Connecting Coil-to-Globule Transitions to Full Phase Diagrams for Intrinsically Disordered Proteins

The Protein Folding Problem: The Role of Theory

The protein folding problem was first articulated as question of how order arose from disorder in proteins: How did the various native structures of proteins arise from interatomic driving forces encoded within their amino acid sequences, and how did they fold so fast? These matters have now been largely resolved by theory and statistical mechanics combined with experiments. There are general principles. Chain randomness is overcome by solvation-based codes. And in the needle-in-a-haystack metaphor, native states are found efficiently because protein haystacks (conformational ensembles) are funnel-shaped. Order-disorder theory has now grown to encompass a large swath of protein physical science across biology.

Intramolecular interactions play key role in stabilization of pHLIP at acidic conditions

The pH-Low Insertion Peptide (pHLIP) is a membrane-active peptide that spontaneously folds into a transmembrane α-helix upon acidification. This activity enables pHLIP to potentially act as a vector for drugs related to diseases characterized by acidosis such as cancer or heart ischemia. Presently, due to aggregation-based effects, formulations of pHLIP are only viable at near-μM concentrations. In addition, since most of pHLIP's measurable qualities involve a membrane, probing the details of pHLIP in the interstitial region is difficult. In attempts to shed light on these issues, we performed constant pH molecular dynamics simulations on pHLIP as well as P20G, a variant with increased helicity, in solution at 0 and 150 mM NaCl over a broad range of pHs. In general, the addition of ions reduced the effective pK_a of the acidic residues in pHLIP. P20G exhibits a higher helicity than pHLIP in general and is more compact than pHLIP at pH values under 4. In terms of charge effects, sodium cations localized predominantly to the C-terminus of the peptide with a high density of acidic residues. Additionally, the salt bridge between R11 and D14 is by far the most favored and particularly so with pHLIP at 150 mM NaCl. We expect that this approach will be a valuable tool to screen variants of pHLIP for favorable properties in solution, an aspect of pHLIP design that to this point has largely been neglected.

Phase separation vs aggregation behavior for model disordered proteins

Liquid-liquid phase separation (LLPS) is widely utilized by the cell to organize and regulate various biochemical processes. Although the LLPS of proteins is known to occur in a sequence-dependent manner, it is unclear how sequence properties dictate the nature of the phase transition and thereby influence condensed phase morphology. In this work, we have utilized grand canonical Monte Carlo simulations for a simple coarse-grained model of disordered proteins to systematically investigate how sequence distribution, sticker fraction, and chain length impact the formation of finite-size aggregates, which can preempt macroscopic phase separation for some sequences. We demonstrate that a normalized sequence charge decoration (SCD) parameter establishes a "soft" predictive criterion for distinguishing when a model protein undergoes macroscopic phase separation vs finite aggregation. Additionally, we find that this order parameter is strongly correlated with the critical density for phase separation, highlighting an unambiguous connection between sequence distribution and condensed phase density. Results obtained from an analysis of the order parameter reveal that at sufficiently long chain lengths, the vast majority of sequences are likely to phase separate. Our results suggest that classical LLPS should be the primary phase transition for disordered proteins when short-ranged attractive interactions dominate and suggest a possible reason behind recent findings of widespread phase separation throughout living cells.

Sequence Determines the Switch in the Fibril Forming Regions in the Low-Complexity FUS Protein and Its Variants

Residues spanning distinct regions of the low-complexity domain of the RNA-binding protein, Fused in Sarcoma (FUS-LC), form fibril structures with different core morphologies. Solid-state NMR experiments show that the 214-residue FUS-LC forms a fibril with an S-bend (core-1, residues 39-95), while the rest of the protein is disordered. In contrast, the fibrils of the C-terminal variant (FUS-LC-C; residues 111-214) have a U-bend topology (core-2, residues 112-150). Absence of the U-bend in FUS-LC implies that the two fibril cores do not coexist. Computer simulations show that these perplexing findings could be understood in terms of the population of sparsely populated fibril-like excited states in the monomer. The propensity to form core-1 is higher compared to core-2. We predict that core-2 forms only in truncated variants that do not contain the core-1 sequence. At the monomer level, sequence-dependent enthalpic effects determine the relative stabilities of the core-1 and core-2 topologies.

Intrinsically disordered protein regions and phase separation: sequence determinants of assembly or lack thereof

Intrinsically disordered protein regions (IDRs) - regions that do not fold into a fixed three-dimensional structure but instead exist in a heterogeneous ensemble of conformations - have recently entered mainstream cell biology in the context of liquid-liquid phase separation (LLPS). IDRs are frequently found to be enriched in phase-separated compartments. Due to this observation, the presence of an IDR in a protein is frequently assumed to be diagnostic of its ability to phase separate. In this review, we clarify the role of IDRs in biological assembly and explore the physical principles through which amino acids can confer the attractive molecular interactions that underlie phase separation. While some disordered regions will robustly drive phase separation, many others will not. We emphasize that rather than 'disorder' driving phase separation, multivalency drives phase separation. As such, whether or not a disordered region is capable of driving phase separation will depend on the physical chemistry encoded within its amino acid sequence. Consequently, an in-depth understanding of that physical chemistry is a prerequisite to make informed inferences on how and why an IDR may be involved in phase separation or, more generally, in protein-mediated intermolecular interactions.

Targeted modulation of protein liquid-liquid phase separation by evolution of amino-acid sequence

Rationally and efficiently modifying the amino-acid sequence of proteins to control their ability to undergo liquid-liquid phase separation (LLPS) on demand is not only highly desirable, but can also help to elucidate which protein features are important for LLPS. Here, we propose a computational method that couples a genetic algorithm to a sequence-dependent coarse-grained protein model to evolve the amino-acid sequences of phase-separating intrinsically disordered protein regions (IDRs), and purposely enhance or inhibit their capacity to phase-separate. We validate the predicted critical solution temperatures of the mutated sequences with ABSINTH, a more accurate all-atom model. We apply the algorithm to the phase-separating IDRs of three naturally occurring proteins, namely FUS, hnRNPA1 and LAF1, as prototypes of regions that exist in cells and undergo homotypic LLPS driven by different types of intermolecular interaction, and we find that the evolution of amino-acid sequences towards enhanced LLPS is driven in these three cases, among other factors, by an increase in the average size of the amino acids. However, the direction of change in the molecular driving forces that enhance LLPS (such as hydrophobicity, aromaticity and charge) depends on the initial amino-acid sequence. Finally, we show that the evolution of amino-acid sequences to modulate LLPS is strongly coupled to the make-up of the medium (e.g. the presence or absence of RNA), which may have significant implications for our understanding of phase separation within the many-component mixtures of biological systems.

A multi-step nucleation process determines the kinetics of prion-like domain phase separation

Compartmentalization by liquid-liquid phase separation (LLPS) has emerged as a ubiquitous mechanism underlying the organization of biomolecules in space and time. Here, we combine rapid-mixing time-resolved small-angle X-ray scattering (SAXS) approaches to characterize the assembly kinetics of a prototypical prion-like domain with equilibrium techniques that characterize its phase boundaries and the size distribution of clusters prior to phase separation. We find two kinetic regimes on the micro- to millisecond timescale that are distinguished by the size distribution of clusters. At the nanoscale, small complexes are formed with low affinity. After initial unfavorable complex assembly, additional monomers are added with higher affinity. At the mesoscale, assembly resembles classical homogeneous nucleation. Careful multi-pronged characterization is required for the understanding of condensate assembly mechanisms and will promote understanding of how the kinetics of biological phase separation is encoded in biomolecules.

Small-Angle X-ray Scattering Signatures of Conformational Heterogeneity and Homogeneity of Disordered Protein Ensembles

An accurate account of disordered protein conformations is of central importance to deciphering the physicochemical basis of biological functions of intrinsically disordered proteins and the folding-unfolding energetics of globular proteins. Physically, disordered ensembles of nonhomopolymeric polypeptides are expected to be heterogeneous, i.e., they should differ from those homogeneous ensembles of homopolymers that harbor an essentially unique relationship between average values of end-to-end distance R_EE and radius of gyration R_g. It was posited recently, however, that small-angle X-ray scattering (SAXS) data on conformational dimensions of disordered proteins can be rationalized almost exclusively by homopolymer ensembles. Assessing this perspective, chain-model simulations are used to evaluate the discriminatory power of SAXS-determined molecular form factors (MFFs) with regard to homogeneous versus heterogeneous ensembles. The general approach adopted here is not bound by any assumption about ensemble encodability, in that the postulated heterogeneous ensembles we evaluated are not restricted to those entailed by simple interaction schemes. Our analysis of MFFs for certain heterogeneous ensembles with more narrowly distributed R_EE and R_g indicates that while they deviate from MFFs of homogeneous ensembles, the differences can be rather small. Remarkably, some heterogeneous ensembles with asphericity and R_EE drastically different from those of homogeneous ensembles can nonetheless exhibit practically identical MFFs, demonstrating that SAXS MFFs do not afford unique characterizations of basic properties of conformational ensembles in general. In other words, the ensemble to MFF mapping is practically many-to-one and likely nonsmooth. Heteropolymeric variations of the R_EE-R_g relationship were further showcased using an analytical perturbation theory developed here for flexible heteropolymers. Ramifications of our findings for interpretation of experimental data are discussed.

Intrachain interaction topology can identify functionally similar intrinsically disordered proteins

Functionally similar IDPs (intrinsically disordered proteins) often have little sequence similarity. This is in stark contrast to folded proteins and poses a challenge for the inverse problem, functional classification of IDPs using sequence alignment. The problem is further compounded because of the lack of structure in IDPs, preventing structural alignment as an alternate tool for classification. Recent advances in heteropolymer theory unveiled a powerful set of sequence-patterning metrics bridging molecular interaction with chain conformation. Focusing only on charge patterning, these set of metrics yield a sequence charge decoration matrix (SCDM). SCDMs can potentially identify functionally similar IDPs not apparent from sequence alignment alone. Here, we illustrate how these information-rich "molecular blueprints" encoded in SCDMs can be used for functional classification of IDPs with specific application in three protein families-Ste50, PSC, and RAM-in which electrostatics is known to be important. For both the Ste50 and PSC protein family, the set of metrics appropriately classifies proteins in functional and nonfunctional groups in agreement with experiment. Furthermore, our algorithm groups synthetic variants of the disordered RAM region of the Notch receptor protein-important in gene expression-in reasonable accordance with classification based on experimentally measured binding constants of RAM and transcription factor. Taken together, the novel classification scheme reveals the critical role of a high-dimensional set of metrics-manifest in self-interaction maps and topology-in functional annotation of IDPs even when there is low sequence homology, providing the much-needed alternate to a traditional sequence alignment tool.

Intrinsically disordered proteins and biomolecular condensates as drug targets

Intrinsically disordered domains represent attractive therapeutic targets because they play key roles in cancer, as well as in neurodegenerative and infectious diseases. They are, however, considered undruggable because they do not form stable binding pockets for small molecules and, therefore, have not been prioritized in drug discovery. Under physiological solution conditions many biomedically relevant intrinsically disordered proteins undergo phase separation processes leading to the formation of mesoscopic highly dynamic assemblies, generally known as biomolecular condensates that define environments that can be quite different from the solutions surrounding them. In what follows, we review key recent findings in this area and show how biomolecular condensation can offer opportunities for modulating the activities of intrinsically disordered targets.

The SARS-CoV-2 nucleocapsid protein is dynamic, disordered, and phase separates with RNA

The SARS-CoV-2 nucleocapsid (N) protein is an abundant RNA-binding protein critical for viral genome packaging, yet the molecular details that underlie this process are poorly understood. Here we combine single-molecule spectroscopy with all-atom simulations to uncover the molecular details that contribute to N protein function. N protein contains three dynamic disordered regions that house putative transiently-helical binding motifs. The two folded domains interact minimally such that full-length N protein is a flexible and multivalent RNA-binding protein. N protein also undergoes liquid-liquid phase separation when mixed with RNA, and polymer theory predicts that the same multivalent interactions that drive phase separation also engender RNA compaction. We offer a simple symmetry-breaking model that provides a plausible route through which single-genome condensation preferentially occurs over phase separation, suggesting that phase separation offers a convenient macroscopic readout of a key nanoscopic interaction.

Design of intrinsically disordered proteins that undergo phase transitions with lower critical solution temperatures

Many naturally occurring elastomers are intrinsically disordered proteins (IDPs) built up of repeating units and they can demonstrate two types of thermoresponsive phase behavior. Systems characterized by lower critical solution temperatures (LCST) undergo phase separation above the LCST whereas systems characterized by upper critical solution temperatures (UCST) undergo phase separation below the UCST. There is congruence between thermoresponsive coil-globule transitions and phase behavior whereby the theta temperatures above or below which the IDPs transition from coils to globules serve as useful proxies for the LCST / UCST values. This implies that one can design sequences with desired values for the theta temperature with either increasing or decreasing radii of gyration above the theta temperature. Here, we show that the Monte Carlo simulations performed in the so-called intrinsic solvation (IS) limit version of the temperature-dependent the ABSINTH (self-Assembly of Biomolecules Studied by an Implicit, Novel, Tunable Hamiltonian) implicit solvation model, yields a useful heuristic for discriminating between sequences with known LCST versus UCST phase behavior. Accordingly, we use this heuristic in a supervised approach, integrate it with a genetic algorithm, combine this with IS limit simulations, and demonstrate that novel sequences can be designed with LCST phase behavior. These calculations are aided by direct estimates of temperature dependent free energies of solvation for model compounds that are derived using the polarizable AMOEBA (atomic multipole optimized energetics for biomolecular applications) forcefield. To demonstrate the validity of our designs, we calculate coil-globule transition profiles using the full ABSINTH model and combine these with Gaussian Cluster Theory calculations to establish the LCST phase behavior of designed IDPs.

Self-Assembly of Silk-like Protein into Nanoscale Bicontinuous Networks under Phase-Separation Conditions

Liquid-liquid phase separation of biomacromolecules is crucial in various inter- and extracellular biological functions. This includes formation of condensates to control, e.g., biochemical reactions and structural assembly. The same phenomenon is also found to be critically important in protein-based high-performance biological materials. Here, we use a well-characterized model triblock protein system to demonstrate the molecular level formation mechanism and structure of its condensate. Large-scale molecular modeling supported by analytical ultracentrifuge characterization combined with our earlier high magnification precision cryo-SEM microscopy imaging leads to deducing that the condensate has a bicontinuous network structure. The bicontinuous network rises from the proteins having a combination of sites with stronger mutual attraction and multiple weakly attractive regions connected by flexible, multiconfigurational linker regions. These attractive sites and regions behave as stickers of varying adhesion strength. For the examined model triblock protein construct, the β-sheet-rich end units are the stronger stickers, while additional weaker stickers, contributing to the condensation affinity, rise from spring-like connections in the flexible middle region of the protein. The combination of stronger and weaker sticker-like connections and the flexible regions between the stickers result in a versatile, liquid-like, self-healing structure. This structure also explains the high flexibility, easy deformability, and diffusion of the proteins, decreasing only 10-100 times in the bicontinuous network formed in the condensate phase in comparison to dilute protein solution. The here demonstrated structure and condensation mechanism of a model triblock protein construct via a combination of the stronger binding regions and the weaker, flexible sacrificial-bond-like network as well as its generalizability via polymer sticker models provide means to not only understand intracellular organization, regulation, and cellular function but also to identify direct control factors for and to enable engineering improved protein and polymer constructs to enhance control of advanced fiber materials, smart liquid biointerfaces, or self-healing matrices for pharmaceutics or bioengineering materials.

The SARS-CoV-2 nucleocapsid protein is dynamic, disordered, and phase separates with RNA

The SARS-CoV-2 nucleocapsid (N) protein is an abundant RNA binding protein critical for viral genome packaging, yet the molecular details that underlie this process are poorly understood. Here we combine single-molecule spectroscopy with all-atom simulations to uncover the molecular details that contribute to N protein function. N protein contains three dynamic disordered regions that house putative transiently-helical binding motifs. The two folded domains interact minimally such that full-length N protein is a flexible and multivalent RNA binding protein. N protein also undergoes liquid-liquid phase separation when mixed with RNA, and polymer theory predicts that the same multivalent interactions that drive phase separation also engender RNA compaction. We offer a simple symmetry-breaking model that provides a plausible route through which single-genome condensation preferentially occurs over phase separation, suggesting that phase separation offers a convenient macroscopic readout of a key nanoscopic interaction.

ALS/FTLD-Linked Mutations in FUS Glycine Residues Cause Accelerated Gelation and Reduced Interactions with Wild-Type FUS

The RNA-binding protein fused in sarcoma (FUS) can form pathogenic inclusions in neurodegenerative diseases like amyotrophic lateral sclerosis (ALS) and frontotemporal lobar dementia (FTLD). Over 70 mutations in Fus are linked to ALS/FTLD. In patients, all Fus mutations are heterozygous, indicating that the mutant drives disease progression despite the presence of wild-type (WT) FUS. Here, we demonstrate that ALS/FTLD-linked FUS mutations in glycine (G) strikingly drive formation of droplets that do not readily interact with WT FUS, whereas arginine (R) mutants form mixed condensates with WT FUS. Remarkably, interactions between WT and G mutants are disfavored at the earliest stages of FUS nucleation. In contrast, R mutants physically interact with the WT FUS such that WT FUS recovers the mutant defects by reducing droplet size and increasing dynamic interactions with RNA. This result suggests disparate molecular mechanisms underlying ALS/FTLD pathogenesis and differing recovery potential depending on the type of mutation.

How do intrinsically disordered protein regions encode a driving force for liquid-liquid phase separation?

Liquid-liquid phase separation is the mechanism underlying the formation of biomolecular condensates. Disordered protein regions often drive phase separation, but the molecular interactions mediating this phenomenon are not well understood, sometimes leading to the conflation that all disordered protein regions drive phase separation. Given the critical role of phase separation in many cellular processes, and that dysfunction of phase separation can lead to debilitating diseases, it is important that we understand the interactions and sequence properties underlying phase behavior. A conceptual framework that divides IDRs into interacting and solvating regions has proven particularly useful, and analytical instantiations and coarse-grained models can test our understanding of the driving forces against experimental phase behavior. Validated simulation paradigms enable the exploration of sequence space to help our understanding of how disordered protein regions can encode phase behavior, which IDRs may mediate phase separation in cells, and which IDRs are highly soluble.

Generalized models for bond percolation transitions of associative polymers

Polymers with stickers-and-spacers architectures can drive phase-separation-aided bond percolation transitions. Here, we present a generalized mean-field model to enable the calculation of bond percolation thresholds for polymers with multiple types of stickers. Further, using graph-based Monte Carlo simulations we demonstrate how cooperativity in bond formation can give rise to reentrant phase behavior. When combined with recent advances for modeling phase separation, our approaches for calculating percolation lines could be useful for modeling hardening transitions for multivalent proteins.

Analytical Theory for Sequence-Specific Binary Fuzzy Complexes of Charged Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are important for biological functions. In contrast to folded proteins, molecular recognition among certain IDPs is "fuzzy" in that their binding and/or phase separation are stochastically governed by the interacting IDPs' amino acid sequences, while their assembled conformations remain largely disordered. To help elucidate a basic aspect of this fascinating yet poorly understood phenomenon, the binding of a homo or heterodimeric pair of polyampholytic IDPs is modeled statistical mechanically using cluster expansion. We find that the binding affinities of binary fuzzy complexes in the model correlate strongly with a newly derived simple "joint sequence charge decoration" parameter readily calculable from the pair of IDPs' sequence charge patterns. Predictions by our analytical theory are in essential agreement with coarse-grained explicit-chain simulations. This computationally efficient theoretical framework is expected to be broadly applicable to rationalizing and predicting sequence-specific IDP-IDP polyelectrostatic interactions.

Molecular dynamics simulations of DNA-DNA and DNA-protein interactions

The all-atom molecular dynamics method can characterize the molecular-level interactions in DNA and DNA-protein systems with unprecedented resolution. Recent advances in computational technologies have allowed the method to reveal the unbiased behavior of such systems at the microseconds time scale, whereas enhanced sampling approaches have matured enough to characterize the interaction free energy with quantitative precision. Here, we describe recent progress toward increasing the realism of such simulations by refining the accuracy of the molecular dynamics force field, and we highlight recent application of the method to systems of outstanding biological interest.