Innovative scattering analysis shows that hydrophobic disordered proteins are expanded in water

Intramolecular structural heterogeneity altered by long-range contacts in an intrinsically disordered protein

Short-range interactions and long-range contacts drive the 3D folding of structured proteins. The proteins' structure has a direct impact on their biological function. However, nearly 40% of the eukaryotes proteome is composed of intrinsically disordered proteins (IDPs) and protein regions that fluctuate between ensembles of numerous conformations. Therefore, to understand their biological function, it is critical to depict how the structural ensemble statistics correlate to the IDPs' amino acid sequence. Here, using small-angle X-ray scattering and time-resolved Förster resonance energy transfer (trFRET), we study the intramolecular structural heterogeneity of the neurofilament low intrinsically disordered tail domain (NFLt). Using theoretical results of polymer physics, we find that the Flory scaling exponent of NFLt subsegments correlates linearly with their net charge, ranging from statistics of ideal to self-avoiding chains. Surprisingly, measuring the same segments in the context of the whole NFLt protein, we find that regardless of the peptide sequence, the segments' structural statistics are more expanded than when measured independently. Our findings show that while polymer physics can, to some level, relate the IDP's sequence to its ensemble conformations, long-range contacts between distant amino acids play a crucial role in determining intramolecular structures. This emphasizes the necessity of advanced polymer theories to fully describe IDPs ensembles with the hope that it will allow us to model their biological function.

Generation of unfolded outer membrane protein ensembles defined by hydrodynamic properties

Outer membrane proteins (OMPs) must exist as an unfolded ensemble while interacting with a chaperone network in the periplasm of Gram-negative bacteria. Here, we developed a method to model unfolded OMP (uOMP) conformational ensembles using the experimental properties of two well-studied OMPs. The overall sizes and shapes of the unfolded ensembles in the absence of a denaturant were experimentally defined by measuring the sedimentation coefficient as a function of urea concentration. We used these data to model a full range of unfolded conformations by parameterizing a targeted coarse-grained simulation protocol. The ensemble members were further refined by short molecular dynamics simulations to reflect proper torsion angles. The final conformational ensembles have polymer properties different from unfolded soluble and intrinsically disordered proteins and reveal inherent differences in the unfolded states that necessitate further investigation. Building these uOMP ensembles advances the understanding of OMP biogenesis and provides essential information for interpreting structures of uOMP-chaperone complexes.

AutoRNC: an automated modeling program for building atomic models of ribosome-nascent chain complexes

The interpretation of experimental studies of co-translational protein folding often benefits from the use of computational methods that seek to model the nascent chain and its interactions with the ribosome. Ribosome-nascent chain (RNC) constructs studied experimentally can vary significantly in size and the extent to which they contain secondary and tertiary structure, and building realistic 3D models of them therefore often requires expert knowledge. To circumvent this issue, we describe here AutoRNC, an automated modeling program capable of constructing large numbers of plausible atomic models of RNCs within minutes. AutoRNC takes input from the user specifying any regions of the nascent chain that contain secondary or tertiary structure and attempts to build conformations compatible with those specifications - and with the constraints imposed by the ribosome - by sampling and progressively piecing together dipeptide conformations extracted from the RCSB. We first show that conformations of completely unfolded proteins built by AutoRNC in the absence of the ribosome have radii of gyration that match well with the corresponding experimental data. We then show that AutoRNC can build plausible conformations for a wide range of RNC constructs for which experimental data have already been reported. Since AutoRNC requires only modest computational resources, we anticipate that it will prove to be a useful hypothesis generator for experimental studies, for example, in providing indications of whether designed constructs are likely to be capable of folding, as well as providing useful starting points for downstream atomic or coarse-grained simulations of the conformational dynamics of RNCs.

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

Denatured, unfolded, and intrinsically disordered proteins (collectively referred to here as unfolded proteins) can be described using analytical polymer models. These models capture various polymeric properties and can be fit to simulation results or experimental data. However, the model parameters commonly require users' decisions, making them useful for data interpretation but less clearly applicable as stand-alone reference models. Here we use all-atom simulations of polypeptides in conjunction with polymer scaling theory to parameterize an analytical model of unfolded polypeptides that behave as ideal chains (ν = 0.50). The model, which we call the analytical Flory random coil (AFRC), requires only the amino acid sequence as input and provides direct access to probability distributions of global and local conformational order parameters. The model defines a specific reference state to which experimental and computational results can be compared and normalized. As a proof-of-concept, we use the AFRC to identify sequence-specific intramolecular interactions in simulations of disordered proteins. We also use the AFRC to contextualize a curated set of 145 different radii of gyration obtained from previously published small-angle X-ray scattering experiments of disordered proteins. The AFRC is implemented as a stand-alone software package and is also available via a Google Colab notebook. In summary, the AFRC provides a simple-to-use reference polymer model that can guide intuition and aid in interpreting experimental or simulation results.

The Action of Chemical Denaturants: From Globular to Intrinsically Disordered Proteins

Proteins perform their many functions by adopting either a minimal number of strictly similar conformations, the native state, or a vast ensemble of highly flexible conformations. In both cases, their structural features are highly influenced by the chemical environment. Even though a plethora of experimental studies have demonstrated the impact of chemical denaturants on protein structure, the molecular mechanism underlying their action is still debated. In the present review, after a brief recapitulation of the main experimental data on protein denaturants, we survey both classical and more recent interpretations of the molecular basis of their action. In particular, we highlight the differences and similarities of the impact that denaturants have on different structural classes of proteins, i.e., globular, intrinsically disordered (IDP), and amyloid-like assemblies. Particular attention has been given to the IDPs, as recent studies are unraveling their fundamental importance in many physiological processes. The role that computation techniques are expected to play in the near future is illustrated.

Interaction of the tau fibrils with the neuronal membrane

Tau proteins are recently gaining a lot of interest due to their active role in causing a range of tauopathies. Molecular mechanisms underlying the tau interaction with the neuronal membrane are hitherto unknown and difficult to characterize using experimental methods. Using the cryo-EM structure of the tau-fibrils we have used atomistic molecular dynamics simulation to model the tau fibril and neuronal membrane interaction using explicit solvation. The dynamics and structural characteristics of the tau fibril with the neuronal membrane are compared to the tau fibril in the aqueous phase to corroborate the effect of the neuronal membrane in the tau structure. Tau fibrils have been modelled using CHARMM-36m force field and the six component neuronal membrane composition is taken from the earlier simulation results. The timescale conceivable in our molecular dynamics simulations is of the order of microseconds which captures the onset of the interaction of the tau fibrils with the neuronal membrane. This interaction is found to impact the tau pathogenesis that finally causes neuronal toxicity. Our study initiates the understanding of tau conformational ensemble in the presence of neuronal membrane and sheds the light on the significant tau-membrane interactions.

Interpreting Transient Interactions of Intrinsically Disordered Proteins

The flexible nature of intrinsically disordered proteins (IDPs) gives rise to a conformational ensemble with a diverse set of conformations. The simplest way to describe this ensemble is through a homopolymer model without any specific interactions. However, there has been growing evidence that the conformational properties of IDPs and their relevant functions can be affected by transient interactions between specific and even nonlocal pairs of amino acids. Interpreting these interactions from experimental methods, each of which is most sensitive to a different distance regime referred to as probing length, remains a challenging and unsolved problem. Here, we first show that transient interactions can be realized between short fragments of charged amino acids by generating conformational ensembles using model disordered peptides and coarse-grained simulations. Using these ensembles, we investigate how sensitive different types of experimental measurements are to the presence of transient interactions. We find methods with shorter probing lengths to be more appropriate for detecting these transient interactions, but one experimental method is not sufficient due to the existence of other weak interactions typically seen in IDPs. Finally, we develop an adjusted polymer model with an additional short-distance peak which can robustly reproduce the distance distribution function from two experimental measurements with complementary short and long probing lengths. This new model can suggest whether a homopolymer model is insufficient for describing a specific IDP and meets the challenge of quantitatively identifying specific, transient interactions from a background of nonspecific, weak interactions.

Biophysical and Integrative Characterization of Protein Intrinsic Disorder as a Prime Target for Drug Discovery

Protein intrinsic disorder is increasingly recognized for its biological and disease-driven functions. However, it represents significant challenges for biophysical studies due to its high conformational flexibility. In addressing these challenges, we highlight the complementary and distinct capabilities of a range of experimental and computational methods and further describe integrative strategies available for combining these techniques. Integrative biophysics methods provide valuable insights into the sequence–structure–function relationship of disordered proteins, setting the stage for protein intrinsic disorder to become a promising target for drug discovery. Finally, we briefly summarize recent advances in the development of new small molecule inhibitors targeting the disordered N-terminal domains of three vital transcription factors.

The analytical Flory random coil is a simple-to-use reference model for unfolded and disordered proteins

Denatured, unfolded, and intrinsically disordered proteins (collectively referred to here as unfolded proteins) can be described using analytical polymer models. These models capture various polymeric properties and can be fit to simulation results or experimental data. However, the model parameters commonly require users' decisions, making them useful for data interpretation but less clearly applicable as stand-alone reference models. Here we use all-atom simulations of polypeptides in conjunction with polymer scaling theory to parameterize an analytical model of unfolded polypeptides that behave as ideal chains (ν = 0.50). The model, which we call the analytical Flory Random Coil (AFRC), requires only the amino acid sequence as input and provides direct access to probability distributions of global and local conformational order parameters. The model defines a specific reference state to which experimental and computational results can be compared and normalized. As a proof-of-concept, we use the AFRC to identify sequence-specific intramolecular interactions in simulations of disordered proteins. We also use the AFRC to contextualize a curated set of 145 different radii of gyration obtained from previously published small-angle X-ray scattering experiments of disordered proteins. The AFRC is implemented as a stand-alone software package and is also available via a Google colab notebook. In summary, the AFRC provides a simple-to-use reference polymer model that can guide intuition and aid in interpreting experimental or simulation results.

Phase Separation in Biology and Disease; Current Perspectives and Open Questions

In the past almost 15 years, we witnessed the birth of a new scientific field focused on the existence, formation, biological functions, and disease associations of membraneless bodies in cells, now referred to as biomolecular condensates. Pioneering studies from several laboratories [reviewed in1-3] supported a model wherein biomolecular condensates associated with diverse biological processes form through the process of phase separation. These and other findings that followed have revolutionized our understanding of how biomolecules are organized in space and time within cells to perform myriad biological functions, including cell fate determination, signal transduction, endocytosis, regulation of gene expression and protein translation, and regulation of RNA metabolism. Further, condensates formed through aberrant phase transitions have been associated with numerous human diseases, prominently including neurodegeneration and cancer. While in some cases, rigorous evidence supports links between formation of biomolecular condensates through phase separation and biological functions, in many others such links are less robustly supported, which has led to rightful scrutiny of the generality of the roles of phase separation in biology and disease.4-7 During a week-long workshop in March 2022 at the Telluride Science Research Center (TSRC) in Telluride, Colorado, ∼25 scientists addressed key questions surrounding the biomolecular condensates field. Herein, we present insights gained through these discussions, addressing topics including, roles of condensates in diverse biological processes and systems, and normal and disease cell states, their applications to synthetic biology, and the potential for therapeutically targeting biomolecular condensates.

Deep mining of the protein energy landscape

For over half a century, it has been known that protein molecules naturally undergo extensive structural fluctuations, and that these internal motions are intimately related to their functional properties. The energy landscape view has provided a powerful framework for describing the various physical states that proteins visit during their lifetimes. This Perspective focuses on the commonly neglected and often disparaged axis of the protein energy landscape: entropy. Initially seen largely as a barrier to functionally relevant states of protein molecules, it has recently become clear that proteins retain considerable conformational entropy in the "native" state, and that this entropy can and often does contribute significantly to the free energy of fundamental protein properties, processes, and functions. NMR spectroscopy, molecular dynamics simulations, and emerging crystallographic views have matured in parallel to illuminate dynamic disorder of the "ground state" of proteins and their importance in not only transiting between biologically interesting structures but also greatly influencing their stability, cooperativity, and contribution to critical properties such as allostery.

The Role of Transient Intermediate Structures in the Unfolding of the Trp-Cage Fast-Folding Protein: Generating Ensembles from Time-Resolved X-ray Solution Scattering with Genetic Algorithms

The Trp-cage miniprotein is one of the smallest systems to exhibit a stable secondary structure and fast-folding dynamics, serving as an apt model system to study transient intermediates with both experimental and computational analyses. Previous spectroscopic characterizations that have been done on Trp-cage have inferred a single stable intermediate on a pathway from folded to unfolded basins. We aim to bridge the understanding of Trp-cage structural folding dynamics on microsecond-time scales, by utilizing time-resolved X-ray solution scattering to probe the temperature-induced unfolding pathway. Our results indicate the formation of a conformationally extended intermediate on the time scale of 1 μs, which undergoes complete unfolding within 5 μs. We further investigated the atomistic structural details of the unfolding pathway using a genetic algorithm to generate ensemble model fits to the scattering profiles. This analysis paves the way for direct benchmarking of theoretical models of protein folding ensembles produced with molecular dynamics simulations.

Factors That Control the Force Needed to Unfold a Membrane Protein in Silico Depend on the Mode of Denaturation

Single-molecule force spectroscopy methods, such as AFM and magnetic tweezers, have proved extremely beneficial in elucidating folding pathways for soluble and membrane proteins. To identify factors that determine the force rupture levels in force-induced membrane protein unfolding, we applied our near-atomic-level Upside molecular dynamics package to study the vertical and lateral pulling of bacteriorhodopsin (bR) and GlpG, respectively. With our algorithm, we were able to selectively alter the magnitudes of individual interaction terms and identify that, for vertical pulling, hydrogen bond strength had the strongest effect, whereas other non-bonded protein and membrane-protein interactions had only moderate influences, except for the extraction of the last helix where the membrane-protein interactions had a stronger influence. The up-down topology of the transmembrane helices caused helices to be pulled out as pairs. The rate-limiting rupture event often was the loss of H-bonds and the ejection of the first helix, which then propagated tension to the second helix, which rapidly exited the bilayer. The pulling of the charged linkers across the membrane had minimal influence, as did changing the bilayer thickness. For the lateral pulling of GlpG, the rate-limiting rupture corresponded to the separation of the helices within the membrane, with the H-bonds generally being broken only afterward. Beyond providing a detailed picture of the rupture events, our study emphasizes that the pulling mode greatly affects the factors that determine the forces needed to unfold a membrane protein.

Improved predictions of phase behaviour of intrinsically disordered proteins by tuning the interaction range

The formation and viscoelastic properties of condensates of intrinsically disordered proteins (IDPs) is dictated by amino acid sequence and solution conditions. Because of the involvement of biomolecular condensates in cell physiology and disease, advancing our understanding of the relationship between protein sequence and phase separation (PS) may have important implications in the formulation of new therapeutic hypotheses. Here, we present CALVADOS 2, a coarse-grained model of IDPs that accurately predicts conformational properties and propensities to undergo PS for diverse sequences and solution conditions. In particular, we systematically study the effect of varying the range of the nonionic interactions and use our findings to improve the temperature scale of the model. We further optimize the residue-specific model parameters against experimental data on the conformational properties of 55 proteins, while also leveraging 70 hydrophobicity scales from the literature to avoid overfitting the training data. Extensive testing shows that the model accurately predicts chain compaction and PS propensity for sequences of diverse length and charge patterning, as well as at different temperatures and salt concentrations.

Assessment of models for calculating the hydrodynamic radius of intrinsically disordered proteins

Diffusion measurements by pulsed-field gradient NMR and fluorescence correlation spectroscopy can be used to probe the hydrodynamic radius of proteins, which contains information about the overall dimension of a protein in solution. The comparison of this value with structural models of intrinsically disordered proteins is nonetheless impaired by the uncertainty of the accuracy of the methods for computing the hydrodynamic radius from atomic coordinates. To tackle this issue, we here build conformational ensembles of 11 intrinsically disordered proteins that we ensure are in agreement with measurements of compaction by small-angle x-ray scattering. We then use these ensembles to identify the forward model that more closely fits the radii derived from pulsed-field gradient NMR diffusion experiments. Of the models we examined, we find that the Kirkwood-Riseman equation provides the best description of the hydrodynamic radius probed by pulsed-field gradient NMR experiments. While some minor discrepancies remain, our results enable better use of measurements of the hydrodynamic radius in integrative modeling and for force field benchmarking and parameterization.

Improved predictions of phase behaviour of intrinsically disordered proteins by tuning the interaction range

The formation and viscoelastic properties of condensates of intrinsically disordered proteins (IDPs) is dictated by amino acid sequence and solution conditions. Because of the involvement of biomolecular condensates in cell physiology and disease, advancing our understanding of the relationship between protein sequence and phase separation (PS) may have important implications in the formulation of new therapeutic hypotheses. Here, we present CALVADOS 2, a coarse-grained model of IDPs that accurately predicts conformational properties and propensities to undergo PS for diverse sequences and solution conditions. In particular, we systematically study the effect of varying the range of the nonionic interactions and use our findings to improve the temperature scale of the model. We further optimize the residue-specific model parameters against experimental data on the conformational properties of 55 proteins, while also leveraging 70 hydrophobicity scales from the literature to avoid overfitting the training data. Extensive testing shows that the model accurately predicts chain compaction and PS propensity for sequences of diverse length and charge patterning, as well as at different temperatures and salt concentrations.

The Protein Unfolded State: One, No One and One Hundred Thousand

Many in vitro studies, in which proteins have been unfolded by the action of a variety of physical or chemical agents, have led to the definition of a folded versus an unfolded state and to the question of what is the nature of the unfolded state. The unstructured nature of this state could suggest that "the" unfolded state is a unique entity which holds true for all kinds of unfolding processes. This assumption has to be questioned because the unfolding processes under different stress conditions are dictated by entirely different mechanisms. As a consequence, it can be easily understood that the final state, generically referred to as "the unfolded state", can be completely different for each of the unfolding processes. The present review examines recent data on the characteristics of the unfolded states emerging from experiments under different conditions, focusing specific attention to the level of compaction of the unfolded species.

Condensates formed by prion-like low-complexity domains have small-world network structures and interfaces defined by expanded conformations

Biomolecular condensates form via coupled associative and segregative phase transitions of multivalent associative macromolecules. Phase separation coupled to percolation is one example of such transitions. Here, we characterize molecular and mesoscale structural descriptions of condensates formed by intrinsically disordered prion-like low complexity domains (PLCDs). These systems conform to sticker-and-spacers architectures. Stickers are cohesive motifs that drive associative interactions through reversible crosslinking and spacers affect the cooperativity of crosslinking and overall macromolecular solubility. Our computations reproduce experimentally measured sequence-specific phase behaviors of PLCDs. Within simulated condensates, networks of reversible inter-sticker crosslinks organize PLCDs into small-world topologies. The overall dimensions of PLCDs vary with spatial location, being most expanded at and preferring to be oriented perpendicular to the interface. Our results demonstrate that even simple condensates with one type of macromolecule feature inhomogeneous spatial organizations of molecules and interfacial features that likely prime them for biochemical activity.

Protein structural transitions critically transform the network connectivity and viscoelasticity of RNA-binding protein condensates but RNA can prevent it

Biomolecular condensates, some of which are liquid-like during health, can age over time becoming gel-like pathological systems. One potential source of loss of liquid-like properties during ageing of RNA-binding protein condensates is the progressive formation of inter-protein β-sheets. To bridge microscopic understanding between accumulation of inter-protein β-sheets over time and the modulation of FUS and hnRNPA1 condensate viscoelasticity, we develop a multiscale simulation approach. Our method integrates atomistic simulations with sequence-dependent coarse-grained modelling of condensates that exhibit accumulation of inter-protein β-sheets over time. We reveal that inter-protein β-sheets notably increase condensate viscosity but does not transform the phase diagrams. Strikingly, the network of molecular connections within condensates is drastically altered, culminating in gelation when the network of strong β-sheets fully percolates. However, high concentrations of RNA decelerate the emergence of inter-protein β-sheets. Our study uncovers molecular and kinetic factors explaining how the accumulation of inter-protein β-sheets can trigger liquid-to-solid transitions in condensates, and suggests a potential mechanism to slow such transitions down.

In this work the authors propose a multiscale computational approach, integrating atomistic and coarse-grained models simulations, to study the thermodynamic and kinetic factors playing a major role in the liquid-to-solid transition of biomolecular condensates. It is revealed how the gradual accumulation of inter-protein β-sheets increases the viscosity of functional liquid-like condensates, transforming them into gel-like pathological aggregates, and it is also shown how high concentrations of RNA can decelerate such transition.

Post-translational modifications in liquid-liquid phase separation: a comprehensive review

Liquid-liquid phase separation (LLPS) has received significant attention in recent biological studies. It refers to a phenomenon that biomolecule exceeds the solubility, condensates and separates itself from solution in liquid like droplets formation. Our understanding of it has also changed from memebraneless organelles to compartmentalization, muti-functional crucibles, and reaction regulators. Although this phenomenon has been employed for a variety of biological processes, recent studies mainly focus on its physiological significance, and the comprehensive research of the underlying physical mechanism is limited. The characteristics of side chains of amino acids and the interaction tendency of proteins function importantly in regulating LLPS thus should be pay more attention on. In addition, the importance of post-translational modifications (PTMs) has been underestimated, despite their abundance and crucial functions in maintaining the electrostatic balance. In this review, we first introduce the driving forces and protein secondary structures involved in LLPS and their different physical functions in cell life processes. Subsequently, we summarize the existing reports on PTM regulation related to LLPS and analyze the underlying basic principles, hoping to find some common relations between LLPS and PTM. Finally, we speculate several unreported PTMs that may have a significant impact on phase separation basing on the findings.

Rules of Physical Mathematics Govern Intrinsically Disordered Proteins

In stark contrast to foldable proteins with a unique folded state, intrinsically disordered proteins and regions (IDPs) persist in perpetually disordered ensembles. Yet an IDP ensemble has conformational features-even when averaged-that are specific to its sequence. In fact, subtle changes in an IDP sequence can modulate its conformational features and its function. Recent advances in theoretical physics reveal a set of elegant mathematical expressions that describe the intricate relationships among IDP sequences, their ensemble conformations, and the regulation of their biological functions. These equations also describe the molecular properties of IDP sequences that predict similarities and dissimilarities in their functions and facilitate classification of sequences by function, an unmet challenge to traditional bioinformatics. These physical sequence-patterning metrics offer a promising new avenue for advancing synthetic biology at a time when multiple novel functional modes mediated by IDPs are emerging.

Residual Structure in the Denatured State of the Fast-Folding UBA(1) Domain from the Human DNA Excision Repair Protein HHR23A

The structure of the first ubiquitin-associated domain from HHR23A, UBA(1), was determined by X-ray crystallography at a 1.60 Å resolution, and its stability, folding kinetics, and residual structure under denaturing conditions have been investigated. The concentration dependence of thermal denaturation and size-exclusion chromatography indicate that UBA(1) is monomeric. Guanidine hydrochloride (GdnHCl) denaturation experiments reveal that the unfolding free energy, ΔGu°'(H2O), of UBA(1) is 2.4 kcal mol-1. Stopped-flow folding kinetics indicates sub-millisecond folding with only proline isomerization phases detectable at 25 °C. The full folding kinetics are observable at 4 °C, yielding a folding rate constant, kf, in the absence of a denaturant of 13,000 s-1 and a Tanford β-value of 0.80, consistent with a compact transition state. Evaluation of the secondary structure via circular dichroism shows that the residual helical structure in the denatured state is replaced by polyproline II structure as the GdnHCl concentration increases. Analysis of NMR secondary chemical shifts for backbone 15NH, 13CO, and 13Cα atoms between 4 and 7 M GdnHCl shows three islands of residual helical secondary structure that align in sequence with the three native-state helices. Extrapolation of the NMR data to 0 M GdnHCl demonstrates that helical structure would populate to 17-33% in the denatured state under folding conditions. Comparison with NMR data for a peptide corresponding to helix 1 indicates that this helix is stabilized by transient tertiary interactions in the denatured state of UBA(1). The high helical content in the denatured state, which is enhanced by transient tertiary interactions, suggests a diffusion-collision folding mechanism.

NMR Provides Unique Insight into the Functional Dynamics and Interactions of Intrinsically Disordered Proteins

Intrinsically disordered proteins are ubiquitous throughout all known proteomes, playing essential roles in all aspects of cellular and extracellular biochemistry. To understand their function, it is necessary to determine their structural and dynamic behavior and to describe the physical chemistry of their interaction trajectories. Nuclear magnetic resonance is perfectly adapted to this task, providing ensemble averaged structural and dynamic parameters that report on each assigned resonance in the molecule, unveiling otherwise inaccessible insight into the reaction kinetics and thermodynamics that are essential for function. In this review, we describe recent applications of NMR-based approaches to understanding the conformational energy landscape, the nature and time scales of local and long-range dynamics and how they depend on the environment, even in the cell. Finally, we illustrate the ability of NMR to uncover the mechanistic basis of functional disordered molecular assemblies that are important for human health.

Improving Martini 3 for Disordered and Multidomain Proteins

Coarse-grained molecular dynamics simulations are a useful tool to determine conformational ensembles of proteins. Here, we show that the coarse-grained force field Martini 3 underestimates the global dimensions of intrinsically disordered proteins (IDPs) and multidomain proteins when compared with small-angle X-ray scattering (SAXS) data and that increasing the strength of protein-water interactions favors more expanded conformations. We find that increasing the strength of interactions between protein and water by ca. 10% results in improved agreement with the SAXS data for IDPs and multidomain proteins. We also show that this correction results in a more accurate description of self-association of IDPs and folded proteins and better agreement with paramagnetic relaxation enhancement data for most IDPs. While simulations with this revised force field still show deviations to experiments for some systems, our results suggest that it is overall a substantial improvement for coarse-grained simulations of soluble proteins.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

Modeling the Structure and Interactions of Intrinsically Disordered Peptides with Multiple Replica, Metadynamics-Based Sampling Methods and Force-Field Combinations

Intrinsically disordered proteins play a key role in many biological processes, including the formation of biomolecular condensates within cells. A detailed characterization of their configurational ensemble and structure-function paradigm is crucial for understanding their biological activity and for exploiting them as building blocks in material sciences. In this work, we incorporate bias-exchange metadynamics and parallel-tempering well-tempered metadynamics with CHARMM36m and CHARMM22* to explore the structural and thermodynamic characteristics of a short archetypal disordered sequence derived from a DEAD-box protein. The conformational landscapes emerging from our simulations are largely congruent across methods and force fields. Nevertheless, differences in fine details emerge from varying combinations of force-fields and sampling methods. For this protein, our analysis identifies features that help to explain the low propensity of this sequence to undergo self-association in vitro, which are common to all force-field/sampling method combinations. Overall, our work demonstrates the importance of using multiple force-field and sampling method combinations for accurate structural and thermodynamic information in the study of disordered proteins.

Protein chain collapse modulation and folding stimulation by GroEL-ES

The collapse of polypeptides is thought important to protein folding, aggregation, intrinsic disorder, and phase separation. However, whether polypeptide collapse is modulated in cells to control protein states is unclear. Here, using integrated protein manipulation and imaging, we show that the chaperonin GroEL-ES can accelerate the folding of proteins by strengthening their collapse. GroEL induces contractile forces in substrate chains, which draws them into the cavity and triggers a general compaction and discrete folding transitions, even for slow-folding proteins. This collapse enhancement is strongest in the nucleotide-bound states of GroEL and is aided by GroES binding to the cavity rim and by the amphiphilic C-terminal tails at the cavity bottom. Collapse modulation is distinct from other proposed GroEL-ES folding acceleration mechanisms, including steric confinement and misfold unfolding. Given the prevalence of collapse throughout the proteome, we conjecture that collapse modulation is more generally relevant within the protein quality control machinery.

Deciphering how naturally occurring sequence features impact the phase behaviours of disordered prion-like domains

Prion-like low-complexity domains (PLCDs) have distinctive sequence grammars that determine their driving forces for phase separation. Here we uncover the physicochemical underpinnings of how evolutionarily conserved compositional biases influence the phase behaviour of PLCDs. We interpret our results in the context of the stickers-and-spacers model for the phase separation of associative polymers. We find that tyrosine is a stronger sticker than phenylalanine, whereas arginine is a context-dependent auxiliary sticker. In contrast, lysine weakens sticker-sticker interactions. Increasing the net charge per residue destabilizes phase separation while also weakening the strong coupling between single-chain contraction in dilute phases and multichain interactions that give rise to phase separation. Finally, glycine and serine residues act as non-equivalent spacers, and thus make the glycine versus serine contents an important determinant of the driving forces for phase separation. The totality of our results leads to a set of rules that enable comparative estimates of composition-specific driving forces for PLCD phase separation.

Deciphering how naturally occurring sequence features impact the phase behaviours of disordered prion-like domains

Prion-like low-complexity domains (PLCDs) have distinctive sequence grammars that determine their driving forces for phase separation. Here we uncover the physicochemical underpinnings of how evolutionarily conserved compositional biases influence the phase behaviour of PLCDs. We interpret our results in the context of the stickers-and-spacers model for the phase separation of associative polymers. We find that tyrosine is a stronger sticker than phenylalanine, whereas arginine is a context-dependent auxiliary sticker. In contrast, lysine weakens sticker-sticker interactions. Increasing the net charge per residue destabilizes phase separation while also weakening the strong coupling between single-chain contraction in dilute phases and multichain interactions that give rise to phase separation. Finally, glycine and serine residues act as non-equivalent spacers, and thus make the glycine versus serine contents an important determinant of the driving forces for phase separation. The totality of our results leads to a set of rules that enable comparative estimates of composition-specific driving forces for PLCD phase separation.

Lipid bilayer induces contraction of the denatured state ensemble of a helical-bundle membrane protein

Defining the denatured state ensemble (DSE) and disordered proteins is essential to understanding folding, chaperone action, degradation, and translocation. As compared with water-soluble proteins, the DSE of membrane proteins is much less characterized. Here, we measure the DSE of the helical membrane protein GlpG of Escherichia coli (E. coli) in native-like lipid bilayers. The DSE was obtained using our steric trapping method, which couples denaturation of doubly biotinylated GlpG to binding of two streptavidin molecules. The helices and loops are probed using limited proteolysis and mass spectrometry, while the dimensions are determined using our paramagnetic biotin derivative and double electron-electron resonance spectroscopy. These data, along with our Upside simulations, identify the DSE as being highly dynamic, involving the topology changes and unfolding of some of the transmembrane (TM) helices. The DSE is expanded relative to the native state but only to 15 to 75% of the fully expanded condition. The degree of expansion depends on the local protein packing and the lipid composition. E. coli's lipid bilayer promotes the association of TM helices in the DSE and, probably in general, facilitates interhelical interactions. This tendency may be the outcome of a general lipophobic effect of proteins within the cell membranes.

Synergies of Single Molecule Fluorescence and NMR for the Study of Intrinsically Disordered Proteins

Single molecule fluorescence and nuclear magnetic resonance spectroscopy (NMR) are two very powerful techniques for the analysis of intrinsically disordered proteins (IDPs). Both techniques have individually made major contributions to deciphering the complex properties of IDPs and their interactions, and it has become evident that they can provide very complementary views on the distance-dynamics relationships of IDP systems. We now review the first approaches using both NMR and single molecule fluorescence to decipher the molecular properties of IDPs and their interactions. We shed light on how these two techniques were employed synergistically for multidomain proteins harboring intrinsically disordered linkers, for veritable IDPs, but also for liquid–liquid phase separated systems. Additionally, we provide insights into the first approaches to use single molecule Förster resonance energy transfer (FRET) and NMR for the description of multiconformational models of IDPs.

Quantitative Description of Intrinsically Disordered Proteins Using Single-Molecule FRET, NMR, and SAXS

Studying the conformational landscape of intrinsically disordered and partially folded proteins is challenging and only accessible to a few solution state techniques, such as nuclear magnetic resonance (NMR), small-angle scattering techniques, and single-molecule Förster resonance energy transfer (smFRET). While each of the techniques is sensitive to different properties of the disordered chain, such as local structural propensities, overall dimension, or intermediate- and long-range contacts, conformational ensembles describing intrinsically disordered proteins (IDPs) accurately should ideally respect all of these properties. Here we develop an integrated approach using a large set of FRET efficiencies and fluorescence lifetimes, NMR chemical shifts, and paramagnetic relaxation enhancements (PREs), as well as small-angle X-ray scattering (SAXS) to derive quantitative conformational ensembles in agreement with all parameters. Our approach is tested using simulated data (five sets of PREs and 15 FRET efficiencies) and validated experimentally on the example of the disordered domain of measles virus phosphoprotein, providing new insights into the conformational landscape of this viral protein that comprises transient structural elements and is more compact than an unfolded chain throughout its length. Rigorous cross-validation using FRET efficiencies, fluorescence lifetimes, and SAXS demonstrates the predictive nature of the calculated conformational ensembles and underlines the potential of this strategy in integrative dynamic structural biology.

'RNA modulation of transport properties and stability in phase-separated condensates

One of the key mechanisms employed by cells to control their spatiotemporal organization is the formation and dissolution of phase-separated condensates. The balance between condensate assembly and disassembly can be critically regulated by the presence of RNA. In this work, we use a chemically-accurate sequence-dependent coarse-grained model for proteins and RNA to unravel the impact of RNA in modulating the transport properties and stability of biomolecular condensates. We explore the phase behavior of several RNA-binding proteins such as FUS, hnRNPA1, and TDP-43 proteins along with that of their corresponding prion-like domains and RNA recognition motifs from absence to moderately high RNA concentration. By characterizing the phase diagram, key molecular interactions, surface tension, and transport properties of the condensates, we report a dual RNA-induced behavior: on the one hand, RNA enhances phase separation at low concentration as long as the RNA radius of gyration is comparable to that of the proteins, whereas at high concentration, it inhibits the ability of proteins to self-assemble independently of its length. On the other hand, along with the stability modulation, the viscosity of the condensates can be considerably reduced at high RNA concentration as long as the length of the RNA chains is shorter than that of the proteins. Conversely, long RNA strands increase viscosity even at high concentration, but barely modify protein self-diffusion which mainly depends on RNA concentration and on the effect RNA has on droplet density. On the whole, our work rationalizes the different routes by which RNA can regulate phase separation and condensate dynamics, as well as the subsequent aberrant rigidification implicated in the emergence of various neuropathologies and age-related diseases.

'RNA modulation of transport properties and stability in phase-separated condensates

One of the key mechanisms employed by cells to control their spatiotemporal organization is the formation and dissolution of phase-separated condensates. The balance between condensate assembly and disassembly can be critically regulated by the presence of RNA. In this work, we use a chemically-accurate sequence-dependent coarse-grained model for proteins and RNA to unravel the impact of RNA in modulating the transport properties and stability of biomolecular condensates. We explore the phase behavior of several RNA-binding proteins such as FUS, hnRNPA1, and TDP-43 proteins along with that of their corresponding prion-like domains and RNA recognition motifs from absence to moderately high RNA concentration. By characterizing the phase diagram, key molecular interactions, surface tension, and transport properties of the condensates, we report a dual RNA-induced behavior: on the one hand, RNA enhances phase separation at low concentration as long as the RNA radius of gyration is comparable to that of the proteins, whereas at high concentration, it inhibits the ability of proteins to self-assemble independently of its length. On the other hand, along with the stability modulation, the viscosity of the condensates can be considerably reduced at high RNA concentration as long as the length of the RNA chains is shorter than that of the proteins. Conversely, long RNA strands increase viscosity even at high concentration, but barely modify protein self-diffusion which mainly depends on RNA concentration and on the effect RNA has on droplet density. On the whole, our work rationalizes the different routes by which RNA can regulate phase separation and condensate dynamics, as well as the subsequent aberrant rigidification implicated in the emergence of various neuropathologies and age-related diseases.

Refining conformational ensembles of flexible proteins against small-angle x-ray scattering data

Intrinsically disordered proteins and flexible regions in multidomain proteins display substantial conformational heterogeneity. Characterizing the conformational ensembles of these proteins in solution typically requires combining one or more biophysical techniques with computational modeling or simulations. Experimental data can either be used to assess the accuracy of a computational model or to refine the computational model to get a better agreement with the experimental data. In both cases, one generally needs a so-called forward model (i.e., an algorithm to calculate experimental observables from individual conformations or ensembles). In many cases, this involves one or more parameters that need to be set, and it is not always trivial to determine the optimal values or to understand the impact on the choice of parameters. For example, in the case of small-angle x-ray scattering (SAXS) experiments, many forward models include parameters that describe the contribution of the hydration layer and displaced solvent to the background-subtracted experimental data. Often, one also needs to fit a scale factor and a constant background for the SAXS data but across the entire ensemble. Here, we present a protocol to dissect the effect of the free parameters on the calculated SAXS intensities and to identify a reliable set of values. We have implemented this procedure in our Bayesian/maximum entropy framework for ensemble refinement and demonstrate the results on four intrinsically disordered proteins and a protein with three domains connected by flexible linkers. Our results show that the resulting ensembles can depend on the parameters used for solvent effects and suggest that these should be chosen carefully. We also find a set of parameters that work robustly across all proteins.

Accurate model of liquid-liquid phase behavior of intrinsically disordered proteins from optimization of single-chain properties

Many intrinsically disordered proteins (IDPs) may undergo liquid-liquid phase separation (LLPS) and participate in the formation of membraneless organelles in the cell, thereby contributing to the regulation and compartmentalization of intracellular biochemical reactions. The phase behavior of IDPs is sequence dependent, and its investigation through molecular simulations requires protein models that combine computational efficiency with an accurate description of intramolecular and intermolecular interactions. We developed a general coarse-grained model of IDPs, with residue-level detail, based on an extensive set of experimental data on single-chain properties. Ensemble-averaged experimental observables are predicted from molecular simulations, and a data-driven parameter-learning procedure is used to identify the residue-specific model parameters that minimize the discrepancy between predictions and experiments. The model accurately reproduces the experimentally observed conformational propensities of a set of IDPs. Through two-body as well as large-scale molecular simulations, we show that the optimization of the intramolecular interactions results in improved predictions of protein self-association and LLPS.

Accurate model of liquid-liquid phase behavior of intrinsically disordered proteins from optimization of single-chain properties

Many intrinsically disordered proteins (IDPs) may undergo liquid-liquid phase separation (LLPS) and participate in the formation of membraneless organelles in the cell, thereby contributing to the regulation and compartmentalization of intracellular biochemical reactions. The phase behavior of IDPs is sequence dependent, and its investigation through molecular simulations requires protein models that combine computational efficiency with an accurate description of intramolecular and intermolecular interactions. We developed a general coarse-grained model of IDPs, with residue-level detail, based on an extensive set of experimental data on single-chain properties. Ensemble-averaged experimental observables are predicted from molecular simulations, and a data-driven parameter-learning procedure is used to identify the residue-specific model parameters that minimize the discrepancy between predictions and experiments. The model accurately reproduces the experimentally observed conformational propensities of a set of IDPs. Through two-body as well as large-scale molecular simulations, we show that the optimization of the intramolecular interactions results in improved predictions of protein self-association and LLPS.

Beta turn propensity and a model polymer scaling exponent identify intrinsically disordered phase-separating proteins

The complex cellular milieu can spontaneously demix, or phase separate, in a process controlled in part by intrinsically disordered (ID) proteins. A protein's propensity to phase separate is thought to be driven by a preference for protein-protein over protein-solvent interactions. The hydrodynamic size of monomeric proteins, as quantified by the polymer scaling exponent (v), is driven by a similar balance. We hypothesized that mean v, as predicted by protein sequence, would be smaller for proteins with a strong propensity to phase separate. To test this hypothesis, we analyzed protein databases containing subsets of proteins that are folded, disordered, or disordered and known to spontaneously phase separate. We find that the phase-separating disordered proteins, on average, had lower calculated values of v compared with their non-phase-separating counterparts. Moreover, these proteins had a higher sequence-predicted propensity for β-turns. Using a simple, surface area-based model, we propose a physical mechanism for this difference: transient β-turn structures reduce the desolvation penalty of forming a protein-rich phase and increase exposure of atoms involved in π/sp2 valence electron interactions. By this mechanism, β-turns could act as energetically favored nucleation points, which may explain the increased propensity for turns in ID regions (IDRs) utilized biologically for phase separation. Phase-separating IDRs, non-phase-separating IDRs, and folded regions could be distinguished by combining v and β-turn propensity. Finally, we propose a new algorithm, ParSe (partition sequence), for predicting phase-separating protein regions, and which is able to accurately identify folded, disordered, and phase-separating protein regions based on the primary sequence.

Denatured State Conformational Biases in Three-Helix Bundles Containing Divergent Sequences Localize near Turns and Helix Capping Residues

Rhodopseudomonas palustris cytochrome c', a four-helix bundle, and the second ubiquitin-associated domain, UBA(2), a three-helix bundle from the human homologue of yeast Rad23, HHR23A, deviate from random coil behavior under denaturing conditions in a fold-specific manner. The random coil deviations in each of these folds occur near interhelical turns and loops in their tertiary structures. Here, we examine an additional three-helix bundle with an identical fold to UBA(2), but a highly divergent sequence, the first ubiquitin-associated domain, UBA(1), of HHR23A. We use histidine-heme loop formation methods, employing eight single histidine variants, to probe for denatured state conformational bias of a UBA(1) domain fused to the N-terminus of iso-1-cytochrome c (iso-1-Cytc). Guanidine hydrochloride (GuHCl) denaturation shows that the iso-1-Cytc domain unfolds first, followed by the UBA(1) domain. Denatured state (4 and 6 M GuHCl) histidine-heme loop formation studies show that as the size of the histidine-heme loop increases, loop stability decreases, as expected for the Jacobson-Stockmayer relationship. However, loops formed with His35, His31, and His15, of UBA(1), are 0.6-1.1 kcal/mol more stable than expected from the Jacobson-Stockmayer relationship, confirming the importance of deviations of the denatured state from random coil behavior near interhelical turns of helical domains for facilitating folding to the correct topology. For UBA(1) and UBA(2), hydrophobic clusters on either side of the turns partially explain deviations from random coil behavior; however, helix capping also appears to be important.

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.

In Silico Modeling of the Influence of Environment on Amyloid Folding Using FOD-M Model

The role of the environment in amyloid formation based on the fuzzy oil drop model (FOD) is discussed here. This model assumes that the hydrophobicity distribution within a globular protein is consistent with a 3D Gaussian (3DG) distribution. Such a distribution is interpreted as the idealized effect of the presence of a polar solvent-water. A chain with a sequence of amino acids (which are bipolar molecules) determined by evolution recreates a micelle-like structure with varying accuracy. The membrane, which is a specific environment with opposite characteristics to the polar aquatic environment, directs the hydrophobic residues towards the surface. The modification of the FOD model to the FOD-M form takes into account the specificity of the cell membrane. It consists in "inverting" the 3DG distribution (complementing the Gaussian distribution), which expresses the exposure of hydrophobic residues on the surface. It turns out that the influence of the environment for any protein (soluble or membrane-anchored) is the result of a consensus factor expressing the participation of the polar environment and the "inverted" environment. The ratio between the proportion of the aqueous and the "reversed" environment turns out to be a characteristic property of a given protein, including amyloid protein in particular. The structure of amyloid proteins has been characterized in the context of prion, intrinsically disordered, and other non-complexing proteins to cover a wider spectrum of molecules with the given characteristics based on the FOD-M model.

Integrating single-molecule spectroscopy and simulations for the study of intrinsically disordered proteins

Over the last two decades, intrinsically disordered proteins and protein regions (IDRs) have emerged from a niche corner of biophysics to be recognized as essential drivers of cellular function. Various techniques have provided fundamental insight into the function and dysfunction of IDRs. Among these techniques, single-molecule fluorescence spectroscopy and molecular simulations have played a major role in shaping our modern understanding of the sequence-encoded conformational behavior of disordered proteins. While both techniques are frequently used in isolation, when combined they offer synergistic and complementary information that can help uncover complex molecular details. Here we offer an overview of single-molecule fluorescence spectroscopy and molecular simulations in the context of studying disordered proteins. We discuss the various means in which simulations and single-molecule spectroscopy can be integrated, and consider a number of studies in which this integration has uncovered biological and biophysical mechanisms.

The Proteome Folding Problem and Cellular Proteostasis

Stunning advances have been achieved in addressing the protein folding problem, providing deeper understanding of the mechanisms by which proteins navigate energy landscapes to reach their native states and enabling powerful algorithms to connect sequence to structure. However, the realities of the in vivo protein folding problem remain a challenge to reckon with. Here, we discuss the concept of the "proteome folding problem"-the problem of how organisms build and maintain a functional proteome-by admitting that folding energy landscapes are characterized by many misfolded states and that cells must deploy a network of chaperones and degradation enzymes to minimize deleterious impacts of these off-pathway species. The resulting proteostasis network is an inextricable part of in vivo protein folding and must be understood in detail if we are to solve the proteome folding problem. We discuss how the development of computational models for the proteostasis network's actions and the relationship to the biophysical properties of the proteome has begun to offer new insights and capabilities.

On the potential of machine learning to examine the relationship between sequence, structure, dynamics and function of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) constitute a broad set of proteins with few uniting and many diverging properties. IDPs-and intrinsically disordered regions (IDRs) interspersed between folded domains-are generally characterized as having no persistent tertiary structure; instead they interconvert between a large number of different and often expanded structures. IDPs and IDRs are involved in an enormously wide range of biological functions and reveal novel mechanisms of interactions, and while they defy the common structure-function paradigm of folded proteins, their structural preferences and dynamics are important for their function. We here discuss open questions in the field of IDPs and IDRs, focusing on areas where machine learning and other computational methods play a role. We discuss computational methods aimed to predict transiently formed local and long-range structure, including methods for integrative structural biology. We discuss the many different ways in which IDPs and IDRs can bind to other molecules, both via short linear motifs, as well as in the formation of larger dynamic complexes such as biomolecular condensates. We discuss how experiments are providing insight into such complexes and may enable more accurate predictions. Finally, we discuss the role of IDPs in disease and how new methods are needed to interpret the mechanistic effects of genomic variants in IDPs.

EVALUATION OF BLOOD OXYGEN SATURATION OF HIGH JUMPERS BASED ON ISOKINETIC TEST

ABSTRACT Introduction: An isokinetic test refers to the test of the force of a muscle or muscle group during centripetal and centrifugal movements at a constant speed in the whole range of joint motion by means of a isokinetic force tester. Objective: To explore the application of the knee centripetal flexor and extensor muscle groups in the blood oxygen saturation of high jumpers. Methods: Eighteen teenage female high jumper athletes above level 2 in a city sports school were selected. Their ages was 16.89±1.02 years old; height, 168.31±6.32cm; weight, 55.36±6.75kg. Results: At 60° S and 120° S test speed, the peak moment of the extensor muscle group on the same side of the knee was significantly greater than that of the flexor muscle group (P<0.05), while at 240° S test speed, it was the opposite. There was a significant difference in the peak moment of the flexor muscle group on the left and right side of the knee (P<0.01). Conclusions: The function of the dynamic muscle strength test system is one of the methods of studying the human muscle function. and can be used to test and evaluate the general strength of athletes. Level of evidence II; Therapeutic studies - investigation of treatment results.