allow the minimal proteins to establish multivalent transient interactions (Fig 1 Right). Additionally, RNA strands in our minimal model are represented as fully flexible self-repulsive PHS polymers that can interact attractively with RBPs via mid-range non-specific interactions (see S1 Text and Ref. [69] for further details on the model potentials and parameters). Each minimal RNA bead accounts for tens of nucleotides and has the same size as the protein beads [69]. As in the residue-resolution coarse-grained model, an implicit solvent is used; 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.

To measure the stability of the RBP–RNA condensates, we compute phase diagrams of the different systems in the temperature–density plane by means of Direct Coexistence (DC) simulations [117, 118]. Within the DC approach, the two coexisting phases of the system are placed in the same simulation box; in our case, a high-density protein liquid and a very low-density one. We employ a rectangular box, 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 cannot interact with themselves across the periodic boundaries [50]. We then run NVT MD simulations until equilibrium is reached. Once the simulations have converged, we measure the equilibrium coexisting densities of both phases along the long side of the box, excluding the fluctuations of the interfaces and keeping the center of mass of the system fixed. We repeat this procedure at different temperatures until we reach supercritical temperatures, where no phase separation is observed any longer. Then, to avoid finite system-size effects close to the critical point, we evaluate the critical temperature (T) and density (ρ) using the law of critical exponents and rectilinear diameters [119] (as shown in Refs. [69, 91]). Fig 2(a) (Top and Bottom panels) depicts phase-separated systems computed via DC simulations, while Fig 2(b) (Top panel) shows supercrticial systems (i.e., no phase separation).

Fig 2

(a) Direct Coexistence simulations of FUS/RNA (left) and scaffold proteins/RNA (right) using short RNA strands (top; 50-mer polyU and 10-bead RNA chains in the FUS and the minimal scaffold protein system respectively) and long RNA strands (bottom; 400-mer and 250-bead RNA chains in the FUS and the minimal scaffold protein system respectively) at T/T = 1.01, where T corresponds to the pure protein critical temperature of each system. (b) Direct Coexistence simulations of PR25/RNA (left) and cognate proteins/RNA (right) using both short RNA strands (top; 40-mer polyU and 10-bead polyU RNA chains in the PR25 and RNA cognate protein system respectively) and long RNA strands (bottom; 400-mer and 250-bead RNA chains in the PR25 and RNA cognate protein system respectively) at T/T = 1.01, where T corresponds to the pure critical temperature of FUS (left) and scaffold proteins (right), as in panel (a).

Results and discussions

Impact of RNA length in the phase behaviour of FUS versus PR25 condensates

Using MD simulations of our protein/RNA sequence-specific Mpipi model [57], we first investigate the effect of adding disordered polyU single-stranded RNA chains to RBPs condensates, and varying the length of the polyU (while keeping the total amount of U nucleotides and protein constant). Specifically, we compare the effects of RNA length in the phase behaviour of two different RBPs: (1) FUS, which can phase separate on its own at physiological conditions via homotypic protein–protein interactions, and (2) PR25, which only undergoes LLPS at physiological conditions in the presence of RNA (Fig A in the S1 Text) via heterotypic RNA–protein interactions [48, 103, 114].

For the different FUS/RNA systems, regardless of the length of the RNA strands in each case, we always add a total amount of U nucleotides to get a constant U/FUS mass ratio of 0.096; that is because this ratio enhances phase separation with respect to the pure FUS system. Importantly, the net charge of the system at this RNA/protein mass ratio is very low (−42e) and has been shown to ensure the maximum condensate stability of FUS as a function of RNA concentration [50]. Specifically, we test six polyU lenghts: (i) 32 polyU chains of 25 nucleotides each, (ii) 16 polyU chains of 50 nucleotides each, (iii) 8 polyU chains of 100 nucleotides each, (iv) 4 polyU chains of 200 nucleotides each, (v) 2 polyU chains of 400 nucleotides each, and (vi) 1 polyU chains of 800 nucleotides each (further details on these systems are provided in Table A of the S1 Text). In all these systems (Fig 3(a)), we observe a moderate increase in the critical temperature of FUS when RNA is added, independently of the length of RNA; i.e., all FUS+polyU systems we simulate have very similar critical temperatures within the uncertainty.

Fig 3

(a) Temperature–density phase diagrams of FUS with polyU RNA of different lengths at a constant polyU/FUS mass ratio of 0.096, and for a pure system of FUS (black curve). The length of polyU RNA strands range from 25-nucleotide to 800-nucleotide. (b) Temperature–density phase diagrams of PR25 with RNA at different lengths at a constant RNA/PR25 mass ratio of 1.20. RNA lengths range from 20-nucleotide to 800-nucleotide strands. To verify that our simulations are not affected by finite size effects, we repeated our simulations with 60 chains of 80-nt each (instead of 30 polyU chains), while keeping the RNA/PR25 mass ratio constant, and computed the coexistence densities (black empty triangles). In both (a) and (b) panels, filled circles represent the coexisting densities evaluated from DC simulations while empty circles depict the critical temperatures estimated from the law of rectilinear diameters and critical exponents [119] near the critical temperature. The error bars in the coexistence densities represent standard deviations, while those of the critical points represent the extrapolated uncertainty when applying the law of rectilinear diameters and critical exponents. Temperature in both panels has been normalized by the critical temperature of pure FUS, T = 355 K (black empty circle in (a)). Representative snapshots of the DC simulations used to compute the phase diagrams of both systems for a given RNA strand length (a) FUS–polyU (2x400-nt) and b) PR25–polyU (6x400-nt)) under phase-separating conditions are included below. The same color code employed in Fig 1 applies here.

To determine if proteins that phase separate by complex coacervation exhibit a similar trend, we next investigate the effect of RNA length on PR25–polyU mixtures using the Mpipi model. In this case, we fix the polyU/PR25 mass ratio to 1.20 (net system charge of 0e), which maximizes the size of the coexistence region for the smallest length of polyU used (20 nucleotides). We then test five different polyU lengths: (i) 120 polyU chains of 20 nucleotides each, (ii) 60 polyU chains of 40 nucleotides each, (iii) 30 polyU chains of 80 nucleotides each, (iv) 6 polyU chains of 400 nucleotides each, (v) 3 polyU chains of 800 nucleotides each (further details on these systems are provided in Table A of the S1 Text). The dependence of the phase behaviour of PR25 on RNA length is strikingly different (Fig 3(b)): the size of the coexistence region for PR25+polyU now grows continuously as the length of polyU increases. To confirm that our results are not affected by significant finite size effects, we perform additional simulations for a system composed of 60 polyU chains of 80 nucleotides each keeping the same polyU/PR25 mass ratio (black empty triangles in Fig 3(b)). Indeed, lengthening RNA from 20 to 800 nucleotides increases the critical temperature by as much as 50%. This observation is significant, since while increasing the RNA length, we have maintained a constant nucleotide concentration, which ensures that the total number of binding sites in the RNA molecules available for protein binding is the same in all cases.

To elucidate the molecular origin of this important difference, we compute the percentage of LLPS-stabilizing contacts per unit of volume at 350 K (T/Tc,FUS ∼1) for FUS (Fig 4(a)), and 300 K in the case of PR25 (T/Tc,FUS ∼0.85 (Fig 4(b)). Note that for both systems, we normalize the temperatures using the critical temperature of FUS because PR25 cannot phase separate on its own (Fig A in S1 Text). A sketch of the local order parameter to compute the contacts is provided in Fig 4(c). These temperatures were chosen as the highest temperatures at which phase separation is observed for each protein at all RNA lengths. We find that FUS+polyU condensates are mostly stabilized by protein–protein interactions, and more modestly contributed by protein–RNA interactions (Fig 4(a)). Moreover, the contribution of electrostatic interactions to the condensate liquid-network connectivity (including protein–protein and protein–RNA contacts) is rather modest (< 10%) when compared to non-electrostatic LLPS-stabilizing interactions (Fig G of the S1 Text). Our results suggest that within FUS condensates, where FUS acts as the scaffold, a moderate concentration of RNA creates a few more bridges among the scaffolds; i.e., RNA increases the effective valency of FUS within the condensate or as a co-scaffold in phase separation [121, 122]. In agreement with the well-known RNA concentration-dependent reentrant behaviour of RNA-binding proteins [27, 42, 47, 48], increasing the concentration of polyU in our FUS–polyU simulations, at constant RNA length eventually results in dissolution of the condensates (as shown by simulations in Ref. [50]). At physiological conditions, FUS–FUS interactions are sufficient to drive the system to phase separate [123]. Addition of a moderate amount of RNA creates more connections between FUS proteins by directly binding to free sites on FUS [27] (especially via specific RNA–RRM interactions and promiscous electrostatic and π-π interactions [32, 40–46, 50]. High amounts of RNA begin to outcompete the FUS–FUS connections and introduce electrostatic repulsion, which together eventually inhibit LLPS.

Fig 4

Density of LLPS-stabilizing intermolecular contacts within condensates as a function of RNA length plotted separately for protein–protein interactions (black symbols) and protein–RNA interactions (green symbols) for FUS–polyU (a) and PR25–polyU mixtures (b). The temperature at which the intermolecular contacts were computed was T/Tc,FUS = 0.99 for FUS–RNA systems, and T/Tc,FUS = 0.85 for PR25–RNA mixtures. Error bars depict the computed standard deviation in the number of molecular contacts. (c) Representative snapshot of a bulk FUS–polyU condensate to illustrate the employed cut-off distance (R) criterion to identify protein--protein and protein--RNA contacts. The same color code described in Fig 1 applies here. (d) Critical temperature versus RNA length for FUS–RNA (red) and PR25–RNA (blue) systems. The RNA/protein mass ratio of all systems was kept constant at 0.096 for FUS–RNA systems and at 1.20 for PR25–RNA mixtures.

At moderate concentrations, RNA marginally increases the connectivity of an already sufficiently connected condensed liquid network [48]. This is evident from the density of FUS–FUS and FUS–RNA contacts remaining almost constant as the length of the RNA strands increases (Fig 4(a)), following the same trend of critical points as a function of RNA length in the mixtures (Fig 4(d)). We reason that RNA length does not have a strong impact in the stability of FUS condensates because: (1) the total number of FUS–RNA bonds is low enough that the competition between RNA–RNA repulsion among short RNA chains (that would be reduced by the covalent bonds among longer RNA chains) and RNA–FUS attraction becomes unimportant, and (2) FUS is a large protein that offers many distant RNA-binding sites that are equally viable for moderately short RNA chains that repel each other, or for long RNA chains that are stitched together by covalent bonds, as long they have a comparable radius of gyration to that of the proteins [50]. Despite this, we note that experiments have reported how RNA length can modulate the stability of some RNA-binding proteins such as FUS [124] or LAF-1 [125]. However, in those cases the difference in stability was observed at very short lengths (i.e., ∼20–40 nucleotides), where the RNA strands were much smaller than the proteins themselves. In fact, when RNA is not long enough to bind to more than one protein at the same time, it can hinder the association with other proteins [50]. Our results argue that for RBPs that exhibit homotypic LLPS (Fig 4(a)), the effect of increasing the RNA length beyond the minimum required to bridge at least two RBPs is expected to be marginal (Fig 4(d)).

In contrast, PR25 condensates are mostly stabilized by PR25–polyU interactions (with a higher contribution of electrostatic interactions than those observed in FUS–polyU condensates, Fig G of the S1 Text), and only modestly by protein–protein interactions (Fig 4(b)), as expected from their complex coacervation being dependent on the presence of polyU. We speculate that the considerable abundance of R–U interactions—which significantly facilitate LLPS due to their charge–charge and π–π contributions—might explain the much higher densities of PR25–polyU versus polyU–FUS condensates in our simulations. Indeed, charged-matched in vitro polyR–polyU condensates exhibit very high viscosities [126]. Furthermore, consistent with the increase of the critical temperature with RNA length (Fig 4(d)), the density of protein–RNA intermolecular contacts increases significantly as the RNA lengthens, especially at chain lengths of hundreds of nucleotides (i.e., 800-mer polyU chains in our simulations; Fig 4(b)). Because PR25 must bind to RNA to form a liquid network, adding covalent bonds within the RNA chains—for instance, by replacing 40 strands of 20 nucleotides by one strand of 800 nucleotides—increases the PR25+RNA critical temperature by zipping together large chunks of RNA that would otherwise be driven away by the dominant RNA–RNA electrostatic repulsion at physiological conditions. Thus, increasing the length of an RNA chain at constant nucleotide concentration, allows a higher density of PR25 bonds per RNA length, and an overall higher connected condensed liquid.

The distinct behaviour of FUS–polyU versus PR25–polyU condensates emerges also with a different residue-resolution coarse-grained model [56] (Figs D and E of the S1 Text). We note also that the behaviour is unlikely explained simply by the RNA strands being longer than PR25 peptides in our simulations. Indeed, the FUS–polyU behaviour also holds for long polyU strands of 200-nt with significantly larger radius of gyration for polyU (R >100Å) [50] than FUS (Fig C in S1 Text). Furthermore, when approaching the critical temperature of the PR25–polyU mixtures (and also in FUS–polyU mixtures), the number of contacts significantly decreases (Fig F of the S1 Text), independently of the RNA length. A consistent RNA-driven LLPS behaviour, to that observed here, has been experimentally found for the P-granule protein PGL-3, which has limited LLPS propensity in absence of RNA [127]. However, in presence of long (>600-mer) RNA strands, its ability to phase separate increases considerably [127]. Also consistent with our observations, enrichment of long mRNA in stress granules [28, 128, 129] and NEAT1 RNA (∼23000-mer non-coding RNA transcripts) in paraspeckles [130, 131] promotes phase-separation of such membraneless organelles.

RNA length has distinct effects on the stability of condensates driven by homotypic versus heterotypic interactions

To test the universality of these observations, we now employ our minimal protein model [69, 98–100], in which proteins are represented as patchy colloids [91] and RNA as a self-repulsive (pseudo hard-sphere) flexible chain [69]. This allows us to go beyond protein sequence and specific molecular features, and assess the thermodynamic parameters that explain the general differences between the impact of RNA length on homotypic phase separation versus RNA–protein complex coacervation.

We start by computing the phase diagram of a minimal scaffold protein that, like FUS, is able to phase separate on its own via homotypic interactions. The scaffold protein is represented by a patchy particle decorated with 3-binding sites in a planar arrangement separated by 120 degrees angles (Fig 1 Right). Reducing the behaviour of a multi-domain protein, with its rich conformational ensemble, to a patchy particle is undoubtedly a strong simplification. However, such an approximation allows us to look at the problem from a condensed matter perspective, and identify general parameters that explain the observed behaviour. Indeed, patchy particle models can capture the effects of protein valency, binding affinity, and binding-site topology in the modulation of protein phase diagrams [98, 99, 120]. As shown in Ref. [69], below a reduced temperature of T* = 0.09 (see details on reduced units in S1 Text), the scaffold proteins undergo phase separation (black curve of Fig 5(a)). We note that density is expressed as ‘reduced number density’, which avoids computing absolute density from the arbitrary choice of the particle mass. To map mass densities from our minimal model to realistic systems, one would need to assign the mass molecule to the patchy particle, and then tune the number of binding-sites, topology, and interaction strength to recapitulate the experimental values. Importantly, we find that with our minimal scaffold model, when adding self-avoiding flexible polymers that mimic RNA, we qualitatively recapitulate the impact on phase behaviour that we observed for FUS (Fig 3(a)) with our residue-resolution coarse-grained simulations. That is, adding a moderate concentration of RNA (a RNA bead/protein ratio of 0.25), increases the critical temperature modestly (by about ∼ 35%), but changing the length of RNA (while keeping the protein/RNA bead concentration constant) has a marginal effect on the critical temperature (Fig 5(a)).

Fig 5

(a) Phase diagram in the temperature–density plane for a scaffold protein that, like FUS, can phase separate via homotypic protein interactions (black curve), and for mixtures of a fixed RNA/protein concentration using different RNA strand lengths as indicated in the legend. (b) Phase diagram in the temperature-density plane for a cognate protein that, like PR25, does not exhibit LLPS on its own, and that only undergoes LLPS upon addition of RNA. The RNA concentration in both panels was kept constant in all simulations at a 0.25 nucleotide/protein ratio. Filled circles represent the coexisting densities evaluated from DC simulations, while empty circles depict the critical temperatures estimated from the law of rectilinear diameters and critical exponents near the critical temperature [119]. The error bars in the coexistence densities represent the standard deviation, while those of the critical points represent the extrapolated uncertainty when applying the law of rectilinear diameters and critical exponents. Temperature in both panels has been normalized by the critical temperature of the pure scaffold system, in reduced units (empty black circle in (a)).

Now we focus on the phase behaviour of a minimal cognate protein that, like PR25, cannot phase separate on its own (Fig 5(b) and Fig B of S1 Text). Our cognate proteins are represented by patchy particles with 2-binding sites in a polar arrangement, which by construction can only form linear chains and not the 3-dimensional percolated network that sustains a condensate [87, 91, 100]). For the minimal cognate proteins, we obtain a phase behavior similar to that of PR25; when increasing the length of RNA (while keeping the RNA bead/protein ratio constant at 0.25), the critical temperature of the mixture considerably increases (Fig 5(b)). However, after reaching a certain RNA length that is much longer that the size of the proteins (i.e., ∼50 times longer, which in this minimal model can be tested) [50], the LLPS enhancement plateaus. We have chosen a value of the RNA bead/protein ratio (0.25) that results in RNA-driven enhancement of phase separation. Drastically changing the RNA bead/protein ratio in our minimal simulations can give rise to distinctly different scenarios. On the one hand, very small ratios (<0.1), would lead to very minor impact of RNA on condensate stability. On the other, very large ratios (above 0.5 [132]) would result in the coating of RNA with proteins, rather than in the formation of mixed protein–RNA condensates.

Next we analyze the density of protein–protein and protein–RNA contacts as a function of RNA length (Fig 6(a) and 6(b)), to further elucidate the origins of the distinct behavior for scaffold and cognate proteins. We observe a similar trend in terms of the predicted liquid-network connectivity with our minimal model as that found using sequence-dependent coarse-grained simulations (Fig 4(a) and 4(b)), therefore, highlighting the key role of valency in our observations. When LLPS is mainly driven by homotypic scaffold–scaffold interactions, scaffold–scaffold and scaffold–RNA contacts remain roughly constant as the length of RNA increases. In contrast, when LLPS is significantly driven by RNA–protein (i.e., cognate protein) heterotypic interactions, the number of cognate–RNA contacts considerably augments with RNA length (until the RNA size is much larger than that of the proteins; Fig 6(b)). For the minimal scaffold proteins, the increase in scaffold–scaffold and scaffold–RNA contacts with RNA length is smaller than a 5–10% (Fig 6(a)). In contrast, for cognate proteins such increase is higher than a factor of 3, which is a significant difference considering that in both cases RNA/protein ratios are kept constant. The variation in the critical temperature as a function of RNA length is depicted in Fig 6(c), where the consequences of the dissimilar liquid-network connectivity [100] that both type of proteins establish upon demixing—homotypic vs. heterotypic interactions—manifest.

Fig 6

Density of LLPS-stabilizing contacts as a function of RNA length plotted separately for protein–protein contacts (black symbols) and protein–RNA contacts (green symbols) for a minimal RNA-binding scaffold protein model wherein scaffold proteins can phase separate via homotypic interactions (a), and an RNA-binding cognate protein model wherein cognate proteins can only phase separate via heterotypic RNA–protein interactions (b). Calculations are performed at for the RNA/scaffold system and for the RNA/cognate protein system. Error bars depict the computed standard deviation in the number of molecular contacts. The RNA/protein concentration was kept at a constant nucleotide/protein ratio of 0.25 in both cases. (c) Critical temperature versus RNA length plot for both mixtures, scaffold proteins + RNA (red) and cognate proteins + RNA (blue).

In agreement with the preceding results, Zacco et al. [25] found that longer RNA strands present weaker dissociation constants with N-RRM1–2 domains of TDP-43 (which, like PR25, cannot phase separate on their own at physiological conditions) than 3-fold shorter RNA strands. Moreover, it has been recently shown that length and charge segregation in the IDR domain of VRN1-like proteins has a critical impact on modulating DNA-induced VRN1 phase separation, where liquid-like, gel-like or no phase-separation behaviour can be favoured depending on the IDR length and the presence of neutral vs. charged residues [133]. Another study by Maharana et al. [27] showed that smaller RNAs are more potent than larger ones in solubilizing protein condensates at high RNA concentration, which in turn, indirectly supports our observations that very short RNA strands can remotely promote LLPS for proteins that heavily rely on heterotypic interactions. Furthermore, besides controlling condensate stability, RNA has been suggested to play a critical role in regulating the dynamics of many membraneless organelles [21, 27, 32, 134, 135]. In that respect, Zhang et al. [136] showed that the RNA-binding protein Whi3 phase separates into liquid-like droplets wherein biophysical properties can be subtly tuned by changing the concentration and length of the mRNA binding partner, finding that larger RNA content increases Whi3 droplet viscosity. RNA has been shown to yield opposite effects in LAF-1 condensates when short strands (50 nt) were introduced [40]. Nonetheless, when long RNAs were used (up to 3,000 nt), LAF-1 condensates presented significantly higher viscosity [41]. Since the impact of RNA length and concentration on condensate density has been recently shown to be a good proxy of condensate dynamics (i.e., droplet viscosity and protein diffusion) [27, 41, 50], the reported variations in droplet density as a function of RNA length and temperature presented here in Figs 3 and 5, can be also considered as good indicators of the impact that RNA length produces on RBP–RNA droplet transport properties. Therefore, RNA lengths that promote higher droplet density should also lead to enhancements in droplet viscosity [50, 126].

Conclusions

Using a multiscale simulation approach we demonstrate how variations in RNA length can yield non-trivial effects in the stability of RBP condensates. We find that in condensates sustained by homotypic protein–protein interactions, RNA behaves as a LLPS enhancer that subtly augments the stability of the condensates irrespective of its length. In contrast, in condensates sustained by heterotypic protein–RNA interactions, we find that RNA acts as a LLPS enabler that increases the stability of the condensates in a RNA length-dependent manner.

Our findings for FUS and PR25 polyU systems using sequence-dependent coarse-grained simulations in parellel with our results for the miminal protein/RNA model suggest that when protein–protein LLPS-stabilising interactions are substantially higher than protein–RNA contacts, like in FUS or in our archetypal scaffold protein model, it is the RNA concentration rather than its chain length what critically modulates the condensate stability (at least for strands larger than 50–80 nucleotides or of comparable length to that of the proteins). Nevertheless, when protein–RNA intermolecular contacts contribute similarly or even higher than homotypic protein–protein interactions, like in PR25 peptides or in our minimal cognate–RNA model, not only the RNA concentration, but also the RNA chain length plays a major role in controlling RBP condensate stability. Our study demonstrates that RNA participation in biological phase transitions is not uniform and argues that RNA parameters should be considered as important as those of proteins with respect to the regulation of the stability and mesoscale properties of condensates.

Model description and computational details of the sequence-dependent high-resolution model and the minimal model.

Mpipi model, full-FUS sequence, patchy particle protein/RNA model, Direct Coexistence calculations for extracting phase diagrams, and calculation of protein/RNA molecular contacts. Table A. System sizes and simulation details. Summary of the simulation details of the employed systems: Total number of proteins (N), total number of RNA nucleotides (or RNA beads in the minimal model; N), total number of RNA chains (N), length of the RNA chains (L), net charge of the system, box dimensions (in x/Å, y/Å, z/Å), and estimated critical temperature (T in K for the high-resolution Mpipi model and in reduced units for the minimal CG model). Fig A. Direct Coexistence simulation of PR. Snapshot of a pure PR25 Direct coexistence simulation at T/T = 0.5. As it can be seen, in absence of RNA, PR25 cannot undergo LLPS (even at low temperatures). The same colour code employed in Fig 1 of the main text has been employed here. Fig B. Direct Coexistence simulation of cognate proteins in absence of RNA. Snapshot of a pure cognate system Direct Coexistence simulation at T/T = 0.6. As it can be seen, in absence of RNA, the cognate protein cannot undergo LLPS (even at low temperatures). The same colour code employed in Fig 1 of the main text has been employed here. Fig C. Radius of gyration of FUS and PR. Radius of gyration (R) distribution function for: a) FUS within a FUS-polyU(400-nt) condensate (green curve) and FUS in the dilute phase (black curve) at T/Tc,FUS = 0.96. b) PR25 within a PR25-polyU(400-nt) condensate (green curve) and PR25 in the dilute phase (black curve) at T/Tc,FUS = 0.85. The polyU/FUS mass ratio was kept constant at a value of 0.096, while the polyU/PR25 mass ratio at a value of 1.20. Fig D. Phase diagrams of FUS-polyU and PR. Temperature–density phase diagrams of FUS with polyU of different lengths at a constant polyU/FUS mass ratio of 0.16, and for a pure system of FUS (black curve). (b) Temperature–density phase diagrams of PR25 with RNA at different lengths at a constant RNA/PR25 mass ratio of 0.57. In both (a) and (b) panels, filled circles represent the coexisting densities evaluated from DC simulations while empty circles depict the critical temperatures estimated from the law of rectilinear diameters and critical exponents near the critical temperature. Temperature in both panels has been normalized by the critical temperature of pure FUS, T = 309K (black empty circle in (a)). Fig E. Intermolecular contacts of FUS-polyU and PR. Density of LLPS-stabilizing intermolecular contacts within condensates as a function of RNA length plotted separately for protein–protein interactions (black symbols) and protein–RNA interactions (green symbols) for FUS-polyU (a) and PR25-polyU mixtures (b). The temperature at which the intermolecular contacts were computed was T/Tc,FUS = 1.13 for FUS–RNA systems and T/Tc,FUS = 0.924 for PR25–RNA mixtures (the highest temperature at which all systems with distinct RNA lengths can phase separate). (c) Critical temperature versus RNA length for FUS–RNA (black) and PR25–RNA (blue) systems. Fig F. Intermolecular contacts of FUS-polyU and PR. Density of LLPS-stabilizing intermolecular contacts within the condensates (plotted separately for protein–protein interactions, black circles, and protein–RNA interactions, red circles) as a function of temperature (T/T) for: a) FUS+polyU(400-nt), and b) PR25+polyU(400-nt) condensates. The polyU/FUS mass ratio was kept constant at a value of 0.096 for all FUS simulations, while the polyU/PR25 mass ratio was kept constant at a value of 1.20 for all PR25 simulations at every studied temperature. Fig G. Electrostatic . Electrostatic (black symbols) vs. non-electrostatic (red symbols) contribution to the potential attractive interactions (molecular contacts sustaining phase-separated condensates) as a function of RNA length for FUS+polyU condensates (filled circles) and PR25+polyU condensates (empty squares). The temperature at which the intermolecular contacts were computed was T/Tc,FUS = 0.99 for FUS–RNA systems, and T/Tc,FUS = 0.85 for PR25–RNA mixtures. Error bars depict the computed standard deviation in the percentage contribution of electrostatic vs. non-electrostatic interactions. The polyU/FUS mass ratio was kept constant at a value of 0.096 for FUS-polyU simulations, and at a polyU/PR25 mass ratio of 1.20 in PR25-polyU simulations.

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