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.
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/Tc = 1.01, where Tc 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/Tc = 1.01, where Tc corresponds to the pure critical temperature of FUS (left) and scaffold proteins (right), as in panel (a).
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, Tc,FUS = 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.
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 (Rc) 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.
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)).
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).