The Analytical Flory Random Coil Is a Simple-to-Use Reference Model for Unfolded and Disordered Proteins

Noncovalent Lasso Entanglements are Common in Experimentally Derived Intrinsically Disordered Protein Ensembles and Strongly Influenced by Protein Length and Charge

Noncovalent lasso entanglements are conformations in which a protein backbone segment forms a loop closed by noncovalent interactions and that loop is threaded one or more times by either the N- or C-terminal segment of the backbone or both. While these entanglements are common in globular proteins, their presence in intrinsically disordered proteins or regions (IDPs/IDRs) remains largely unexplored. Here, we examine whether IDPs/IDRs in their monomeric form populate these conformations and how sequence length and charge composition influence entanglement prevalence. Using experimentally derived IDP/IDR ensembles from the Protein Ensemble Database, we find that 48% (199 of 416) of its entries contain subpopulations with entangled conformations, with 25% of entries having conformational ensembles in which 50% or more are entangled. This includes IDPs such as nuclear pore complex protein Nup153, nonstructural protein V of Hendra virus, and Eukaryotic initiation factor 4F subunit p150. Using molecular simulations, we find that (i) entanglements are most prevalent in weak polyampholytes and polyelectrolytes, and strong polyampholytes but rare in strong polyelectrolytes; (ii) entanglement populations increase with IDP length; (iii) entanglement probability positively correlates with chain compaction; and (iv) most IDPs/IDRs in the human proteome exhibit entangled conformations. A GO enrichment analysis reveals that the entanglement probability correlates with IDP/IDR function and subcellular localization. Thus, these findings indicate that noncovalent lasso entanglements are a widespread structural feature of IDPs/IDRs and have the potential to be biologically relevant.

Disentangling Folding from Energetic Traps in Simulations of Disordered Proteins

Protein conformational heterogeneity plays an essential role in a myriad of different biological processes. Extensive conformational heterogeneity is especially characteristic of intrinsically disordered proteins and protein regions (collectively IDRs), which lack a well-defined three-dimensional structure and instead rapidly exchange between a diverse ensemble of configurations. An emerging paradigm recognizes that the conformational biases encoded in IDR ensembles can play a central role in their biological function, necessitating understanding these sequence-ensemble relations. All-atom simulations have provided critical insight into our modern understanding of the solution behavior of IDRs. However, effectively exploring the accessible conformational space associated with large, heterogeneous ensembles is challenging. In particular, identifying poorly sampled or energetically trapped regions of disordered proteins in simulations often relies on qualitative assessment based on visual inspection of simulations and/or analysis data. These approaches, while convenient, run the risk of masking poorly sampled simulations. In this work, we present an algorithm for quantifying per-residue local conformational heterogeneity in protein simulations. Our work builds on prior work and compares the similarity between backbone dihedral angle distributions generated from molecular simulations in a limiting polymer model and across independent all-atom simulations. In this regime, the polymer model serves as a statistical reference model for extensive conformational heterogeneity in a real chain. Quantitative comparisons of probability vectors generated from these simulations reveal the extent of conformational sampling in a simulation, enabling us to distinguish between situations in which protein regions are well-sampled, poorly sampled, or folded. To demonstrate the effectiveness of this approach, we apply our algorithm to several toy, synthetic, and biological systems. Accurately assessing local conformational sampling in simulations of IDRs will help better quantify new enhanced sampling methods, ensure force field comparisons are equivalent, and provide confidence that conclusions drawn from simulations are robust.

Deep generative modeling of temperature-dependent structural ensembles of proteins

Deep learning has revolutionized protein structure prediction, but capturing conformational ensembles and structural variability remains an open challenge. While molecular dynamics (MD) is the foundation method for simulating biomolecular dynamics, it is computationally expensive. Recently, deep learning models trained on MD have made progress in generating structural ensembles at reduced cost. However, they remain limited in modeling atomistic details and, crucially, incorporating the effect of environmental factors. Here, we present aSAM (atomistic structural autoencoder model), a latent diffusion model trained on MD to generate heavy atom protein ensembles. Unlike most methods, aSAM models atoms in a latent space, greatly facilitating accurate sampling of side chain and backbone torsion angle distributions. Additionally, we extended aSAM into the first reported transferable generator conditioned on temperature, named aSAMt. Trained on the large and open mdCATH dataset, aSAMt captures temperature-dependent ensemble properties and demonstrates generalization beyond training temperatures. By comparing aSAMt ensembles to long MD simulations of fast folding proteins, we find that high-temperature training enhances the ability of deep generators to explore energy landscapes. Finally, we also show that our MD-based aSAMt can already capture experimentally observed thermal behavior of proteins. Our work is a step towards generalizable ensemble generation to complement physics-based approaches.

Molecular insights into the interaction between a disordered protein and a folded RNA

Intrinsically disordered protein regions (IDRs) are well established as contributors to intermolecular interactions and the formation of biomolecular condensates. In particular, RNA-binding proteins (RBPs) often harbor IDRs in addition to folded RNA-binding domains that contribute to RBP function. To understand the dynamic interactions of an IDR-RNA complex, we characterized the RNA-binding features of a small (68 residues), positively charged IDR-containing protein, Small ERDK-Rich Factor (SERF). At high concentrations, SERF and RNA undergo charge-driven associative phase separation to form a protein- and RNA-rich dense phase. A key advantage of this model system is that this threshold for demixing is sufficiently high that we could use solution-state biophysical methods to interrogate the stoichiometric complexes of SERF with RNA in the one-phase regime. Herein, we describe our comprehensive characterization of SERF alone and in complex with a small fragment of the HIV-1 Trans-Activation Response (TAR) RNA with complementary biophysical methods and molecular simulations. We find that this binding event is not accompanied by the acquisition of structure by either molecule; however, we see evidence for a modest global compaction of the SERF ensemble when bound to RNA. This behavior likely reflects attenuated charge repulsion within SERF via binding to the polyanionic RNA and provides a rationale for the higher-order assembly of SERF in the context of RNA. We envision that the SERF-RNA system will lower the barrier to accessing the details that support IDR-RNA interactions and likewise deepen our understanding of the role of IDR-RNA contacts in complex formation and liquid-liquid phase separation.

Molecular insights into the interaction between a disordered protein and a folded RNA

Intrinsically disordered protein regions (IDRs) are well-established as contributors to intermolecular interactions and the formation of biomolecular condensates. In particular, RNA-binding proteins (RBPs) often harbor IDRs in addition to folded RNA-binding domains that contribute to RBP function. To understand the dynamic interactions of an IDR-RNA complex, we characterized the RNA-binding features of a small (68 residues), positively charged IDR-containing protein, SERF. At high concentrations, SERF and RNA undergo charge-driven associative phase separation to form a protein- and RNA-rich dense phase. A key advantage of this model system is that this threshold for demixing is sufficiently high that we could use solution-state biophysical methods to interrogate the stoichiometric complexes of SERF with RNA in the one-phase regime. Herein, we describe our comprehensive characterization of SERF alone and in complex with a small fragment of the HIV-1 TAR RNA (TAR) with complementary biophysical methods and molecular simulations. We find that this binding event is not accompanied by the acquisition of structure by either molecule; however, we see evidence for a modest global compaction of the SERF ensemble when bound to RNA. This behavior likely reflects attenuated charge repulsion within SERF via binding to the polyanionic RNA and provides a rationale for the higher-order assembly of SERF in the context of RNA. We envision that the SERF-RNA system will lower the barrier to accessing the details that support IDR-RNA interactions and likewise deepen our understanding of the role of IDR-RNA contacts in complex formation and liquid-liquid phase separation.

Map conformational landscapes of intrinsically disordered proteins with polymer physics quantities

Disordered proteins are conformationally flexible proteins that are biologically important and have been implicated in devastating diseases such as Alzheimer's disease and cancer. Unlike stably folded structured proteins, disordered proteins sample a range of different conformations that needs to be accounted for. Here, we treat disordered proteins as polymer chains, and compute a dimensionless quantity called instantaneous shape ratio (Rs), as Rs = Ree2/Rg2, where Ree is end-to-end distance and Rg is radius of gyration. Extended protein conformations tend to have high Ree compared with Rg, and thus have high Rs values, whereas compact conformations have smaller Rs values. We use a scatter plot of Rs (representing shape) against Rg (representing size) as a simple map of conformational landscapes. We first examine the conformational landscape of simple polymer models such as Random Walk, Self-Avoiding Walk, and Gaussian Walk (GW), and we notice that all protein/polymer maps lie within the boundaries of the GW map. We thus use the GW map as a reference and, to assess conformational diversity, we compute the fraction of the GW conformations (fC) covered by each protein/polymer. Disordered proteins all have high fC scores, consistent with their disordered nature. Each disordered protein accesses a different region of the reference map, revealing differences in their conformational ensembles. We additionally examine the conformational maps of the nonviral gene delivery vector polyethyleneimine at various protonation states, and find that they resemble disordered proteins, with coverage of the reference map decreasing with increasing protonation state, indicating decreasing conformational diversity. We propose that our method of combining Rs and Rg in a scatter plot generates a simple, meaningful map of the conformational landscape of a disordered protein, which in turn can be used to assess conformational diversity of disordered proteins.

Multiphosphorylation-Dependent Recognition of Anti-pS2 Antibodies against RNA Polymerase II C-Terminal Domain Revealed by Chemical Synthesis

Phosphorylation is a major constituent of the CTD code, which describes the set of post-translational modifications on 52 repeats of a YSPTSPS consensus heptad that orchestrates the binding of regulatory proteins to the C-terminal domain (CTD) of RNA polymerase II. Phospho-specific antibodies are used to detect CTD phosphorylation patterns. However, their recognition repertoire is underexplored due to limitations in the synthesis of long multiphosphorylated peptides. Herein, we describe the development of a synthesis strategy that provides access to multiphosphorylated CTD peptides in high purity without HPLC purification for immobilization onto microtiter plates. Native chemical ligation was used to assemble 12 heptad repeats in various phosphoforms. The synthesis of >60 CTD peptides, 48-90 amino acids in length and containing up to 6 phosphosites, enabled a detailed and rapid analysis of the binding characteristics of different anti-pSer2 antibodies. The three antibodies tested showed positional selectivity with marked differences in the affinity of the antibodies for pSer2-containing peptides. Furthermore, the length of the phosphopeptides allowed a systematic analysis of the multivalent chelate-type interactions. The absence of multivalency-induced binding enhancements is probably due to the high flexibility of the CTD scaffold. The effect of clustered phosphorylation proved to be more complex. Recognition of pSer2 by anti-pSer2-antibodies can be prevented and, perhaps surprisingly, enhanced by the phosphorylation of "bystander" amino acids in the vicinity. The results have relevance for functional analysis of the CTD in cell biological experiments.

Disordered clock protein interactions and charge blocks turn an hourglass into a persistent circadian oscillator

Organismal physiology is widely regulated by the molecular circadian clock, a feedback loop composed of protein complexes whose members are enriched in intrinsically disordered regions. These regions can mediate protein-protein interactions via SLiMs, but the contribution of these disordered regions to clock protein interactions had not been elucidated. To determine the functionality of these disordered regions, we applied a synthetic peptide microarray approach to the disordered clock protein FRQ in Neurospora crassa. We identified residues required for FRQ's interaction with its partner protein FRH, the mutation of which demonstrated FRH is necessary for persistent clock oscillations but not repression of transcriptional activity. Additionally, the microarray demonstrated an enrichment of FRH binding to FRQ peptides with a net positive charge. We found that positively charged residues occurred in significant "blocks" within the amino acid sequence of FRQ and that ablation of one of these blocks affected both core clock timing and physiological clock output. Finally, we found positive charge clusters were a commonly shared molecular feature in repressive circadian clock proteins. Overall, our study suggests a mechanistic purpose for positive charge blocks and yielded insights into repressive arm protein roles in clock function.

Direct prediction of intrinsically disordered protein conformational properties from sequence

Intrinsically disordered regions (IDRs) are ubiquitous across all domains of life and play a range of functional roles. While folded domains are generally well described by a stable three-dimensional structure, IDRs exist in a collection of interconverting states known as an ensemble. This structural heterogeneity means that IDRs are largely absent from the Protein Data Bank, contributing to a lack of computational approaches to predict ensemble conformational properties from sequence. Here we combine rational sequence design, large-scale molecular simulations and deep learning to develop ALBATROSS, a deep-learning model for predicting ensemble dimensions of IDRs, including the radius of gyration, end-to-end distance, polymer-scaling exponent and ensemble asphericity, directly from sequences at a proteome-wide scale. ALBATROSS is lightweight, easy to use and accessible as both a locally installable software package and a point-and-click-style interface via Google Colab notebooks. We first demonstrate the applicability of our predictors by examining the generalizability of sequence-ensemble relationships in IDRs. Then, we leverage the high-throughput nature of ALBATROSS to characterize the sequence-specific biophysical behavior of IDRs within and between proteomes.

Protein ensemble modeling and analysis with MMMx

Proteins, especially of eukaryotes, often have disordered domains and may contain multiple folded domains whose relative spatial arrangement is distributed. The MMMx ensemble modeling and analysis toolbox (https://github.com/gjeschke/MMMx) can support the design of experiments to characterize the distributed structure of such proteins, starting from AlphaFold2 predictions or folded domain structures. Weak order can be analyzed with reference to a random coil model or to peptide chains that match the residue-specific Ramachandran angle distribution of the loop regions and are otherwise unrestrained. The deviation of the mean square end-to-end distance of chain sections from their average over sections of the same sequence length reveals localized compaction or expansion of the chain. The shape sampled by disordered chains is visualized by superposition in the principal axes frame of their inertia tensor. Ensembles of different sizes and with weighted conformers can be compared based on a similarity parameter that abstracts from the ensemble width.

SOURSOP: A Python Package for the Analysis of Simulations of Intrinsically Disordered Proteins

Conformational heterogeneity is a defining hallmark of intrinsically disordered proteins and protein regions (IDRs). The functions of IDRs and the emergent cellular phenotypes they control are associated with sequence-specific conformational ensembles. Simulations of conformational ensembles that are based on atomistic and coarse-grained models are routinely used to uncover the sequence-specific interactions that may contribute to IDR functions. These simulations are performed either independently or in conjunction with data from experiments. Functionally relevant features of IDRs can span a range of length scales. Extracting these features requires analysis routines that quantify a range of properties. Here, we describe a new analysis suite simulation analysis of unfolded regions of proteins (SOURSOP), an object-oriented and open-source toolkit designed for the analysis of simulated conformational ensembles of IDRs. SOURSOP implements several analysis routines motivated by principles in polymer physics, offering a unique collection of simple-to-use functions to characterize IDR ensembles. As an extendable framework, SOURSOP supports the development and implementation of new analysis routines that can be easily packaged and shared.

Excluded Volume and Weak Interactions in Crowded Solutions Modulate Conformations and RNA Binding of an Intrinsically Disordered Tail

The cellular milieu is a solution crowded with a significant concentration of different components (proteins, nucleic acids, metabolites, etc.). Such a crowded environment affects protein conformations, dynamics, and interactions. Intrinsically disordered proteins and regions are particularly sensitive to these effects. Here, we investigate the impact on an intrinsically disordered tail that flanks a folded domain, the N-terminal domain, and the RNA-binding domain of the SARS-CoV-2 nucleocapsid protein. We mimic the crowded environment of the cell using polyethylene glycol (PEG) and study its impact on protein conformations using single-molecule Förster resonance energy transfer. We found that high-molecular-weight PEG induces a collapse of the disordered N-terminal tail, whereas low-molecular-weight PEG induces a chain expansion. Our data can be explained by accounting for two opposing contributions: favorable interactions between the protein and crowder molecules and screening of excluded volume interactions. We further characterized the interaction between protein and RNA in the presence of crowding agents. While for all PEG molecules tested, we observed an increase in the binding affinity, the trend is not monotonic as a function of the degree of PEG polymerization. This points to the role of nonspecific protein-PEG interactions on binding in addition to the entropic effects due to crowding. To separate the enthalpic and entropic components of the effects, we investigated the temperature dependence of the association constants in the absence and presence of crowders. Finally, we compared the effects of crowding across mutations in the disordered region and found that the threefold difference in association constants for two naturally occurring variants of the SARS-CoV-2 nucleocapsid protein is reduced to almost identical affinities in the presence of crowders. Overall, our data provide new insights into understanding and modeling the contribution of crowding effects on disordered regions, including the impact of interactions between proteins and crowders and their interplay when binding a ligand.