Desolvation-related PMF features of intermolecular interactions.

(A) Potential of mean force along the intermolecular distances for the amino acid analogues from all-atom MD simulations with different solvent polarities. (B) Schematic diagram of desolvation effects. (C) Pairwise effective potential incorporating desolvation-inspired terms. Different curves correspond to different desolvation parameters.

Thermodynamic regulation and microscopic mechanisms of desolvation-mediated phase separation.

(A) Baseline phase diagram of the poly-50 system using the standard HPS model. (B) Representative simulation snapshots visualizing the transition from a stable condensate (T ∗ = 2.58) to a near-critical state (T ∗ = 2.98) and a homogeneous solution (T ∗ = 3.18). (C) Time-averaged density profiles along the z-axis identifying the coexisting dense and dilute phases. (D, E) Macroscopic phase boundaries under varying desolvation barrier heights ϵb (D) and solvent-separated potential depths ϵss (E). Insets show the monotonic dependence of Tc on the respective parameters. The lower panels schematically illustrate how changes in ϵb and ϵss alter the distribution of residue-pair configurations. The small circles indicate schematic populations of residue-pair configurations along the potential profile, with denser circles representing a higher population. (F, G) Renormalized phase behavior plotted against normalized temperature T ∗/Tc for varying ϵb (F) and varying ϵss (G).

Effect of desolvation on protein conformations.

(A) Schematic illustration of the conformational distributions of the protein in the high- and low-density phases under different desolvation parameters. (B–C) Distribution of Rg with different ϵb (B) and ϵss (C) at . The solid and dashed lines represent the results for the condensed and dilute phases, respectively. The inset illustrates the mean value of Rg as a function of desolvation parameters. (D) Correlation between temperature difference and the averaged Rg difference between two phases. The purple and yellow dashed lines represent linear fits to the data obtained at low- and high-simulation-temperature regimes, respectively. The inset displays the improved linearity obtained when the temperature difference is rescaled by the simulation temperature, . (E) Correlation between the density difference and Rg difference in the two phases with varying temperatures and desolvation parameters. The plot is shown on a log–log scale.

Desolvation-mediated modulation of diffusion and coarsening dynamics.

(A) Snapshots of phase-separation dynamics after a temperature quench and the subsequent FRAP-like analysis of chain self-diffusion in an equilibrated slab. Upper snapshots show the simulation box along the z-axis at tsim = 0, 10, and 500 ns. The vertical schematic summarizes the dynamical progression described in the main text, from the post-quench spinodal instability to kinetic arrest, domain coarsening, and dynamic equilibrium. Lower panels show enlarged slab views for tracking chains initially located near the slab center, with the TAMSD plot quantifying their mobility. (B) Density profiles along the z-axis for the entire system (orange) and for the highlighted chains (red) at different time lags, with and without desolvation. Shaded histograms show instantaneous snapshots, and solid curves represent normalized time averages over 1 μs. (C) Diffusion coefficients as a function of the desolvation strength (ϵb, ϵss) and dense-phase density (ρdense) at different temperatures. (D) Reduced diffusion coefficient versus quench depth for varying ϵb. The schematic insets summarize the reduced chain mobility observed for higher desolvation barriers at comparable quench depths. (E) Schematic illustration of the three-stage phase-separation mechanism, including early density-fluctuation growth, a transiently arrested plateau, and late-stage coarsening. In the zoom-in view, yellow beads denote residues involved in transient inter-chain contacts, and black springs denote schematic network connections formed by these contacts. (F, G) Kinetics of density fluctuations and domain growth under varying ϵb (F) and ϵss (G). Top panels show the time evolution of the normalized density variance , with the inset showing the characteristic time τ1/2. Bottom panels show the growth of the average slab size ⟨ξ⟩ on a logarithmic scale. The colored timeline highlights the initial fluctuation, plateau, and late-stage coarsening regimes.

Parameterization of desolvation terms for the HPS and CALVADOS2 models based on IDPs.

(A) Schematic workflow of the desolvation parameterization. (B) Correlation between experimental Rg and simulation Rg for the original HPS model (blue) and the revised HPS model with default desolvation scales (αb = 0.33 and αss = 0.06) (purple). The for different models are also shown. (C) Correlation between experimental Rg and simulation Rg for the original CALVADOS2 model (orange), the revised CALVADOS2 model with default desolvation (yellow), and the revised CALVADOS2 model with optimized desolvation (αb = 0.3, αss = 0.03 and ϵ = 0.262 kcal/mol, red). (D) Coexistence curves of FUS LC simulated with the original HPS model (blue), the revised HPS model with default desolvation scales (purple), the energy-rescaled HPS model (green), the default CALVADOS2 model (orange), and the revised CALVADOS2 model with optimized desolvation scales (red). The green shaded regions highlight the deviations of the desolvation models relative to the original frameworks.

Global desolvation coefficients αb and αss used in the HPS and CALVADOS2 frameworks.

The HPS baseline coefficients were obtained by averaging values fitted to the all-atom analogue PMFs, whereas the CALVADOS2 coefficients and global energy scale ϵ were selected through optimization against experimental Rg data.

Summary of the production run parameters for all-atom molecular dynamics simulations.

Summary of the coarse-grained molecular dynamics simulation parameters used in the slab simulations.

Desolvation-related PMF features and fitted parameters from all-atom analogue simulations.

(A-D) PMFs obtained from all-atom simulations of representative amino-acid analogue pairs, together with fits using the desolvation-aware effective potential in Equation 1. (E) Overlay of fitted PMF profiles for different analogue pairs, illustrating the shared double-minimum/barrier structure and the pair-dependent variation in desolvation features. (F) Desolvation coefficients αb and αss obtained by expressing the fitted barrier height and solvent-separated minimum depth relative to the global reference energy scale ϵ used in the effective potential.

Microscopic residue-pair distributions and integrated effective attraction under varying desolvation parameters.

(A, B) Schematic illustration of the effective pair potential corresponding to different values of ϵb or ϵss. (C, D) Radial distribution functions of all residue pairs under varying ϵb (C) or ϵss (D) at the same reduced temperature, T ∗ = 1.49. (E, F) Radial distribution functions of all residue pairs in the dense phase at the same normalized temperature . (G, H) Bead-level second virial coefficient (B2/σ3) calculated from the effective pair potential under varying ϵb at fixed ϵss = 0.02 kcal/mol (G) and varying ϵss at fixed ϵb = 0.12 kcal/mol (H).

Optimization of the CALVADOS2 + desolvation energy scale using experimental Rg data.

(A, C, E, G) Correlations between experimental and simulated Rg values for the IDP dataset under selected desolvation-parameter combinations. Each panel corresponds to simulations performed at fixed αb and αss with different values of the overall energy scale ϵ. (B, D, F, H) Corresponding values as a function of ϵ, used to identify the optimal energy scale for each desolvation-parameter set. The optimized ϵ values are indicated in each panel.

Global scan of CALVADOS2 + desolvation parameter combinations against experimental Rg values.

Comparison between experimental and simulated Rg values for different combinations of αb and αss, with the overall energy scale (ϵ) optimized separately for each parameter set. The corresponding optimized (ϵ) values are shown to illustrate how the energy rescaling compensates for different desolvation strengths while preserving agreement with single-chain dimensions.

Single-chain Rg comparison of FUS LC under different coarse-grained model variants.

Single-chain radius of gyration of FUS LC simulated using the original HPS model, HPS + desolvation, energy-rescaled HPS, original CALVADOS2, and CALVADOS2 + desolvation models. The energy-rescaled HPS model was included to separate the effect of global interaction-strength rescaling from the effect of adding desolvation terms.

Phase behavior of the LAF-1 RGG domain simulated with CALVA-DOS2 and CALVADOS2 + desolvation.

Coexistence curves of the LAF-1 RGG domain simulated using the original CALVADOS2 model and the desolvation-aware CALVADOS2 model. Symbols show the coexisting dilute- and dense-phase densities obtained from slab simulations at different simulation temperatures, and dashed curves represent binodal fits using the same critical-scaling procedure as in the main text.