Statistical coil model of the unfolded state: resolving the reconciliation problem

Wet Conformation of Prion-Like Domain and Intimate Correlation of Hydration and Conformational Fluctuations

Proteins with prion-like domains (PLDs) are involved in neurodegeneration-associated aggregation and are prevalent in liquid-like membrane-less organelles. These PLDs contain amyloidogenic stretches but can maintain dynamic disordered conformations, even in the condensed phase. However, the molecular mechanism underlying such intricate conformational properties of PLDs remains elusive. Here we employed molecular dynamics simulations to investigate the conformational properties of a prototypical PLD system (i.e., FUS PLD). According to our simulation results, PLD adopts a wet collapsed conformation, wherein most residues maintain sufficient hydration with the abundance of internal water. These internal water molecules can rapidly exchange between the protein interior and the bulk, enabling intensive coupling of the entire protein with its hydration environment. The dynamic exchange of water molecules is intimately correlated to the overall conformational fluctuations of PLD. Furthermore, the abundance of dynamic internal water suppresses the formation of aggregation-prone ordered structures. These results collectively elucidate the crucial role of internal water in sustaining the dynamic disordered conformation of the PLD and inhibiting its aggregation propensity.

Proline Analogues

Within the canonical repertoire of the amino acid involved in protein biogenesis, proline plays a unique role as an amino acid presenting a modified backbone rather than a side-chain. Chemical structures that mimic proline but introduce changes into its specific molecular features are defined as proline analogues. This review article summarizes the existing chemical, physicochemical, and biochemical knowledge about this peculiar family of structures. We group proline analogues from the following compounds: substituted prolines, unsaturated and fused structures, ring size homologues, heterocyclic, e.g., pseudoproline, and bridged proline-resembling structures. We overview (1) the occurrence of proline analogues in nature and their chemical synthesis, (2) physicochemical properties including ring conformation and cis/trans amide isomerization, (3) use in commercial drugs such as nirmatrelvir recently approved against COVID-19, (4) peptide and protein synthesis involving proline analogues, (5) specific opportunities created in peptide engineering, and (6) cases of protein engineering with the analogues. The review aims to provide a summary to anyone interested in using proline analogues in systems ranging from specific biochemical setups to complex biological systems.

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 or simulate the nascent chain and its interactions with the ribosome. Building realistic 3D models of ribosome-nascent chain (RNC) constructs often requires expert knowledge, so 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 Research Collaboratory for Structural Bioinformatics Protein Data Bank (RCSB). Despite using only modest computational resources, we show here that AutoRNC can build plausible conformations for a wide range of RNC constructs for which experimental data have already been reported.

How hydrophobicity, side chains, and salt affect the dimensions of disordered proteins

Despite the generally accepted role of the hydrophobic effect as the driving force for folding, many intrinsically disordered proteins (IDPs), including those with hydrophobic content typical of foldable proteins, behave nearly as self-avoiding random walks (SARWs) under physiological conditions. Here, we tested how temperature and ionic conditions influence the dimensions of the N-terminal domain of pertactin (PNt), an IDP with an amino acid composition typical of folded proteins. While PNt contracts somewhat with temperature, it nevertheless remains expanded over 10-58°C, with a Flory exponent, ν, >0.50. Both low and high ionic strength also produce contraction in PNt, but this contraction is mitigated by reducing charge segregation. With 46% glycine and low hydrophobicity, the reduced form of snow flea anti-freeze protein (red-sfAFP) is unaffected by temperature and ionic strength and persists as a near-SARW, ν ~ 0.54, arguing that the thermal contraction of PNt is due to stronger interactions between hydrophobic side chains. Additionally, red-sfAFP is a proxy for the polypeptide backbone, which has been thought to collapse in water. Increasing the glycine segregation in red-sfAFP had minimal effect on ν. Water remained a good solvent even with 21 consecutive glycine residues (ν > 0.5), and red-sfAFP variants lacked stable backbone hydrogen bonds according to hydrogen exchange. Similarly, changing glycine segregation has little impact on ν in other glycine-rich proteins. These findings underscore the generality that many disordered states can be expanded and unstructured, and that the hydrophobic effect alone is insufficient to drive significant chain collapse for typical protein sequences.

Using NMR diffusion data to validate MD models of disordered proteins: Test case of N-terminal tail of histone H4

MD simulations can provide uniquely detailed models of intrinsically disordered proteins (IDPs). However, these models need careful experimental validation. The coefficient of translational diffusion Dtr, measurable by pulsed field gradient NMR, offers a potentially useful piece of experimental information related to the compactness of the IDP's conformational ensemble. Here, we investigate, both experimentally and via the MD modeling, the translational diffusion of a 25-residue N-terminal fragment from histone H4 (N-H4). We found that the predicted values of Dtr, as obtained from mean-square displacement of the peptide in the MD simulations, are largely determined by the viscosity of the MD water (which has been reinvestigated as a part of our study). Beyond that, our analysis of the diffusion data indicates that MD simulations of N-H4 in the TIP4P-Ew water give rise to an overly compact conformational ensemble for this peptide. In contrast, TIP4P-D and OPC simulations produce the ensembles that are consistent with the experimental Dtr result. These observations are supported by the analyses of the 15N spin relaxation rates. We also tested a number of empirical methods to predict Dtr based on IDP's coordinates extracted from the MD snapshots. In particular, we show that the popular approach involving the program HYDROPRO can produce misleading results. This happens because HYDROPRO is not intended to predict the diffusion properties of highly flexible biopolymers such as IDPs. Likewise, recent empirical schemes that exploit the relationship between the small-angle x-ray scattering-informed conformational ensembles of IDPs and the respective experimental Dtr values also prove to be problematic. In this sense, the first-principle calculations of Dtr from the MD simulations, such as demonstrated in this work, should provide a useful benchmark for future efforts in this area.

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 relevance of short peptides for an understanding of unfolded and intrinsically disordered proteins

Over the last thirty years the unfolded state of proteins has attracted considerable interest owing to the discovery of intrinsically disordered proteins which perform a plethora of functions despite resembling unfolded proteins to a significant extent. Research on both, unfolded and disordered proteins has revealed that their conformational properties can deviate locally from random coil behavior. In this context results from work on short oligopeptides suggest that individual amino acid residues sample the sterically allowed fraction of the Ramachandran plot to a different extent. Alanine has been found to exhibit a peculiarity in that it has a very high propensity for adopting polyproline II like conformations. This Perspectives article reviews work on short peptides aimed at exploring the Ramachandran distributions of amino acid residues in different contexts with experimental and computational means. Based on the thus provided overview the article discussed to what extent short peptides can serve as tools for exploring unfolded and disordered proteins and as benchmarks for the development of a molecular dynamics force field.

Statistical proofs of the interdependence between nearest neighbor effects on polypeptide backbone conformations

Backbone dihedral angles ϕ and ψ are the main structural descriptors of proteins and peptides. The distribution of these angles has been investigated over decades as they are essential for the validation and refinement of experimental measurements, as well as for structure prediction and design methods. The dependence of these distributions, not only on the nature of each amino acid but also on that of the closest neighbors, has been the subject of numerous studies. Although neighbor-dependent distributions are nowadays generally accepted as a good model, there is still some controversy about the combined effects of left and right neighbors. We have investigated this question using rigorous methods based on recently-developed statistical techniques. Our results unambiguously demonstrate that the influence of left and right neighbors cannot be considered independently. Consequently, three-residue fragments should be considered as the minimal building blocks to investigate polypeptide sequence-structure relationships.

Exploring Nearest Neighbor Interactions and Their Influence on the Gibbs Energy Landscape of Unfolded Proteins and Peptides

The Flory isolated pair hypothesis (IPH) is one of the corner stones of the random coil model, which is generally invoked to describe the conformational dynamics of unfolded and intrinsically disordered proteins (IDPs). It stipulates, that individual residues sample the entire sterically allowed space of the Ramachandran plot without exhibiting any correlations with the conformational dynamics of its neighbors. However, multiple lines of computational, bioinformatic and experimental evidence suggest that nearest neighbors have a significant influence on the conformational sampling of amino acid residues. This implies that the conformational entropy of unfolded polypeptides and proteins is much less than one would expect based on the Ramachandran plots of individual residues. A further implication is that the Gibbs energies of residues in unfolded proteins or polypeptides are not additive. This review provides an overview of what is currently known and what has yet to be explored regarding nearest neighbor interactions in unfolded proteins.

Randomizing of Oligopeptide Conformations by Nearest Neighbor Interactions between Amino Acid Residues

Flory’s random coil model assumes that conformational fluctuations of amino acid residues in unfolded poly(oligo)peptides and proteins are uncorrelated (isolated pair hypothesis, IPH). This implies that conformational energies, entropies and solvation free energies are all additive. Nearly 25 years ago, analyses of coil libraries cast some doubt on this notion, in that they revealed that aromatic, but also β-branched side chains, could change the ³J(H^NH^Cα) coupling of their neighbors. Since then, multiple bioinformatical, computational and experimental studies have revealed that conformational propensities of amino acids in unfolded peptides and proteins depend on their nearest neighbors. We used recently reported and newly obtained Ramachandran plots of tetra- and pentapeptides with non-terminal homo- and heterosequences of amino acid residues to quantitatively determine nearest neighbor coupling between them with a Ising type model. Results reveal that, depending on the choice of amino acid residue pairs, nearest neighbor interactions either stabilize or destabilize pairs of polyproline II and β-strand conformations. This leads to a redistribution of population between these conformations and a reduction in conformational entropy. Interactions between residues in polyproline II and turn(helix)-forming conformations seem to be cooperative in most cases, but the respective interaction parameters are subject to large statistical errors.

Mechanism of Thermal Protein Aggregation: Experiments and Molecular Dynamics Simulations on the High-Temperature Behavior of Myoglobin

Proteins that encounter unfavorable solvent conditions are prone to aggregation, a phenomenon that remains poorly understood. This work focuses on myoglobin (Mb) as a model protein. Upon heating, Mb produces amorphous aggregates. Thermal unfolding experiments at low concentration (where aggregation is negligible), along with centrifugation assays, imply that Mb aggregation proceeds via globally unfolded conformers. This contrasts studies on other proteins that emphasized the role of partially folded structures as aggregate precursors. Molecular dynamics (MD) simulations were performed to gain insights into the mechanism by which heat-unfolded Mb molecules associate with one another. A prerequisite for these simulations was the development of a method for generating monomeric starting structures. Periodic boundary condition artifacts necessitated the implementation of a partially immobilized water layer lining the walls of the simulation box. Aggregation simulations were performed at 370 K to track the assembly of monomeric Mb into pentameric species. Binding events were preceded by multiple unsuccessful encounters. Even after association, protein-protein contacts remained in flux. Binding was mediated by hydrophobic contacts, along with salt bridges that involved hydrophobically embedded Lys residues. Overall, this work illustrates that atomistic MD simulations are well suited for garnering insights into protein aggregation mechanisms.

Accurate prediction of protein torsion angles using evolutionary signatures and recurrent neural network

The amino acid sequence of a protein contains all the necessary information to specify its shape, which dictates its biological activities. However, it is challenging and expensive to experimentally determine the three-dimensional structure of proteins. The backbone torsion angles play a critical role in protein structure prediction, and accurately predicting the angles can considerably advance the tertiary structure prediction by accelerating efficient sampling of the large conformational space for low energy structures. Here we first time propose evolutionary signatures computed from protein sequence profiles, and a novel recurrent architecture, termed ESIDEN, that adopts a straightforward architecture of recurrent neural networks with a small number of learnable parameters. The ESIDEN can capture efficient information from both the classic and new features benefiting from different recurrent architectures in processing information. On the other hand, compared to widely used classic features, the new features, especially the Ramachandran basin potential, provide statistical and evolutionary information to improve prediction accuracy. On four widely used benchmark datasets, the ESIDEN significantly improves the accuracy in predicting the torsion angles by comparison to the best-so-far methods. As demonstrated in the present study, the predicted angles can be used as structural constraints to accurately infer protein tertiary structures. Moreover, the proposed features would pave the way to improve machine learning-based methods in protein folding and structure prediction, as well as function prediction. The source code and data are available at the website https://kornmann.bioch.ox.ac.uk/leri/resources/download.html .

Tandem domain structure determination based on a systematic enumeration of conformations

Protein structure determination is undergoing a change of perspective due to the larger importance taken in biology by the disordered regions of biomolecules. In such cases, the convergence criterion is more difficult to set up and the size of the conformational space is a obstacle to exhaustive exploration. A pipeline is proposed here to exhaustively sample protein conformations using backbone angle limits obtained by nuclear magnetic resonance (NMR), and then to determine the populations of conformations. The pipeline is applied to a tandem domain of the protein whirlin. An original approach, derived from a reformulation of the Distance Geometry Problem is used to enumerate the conformations of the linker connecting the two domains. Specifically designed procedure then permit to assemble the domains to the linker conformations and to optimize the tandem domain conformations with respect to two sets of NMR measurements: residual dipolar couplings and paramagnetic resonance enhancements. The relative populations of optimized conformations are finally determined by fitting small angle X-ray scattering (SAXS) data. The most populated conformation of the tandem domain is a semi-closed one, fully closed and more extended conformations being in minority, in agreement with previous observations. The SAXS and NMR data show different influences on the determination of populations.

CheSPI: chemical shift secondary structure population inference

NMR chemical shifts (CSs) are delicate reporters of local protein structure, and recent advances in random coil CS (RCCS) prediction and interpretation now offer the compelling prospect of inferring small populations of structure from small deviations from RCCSs. Here, we present CheSPI, a simple and efficient method that provides unbiased and sensitive aggregate measures of local structure and disorder. It is demonstrated that CheSPI can predict even very small amounts of residual structure and robustly delineate subtle differences into four structural classes for intrinsically disordered proteins. For structured regions and proteins, CheSPI provides predictions for up to eight structural classes, which coincide with the well-known DSSP classification. The program is freely available, and can either be invoked from URL www.protein-nmr.org as a web implementation, or run locally from command line as a python program. CheSPI generates comprehensive numeric and graphical output for intuitive annotation and visualization of protein structures. A number of examples are provided.

Effects of pH on an IDP conformational ensemble explored by molecular dynamics simulation

The conformational ensemble of intrinsically disordered proteins, such as α-synuclein, are responsible for their function and malfunction. Misfolding of α-synuclein can lead to neurodegenerative diseases, and the ability to study their conformations and those of other intrinsically disordered proteins under varying physiological conditions can be crucial to understanding and preventing pathologies. In contrast to well-folded peptides, a consensus feature of IDPs is their low hydropathy and high charge, which makes their conformations sensitive to pH perturbation. We examine a prominent member of this subset of IDPs, α-synuclein, using a divide-and-conquer scheme that provides enhanced sampling of IDP structural ensembles. We constructed conformational ensembles of α-synuclein under neutral (pH ~ 7) and low (pH ~ 3) pH conditions and compared our results with available information obtained from smFRET, SAXS, and NMR studies. Specifically, α-synuclein has been found to in a more compact state at low pH conditions and the structural changes observed are consistent with those from experiments. We also characterize the conformational and dynamic differences between these ensembles and discussed the implication on promoting pathogenic fibril formation. We find that under low pH conditions, neutralization of negatively charged residues leads to compaction of the C-terminal portion of α-synuclein while internal reorganization allows α-synuclein to maintain its overall end-to-end distance. We also observe different levels of intra-protein interaction between three regions of α-synuclein at varying pH and a shift towards more hydrophilic interactions with decreasing pH.

Complex Morphogenesis by a Model Intrinsically Disordered Protein

The development of intricate and complex self-assembling structures in the micrometer range, such as biomorphs, is a major challenge in materials science. Although complex structures can be obtained from self-assembling materials as they segregate from solution, their size is usually in the nanometer range or requires accessory techniques. Previous studies with intrinsically disordered proteins (IDPs) have shown that the active interplay of different molecular interactions provides access to new and more complex nanostructures. As such, it is hypothesized that enriching the variety of intra- and intermolecular interactions in a model IDP will widen the landscape of sophisticated intermediate structures that can be accessed. In this study, a model silk-elastin-like recombinamer capable of interacting via three non-covalent interactions, namely hydrophobic, ion-pairing, and H-bonding is built. This model material is shown to self-assemble into complex stable micrometer-sized biomorphs. Variation of the block composition, pH, and temperature demonstrates the necessary interplay of all three interactions for the formation of such complex structures.

Comprehensive Structural and Thermodynamic Analysis of Prefibrillar WT α-Synuclein and Its G51D, E46K, and A53T Mutants by a Combination of Small-Angle X-ray Scattering and Variational Bayesian Weighting

The in solution synchrotron small-angle X-ray scattering SAXS technique has been used to investigate an intrinsically disordered protein (IDP) related to Parkinson's disease, the α-synuclein (α-syn), in prefibrillar diluted conditions. SAXS experiments have been performed as a function of temperature and concentration on the wild type (WT) and on the three pathogenic mutants G51D, E46K, and A53T. To identify the conformers that populate WT α-syn and the pathogenic mutants in prefibrillar conditions, scattering data have been analyzed by a new variational bayesian weighting method (VBWSAS) based on an ensemble of conformers, which includes unfolded monomers, trimers, and tetramers, both in helical-rich and strand-rich forms. The developed VBWSAS method uses a thermodynamic scheme to account for temperature and concentration effects and considers long-range protein-protein interactions in the framework of the random phase approximation. The global analysis of the whole set of data indicates that WT α-syn is mostly present as unfolded monomers and trimers (helical-rich trimers at low T and strand-rich trimers at high T), but not tetramers, as previously derived by several studies. On the contrary, different conformer combinations characterize mutants. In the α-syn G51D mutant, the most abundant aggregates at all the temperatures are strand-rich tetramers. Strand-rich tetramers are also the predominant forms in the A53T mutant, but their weight decreases with temperature. Only monomeric conformers, with a preference for the ones with the smallest sizes, are present in the E46K mutant. The derived conformational behavior then suggests a different availability of species prone to aggregate, depending on mutation, temperature, and concentration and accounting for the different neurotoxicity of α-syn variants. Indeed, this approach may be of pivotal importance to describe conformational and aggregational properties of other IDPs.

Hierarchical Ensembles of Intrinsically Disordered Proteins at Atomic Resolution in Molecular Dynamics Simulations

Intrinsically disordered proteins (IDPs) constitute a large fraction of the human proteome and are critical in the regulation of cellular processes. A detailed understanding of the conformational dynamics of IDPs could help to elucidate their roles in health and disease. However, the inherent flexibility of IDPs makes structural studies and their interpretation challenging. Molecular dynamics (MD) simulations could address this challenge in principle, but inaccuracies in the simulation models and the need for long simulations have stymied progress. To overcome these limitations, we adopt a hierarchical approach that builds on the "flexible-meccano" model reported by Bernadó et al. (J. Am. Chem. Soc. 2005, 127, 17968-17969). First, we exhaustively sample small IDP fragments in all-atom simulations to capture their local structures. Then, we assemble the fragments into full-length IDPs to explore the stereochemically possible global structures of IDPs. The resulting ensembles of three-dimensional structures of full-length IDPs are highly diverse, much more so than in standard MD simulation. For the paradigmatic IDP α-synuclein, our ensemble captures both the local structure, as probed by nuclear magnetic resonance spectroscopy, and its overall dimension, as obtained from small-angle X-ray scattering in solution. By generating representative and meaningful starting ensembles, we can begin to exploit the massive parallelism afforded by current and future high-performance computing resources for atomic-resolution characterization of IDPs.

Impact of Heat on Coil Hydrodynamic Size Yields the Energetics of Denatured State Conformational Bias

Conformational equilibria in the protein denatured state have key roles regulating folding, stability, and function. The extent of conformational bias in the protein denatured state under folding conditions, however, has thus far proven elusive to quantify, particularly with regard to its sequence dependence and energetic character. To better understand the structural preferences of the denatured state, we analyzed both the sequence dependence to the mean hydrodynamic size of disordered proteins in water and the impact of heat on the coil dimensions, showing that the sequence dependence and thermodynamic energies associated with intrinsic biases for the α and polyproline II (PPII) backbone conformations can be obtained. Experiments that evaluate how the hydrodynamic size changes with compositional changes in the protein reveal amino acid specific preferences for PPII that are in good quantitative agreement with calorimetry-measured values from unfolded peptides and those inferred by survey of the protein coil library. At temperatures above 25 °C, the denatured state follows the predictions of a PPII-dominant ensemble. Heat effects on coil hydrodynamic size indicate the α bias is comparable to the PPII bias at cold temperatures. Though historically thought to give poor resolution to structural details, the hydrodynamic size of the unfolded state is found to be an effective reporter on the extent of the biases for the α and PPII backbone conformations.

The Evolution of Tau Phosphorylation and Interactions

Tau is a neuronal microtubule-associated protein (MAP) that is involved in the regulation of axonal microtubule assembly. However, as a protein with intrinsically disordered regions (IDRs), tau also interacts with many other partners in addition to microtubules. Phosphorylation at selected sites modulates tau's various intracellular interactions and regulates the properties of IDRs. In Alzheimer's disease (AD) and other tauopathies, tau exhibits pathologically increased phosphorylation (hyperphosphorylation) at selected sites and aggregates into neurofibrillary tangles (NFTs). By bioinformatics means, we tested the hypothesis that the sequence of tau has changed during the vertebrate evolution in a way that novel interactions developed and also the phosphorylation pattern was affected, which made tau prone to the development of tauopathies. We report that distinct regions of tau show functional specialization in their molecular interactions. We found that tau's amino-terminal region, which is involved in biological processes related to "membrane organization" and "regulation of apoptosis," exhibited a strong evolutionary increase in protein disorder providing the basis for the development of novel interactions. We observed that the predicted phosphorylation sites have changed during evolution in a region-specific manner, and in some cases the overall number of phosphorylation sites increased owing to the formation of clusters of phosphorylatable residues. In contrast, disease-specific hyperphosphorylated sites remained highly conserved. The data indicate that novel, non-microtubule related tau interactions developed during evolution and suggest that the biological processes, which are mediated by these interactions, are of pathological relevance. Furthermore, the data indicate that predicted phosphorylation sites in some regions of tau, including a cluster of phosphorylatable residues in the alternatively spliced exon 2, have changed during evolution. In view of the "antagonistic pleiotropy hypothesis" it may be worth to take disease-associated phosphosites with low evolutionary conservation as relevant biomarkers into consideration.

On the Interpretation of Force-Induced Unfolding Studies of Membrane Proteins Using Fast Simulations

Single-molecule force spectroscopy has proven extremely beneficial in elucidating folding pathways for membrane proteins. Here, we simulate these measurements, conducting hundreds of unfolding trajectories using our fast Upside algorithm for slow enough speeds to reproduce key experimental features that may be missed using all-atom methods. The speed also enables us to determine the logarithmic dependence of pulling velocities on the rupture levels to better compare to experimental values. For simulations of atomic force microscope measurements in which force is applied vertically to the C-terminus of bacteriorhodopsin, we reproduce the major experimental features including even the back-and-forth unfolding of single helical turns. When pulling laterally on GlpG to mimic the experiment, we observe quite different behavior depending on the stiffness of the spring. With a soft spring, as used in the experimental studies with magnetic tweezers, the force remains nearly constant after the initial unfolding event, and a few pathways and a high degree of cooperativity are observed in both the experiment and simulation. With a stiff spring, however, the force drops to near zero after each major unfolding event, and numerous intermediates are observed along a wide variety of pathways. Hence, the mode of force application significantly alters the perception of the folding landscape, including the number of intermediates and the degree of folding cooperativity, important issues that should be considered when designing experiments and interpreting unfolding data.

Commonly used FRET fluorophores promote collapse of an otherwise disordered protein

The dimensions that unfolded proteins, including intrinsically disordered proteins (IDPs), adopt in the absence of denaturant remain controversial. We developed an analysis procedure for small-angle X-ray scattering (SAXS) profiles and used it to demonstrate that even relatively hydrophobic IDPs remain nearly as expanded in water as they are in high denaturant concentrations. In contrast, as demonstrated here, most fluorescence resonance energy transfer (FRET) measurements have indicated that relatively hydrophobic IDPs contract significantly in the absence of denaturant. We use two independent approaches to further explore this controversy. First, using SAXS we show that fluorophores employed in FRET can contribute to the observed discrepancy. Specifically, we find that addition of Alexa-488 to a normally expanded IDP causes contraction by an additional 15%, a value in reasonable accord with the contraction reported in FRET-based studies. Second, using our simulations and analysis procedure to accurately extract both the radius of gyration (R_g) and end-to-end distance (R_ee) from SAXS profiles, we tested the recent suggestion that FRET and SAXS results can be reconciled if the R_g and R_ee are "uncoupled" (i.e., no longer simply proportional), in contrast to the case for random walk homopolymers. We find, however, that even for unfolded proteins, these two measures of unfolded state dimensions remain proportional. Together, these results suggest that improved analysis procedures and a correction for significant, fluorophore-driven interactions are sufficient to reconcile prior SAXS and FRET studies, thus providing a unified picture of the nature of unfolded polypeptide chains in the absence of denaturant.

Investigating the Formation of Structural Elements in Proteins Using Local Sequence-Dependent Information and a Heuristic Search Algorithm

Structural elements inserted in proteins are essential to define folding/unfolding mechanisms and partner recognition events governing signaling processes in living organisms. Here, we present an original approach to model the folding mechanism of these structural elements. Our approach is based on the exploitation of local, sequence-dependent structural information encoded in a database of three-residue fragments extracted from a large set of high-resolution experimentally determined protein structures. The computation of conformational transitions leading to the formation of the structural elements is formulated as a discrete path search problem using this database. To solve this problem, we propose a heuristically-guided depth-first search algorithm. The domain-dependent heuristic function aims at minimizing the length of the path in terms of angular distances, while maximizing the local density of the intermediate states, which is related to their probability of existence. We have applied the strategy to two small synthetic polypeptides mimicking two common structural motifs in proteins. The folding mechanisms extracted are very similar to those obtained when using traditional, computationally expensive approaches. These results show that the proposed approach, thanks to its simplicity and computational efficiency, is a promising research direction.

Characterization of intrinsically disordered proteins and their dynamic complexes: From in vitro to cell-like environments

Over the last two decades, it has become increasingly clear that a large fraction of the human proteome is intrinsically disordered or contains disordered segments of significant length. These intrinsically disordered proteins (IDPs) play important regulatory roles throughout biology, underlining the importance of understanding their conformational behavior and interaction mechanisms at the molecular level. Here we review recent progress in the NMR characterization of the structure and dynamics of IDPs in various functional states and environments. We describe the complementarity of different NMR parameters for quantifying the conformational propensities of IDPs in their isolated and phosphorylated states, and we discuss the challenges associated with obtaining structural models of dynamic protein-protein complexes involving IDPs. In addition, we review recent progress in understanding the conformational behavior of IDPs in cell-like environments such as in the presence of crowding agents, in membrane-less organelles and in the complex environment of the human cell.

What Drives 15N Spin Relaxation in Disordered Proteins? Combined NMR/MD Study of the H4 Histone Tail

Backbone (¹⁵N) NMR relaxation is one of the main sources of information on dynamics of disordered proteins. Yet, we do not know very well what drives ¹⁵N relaxation in such systems, i.e., how different forms of motion contribute to the measurable relaxation rates. To address this problem, we have investigated, both experimentally and via molecular dynamics simulations, the dynamics of a 26-residue peptide imitating the N-terminal portion of the histone protein H4. One part of the peptide was found to be fully flexible, whereas the other part features some transient structure (a hairpin stabilized by hydrogen bonds). The following motional modes proved relevant for ¹⁵N relaxation. 1) Sub-picosecond librations attenuate relaxation rates according to S² ∼0.85-0.90. 2) Axial peptide-plane fluctuations along a stretch of the peptide chain contribute to relaxation-active dynamics on a fast timescale (from tens to hundreds of picoseconds). 3) φ/ψ backbone jumps contribute to relaxation-active dynamics on both fast (from tens to hundreds of picoseconds) and slow (from hundreds of picoseconds to a nanosecond) timescales. The major contribution is from polyproline II (PPII) ↔ β transitions in the Ramachandran space; in the case of glycine residues, the major contribution is from PPII ↔ (β) ↔ rPPII transitions, in which rPPII is the mirror-image (right-handed) version of the PPII geometry, whereas β geometry plays the role of an intermediate state. 4) Reorientational motion of certain (sufficiently long-lived) elements of transient structure, i.e., rotational tumbling, contributes to slow relaxation-active dynamics on ∼1-ns timescale (however, it is difficult to isolate this contribution). In conclusion, recent advances in the area of force-field development have made it possible to obtain viable Molecular Dynamics models of protein disorder. After careful validation against the experimental relaxation data, these models can provide a valuable insight into mechanistic origins of spin relaxation in disordered peptides and proteins.

Exploring Peptide⁻Solvent Interactions: A Computational Study

The dilemma of reconciling the contradictory evidence regarding the conformation of long solvated peptide chains is the so-called "reconciliation problem". Clues regarding the stability of certain conformations likely lie in the electronic structure at the peptide⁻solvent interface, but the peptide⁻solvent interaction is not fully understood. Here, we study the influence of aqueous solvent on peptide conformations by using classical molecular dynamics (MD) and quantum mechanical/molecular mechanical (QM/MM) energy calculations. The model systems include an 11-residue peptide, X 2 A 7 O 2 (XAO), where X, A, and O denote diaminobutyric acid, alanine, and ornithine, respectively, and a 9-mer (Arg-Pro-Pro-Gly-Phe-Ser-Ala-Phe-Lys). Spectroscopic and MD data present conflicting evidence regarding the structure of XAO in water; some results indicate that XAO adopts a polyproline II (P II ) conformation, whereas other findings suggest that XAO explores a range of conformations. To investigate this contradiction, we present here the results of MD simulations of XAO and the 9-mer in aqueous solution, combined with QM/MM energy calculations.

Universal Implementation of a Residue-Specific Force Field Based on CMAP Potentials and Free Energy Decomposition

The coupling between neighboring backbone ϕ and ψ dihedral angles (torsions) has been well appreciated in protein force field development, as in correction map (CMAP) potentials. However, although preferences of backbone torsions are significantly affected by side-chain conformation, there has been no easy way to optimize this coupling. Herein, we prove that the three-dimensional (3D) free energy hypersurface of joint (ϕ, ψ, χ₁) torsions can be decomposed into three separated 2D surfaces. Thus, each of the 2D torsional surfaces can be efficiently and automatically optimized using a CMAP potential. This strategy is then used to reparameterize an AMBER force field such that the resulting χ₁-dependent backbone conformational preference can agree excellently with the reference protein coil library statistics. In various validation simulations (including the folding of seven peptides/proteins, backbone dynamics of three folded proteins, and two intrinsically disordered peptides), the new RSFF2C (residue-specific force field with CMAP potentials) force field gives similar or better performance compared with RSFF2. This strategy can be used to implement our RSFF force fields into a variety of molecular dynamics packages easily.

Annexins A2 and A6 interact with the extreme N terminus of tau and thereby contribute to tau's axonal localization

During neuronal development, the microtubule-associated protein tau becomes enriched in the axon, where it remains concentrated in the healthy brain. In tauopathies such as Alzheimer's disease, tau redistributes from the axon to the somatodendritic compartment. However, the cellular mechanism that regulates tau's localization remains unclear. We report here that tau interacts with the Ca²⁺-regulated plasma membrane-binding protein annexin A2 (AnxA2) via tau's extreme N terminus encoded by the first exon (E1). Bioinformatics analysis identified two conserved eight-amino-acids-long motifs within E1 in mammals. Using a heterologous yeast system, we found that disease-related mutations and pseudophosphorylation of Tyr-18, located within E1 but outside of the two conserved regions, do not influence tau's interaction with AnxA2. We further observed that tau interacts with the core domain of AnxA2 in a Ca²⁺-induced open conformation and interacts also with AnxA6. Moreover, lack of E1 moderately increased tau's association rate to microtubules, consistent with the supposition that the presence of the tau-annexin interaction reduces the availability of tau to interact with microtubules. Of note, intracellular competition through overexpression of E1-containing constructs reduced tau's axonal enrichment in primary neurons. Our results suggest that the E1-mediated tau-annexin interaction contributes to the enrichment of tau in the axon and is involved in its redistribution in pathological conditions.

Modeling the Early Stages of Phase Separation in Disordered Elastin-like Proteins

Elastin-like proteins (ELPs) are known to undergo liquid-liquid phase separation reversibly above a concentration-dependent transition temperature. Previous studies suggested that, as temperature increases, ELPs experience an increased propensity for type II β-turns. However, how the ELPs behave below the phase transition temperature itself is still elusive. Here, we investigate the importance of β-turn formation during the early stages of ELP self-association. We examined the behavior of two ELPs, a 150-repeat construct that had been investigated previously (ELP[V5G3A2-150] as well as a new 40-repeat construct (ELP40) suitable for nuclear magnetic resonance measurements. Structural analysis of ELP40 reveals a disordered conformation, and chemical shifts throughout the sequence are insensitive to changes in temperature over 20°C. However, a low population of β-turn conformation cannot be ruled out based on chemical shifts alone. To examine the structural consequences of β-turns in ELPs, a series of structural ensembles of ELP[V5G3A2-150] were generated, incorporating differing amounts of β-turn bias throughout the chain. To mimic the early stages of the phase change, two monomers were paired, assuming preferential interaction at β-turn regions. This approach was justified by the observation that buried hydrophobic turns are commonly observed to interact in the Protein Data Bank. After dimerization, the ensemble-averaged hydrodynamic properties were calculated for each degree of β-turn bias, and the results were compared with analytical ultracentrifugation experiments at various temperatures. We find that the temperature dependence of the sedimentation coefficient (s20,wo) can be reproduced by increasing the β-turn content in the structural ensemble. This analysis allows us to estimate the presence of β-turns and weak associations under experimental conditions. Because disordered proteins frequently exhibit weak biases in secondary structure propensity, these experimentally-driven ensemble calculations may complement existing methods for modeling disordered proteins generally.

Hypothesis: structural heterogeneity of the unfolded proteins originating from the coupling of the local clusters and the long-range distance distribution

We propose a hypothesis that explains two apparently contradicting observations for the heterogeneity of the unfolded proteins. First, the line confocal method of the single-molecule Förster resonance energy transfer (sm-FRET) spectroscopy revealed that the unfolded proteins possess broad peaks in the FRET efficiency plot, implying the significant heterogeneity that lasts longer than milliseconds. Second, the fluorescence correlation method demonstrated that the unfolded proteins fluctuate in the time scale shorter than 100 ns. To formulate the hypothesis, we first summarize the recent consensus for the structure and dynamics of the unfolded proteins. We next discuss the conventional method of the sm-FRET spectroscopy and its limitations for the analysis of the unfolded proteins, followed by the advantages of the line confocal method that revealed the heterogeneity. Finally, we propose that the structural heterogeneity formed by the local clustering of hydrophobic residues modulates the distribution of the long-range distance between the labeled chromophores, resulting in the broadening of the peak in the FRET efficiency plot. A clustering of hydrophobic residues around the chromophore might further contribute to the broadening. The proposed clusters are important for the understanding of protein folding mechanism.

An Efficient Method for Estimating the Hydrodynamic Radius of Disordered Protein Conformations

Intrinsically disordered proteins play important roles throughout biology, yet our understanding of the relationship between their sequences, structural properties, and functions remains incomplete. The dynamic nature of these proteins, however, makes them difficult to characterize structurally. Many disordered proteins can attain both compact and expanded conformations, and the level of expansion may be regulated and important for function. Experimentally, the level of compaction and shape is often determined either by small-angle x-ray scattering experiments or pulsed-field-gradient NMR diffusion measurements, which provide ensemble-averaged estimates of the radius of gyration and hydrodynamic radius, respectively. Often, these experiments are interpreted using molecular simulations or are used to validate them. We here provide, to our knowledge, a new and efficient method to calculate the hydrodynamic radius of a disordered protein chain from a model of its structural ensemble. In particular, starting from basic concepts in polymer physics, we derive a relationship between the radius of gyration of a structure and its hydrodynamic ratio, which in turn can be used, for example, to compare a simulated ensemble of conformations to NMR diffusion measurements. The relationship may also be valuable when using NMR diffusion measurements to restrain molecular simulations.

Molecular Determinants of Temperature Dependence of Protein Volume Change upon Unfolding

Pressure is a well-known environmental stressor that can either stabilize or destabilize proteins. The volumetric change upon protein unfolding determines the effect of pressure on protein stability, where negative volume changes destabilized proteins at high pressures. High temperature often accompanies high pressure, for example, in the ocean depths near hydrothermal vents or near faults, so it is important to study the effect of temperature on the volumetric change upon unfolding. We previously detailed the magnitude and sign of the molecular determinants of volumetric change, allowing us to quantitatively predict the volumetric change upon protein unfolding. Here, we present a comprehensive analysis of the temperature dependence of the volumetric components of proteins, showing that hydration volume is the primary component that defines expansivities of the native and unfolded states and void volume only contributes slightly to the folded state expansivity.

Simple MD-based model for oxidative folding of peptides and proteins

Significant strides have been recently made to fold peptides and small proteins in silico using MD simulations. However, facilities are currently lacking to include disulfide bonding in the MD models of protein folding. To address this problem, we have developed a simple empirical protocol to model formation of disulfides, which is perturbation-free, retains the same speed as conventional MD simulations and allows one to control the reaction rate. The new protocol has been tested on 15-aminoacid peptide guanylin containing four cysteine residues; the net simulation time using Amber ff14SB force field was 61 μs. The resulting isomer distribution is in qualitative agreement with experiment, suggesting that oxidative folding of guanylin in vitro occurs under kinetic control. The highly stable conformation of the so-called isomer 2(B) has been obtained for full-length guanylin, which is significantly different from the poorly ordered structure of the truncated peptide PDB ID 1GNB. In addition, we have simulated oxidative folding of guanylin within the 94-aminoacid prohormone proguanylin. The obtained structure is in good agreement with the NMR coordinates 1O8R. The proposed modeling strategy can help to explore certain fundamental aspects of protein folding and is potentially relevant for manufacturing of synthetic peptides and recombinant proteins.

Mechanism of Initiation, Association, and Formation of Amyloid Fibrils Modeled with the N-Terminal Peptide Fragment, IKYLEFIS, of Myoglobin G-Helix

Some peptides and proteins undergo self-aggregation under certain conditions, leading to amyloid fibrils formation, which is related to many disease conditions. It is important to understand such amyloid fibrils formation to provide mechanistic detail that governs the process. A predominantly α-helical myoglobin has been reported recently to readily form amyloid fibrils at a higher temperature, similar to its G-helix segment. Here, we have investigated the mechanism of amyloid fibrils formation by performing multiple long molecular dynamics simulations (27 μs) on the N-terminal segment of the G-helix of myoglobin. These simulations resulted in the formation of a single-layered tetrameric β-sheet with mixed parallel and antiparallel β-strands and this is the most common event irrespective of many different starting structures. Formation of the single-layered tetrameric β-sheet takes place following three distinctive pathways. The process of fibril initiation is dependent on temperature. Further, this study provides mechanistic insights into the formation of multilayered fibrilar structure, which could be applicable to a wider variety of peptides or proteins to understand the amyloidogenesis.

Construction and comparison of the statistical coil states of unfolded and intrinsically disordered proteins from nearest-neighbor corrected conformational propensities of short peptides

Assessing the influence of nearest neighbors on the conformational ensemble of amino acid residues in unfolded and intrinsically disordered proteins and peptides is pivotal for a thorough understanding of the statistical coil state of unfolded proteins as well as of the energetics of the folding process. Research aimed at exploring nearest neighbor interactions has mostly focused on the analysis of restricted coil libraries that reflect conformational distributions in loops connecting more regular secondary structure segments. Recently, however, Toal et al. reported an experimentally based structural analysis of selected xy-pairs in GxyG tetrapeptides, which revealed quantitative information about conformational changes induced by nearest-neighbor interactions (Eur. J. Chem., 2015, 21, 5173-5192). Here, we perform analyses of Ramachandran plots of xy-pairs in GxyG and in coil libraries (Ting et al., PLOS CompBiol, 2010, 6, e1000763) using Hellinger distances as a quantitative measure of dissimilarities between Ramachandran distributions. Our analysis reveals that nearest-neighbor effects inferred from the above coil library are much less pronounced than corresponding structural changes observed for GxyG peptides. To determine whether nearest-neighbor induced conformational changes observed for GxyG can be utilized for the analysis of unfolded proteins, we analyzed sets of ³J(H^HH^α) coupling constants of three different unfolded proteins, namely the 130-residue fragment of the Staphylococcus aureus fibronectin-binding protein (FnBPc), denatured hen lysozyme, and the htau40 protein. For the first two proteins we found statistically meaningful correlations between predicted nearest-neighbor induced changes of ³J(H^HH^α) and experimentally observed deviations from corresponding coupling constants of GxG peptides in water, which we used as reference system with minimal nearest-neighbor interactions. This observation is in line with the NMR based understanding of these proteins being predominantly statistical coils. For htau40, however, which is known to exhibit residual structure and large deviations form statistical coil expectations, these correlations are weak or absent. Our results thus underscore the importance of nearest-neighbor interactions for a complete physical description of an ideal statistical coil state of a protein.

Dynamic Descriptions of Highly Flexible Molecules from NMR Dipolar Couplings: Physical Basis and Limitations

Biomolecules that control physiological function by changing their conformation play key roles in biology and remain poorly characterized. NMR dipolar couplings (DCs) depend intrinsically on both molecular shape and structural fluctuations, thereby providing the enticing prospect of tracking these conformational changes at atomic detail. Although this dual dependence has until now severely complicated analysis of DCs from highly dynamic systems, general approaches have recently been proposed that simplify interpretation of experimental DCs, by entirely eliminating molecular alignment from the analysis. Using simple and intuitive simulation of target ensembles, we investigate the impact of such approaches on the resulting descriptions of the conformational energy landscape. We find that ensemble descriptions of highly flexible systems derived from DCs without explicit consideration of the alignment properties of the constituent conformations can be compromised and inaccurate, despite exhibiting high correlation with experimental measurement.

Systemic and network functions of the microtubule-associated protein tau: Implications for tau-based therapies

Tau is a microtubule-associated neuronal protein, whose primary role was long thought to regulate axonal microtubule assembly. Tau is subject to many posttranslational modifications and can aggregate into neurofibrillary tangles, which are considered to be a hallmark of several neurodegenerative diseases collectively called "tauopathies". The most common tauopathy is Alzheimer's disease, where tau pathology correlates with sites of neurodegeneration. Tau belongs to the class of intrinsically disordered proteins, which are known to interact with many partners and are considered to be involved in various signaling, regulation and recognition processes. Thus more recent evidence indicates that tau functionally interacts with many proteins and different cellular structures, which may have an important physiological role and may be involved in neurodegenerative processes. Furthermore, tau can be released from neurons and exert functional effects on other cells. This review article weighs the evidence that tau has subtle but important systemic effects on neuronal network function by maintaining physiological neuronal transmission and synaptic plasticity, which are possibly independent from tau's microtubule modulating activities. Implications for tau-based therapeutic approaches are discussed.

Perplexing cooperative folding and stability of a low-sequence complexity, polyproline 2 protein lacking a hydrophobic core

The burial of hydrophobic side chains in a protein core generally is thought to be the major ingredient for stable, cooperative folding. Here, we show that, for the snow flea antifreeze protein (sfAFP), stability and cooperativity can occur without a hydrophobic core, and without α-helices or β-sheets. sfAFP has low sequence complexity with 46% glycine and an interior filled only with backbone H-bonds between six polyproline 2 (PP2) helices. However, the protein folds in a kinetically two-state manner and is moderately stable at room temperature. We believe that a major part of the stability arises from the unusual match between residue-level PP2 dihedral angle bias in the unfolded state and PP2 helical structure in the native state. Additional stabilizing factors that compensate for the dearth of hydrophobic burial include shorter and stronger H-bonds, and increased entropy in the folded state. These results extend our understanding of the origins of cooperativity and stability in protein folding, including the balance between solvent and polypeptide chain entropies.

Molecular determinant of the effects of hydrostatic pressure on protein folding stability

Hydrostatic pressure is an important environmental variable that plays an essential role in biological adaptation for many extremophilic organisms (for example, piezophiles). Increase in hydrostatic pressure, much like increase in temperature, perturbs the thermodynamic equilibrium between native and unfolded states of proteins. Experimentally, it has been observed that increase in hydrostatic pressure can both increase and decrease protein stability. These observations suggest that volume changes upon protein unfolding can be both positive and negative. The molecular details of this difference in sign of volume changes have been puzzling the field for the past 50 years. Here we present a comprehensive thermodynamic model that provides in-depth analysis of the contribution of various molecular determinants to the volume changes upon protein unfolding. Comparison with experimental data shows that the model allows quantitative predictions of volume changes upon protein unfolding, thus paving the way to proteome-wide computational comparison of proteins from different extremophilic organisms.

Proteins can be both stabilized and destabilized by pressure. Here the authors analyse the factors contributing to both negative and positive protein volume change upon denaturation, and shed light on the molecular determinants allowing proteins to be stable at high pressures.

Shedding light on the extra thermal stability of thermophilic proteins

An entropic stabilization mechanism has recently gained attention and credibility as the physical ground for the extra thermal stability of globular proteins from thermophilic microorganisms. An empirical result, obtained from the analysis of thermodynamic data for a large set of proteins, strengthens the general reliability of the theoretical approach originally devised to rationalize the occurrence of cold denaturation [Graziano, PCCP 2014, 16, 21755-21767]. It is shown that this theoretical approach can readily account for the entropic stabilization mechanism. On decreasing the conformational entropy gain associated with denaturation, the thermal stability of a model globular protein increases markedly.