Transfer Free Energies of Test Proteins Into Crowded Protein Solutions Have Simple Dependence on Crowder Concentration.

The effects of macromolecular crowding on the thermodynamic properties of test proteins are determined by the latter's transfer free energies from a dilute solution to a crowded solution. The transfer free energies in turn are determined by effective protein-crowder interactions. When these interactions are modeled at the all-atom level, the transfer free energies may defy simple predictions. Here we investigated the dependence of the transfer free energy (Δµ) on crowder concentration. We represented both the test protein and the crowder proteins atomistically, and used a general interaction potential consisting of hard-core repulsion, non-polar attraction, and solvent-screened electrostatic terms. The chemical potential was rigorously calculated by FMAP (Qin and Zhou, 2014), which entails expressing the protein-crowder interaction terms as correlation functions and evaluating them via fast Fourier transform (FFT). To high accuracy, the transfer free energy can be decomposed into an excluded-volume component (Δµe-v), arising from the hard-core repulsion, and a soft-attraction component (Δµs-a), arising from non-polar and electrostatic interactions. The decomposition provides physical insight into crowding effects, in particular why such effects are very modest on protein folding stability. Further decomposition of Δµs-a into non-polar and electrostatic components does not work, because these two types of interactions are highly correlated in contributing to Δµs-a. We found that Δµe-v fits well to the generalized fundamental measure theory (Qin and Zhou, 2010), which accounts for atomic details of the test protein but approximates the crowder proteins as spherical particles. Most interestingly, Δµs-a has a nearly linear dependence on crowder concentration. The latter result can be understood within a perturbed virial expansion of Δµ (in powers of crowder concentration), with Δµe-v as reference. Whereas the second virial coefficient deviates strongly from that of the reference system, higher virial coefficients are close to their reference counterparts, thus leaving the linear term to make the dominant contribution to Δµs-a.

Atomistic Modeling of Intrinsically Disordered Proteins Under Polyethylene Glycol Crowding: Quantitative Comparison with Experimental Data and Implication of Protein-Crowder Attraction.

The malleability of intrinsically disordered proteins (IDPs) has generated great interest in understanding how their conformations respond to crowded cellular environments. Experiments can report gross properties such as fluorescence resonance energy transfer (FRET) efficiency but cannot resolve the conformational ensembles of IDPs and their interactions with macromolecular crowders. Computation can in principle provide the latter information but in practice has been hampered by the enormous expense for realistic modeling of IDPs and crowders and for sufficient conformational sampling. Here, taking advantage of a powerful method called FMAP (fast Fourier transform-based modeling of atomistic protein-crowder interactions), we computed how the conformational ensembles of three IDPs are modified in concentrated polyethylene glycol (PEG) 6000 solutions. We represented the IDPs at the all-atom level and the PEG molecules at a coarse-grained level and calculated the experimental observable, i.e., FRET efficiency. Whereas accounting for only steric repulsion of PEG led to overestimation of crowding effects, quantitative agreement with experimental data was obtained upon including mild IDP-PEG attraction. The present work demonstrates that realistic modeling of IDPs under crowded conditions for direct comparison with experiments is now achievable.

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.

Liquid-Liquid Phase Separation of Patchy Particles Illuminates Diverse Effects of Regulatory Components on Protein Droplet Formation.

Recently many cellular functions have been associated with membraneless organelles, or protein droplets, formed by liquid-liquid phase separation (LLPS). Proteins in these droplets often contain RNA-binding domains, but the effects of RNA on LLPS have been controversial. To gain better understanding on the roles of RNA and other macromolecular regulators, here we used Gibbs-ensemble simulations to determine phase diagrams of two-component patchy particles, as models for mixtures of proteins with regulatory components. Protein-like particles have four patches, with attraction strength εPP; regulatory particles experience mutual steric repulsion but have two attractive patches toward proteins, with the strength εPR tunable. At low εPR, the regulator, due to steric repulsion, preferentially partitions in the dispersed phase, thereby displacing the protein into the droplet phase and promoting LLPS. At moderate εPR, the regulator starts to partition and displace the protein in the droplet phase, but only to weaken bonding networks and thereby suppress LLPS. At εPR > εPP, the enhanced bonding ability of the regulator initially promotes LLPS, but at higher amounts, the resulting displacement of the protein suppresses LLPS. These results illustrate how RNA can have disparate effects on LLPS, thus able to perform diverse functions in different organelles.