Calculating Binodals and Interfacial Tension of Phase-Separated Condensates from Molecular Simulations with Finite-Size Corrections.

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.

SpiDec: Computing binodals and interfacial tension of biomolecular condensates from simulations of spinodal decomposition.

Phase separation of intrinsically disordered proteins (IDPs) is a phenomenon associated with many essential cellular processes, but a robust method to compute the binodal from molecular dynamics simulations of IDPs modeled at the all-atom level in explicit solvent is still elusive, due to the difficulty in preparing a suitable initial dense configuration and in achieving phase equilibration. Here we present SpiDec as such a method, based on spontaneous phase separation via spinodal decomposition that produces a dense slab when the system is initiated at a homogeneous, low density. After illustrating the method on four model systems, we apply SpiDec to a tetrapeptide modeled at the all-atom level and solvated in TIP3P water. The concentrations in the dense and dilute phases agree qualitatively with experimental results and point to binodals as a sensitive property for force-field parameterization. SpiDec may prove useful for the accurate determination of the phase equilibrium of IDPs.

Multiphase organization is a second phase transition within multi-component biomolecular condensates.

We present a mean-field theoretical model, along with molecular dynamics simulations, to show that the multiphase organization of multi-component condensates is a second phase transition. Whereas the first phase transition that leads to the separation of condensates from the bulk phase is driven by the overall attraction among the macromolecular components, the second phase transition can be driven by the disparity in the strength between the self- and cross-species attraction. At a fixed level of disparity in interaction strengths, both of the phase transitions can be observed by decreasing the temperature, leading first to the separation of condensates from the bulk phase and then to component demixing inside condensates. The existence of a critical temperature for demixing and predicted binodals are verified by molecular dynamics simulations of model mixtures.

Macromolecular regulators have matching effects on the phase equilibrium and interfacial tension of biomolecular condensates.

The interfacial tension of phase-separated biomolecular condensates affects their fusion and multiphase organization, and yet how this important property depends on the composition and interactions of the constituent macromolecules is poorly understood. Here we use molecular dynamics simulations to determine the interfacial tension and phase equilibrium of model condensate-forming systems. The model systems consist of binary mixtures of Lennard-Jones particles or chains of such particles. We refer to the two components as drivers and regulators; the former has stronger self-interactions and hence a higher critical temperature (Tc ) for phase separation. In previous work, we have shown that, depending on the relative strengths of driver-regulator and driver-driver interactions, regulators can either promote or suppress phase separation (i.e., increase or decrease Tc ). Here we find that the effects of regulators on Tc quantitatively match the effects on interfacial tension (γ). This important finding means that, when a condensate-forming system experiences a change in macromolecular composition or a change in intermolecular interactions (e.g., by mutation or posttranslational modification, or by variation in solvent conditions such as temperature, pH, or salt), the resulting change in Tc can be used to predict the change in γ and vice versa. We also report initial results showing that disparity in intermolecular interactions drives multiphase coexistence. These findings provide much needed guidance for understanding how biomolecular condensates mediate cellular functions.

Three archetypical classes of macromolecular regulators of protein liquid-liquid phase separation.

Membraneless organelles, corresponding to the droplet phase upon liquid-liquid phase separation (LLPS) of protein or protein-RNA mixtures, mediate myriad cellular functions. Cells use a variety of biochemical signals such as expression level and posttranslational modification to regulate droplet formation and dissolution, but the physical basis of the regulatory mechanisms remains ill-defined and quantitative assessment of the effects is largely lacking. Our computational study predicted that the strength of attraction by droplet-forming proteins dictates whether and how macromolecular regulators promote or suppress LLPS. We experimentally tested this prediction, using the pentamers of SH3 domains and proline-rich motifs (SH35 and PRM5) as droplet-forming proteins. Determination of the changes in phase boundary and the partition coefficients in the droplet phase over a wide range of regulator concentrations yielded both a quantitative measure and a mechanistic understanding of the regulatory effects. Three archetypical classes of regulatory effects were observed. Ficoll 70 at high concentrations indirectly promoted SH35-PRM5 LLPS, by taking up volume in the bulk phase and thereby displacing SH35 and PRM5 into the droplet phase. Lysozyme had a moderate partition coefficient and suppressed LLPS by substituting weaker attraction with SH35 for the stronger SH35-PRM5 attraction in the droplet phase. By forming even stronger attraction with PRM5, heparin at low concentrations partitioned heavily into the droplet phase and promoted LLPS. These characteristics were recapitulated by computational results of patchy particle models, validating the identification of the 3 classes of macromolecular regulators as volume-exclusion promotors, weak-attraction suppressors, and strong-attraction promotors.

Why Do Disordered and Structured Proteins Behave Differently in Phase Separation?

Intracellular membraneless organelles and their myriad cellular functions have garnered tremendous recent interest. It is becoming well accepted that they form via liquid-liquid phase separation (LLPS) of protein mixtures (often including RNA), where the organelles correspond to a protein-rich droplet phase coexisting with a protein-poor bulk phase. The major protein components contain disordered regions and often also RNA-binding domains, and the disordered fragments on their own easily undergo LLPS. By contrast, LLPS for structured proteins has been observed infrequently. The contrasting phase behaviors can be explained by modeling disordered and structured proteins, respectively, as polymers and colloids. These physical models also provide a better understanding of the regulation of droplet formation by cellular signals and its dysregulation leading to diseases.