Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid–liquid phase separation (LLPS) of proteins, we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess roles of electrostatic, hydrophobic, cation–π, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated three different residue–residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation–π interactions consistently accounted for available experimental LLPS data on the wild-type, a charge-scrambled, a phenylalanine-to-alanine (FtoA), and an arginine-to-lysine (RtoK) mutant of Ddx4 IDR. In contrast, interactions based on contact statistics among folded globular protein structures reproduce the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. Consistency between simulation and experiment was also found for RtoK mutants of P-granule protein LAF-1, underscoring that, to a degree, important LLPS-driving π-related interactions are embodied in classical statistical potentials. Further elucidation is necessary, however, especially of phenylalanine’s role in condensate assembly because experiments on FtoA and tyrosine-to-phenylalanine mutants suggest that LLPS-driving phenylalanine interactions are significantly weaker than posited by common statistical potentials. Protein–protein electrostatic interactions are modulated by relative permittivity, which in general depends on aqueous protein concentration. Analytical theory suggests that this dependence entails enhanced interprotein interactions in the condensed phase but more favorable protein–solvent interactions in the dilute phase. The opposing trends lead to only a modest overall impact on LLPS.

Here we investigate the solute-medium interaction and solute-centered dynamics in (RCONH2 + LiX) deep eutectics (DEs) via carrying out time-resolved fluorescence measurements and all-atom molecular dynamics simulations at various temperatures. Alkylamides (RCONH2) considered are acetamide (CH3CONH2), propionamide (CH3CH2CONH2), and butyramide (CH3CH2CH2CONH2); the electrolytes (LiX) are lithium perchlorate (LiClO4), lithium bromide (LiBr), and lithium nitrate (LiNO3). Differential scanning calorimetric measurements reveal glass transition temperatures (T(g)) of these DEs are ~195 K and show a very weak dependence on alkyl chain-length and electrolyte identity. Time-resolved and steady state fluorescence measurements with these DEs have been carried out at six-to-nine different temperatures that are ~100-150 K above their individual T(g)s. Four different solute probes providing a good spread of fluorescence lifetimes have been employed in steady state measurements, revealing strong excitation wavelength dependence of probe fluorescence emission peak frequencies. Extent of this dependence, which shows sensitivity to anion identity, has been found to increase with increase of amide chain-length and decrease of probe lifetime. Time-resolved measurements reveal strong fractional power dependence of average rates for solute solvation and rotation with fraction power being relatively smaller (stronger viscosity decoupling) for DEs containing longer amide and larger (weaker decoupling) for DEs containing perchlorate anion. Representative all-atom molecular dynamics simulations of (CH3CONH2 + LiX) DEs at different temperatures reveal strongly stretched exponential relaxation of wavevector dependent acetamide self dynamic structure factor with time constants dependent both on ion identity and temperature, providing justification for explaining the fluorescence results in terms of temporal heterogeneity and amide clustering in these multi-component melts.

Biomolecular condensates undergirded by phase separations of proteins and nucleic acids serve crucial biological functions. To gain physical insights into their genetic basis, we study how liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) depends on their sequence charge patterns using a continuum Langevin chain model wherein each amino acid residue is represented by a single bead. Charge patterns are characterized by the "blockiness" measure κ and the "sequence charge decoration" (SCD) parameter. Consistent with random phase approximation (RPA) theory and lattice simulations, LLPS propensity as characterized by critical temperature T * cr increases with increasingly negative SCD for a set of sequences showing a positive correlation between κ and −SCD. Relative to RPA, the simulated sequence-dependent variation in T * cr is often-though not alwayssmaller, whereas the simulated critical volume fractions are higher. However, for a set of sequences exhibiting an anti-correlation between κ and −SCD, the simulated T * cr 's are quite insensitive to either parameters. Additionally, we find that blocky sequences that allow for strong electrostatic repulsion can lead to coexistence curves with upward concavity as stipulated by RPA, but the LLPS propensity of a strictly alternating charge sequence was likely overestimated by RPA and lattice models because interchain stabilization of this sequence requires spatial alignments that are difficult to achieve in real space. These results help delineate the utility and limitations of the charge pattern parameters and of RPA, pointing to further efforts necessary for rationalizing the newly observed subtleties.

In view of recent intense experimental and theoretical interests in the biophysics of liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs), heteropolymer models with chain molecules configured as self-avoiding walks on the simple cubic lattice are constructed to study how phase behaviors depend on the sequence of monomers along the chains. To address pertinent general principles, we focus primarily on two fully charged 50-monomer sequences with significantly different charge patterns. Each monomer in our models occupies a single lattice site, and all monomers interact via a screened pairwise Coulomb potential. Phase diagrams are obtained by extensive Monte Carlo sampling performed at multiple temperatures on ensembles of 300 chains in boxes of sizes ranging from 52 × 52 × 52 to 246 × 246 × 246 to simulate a large number of different systems with the overall polymer volume fraction ϕ in each system varying from 0.001 to 0.1. Phase separation in the model systems is characterized by the emergence of a large cluster connected by intermonomer nearest-neighbor lattice contacts and by large fluctuations in local polymer density. The simulated critical temperatures, T, of phase separation for the two sequences differ significantly, whereby the sequence with a more "blocky" charge pattern exhibits a substantially higher propensity to phase separate. The trend is consistent with our sequence-specific random-phase-approximation (RPA) polymer theory, but the variation of the simulated T with a previously proposed "sequence charge decoration" pattern parameter is milder than that predicted by RPA. Ramifications of our findings for the development of analytical theory and simulation protocols of IDP LLPS are discussed.

Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely stretch, momentum, and energy. The linear theory yields two propagating sound modes and one diffusing heat mode. In contrast, the nonlinear theory predicts that, at long times, the sound mode correlations satisfy Kardar-Parisi-Zhang (KPZ) scaling, while the heat mode correlations satisfies Lévy-walk scaling. In the present contribution we report on molecular dynamics simulations of Fermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with the predictions of the theory. We find very good agreement in many cases, but also some deviations.

Here we report results from our molecular dynamics simulations on orientational relaxation and hydrogen bond dynamics of molten acetamide. Signatures for orientational jumps have been detected with jump barrier estimated to be ∼0.7 kBT. Simulated orientational relaxations indicate deviations from hydrodynamics and this deviation has been ascribed to the detected orientational jumps. Simulated free energy surfaces obtained at various distances between the rotating acetamide and its initial and final H-bond acceptors have been found to be symmetric double-well in nature at the transition state. H-bond relaxation times obtained from our simulations corroborate well with the time scales associated with the jump and waiting time distributions, suggesting an interrelationship between jump dynamics and H-bond fluctuations. Jump angle distributions are asymmetric and depict long tails extending to large angles.

Temperature dependent relaxation dynamics, particle motion characteristics, and heterogeneity aspects of deep eutectic solvents (DESs) made of acetamide (CH3CONH2) and urea (NH2CONH2) have been investigated by employing time-resolved fluorescence measurements and all-atom molecular dynamics simulations. Three different compositions (f) for the mixture [fCH3CONH2 + (1 - f)NH2CONH2] have been studied in a temperature range of 328-353 K which is ∼120-145 K above the measured glass transition temperatures (∼207 K) of these DESs but much lower than the individual melting temperature of either of the constituents. Steady state fluorescence emission measurements using probe solutes with sharply different lifetimes do not indicate any dependence on excitation wavelength in these metastable molten systems. Time-resolved fluorescence anisotropy measurements reveal near-hydrodynamic coupling between medium viscosity and rotation of a dissolved dipolar solute. Stokes shift dynamics have been found to be too fast to be detected by the time-resolution (∼70 ps) employed, suggesting extremely rapid medium polarization relaxation. All-atom simulations reveal Gaussian distribution for particle displacements and van Hove correlations, and significant overlap between non-Gaussian (α2) and new non-Gaussian (γ) heterogeneity parameters. In addition, no stretched exponential relaxations have been detected in the simulated wavenumber dependent acetamide dynamic structure factors. All these results are in sharp contrast to earlier observations for ionic deep eutectics with acetamide [Guchhait et al., J. Chem. Phys. 140, 104514 (2014)] and suggest a fundamental difference in interaction and dynamics between ionic and non-ionic deep eutectic solvent systems.

All-atom molecular dynamics simulations have been carried out to investigate orientation jumps of acetamide molecules in three different ionic deep eutectics made of acetamide (CH3CONH2) and lithium salts of bromide (Br(–)), nitrate (NO3(–)) and perchlorate (ClO4(–)) at approximately 80:20 mole ratio and 303 K. Orientational jumps have been dissected into acetamide–acetamide and acetamide–ion catagories. Simulated jump characteristics register a considerable dependence on the anion identity. For example, large angle jumps are relatively less frequent in the presence of NO3(–) than in the presence of the other two anions. Distribution of jump angles for rotation of acetamide molecules hydrogen bonded (H-bonded) to anions has been found to be bimodal in the presence of Br(–) and is qualitatively different from the other two cases. Estimated energy barrier for orientation jumps of these acetamide molecules (H-bonded to anions) differ by a factor of ∼2 between NO3(–) and ClO4(–), the barrier height for the latter being lower and ∼0.5kBT. Relative radial and angular displacements during jumps describe the sequence ClO(4)– > NO3(–) > Br(–) and follow a reverse viscosity trend. Jump barrier for acetamide–acetamide pairs reflects weak dependence on anion identity and remains closer to the magnitude (∼0.7kBT) found for orientation jumps in molten acetamide. Jump time distributions exhibit a power law dependence of the type, P(tjump) ∝ A(tjump/τ)(−β), with both β and τ showing substantial anion dependence. The latter suggests the presence of dynamic heterogeneity in these systems and supports earlier conclusions from time-resolved fluorescence measurements.