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We illustrate three methods for calculating the binodals of phase-separated condensates from molecular simulations. Because molecular simulations can only be carried out for small system sizes, correction for finite sizes may be required for making direct comparison between calculated results and experimental data. We first summarize the three methods and then present detailed implementation of each method on a Lennard-Jones fluid. In the first method, chemical potentials are calculated over a range of particle densities in canonical-ensemble simulations; the densities of the dilute and dense phases at the given temperature are then found by a Maxwell equal-area construction. In Gibbs-ensemble Monte Carlo, the exchange between separated dilute and dense phases is simulated to obtain their densities. Lastly, slab-geometry molecular dynamics simulations model the dilute and dense phases in coexistence and yield not only their densities but also their interfacial tension. The three types of simulations are carried out for a range of system sizes, and the results are scaled to generate the binodals corrected for finite system sizes. Size-corrected interfacial tension is also produced from slab-geometry molecular dynamics simulations.

Dynamics is a crucial link between sequence and function for intrinsically disordered proteins (IDPs). NMR spin relaxation is a powerful technique for characterizing the sequence-dependent backbone dynamics of IDPs. Of particular interest is the15N transverse relaxation rate (R2), which reports on slower dynamics (10s of ns up to 1 μs and beyond). NMR and molecular dynamics (MD) simulations have shown that local interactions and secondary structure formation slow down backbone dynamics and raiseR2. ElevatedR2has been suggested to be indicators of propensities of membrane association, liquid-liquid phase separation, and other functional processes. Here we present a sequence-based method, SeqDYN, for predictingR2of IDPs. TheR2value of a residue is expressed as the product of contributing factors from all residues, which attenuate with increasing sequence distance from the central residue. The mathematical model has 21 parameters, representing the correlation length (where the attenuation is at 50%) and the amplitudes of the contributing factors of the 20 types of amino acids. Training on a set of 45 IDPs reveals a correlation length of 5.6 residues, aromatic and long branched aliphatic amino acids and Arg asR2promotors whereas Gly and short polar amino acids asR2suppressors. The prediction accuracy of SeqDYN is competitive against that of recent MD simulations using IDP-specific force fields. For a structured protein, SeqDYN prediction representsR2in the unfolded state. SeqDYN is available as a web server athttps://zhougroup-uic.github.io/SeqDYNidp/for rapidR2prediction.Significance StatementHow the sequences of intrinsically disordered proteins (IDPs) code for functions is still an enigma. Dynamics, in particular residue-specific dynamics, holds crucial clues. Enormous efforts have been spent to characterize residue-specific dynamics of IDPs, mainly through NMR spin relaxation experiments. Here we present a sequence-based method, SeqDYN, for predicting residue-specific backbone dynamics of IDPs. SeqDYN employs a mathematical model with 21 parameters and is trained on 45 IDPs. It provides not only rapid, accurate prediction but also insightful physical interpretation of sequence-dependent IDP dynamics.

Nonspecific binding of crowder proteins with functional proteins is likely prevalent in vivo, yet direct quantitative evidence, let alone residue-specific information, is scarce. Here we present NMR characterization showing that bovine serum albumin (BSA) weakly but preferentially interacts with HPr. Notably, the binding interface overlaps with that for HPr’s specific partner protein, EIN, leading to competition. The crowder protein thus reduces the EIN-HPr binding affinity and accelerates the dissociation of the native complex. In contrast, Ficoll-70 stabilizes the native complex and slows its dissociation, as one would expect from excluded-volume and microviscosity effects. Our atomistic modeling of macromolecular crowding rationalizes the experimental data, and provides quantitative insights into the energetics of protein-crowder interactions. The integrated NMR and modeling study yields benchmarks for the effects of crowded cellular environments on protein-protein specific interactions, with implications for evolution regarding how nonspecific binding can be minimized or exploited.