Fundamental Aspects of Phase-Separated Biomolecular Condensates.

Biomolecular condensates, formed through phase separation, are upending our understanding in much of molecular, cell, and developmental biology. There is an urgent need to elucidate the physicochemical foundations of the behaviors and properties of biomolecular condensates. Here we aim to fill this need by writing a comprehensive, critical, and accessible review on the fundamental aspects of phase-separated biomolecular condensates. We introduce the relevant theoretical background, present the theoretical basis for the computation and experimental measurement of condensate properties, and give mechanistic interpretations of condensate behaviors and properties in terms of interactions at the molecular and residue levels.

Surface Charge Can Modulate Phase Separation of Multidomain Proteins.

Phase separation has emerged as an important mechanism explaining the formation of certain biomolecular condensates. Biological phase separation is often driven by the multivalent interactions of modular protein domains. Beyond valency, the physical features of folded domains that promote phase separation are poorly understood. We used a model system─the small ubiquitin modifier (SUMO) and its peptide ligand, the SUMO interaction motif (SIM)─to examine how domain surface charge influences multivalency-driven phase separation. Phase separation of polySUMO and polySIM was altered by pH via a change in the protonation state of SUMO surface histidines. These effects were recapitulated by histidine mutations, which modulated SUMO solubility and polySUMO-polySIM phase separation in parallel and were quantitatively explained by atomistic modeling of weak interactions among proteins in the system. Thus, surface charge can tune the phase separation of multivalent proteins, suggesting a means of controlling phase separation biologically, evolutionarily, and therapeutically.

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.

Both Ligands and Macromolecular Crowders Preferentially Bind to Closed Conformations of Maltose Binding Protein.

In cellular environments, proteins not only interact with their specific partners but also encounter a high concentration of bystander macromolecules, or crowders. Nonspecific interactions with macromolecular crowders modulate the activities of proteins, but our knowledge about the rules of nonspecific interactions is still very limited. In previous work, we presented experimental evidence that macromolecular crowders acted competitively in inhibiting the binding of maltose binding protein (MBP) with its ligand maltose. Competition between a ligand and an inhibitor may result from binding to either the same site or different conformations of the protein. Maltose binds to the cleft between two lobes of MBP, and in a series of mutants, the affinities increased with an increase in the extent of lobe closure. Here we investigated whether macromolecular crowders also have a conformational or site preference when binding to MBP. The affinities of a polymer crowder, Ficoll70, measured by monitoring tryptophan fluorescence were 3-6-fold higher for closure mutants than for wild-type MBP. Competition between the ligand and crowder, as indicated by fitting of titration data and directly by nuclear magnetic resonance spectroscopy, and their similar preferences for closed MBP conformations further suggest the scenario in which the crowder, like maltose, preferentially binds to the interlobe cleft of MBP. Similar observations were made for bovine serum albumin as a protein crowder. Conformational and site preferences in MBP-crowder binding allude to the paradigm that nonspecific interactions can possess hallmarks of molecular recognition, which may be essential for intracellular organizations including colocalization of proteins and liquid-liquid phase separation.

Intrinsically Disordered Protein Exhibits Both Compaction and Expansion under Macromolecular Crowding.

Conformational malleability allows intrinsically disordered proteins (IDPs) to respond agilely to their environments, such as nonspecifically interacting with in vivo bystander macromolecules (or crowders). Previous studies have emphasized conformational compaction of IDPs due to steric repulsion by macromolecular crowders, but effects of soft attraction are largely unexplored. Here we studied the conformational ensembles of the IDP FlgM in both polymer and protein crowders by small-angle neutron scattering. As crowder concentrations increased, the mean radius of gyration of FlgM first decreased but then exhibited an uptick. Ensemble optimization modeling indicated that FlgM conformations under protein crowding segregated into two distinct populations, one compacted and one extended. Coarse-grained simulations showed that compacted conformers fit into an interstitial void and occasionally bind to a surrounding crowder, whereas extended conformers snake through interstitial crevices and bind multiple crowders simultaneously. Crowder-induced conformational segregation may facilitate various cellular functions of IDPs.

Prediction of homoprotein and heteroprotein complexes by protein docking and template-based modeling: A CASP-CAPRI experiment.

We present the results for CAPRI Round 30, the first joint CASP-CAPRI experiment, which brought together experts from the protein structure prediction and protein-protein docking communities. The Round comprised 25 targets from amongst those submitted for the CASP11 prediction experiment of 2014. The targets included mostly homodimers, a few homotetramers, and two heterodimers, and comprised protein chains that could readily be modeled using templates from the Protein Data Bank. On average 24 CAPRI groups and 7 CASP groups submitted docking predictions for each target, and 12 CAPRI groups per target participated in the CAPRI scoring experiment. In total more than 9500 models were assessed against the 3D structures of the corresponding target complexes. Results show that the prediction of homodimer assemblies by homology modeling techniques and docking calculations is quite successful for targets featuring large enough subunit interfaces to represent stable associations. Targets with ambiguous or inaccurate oligomeric state assignments, often featuring crystal contact-sized interfaces, represented a confounding factor. For those, a much poorer prediction performance was achieved, while nonetheless often providing helpful clues on the correct oligomeric state of the protein. The prediction performance was very poor for genuine tetrameric targets, where the inaccuracy of the homology-built subunit models and the smaller pair-wise interfaces severely limited the ability to derive the correct assembly mode. Our analysis also shows that docking procedures tend to perform better than standard homology modeling techniques and that highly accurate models of the protein components are not always required to identify their association modes with acceptable accuracy. Proteins 2016; 84(Suppl 1):323-348. © 2016 Wiley Periodicals, Inc.

Calculating Structure Factors of Protein Solutions by Atomistic Modeling of Protein-Protein Interactions.

We present a method, FMAPS(q), for calculating the structure factor, S(q), of a protein solution, by extending our fast Fourier transform-based modeling of atomistic protein-protein interactions (FMAP) approach. The interaction energy consists of steric, nonpolar attractive, and electrostatic terms that are additive among all pairs of atoms between two protein molecules. In the present version, we invoke the free-rotation approximation, such that the structure factor is given by the Fourier transform of the protein center-center distribution function gC(R). At low protein concentrations, gC(R) can be approximated as e-ßW(R), where W(R) is the potential of mean force along the center-center distance R. We calculate W(R) using FMAPB2, a member of the FMAP class of methods that is specialized for the second virial coefficient [Qin and Zhou, J Phys Chem B 123 (2019) 8203-8215]. For higher protein concentrations, we obtain S(q) by a modified random-phase approximation, which is a perturbation around the steric-only energy function. Without adjusting any parameters, the calculated structure factors for lysozyme and bovine serum albumin at various ionic strengths, temperatures, and protein concentrations are all in reasonable agreement with those measured by small-angle X-ray or neutron scattering. This initial success motivates further developments, including removing approximations and parameterizing the interaction energy function.

Using the concept of transient complex for affinity predictions in CAPRI rounds 20-27 and beyond.

Predictions of protein-protein binders and binding affinities have traditionally focused on features pertaining to the native complexes. In developing a computational method for predicting protein-protein association rate constants, we introduced the concept of transient complex after mapping the interaction energy surface. The transient complex is located at the outer boundary of the bound-state energy well, having near-native separation and relative orientation between the subunits but not yet formed most of the short-range native interactions. We found that the width of the binding funnel and the electrostatic interaction energy of the transient complex are among the features predictive of binders and binding affinities. These ideas were very promising for the five affinity-related targets (T43-45, 55, and 56) of CAPRI rounds 20-27. For T43, we ranked the single crystallographic complex as number 1 and were one of only two groups that clearly identified that complex as a true binder; for T44, we ranked the only design with measurable binding affinity as number 4. For the nine docking targets, continuing on our success in previous CAPRI rounds, we produced 10 medium-quality models for T47 and acceptable models for T48 and T49. We conclude that the interaction energy landscape and the transient complex in particular will complement existing features in leading to better prediction of binding affinities.

Folding free energy surfaces of three small proteins under crowding: validation of the postprocessing method by direct simulation.

We have developed a 'postprocessing' method for modeling biochemical processes such as protein folding under crowded conditions (Qin and Zhou 2009 Biophys. J. 97 12-19). In contrast to the direct simulation approach, in which the protein undergoing folding is simulated along with crowders, the postprocessing method requires only the folding simulation without crowders. The influence of the crowders is then obtained by taking conformations from the crowder-free simulation and calculating the free energies of transferring to the crowders. This postprocessing yields the folding free energy surface of the protein under crowding. Here the postprocessing results for the folding of three small proteins under 'repulsive' crowding are validated by those obtained previously by the direct simulation approach (Mittal and Best 2010 Biophys. J. 98 315-20). This validation confirms the accuracy of the postprocessing approach and highlights its distinct advantages in modeling biochemical processes under cell-like crowded conditions, such as enabling an atomistic representation of the test proteins.

Prediction and dissection of widely-varying association rate constants of actin-binding proteins.

Actin is an abundant protein that constitutes a main component of the eukaryotic cytoskeleton. Its polymerization and depolymerization are regulated by a variety of actin-binding proteins. Their functions range from nucleation of actin polymerization to sequestering G-actin in 1∶1 complexes. The kinetics of forming these complexes, with rate constants varying at least three orders of magnitude, is critical to the distinct regulatory functions. Previously we have developed a transient-complex theory for computing protein association mechanisms and association rate constants. The transient complex refers to an intermediate in which the two associating proteins have near-native separation and relative orientation but have yet to form short-range specific interactions of the native complex. The association rate constant is predicted as k(a) = k(a0) e(-ΔG(el*)/k(B)T), where k(a0) is the basal rate constant for reaching the transient complex by free diffusion, and the Boltzmann factor captures the bias of long-range electrostatic interactions. Here we applied the transient-complex theory to study the association kinetics of seven actin-binding proteins with G-actin. These proteins exhibit three classes of association mechanisms, due to their different molecular shapes and flexibility. The 1000-fold k(a) variations among them can mostly be attributed to disparate electrostatic contributions. The basal rate constants also showed variations, resulting from the different shapes and sizes of the interfaces formed by the seven actin-binding proteins with G-actin. This study demonstrates the various ways that actin-binding proteins use physical properties to tune their association mechanisms and rate constants to suit distinct regulatory functions.

Predicting the Sequence-Dependent Backbone Dynamics of Intrinsically Disordered Proteins.

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 the 15N 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 raise R2. Elevated R2 has 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 predicting R2 of IDPs. The R2 value 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 as R2 promotors whereas Gly and short polar amino acids as R2 suppressors. The prediction accuracy of SeqDYN is competitive against that of recent MD simulations using IDP-specific force fields. For a structured protein, SeqDYN prediction represents R2 in the unfolded state. SeqDYN is available as a web server at https://zhougroup-uic.github.io/SeqDYNidp/ for rapid R2 prediction.

Atomistic Modeling of Liquid-Liquid Phase Equilibrium Explains Dependence of Critical Temperature on γ-Crystallin Sequence.

Liquid-liquid phase separation of protein solutions has regained heightened attention for its biological importance and pathogenic relevance. Coarse-grained models are limited when explaining residue-level effects on phase equilibrium. Here we report phase diagrams for γ-crystallins using atomistic modeling. The calculations were made possible by combining our FMAP method for computing chemical potentials and Brownian dynamics simulations for configurational sampling of dense protein solutions, yielding the binodal and critic temperature ( T c ). We obtain a higher T c for a known high- T c γ-crystallin, γF, than for a low- T c paralog, γB. The difference in T c is corroborated by a gap in second virial coefficient. Decomposition of inter-protein interactions reveals one amino-acid substitution between γB and γF, from Ser to Trp at position 130, as the major contributor to the difference in T c . This type of analysis enables us to link phase equilibrium to amino-acid sequence and to design mutations for altering phase equilibrium.

Atomistic modeling of liquid-liquid phase equilibrium explains dependence of critical temperature on γ-crystallin sequence.

Liquid-liquid phase separation of protein solutions has regained heightened attention for its biological importance and pathogenic relevance. Coarse-grained models are limited when explaining residue-level effects on phase equilibrium. Here we report phase diagrams for γ-crystallins using atomistic modeling. The calculations were made possible by combining our FMAP method for computing chemical potentials and Brownian dynamics simulations for configurational sampling of dense protein solutions, yielding the binodal and critic temperature (Tc). We obtain a higher Tc for a known high-Tc γ-crystallin, γF, than for a low-Tc paralog, γB. The difference in Tc is corroborated by a gap in second virial coefficient. Decomposition of inter-protein interactions reveals one amino-acid substitution between γB and γF, from Ser to Trp at position 130, as the major contributor to the difference in Tc. This type of analysis enables us to link phase equilibrium to amino-acid sequence and to design mutations for altering phase equilibrium.

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.

Contrasting factors on the kinetic path to protein complex formation diminish the effects of crowding agents.

The crowded environment of cells poses a challenge for rapid protein-protein association. Yet, it has been established that the rates of association are similar in crowded and in dilute solutions. Here we probe the pathway leading to fast association between TEM1 ß-lactamase and its inhibitor protein BLIP in crowded solutions. We show that the affinity of the encounter complex, the rate of final complex formation, and the structure of the transition state are similar in crowded solutions and in buffer. The experimental results were reproduced by calculations based on the transient-complex theory for protein association. Both experiments and calculations suggest that while crowding agents decrease the diffusion constant of the associating proteins, they also induce an effective excluded-volume attraction between them. The combination of the two opposing effects thus results in nearly identical overall association rates in diluted and crowded solutions.

A method for computing association rate constants of atomistically represented proteins under macromolecular crowding.

In cellular environments, two protein molecules on their way to form a specific complex encounter many bystander macromolecules. The latter molecules, or crowders, affect both the energetics of the interaction between the test molecules and the dynamics of their relative motion. In earlier work (Zhou and Szabo 1991 J. Chem. Phys. 95 5948-52), it has been shown that, in modeling the association kinetics of the test molecules, the presence of crowders can be accounted for by their energetic and dynamic effects. The recent development of the transient-complex theory for protein association in dilute solutions makes it possible to easily incorporate the energetic and dynamic effects of crowders. The transient complex refers to a late on-pathway intermediate, in which the two protein molecules have near-native relative separation and orientation, but have yet to form the many short-range specific interactions of the native complex. The transient-complex theory predicts the association rate constant as k(a) = k(a0)exp(-ΔG*(el)/k(B)T), where k(a0) is the 'basal' rate constant for reaching the transient complex by unbiased diffusion, and the Boltzmann factors captures the influence of long-range electrostatic interactions between the protein molecules. Crowders slow down the diffusion, therefore reducing the basal rate constant (to k(ac0)), and induce an effective interaction energy ΔG(c). We show that the latter interaction energy for atomistic proteins in the presence of spherical crowders is 'long'-ranged, allowing the association rate constant under crowding to be computed as k(ac) = k(ac0)exp[-(ΔG*(el) + ΔG*(c))/k(B)T]. Applications demonstrate that this computational method allows for realistic modeling of protein association kinetics under crowding.

Dissection of the high rate constant for the binding of a ribotoxin to the ribosome.

Restrictocin belongs to a family of site-specific ribonucleases that kill cells by inactivating the ribosome. The restrictocin-ribosome binding rate constant was observed to exceed 10(10) M(-1) s(-1). We have developed a transient-complex theory to model the binding rates of protein-protein and protein-RNA complexes. The theory predicts the rate constant as k(a) = k(a0) exp(-DeltaG(el)*/k(B)T), where k(a0) is the basal rate constant for reaching the transient complex, located at the outer boundary of the bound state, by random diffusion, and DeltaG(el)* is the average electrostatic interaction free energy of the transient complex. Here, we applied the transient-complex theory to dissect the high restrictocin-ribosome binding rate constant. We found that the binding rate of restrictocin to the isolated sarcin/ricin loop is electrostatically enhanced by approximately 300-fold, similar to results found in other protein-protein and protein-RNA complexes. The ribosome provides an additional 10,000-fold rate enhancement because of two synergistic mechanisms afforded by the distal regions of the ribosome. First, they provide additional electrostatic attraction with restrictocin. Second, they reposition the transient complex into a region where local electrostatic interactions of restrictocin with the sarcin/ricin loop are particularly favorable. Our calculations rationalize a host of experimental observations and identify a strategy for designing proteins that bind their targets with high speed.

ReSMAP: Web Server for Predicting Residue-Specific Membrane-Association Propensities of Intrinsically Disordered Proteins.

The functional processes of many proteins involve the association of their intrinsically disordered regions (IDRs) with acidic membranes. We have identified the membrane-association characteristics of IDRs using extensive molecular dynamics (MD) simulations and validated them with NMR spectroscopy. These studies have led to not only deep insight into functional mechanisms of IDRs but also to intimate knowledge regarding the sequence determinants of membrane-association propensities. Here we turned this knowledge into a web server called ReSMAP, for predicting the residue-specific membrane-association propensities from IDR sequences. The membrane-association propensities are calculated from a sequence-based partition function, trained on the MD simulation results of seven IDRs. Robustness of the prediction is demonstrated by leaving one IDR out of the training set. We anticipate there will be many applications for the ReSMAP web server, including rapid screening of IDR sequences for membrane association.

Preferential Interactions of a Crowder Protein with the Specific Binding Site of a Native Protein Complex.

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 nuclear magnetic resonance (NMR) characterization showing that bovine serum albumin weakly but preferentially interacts with the histidine carrier protein (HPr). Notably, the binding interface overlaps with that for HPr's specific partner protein, EIN, leading to competition. The crowder protein thus decreases 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.