Coarse-grained modeling of the intrinsically disordered protein Histatin 5 in solution: Monte Carlo simulations in combination with SAXS

SOP-MULTI: A Self-Organized Polymer-Based Coarse-Grained Model for Multidomain and Intrinsically Disordered Proteins with Conformation Ensemble Consistent with Experimental Scattering Data

Multidomain proteins with long flexible linkers and full-length intrinsically disordered proteins (IDPs) are best defined as an ensemble of conformations rather than a single structure. Determining high-resolution ensemble structures of such proteins poses various challenges by using tools from experimental structural biophysics. Integrative approaches combining available low-resolution ensemble-averaged experimental data and in silico biomolecular reconstructions are now often used for the purpose. However, extensive Boltzmann weighted conformation sampling for large proteins, especially for ones where both the folded and disordered domains exist in the same polypeptide chain, remains a challenge. In this work, we present a 2-site per amino-acid resolution SOP-MULTI force field for simulating coarse-grained models of multidomain proteins. SOP-MULTI combines two well-established self-organized polymer models─: (i) SOP-SC models for folded systems and (ii) SOP-IDP for IDPs. For the SOP-MULTI, we introduce cross-interaction terms between the beads belonging to the folded and disordered regions to generate conformation ensembles for full-length multidomain proteins such as hnRNP A1, TDP-43, G3BP1, hGHR-ECD, TIA1, HIV-1 Gag, polyubiquitin, and FUS. When back-mapped to all-atom resolution, SOP-MULTI trajectories faithfully recapitulate the scattering data over the range of the reciprocal space. We also show that individual folded domains preserve native contacts with respect to solved folded structures, and root-mean-square fluctuations of residues in folded domains match those obtained from all-atom molecular dynamics simulation trajectories of the same folded systems. SOP-MULTI force field is made available as a LAMMPS-compatible user package along with setup codes for generating the required files for any full-length protein with folded and disordered regions.

Impact of Phosphorylation on the Physiological Form of Human alpha-Synuclein in Aqueous Solution

Serine 129 can be phosphorylated in pathological inclusions formed by the intrinsically disordered protein human α-synuclein (AS), a key player in Parkinson's disease and other synucleinopathies. Here, molecular simulations provide insight into the structural ensemble of phosphorylated AS. The simulations allow us to suggest that phosphorylation significantly impacts the structural content of the physiological AS conformational ensemble in aqueous solution, as the phosphate group is mostly solvated. The hydrophobic region of AS contains β-hairpin structures, which may increase the propensity of the protein to undergo amyloid formation, as seen in the nonphysiological (nonacetylated) form of the protein in a recent molecular simulation study. Our findings are consistent with existing experimental data with the caveat of the observed limitations of the force field for the phosphorylated moiety.

Perspectives on solution-based small angle X-ray scattering for protein and biological macromolecule structural biology

Small-angle X-ray scattering (SAXS) is used to extract structural information from a wide variety of non-crystalline samples in different fields (e.g., materials science, physics, chemistry, and biology). This review provides an overview of SAXS as applied to structural biology, specifically for proteins and other biomacromolecules in solution with an emphasis on extracting key structural parameters and the interpretation of SAXS data using a diverse array of techniques. These techniques cover aspects of building and assessing models to describe data measured from monodispersed and ideal dilute samples through to more complicated structurally polydisperse systems. Ab initio modelling, rigid body modelling as well as normal-mode analysis, molecular dynamics, mixed component and structural ensemble modelling are discussed. Dealing with polydispersity both physically in terms of component separation as well as approaching the analysis and modelling of data of mixtures and evolving systems are described, including methods for data decomposition such as single value decomposition/principle component analysis and evolving factor analysis. This review aims to highlight that solution SAXS, with the cohort of developments in data analysis and modelling, is well positioned to build upon the traditional 'single particle view' foundation of structural biology to take the field into new areas for interpreting the structures of proteins and biomacromolecules as population-states and dynamic structural systems.

A pH-Dependent Coarse-Grained Model for Disordered Proteins: Histidine Interactions Modulate Conformational Ensembles

Histidine (His) presents a unique challenge for modeling disordered protein conformations, as it is versatile and occurs in both the neutral (His0) and positively charged (His+) states. These His charge states, which are enabled by its imidazole side chain, influence the electrostatic and short-range interactions of His residues, which potentially engage in cation-π, π-π, and charge-charge interactions. Existing coarse-grained (CG) models often simplify His representation by assigning it an average charge, thereby neglecting these potential short-range interactions. To address this gap, we developed a model for intrinsically disordered proteins (IDPs) that accounts for the properties of histidine (H). The resulting IDPH model is a 21-amino acid CG model incorporating both His charge states. We show that interactions involving previously neglected His0 are critical for accurate modeling at high pH, where they significantly influence the compaction of His-rich IDPs such as Histatin-5 and CPEB4. These interactions contribute to structural stabilizations primarily via His0-His0 and His0-Arg interactions, which are overlooked in models focusing solely on the charged His+ state.

NPEX: Never give up protein exploration with deep reinforcement learning

Elucidating unknown structures of proteins, such as metastable states, is critical in designing therapeutic agents. Protein structure exploration has been performed using advanced computational methods, especially molecular dynamics and Markov chain Monte Carlo simulations, which require untenably long calculation times and prior structural knowledge. Here, we developed an innovative method for protein structure determination called never give up protein exploration (NPEX) with deep reinforcement learning. The NPEX method leverages the soft actor-critic algorithm and the intrinsic reward system, effectively adding a bias potential without the need for prior knowledge. To demonstrate the method's effectiveness, we applied it to four models: a double well, a triple well, the alanine dipeptide, and the tryptophan cage. Compared with Markov chain Monte Carlo simulations, NPEX had markedly greater sampling efficiency. The significantly enhanced computational efficiency and lack of prior domain knowledge requirements of the NPEX method will revolutionize protein structure exploration.

Deeper Insight of the Conformational Ensemble of Intrinsically Disordered Proteins

It is generally known that, unlike structured proteins, intrinsically disordered proteins, IDPs, exhibit various structures and conformers, the so-called conformational ensemble, CoE. This study aims to better understand the conformers that make up the IDP ensemble by decomposing the CoE into groups separated by their radius of gyration, Rg. A common approach to studying CoE for IDPs is to use low-resolution techniques, such as small-angle scattering, and combine those with computer simulations on different length scales. Herein, the well-studied antimicrobial saliva protein histatin 5 was utilized as a model peptide for an IDP; the average intensity curves were obtained from small-angle X-ray scattering; and compared with fully atomistic, explicit water, molecular dynamics simulations; then, the intensity curve was decomposed with respect to the different Rg values; and their secondary structure propensities were investigated. We foresee that this approach can provide important information on the CoE and the individual conformers within; in that case, it will serve as an additional tool for understanding the IDP structure-function relationship on a more detailed level.

Translocation of Antimicrobial Peptides across Model Membranes: The Role of Peptide Chain Length

Cushioned lipid bilayers are structures consisting of a lipid bilayer supported on a solid substrate with an intervening layer of soft material. They offer possibilities for studying the behavior and interactions of biological membranes more accurately under physiological conditions. In this work, we continue our studies of cushion formation induced by histatin 5 (24Hst5), focusing on the effect of the length of the peptide chain. 24Hst5 is a short, positively charged, intrinsically disordered saliva peptide, and here, both a shorter (14Hst5) and a longer (48Hst5) peptide variant were evaluated. Experimental surface active techniques were combined with coarse-grained Monte Carlo simulations to obtain information about these peptides. Results show that at 10 mM NaCl, both the shorter and the longer peptide variants behave like 24Hst5 and a cushion below the bilayer is formed. At 150 mM NaCl, however, no interaction is observed for 24Hst5. On the contrary, a cushion is formed both in the case of 14Hst5 and 48Hst5, and in the latter, an additional thick, diffuse, and highly hydrated layer of peptide and lipid molecules is formed, on top of the bilayer. Similar trends were observed from the simulations, which allowed us to hypothesize that positively charged patches of the amino acids lysine and arginine in all three peptides are essential for them to interact with and translocate over the bilayer. We therefore hypothesize that electrostatic interactions are important for the interaction between the solid-supported lipid bilayers and the peptide depending on the linear charge density through the primary sequence and the positively charged patches in the sequence. The understanding of how, why, and when the cushion is formed opens up the possibility for this system to be used in the research and development of new drugs and pharmaceuticals.

Transferable deep generative modeling of intrinsically disordered protein conformations

Intrinsically disordered proteins have dynamic structures through which they play key biological roles. The elucidation of their conformational ensembles is a challenging problem requiring an integrated use of computational and experimental methods. Molecular simulations are a valuable computational strategy for constructing structural ensembles of disordered proteins but are highly resource-intensive. Recently, machine learning approaches based on deep generative models that learn from simulation data have emerged as an efficient alternative for generating structural ensembles. However, such methods currently suffer from limited transferability when modeling sequences and conformations absent in the training data. Here, we develop a novel generative model that achieves high levels of transferability for intrinsically disordered protein ensembles. The approach, named idpSAM, is a latent diffusion model based on transformer neural networks. It combines an autoencoder to learn a representation of protein geometry and a diffusion model to sample novel conformations in the encoded space. IdpSAM was trained on a large dataset of simulations of disordered protein regions performed with the ABSINTH implicit solvent model. Thanks to the expressiveness of its neural networks and its training stability, idpSAM faithfully captures 3D structural ensembles of test sequences with no similarity in the training set. Our study also demonstrates the potential for generating full conformational ensembles from datasets with limited sampling and underscores the importance of training set size for generalization. We believe that idpSAM represents a significant progress in transferable protein ensemble modeling through machine learning.

Combining Experiments and Simulations to Examine the Temperature-Dependent Behavior of a Disordered Protein

Intrinsically disordered proteins are a class of proteins that lack stable folded conformations and instead adopt a range of conformations that determine their biochemical functions. The temperature-dependent behavior of such disordered proteins is complex and can vary depending on the specific protein and environment. Here, we have used molecular dynamics simulations and previously published experimental data to investigate the temperature-dependent behavior of histatin 5, a 24-residue-long polypeptide. We examined the hypothesis that histatin 5 undergoes a loss of polyproline II (PPII) structure with increasing temperature, leading to more compact conformations. We found that the conformational ensembles generated by the simulations generally agree with small-angle X-ray scattering data for histatin 5, but show some discrepancies with the hydrodynamic radius as probed by pulsed-field gradient NMR spectroscopy, and with the secondary structure information derived from circular dichroism. We attempted to reconcile these differences by reweighting the conformational ensembles against the scattering and NMR data. By doing so, we were in part able to capture the temperature-dependent behavior of histatin 5 and to link the observed decrease in hydrodynamic radius with increasing temperature to a loss of PPII structure. We were, however, unable to achieve agreement with both the scattering and NMR data within experimental errors. We discuss different possible reasons for this including inaccuracies in the force field, differences in conditions of the NMR and scattering experiments, and issues related to the calculation of the hydrodynamic radius from conformational ensembles. Our study highlights the importance of integrating multiple types of experimental data when modeling conformational ensembles of disordered proteins and how environmental factors such as the temperature influence them.

Comparative Performance of Computer Simulation Models of Intrinsically Disordered Proteins at Different Levels of Coarse-Graining

Coarse-graining is commonly used to decrease the computational cost of simulations. However, coarse-grained models are also considered to have lower transferability, with lower accuracy for systems outside the original scope of parametrization. Here, we benchmark a bead-necklace model and a modified Martini 2 model, both coarse-grained models, for a set of intrinsically disordered proteins, with the different models having different degrees of coarse-graining. The SOP-IDP model has earlier been used for this set of proteins; thus, those results are included in this study to compare how models with different levels of coarse-graining compare. The sometimes naive expectation of the least coarse-grained model performing best does not hold true for the experimental pool of proteins used here. Instead, it showed the least good agreement, indicating that one should not necessarily trust the otherwise intuitive notion of a more advanced model inherently being better in model choice.

Enhancing Conformational Sampling for Intrinsically Disordered and Ordered Proteins by Variational Autoencoder

Intrinsically disordered proteins (IDPs) account for more than 50% of the human proteome and are closely associated with tumors, cardiovascular diseases, and neurodegeneration, which have no fixed three-dimensional structure under physiological conditions. Due to the characteristic of conformational diversity, conventional experimental methods of structural biology, such as NMR, X-ray diffraction, and CryoEM, are unable to capture conformational ensembles. Molecular dynamics (MD) simulation can sample the dynamic conformations at the atomic level, which has become an effective method for studying the structure and function of IDPs. However, the high computational cost prevents MD simulations from being widely used for IDPs conformational sampling. In recent years, significant progress has been made in artificial intelligence, which makes it possible to solve the conformational reconstruction problem of IDP with fewer computational resources. Here, based on short MD simulations of different IDPs systems, we use variational autoencoders (VAEs) to achieve the generative reconstruction of IDPs structures and include a wider range of sampled conformations from longer simulations. Compared with the generative autoencoder (AEs), VAEs add an inference layer between the encoder and decoder in the latent space, which can cover the conformational landscape of IDPs more comprehensively and achieve the effect of enhanced sampling. Through experimental verification, the Cα RMSD between VAE-generated and MD simulation sampling conformations in the 5 IDPs test systems was significantly lower than that of AE. The Spearman correlation coefficient on the structure was higher than that of AE. VAE can also achieve excellent performance regarding structured proteins. In summary, VAEs can be used to effectively sample protein structures.

Functional Implications of Dynamic Structures of Intrinsically Disordered Proteins Revealed by High-Speed AFM Imaging

The unique functions of intrinsically disordered proteins (IDPs) depend on their dynamic protean structure that often eludes analysis. High-speed atomic force microscopy (HS-AFM) can conduct this difficult analysis by directly visualizing individual IDP molecules in dynamic motion at sub-molecular resolution. After brief descriptions of the microscopy technique, this review first shows that the intermittent tip-sample contact does not alter the dynamic structure of IDPs and then describes how the number of amino acids contained in a fully disordered region can be estimated from its HS-AFM images. Next, the functional relevance of a dumbbell-like structure that has often been observed on IDPs is discussed. Finally, the dynamic structural information of two measles virus IDPs acquired from their HS-AFM and NMR analyses is described together with its functional implications.

From dilute to concentrated solutions of intrinsically disordered proteins: Interpretation and analysis of collected data

Intrinsically disordered proteins (IDPs) have a broad energy landscape and consequently sample many different conformations in solution. The innate flexibility of IDPs is exploited in their biological function, and in many instances allows a single IDP to regulate a range of processes in vivo. Due to their highly flexible nature, characterizing the structural properties of IDPs is not straightforward. Often solution-based methods such as Nuclear Magnetic Resonance (NMR), Förster Resonance Energy Transfer (FRET), and Small-Angle X-ray Scattering (SAXS) are used. SAXS is indeed a powerful technique to study the structural and conformational properties of IDPs in solution, and from the obtained SAXS spectra, information about the average size, shape, and extent of oligomerization can be determined. In this chapter, we will introduce model-free methods that can be used to interpret SAXS data and introduce methods that can be used to interpret SAXS data beyond analytical models, for example, by using atomistic and different levels of coarse-grained models in combination with molecular dynamics (MD) and Monte Carlo simulations.

Conformational ensembles of intrinsically disordered proteins and flexible multidomain proteins

Intrinsically disordered proteins (IDPs) and multidomain proteins with flexible linkers show a high level of structural heterogeneity and are best described by ensembles consisting of multiple conformations with associated thermodynamic weights. Determining conformational ensembles usually involves the integration of biophysical experiments and computational models. In this review, we discuss current approaches to determine conformational ensembles of IDPs and multidomain proteins, including the choice of biophysical experiments, computational models used to sample protein conformations, models to calculate experimental observables from protein structure, and methods to refine ensembles against experimental data. We also provide examples of recent applications of integrative conformational ensemble determination to study IDPs and multidomain proteins and suggest future directions for research in the field.

Self-Diffusive Properties of the Intrinsically Disordered Protein Histatin 5 and the Impact of Crowding Thereon: A Combined Neutron Spectroscopy and Molecular Dynamics Simulation Study

Intrinsically disordered proteins (IDPs) are proteins that, in comparison with globular/structured proteins, lack a distinct tertiary structure. Here, we use the model IDP, Histatin 5, for studying its dynamical properties under self-crowding conditions with quasi-elastic neutron scattering in combination with full atomistic molecular dynamics (MD) simulations. The aim is to determine the effects of crowding on the center-of-mass diffusion as well as the internal diffusive behavior. The diffusion was found to decrease significantly, which we hypothesize can be attributed to some degree of aggregation at higher protein concentrations, (≥100 mg/mL), as indicated by recent small-angle X-ray scattering studies. Temperature effects are also considered and found to, largely, follow Stokes–Einstein behavior. Simple geometric considerations fail to accurately predict the rates of diffusion, while simulations show semiquantitative agreement with experiments, dependent on assumptions of the ratio between translational and rotational diffusion. A scaling law that previously was found to successfully describe the behavior of globular proteins was found to be inadequate for the IDP, Histatin 5. Analysis of the MD simulations show that the width of the distribution with respect to diffusion is not a simplistic mirroring of the distribution of radius of gyration, hence, displaying the particular features of IDPs that need to be accounted for.

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.

Comment on the Optimal Parameters to Derive Intrinsically Disordered Protein Conformational Ensembles from Small-Angle X-ray Scattering Data Using the Ensemble Optimization Method

The Ensemble Optimization Method (EOM) is a popular approach to describe small-angle X-ray scattering (SAXS) data from highly disordered proteins. The EOM algorithm selects subensembles of coexisting states from large pools of randomized conformations to fit the SAXS data. Based on the unphysical bimodal radius of gyration (R_g) distribution of conformations resulting from the EOM analysis, a recent article (Fagerberg et al. J. Chem. Theory Comput. 2019, 15 (12), 6968-6983) concluded that this approach inadequately described the SAXS data measured for human Histatin 5 (Hst5), a peptide with antifungal properties. Using extensive experimental and synthetic data, we explored the origin of this observation. We found that the one-bead-per-residue coarse-grained representation with averaged scattering form factors (provided in the EOM as an add-on to represent disordered missing loops or domains) may not be appropriate for EOM analyses of scattering data from short (below 50 residues) proteins/peptides. The method of choice for these proteins is to employ atomistic models (e.g., from molecular dynamics simulations) to sample the protein conformational landscape. As a convenient alternative, we have also improved the coarse-grained approach by introducing amino acid specific form factors in the calculations. We also found that, for small proteins, the search for relatively large subensembles of 20-50 conformers (as implemented in the original EOM version) more adequately describes the conformational space sampled in solution than the procedures optimizing the ensemble size. Our observations have been added as recommendations into the information for EOM users to promote the proper utilization of the program for ensemble-based modeling of SAXS data for all types of disordered systems.

Configurational Entropy of Folded Proteins and Its Importance for Intrinsically Disordered Proteins

Many pairwise additive force fields are in active use for intrinsically disordered proteins (IDPs) and regions (IDRs), some of which modify energetic terms to improve the description of IDPs/IDRs but are largely in disagreement with solution experiments for the disordered states. This work considers a new direction-the connection to configurational entropy-and how it might change the nature of our understanding of protein force field development to equally well encompass globular proteins, IDRs/IDPs, and disorder-to-order transitions. We have evaluated representative pairwise and many-body protein and water force fields against experimental data on representative IDPs and IDRs, a peptide that undergoes a disorder-to-order transition, for seven globular proteins ranging in size from 130 to 266 amino acids. We find that force fields with the largest statistical fluctuations consistent with the radius of gyration and universal Lindemann values for folded states simultaneously better describe IDPs and IDRs and disorder-to-order transitions. Hence, the crux of what a force field should exhibit to well describe IDRs/IDPs is not just the balance between protein and water energetics but the balance between energetic effects and configurational entropy of folded states of globular proteins.

Impact of Arginine-Phosphate Interactions on the Reentrant Condensation of Disordered Proteins

Re-entrant condensation results in the formation of a condensed protein regime between two critical ion concentrations. The process is driven by neutralization and inversion of the protein charge by oppositely charged ions. Re-entrant condensation of cationic proteins by the polyvalent anions, pyrophosphate and tripolyphosphate, has previously been observed, but not for citrate, which has similar charge and size compared to the polyphosphates. Therefore, besides electrostatic interactions, other specific interactions between the polyphosphate ions and proteins must contribute. Here, we show that additional attractive interactions between arginine and tripolyphosphate determine the re-entrant condensation and decondensation boundaries of the cationic, intrinsically disordered saliva protein, histatin 5. Furthermore, we show by small-angle X-ray scattering (SAXS) that polyvalent anions cause compaction of histatin 5, as would be expected based solely on electrostatic interactions. Hence, we conclude that arginine-phosphate-specific interactions not only regulate solution properties but also influence the conformational ensemble of histatin 5, which is shown to vary with the number of arginine residues. Together, the results presented here provide further insight into an organizational mechanism that can be used to tune protein interactions in solution of both naturally occurring and synthetic proteins.

High resolution ensemble description of metamorphic and intrinsically disordered proteins using an efficient hybrid parallel tempering scheme

Mapping free energy landscapes of complex multi-funneled metamorphic proteins and weakly-funneled intrinsically disordered proteins (IDPs) remains challenging. While rare-event sampling molecular dynamics simulations can be useful, they often need to either impose restraints or reweigh the generated data to match experiments. Here, we present a parallel-tempering method that takes advantage of accelerated water dynamics and allows efficient and accurate conformational sampling across a wide variety of proteins. We demonstrate the improved sampling efficiency by benchmarking against standard model systems such as alanine di-peptide, TRP-cage and β-hairpin. The method successfully scales to large metamorphic proteins such as RFA-H and to highly disordered IDPs such as Histatin-5. Across the diverse proteins, the calculated ensemble averages match well with the NMR, SAXS and other biophysical experiments without the need to reweigh. By allowing accurate sampling across different landscapes, the method opens doors for sampling free energy landscape of complex uncharted proteins.

The Effects of Chain Length on the Structural Properties of Intrinsically Disordered Proteins in Concentrated Solutions

Intrinsically disordered proteins (IDP) are proteins that sample a heterogeneous ensemble of conformers in solution. An estimated 25–30% of all eukaryotic proteins belong to this class. In vivo, IDPs function under conditions that are highly crowded by other biological macromolecules. Previous research has highlighted that the presence of crowding agents can influence the conformational ensemble sampled by IDPs, resulting in either compaction or expansion. The effects of self-crowding of the disordered protein Histatin 5 has, in an earlier study, been found to have limited influence on the conformational ensemble. In this study, it is examined whether the short chain length of Histatin 5 can explain the limited effects of crowding observed, by introducing (Histatin 5)₂, a tandem repeat of Histatin 5. By utilizing small-angle X-ray scattering, it is shown that the conformational ensemble is conserved at high protein concentrations, in resemblance with Histatin 5, although with a lowered protein concentration at which aggregation arises. Under dilute conditions, atomistic molecular dynamics and coarse-grained Monte Carlo simulations, as well as an established scaling law, predicted more extended conformations than indicated by experimental data, hence implying that (Histatin 5)₂ does not behave as a self-avoiding random walk.

Sampling of the conformational landscape of small proteins with Monte Carlo methods

Computer simulation provides an increasingly realistic picture of large-scale conformational change of proteins, but investigations remain fundamentally constrained by the femtosecond timestep of molecular dynamics simulations. For this reason, many biologically interesting questions cannot be addressed using accessible state-of-the-art computational resources. Here, we report the development of an all-atom Monte Carlo approach that permits the modelling of the large-scale conformational change of proteins using standard off-the-shelf computational hardware and standard all-atom force fields. We demonstrate extensive thermodynamic characterization of the folding process of the α-helical Trp-cage, the Villin headpiece and the β-sheet WW-domain. We fully characterize the free energy landscape, transition states, energy barriers between different states, and the per-residue stability of individual amino acids over a wide temperature range. We demonstrate that a state-of-the-art intramolecular force field can be combined with an implicit solvent model to obtain a high quality of the folded structures and also discuss limitations that still remain.

Development of Charge-Augmented Three-Point Water Model (CAIPi3P) for Accurate Simulations of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are molecules without a fixed tertiary structure, exerting crucial roles in cellular signalling, growth and molecular recognition events. Due to their high plasticity, IDPs are very challenging in experimental and computational structural studies. To provide detailed atomic insight in IDPs' dynamics governing their functional mechanisms, all-atom molecular dynamics (MD) simulations are widely employed. However, the current generalist force fields and solvent models are unable to generate satisfactory ensembles for IDPs when compared to existing experimental data. In this work, we present a new solvation model, denoted as the Charge-Augmented Three-Point Water Model for Intrinsically Disordered Proteins (CAIPi3P). CAIPi3P has been generated by performing a systematic scan of atomic partial charges assigned to the widely popular molecular scaffold of the three-point TIP3P water model. We found that explicit solvent MD simulations employing CAIPi3P solvation considerably improved the small-angle X-ray scattering (SAXS) scattering profiles for three different IDPs. Not surprisingly, this improvement was further enhanced by using CAIPi3P water in combination with the protein force field parametrized for IDPs. We also demonstrated the applicability of CAIPi3P to molecular systems containing structured as well as intrinsically disordered regions/domains. Our results highlight the crucial importance of solvent effects for generating molecular ensembles of IDPs which reproduce the experimental data available. Hence, we conclude that our newly developed CAIPi3P solvation model is a valuable tool for molecular simulations of intrinsically disordered proteins and assessing their molecular dynamics.

Determining Rg of IDPs from SAXS Data

There is a great interest within the research community to understand the structure-function relationship for intrinsically disordered proteins (IDPs); however, the heterogeneous distribution of conformations that IDPs can adopt limits the applicability of conventional structural biology methods. Here, scattering techniques, such as small-angle X-ray scattering, can contribute. In this chapter, we will describe how to make a model-free determination of the radius of gyration by using two different approaches, the Guinier analysis and the pair distance distribution function. The ATSAS package (Franke et al., J Appl Crystallogr 50:1212-1225, 2017) has been used for the evaluation, and throughout the chapter, different examples will be given to illustrate the discussed phenomena, as well as the pros and cons of using the different approaches.

Glutenin and Gliadin, a Piece in the Puzzle of their Structural Properties in the Cell Described through Monte Carlo Simulations

Gluten protein crosslinking is a predetermined process where specific intra- and intermolecular disulfide bonds differ depending on the protein and cysteine motif. In this article, all-atom Monte Carlo simulations were used to understand the formation of disulfide bonds in gliadins and low molecular weight glutenin subunits (LMW-GS). The two intrinsically disordered proteins appeared to contain mostly turns and loops and showed "self-avoiding walk" behavior in water. Cysteine residues involved in intramolecular disulfide bonds were located next to hydrophobic peptide sections in the primary sequence. Hydrophobicity of neighboring peptide sections, synthesis chronology, and amino acid chain flexibility were identified as important factors in securing the specificity of intramolecular disulfide bonds formed directly after synthesis. The two LMW-GS cysteine residues that form intermolecular disulfide bonds were positioned next to peptide sections of lower hydrophobicity, and these cysteine residues are more exposed to the cytosolic conditions, which influence the crosslinking behavior. In addition, coarse-grained Monte Carlo simulations revealed that the protein folding is independent of ionic strength. The potential molecular behavior associated with disulfide bonds, as reported here, increases the biological understanding of seed storage protein function and provides opportunities to tailor their functional properties for different applications.

Optimization of Molecular Dynamics Simulations of c-MYC1-88-An Intrinsically Disordered System

Many of the proteins involved in key cellular regulatory events contain extensive intrinsically disordered regions that are not readily amenable to conventional structure/function dissection. The oncoprotein c-MYC plays a key role in controlling cell proliferation and apoptosis and more than 70% of the primary sequence is disordered. Computational approaches that shed light on the range of secondary and tertiary structural conformations therefore provide the only realistic chance to study such proteins. Here, we describe the results of several tests of force fields and water models employed in molecular dynamics simulations for the N-terminal 88 amino acids of c-MYC. Comparisons of the simulation data with experimental secondary structure assignments obtained by NMR establish a particular implicit solvation approach as highly congruent. The results provide insights into the structural dynamics of c-MYC^1-88, which will be useful for guiding future experimental approaches. The protocols for trajectory analysis described here will be applicable for the analysis of a variety of computational simulations of intrinsically disordered proteins.

Pseudo-Improper-Dihedral Model for Intrinsically Disordered Proteins

We present a new coarse-grained C_α-based protein model with a nonradial multibody pseudo-improper-dihedral potential that is transferable, time-independent, and suitable for molecular dynamics. It captures the nature of backbone and side-chain interactions between amino acid residues by adapting a simple improper dihedral term for a one-bead-per-residue model. It is parameterized for intrinsically disordered proteins and applicable to simulations of such proteins and their assemblies on millisecond time scales.

Hydropathy Patterning Complements Charge Patterning to Describe Conformational Preferences of Disordered Proteins

Understanding the conformational ensemble of an intrinsically disordered protein (IDP) is of great interest due to its relevance to critical intracellular functions and diseases. It is now well established that the polymer scaling behavior can provide a great deal of information about the conformational properties as well as liquid-liquid phase separation of an IDP. It is, therefore, extremely desirable to be able to predict an IDP's scaling behavior from the protein sequence itself. The work in this direction so far has focused on highly charged proteins and how charge patterning can perturb their structural properties. As naturally occurring IDPs are composed of a significant fraction of uncharged amino acids, the rules based on charge content and patterning are only partially helpful in solving the problem. Here, we propose a new order parameter, sequence hydropathy decoration, which can provide a near-quantitative understanding of scaling and structural properties of IDPs devoid of charged residues. We combine this with a charge patterning parameter, sequence charge decoration, to obtain a general equation, parametrized from extensive coarse-grained simulation data, for predicting protein dimensions from the sequence. We finally test this equation against available experimental data and find a semiquantitative match in predicting the scaling behavior. We also provide guidance on how to extend this approach to experimental data, which should be feasible in the near future.

Spontaneous Formation of Cushioned Model Membranes Promoted by an Intrinsically Disordered Protein

In this article, it is shown that by exposing commonly used lipids for biomembrane mimicking studies, to a solution containing the histidine-rich intrinsically disordered protein histatin 5, a protein cushion spontaneously forms underneath the bilayer. The underlying mechanism is attributed to have an electrostatic origin, and it is hypothesized that the observed behavior is due to proton charge fluctuations promoting attractive electrostatic interactions between the positively charged proteins and the anionic surfaces, with concomitant counterion release. Hence, we anticipate that this novel "green" approach of forming cushioned bilayers can be an important tool to mimic the cell membrane without the disturbance of the solid substrate, thereby achieving a further understanding of protein-cell interactions.

Integrating All-Atom and Coarse-Grained Simulations-Toward Understanding of IDPs at Surfaces

We present a scheme for transferring conformational degrees of freedom from all-atom (AA) simulations of an intrinsically disordered protein (IDP) to coarse-grained (CG) Monte Carlo (MC) simulations using conformational swap moves. AA simulations of a single histatin 5 peptide in water were used to obtain a structural ensemble, which is reweighted in a CGMC simulation in the presence of a negatively charged surface. For efficient sampling, the AA trajectory was condensed using two approaches: RMSD clustering (based on the root-mean-square difference in atom positions) and a "naı̈ve" truncation, where only every 100th frame of the trajectory was included in the library. The results show that even libraries with few structures well reproduce the radius of gyration and interaction free energy as functions of the distance from the surface. We further observe that the surface slightly promotes the secondary structure of histatin 5 and more so if using explicit surface charges rather than smeared charges.

Predicting Conformational Properties of Intrinsically Disordered Proteins from Sequence

Intrinsically disordered proteins (IDPs) can adopt a range of conformations from globules to swollen coils. This large range of conformational preferences for different IDPs raises the question of how conformational preferences are encoded by sequence. Global compositional features of a sequence such as the fraction of charged residues and the net charge per residue engender certain conformational biases. However, more specific sequence features such as the patterning of oppositely charged residues, expansion driving residues, or residues that can undergo posttranslational modifications can also influence the conformational ensembles of an IDP. Here, we outline how to calculate important global compositional features and patterning metrics that can be used to classify IDPs into different conformational classes and predict relative changes in conformation for sequences with the same amino acid composition. Although increased effort has been devoted to determining conformational properties of IDPs in recent years, quantitative predictions of conformation directly from sequence remain difficult and often inaccurate. Thus, if quantitative predictions of conformational properties are desired, then sequence-specific simulations must be performed.

Maximum Entropy Optimized Force Field for Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) constitute a significant fraction of eukaryotic proteomes. High-resolution characterization of IDP conformational ensembles can help elucidate their roles in a wide range of biological processes but remains challenging both experimentally and computationally. Here, we present a generic algorithm to improve the accuracy of coarse-grained IDP models using a diverse set of experimental measurements. It combines maximum entropy optimization and least-squares regression to systematically adjust model parameters and improve the agreement between simulation and experiment. We successfully applied the algorithm to derive a transferable force field, which we term the maximum entropy optimized force field (MOFF), for de novo prediction of IDP structures. Statistical analysis of force field parameters reveals features of amino acid interactions not captured by potentials designed to work well for folded proteins. We anticipate its combination of efficiency and accuracy will make MOFF useful for studying the phase separation of IDPs, which drives the formation of various biological compartments.

Extensive tests and evaluation of the CHARMM36IDPSFF force field for intrinsically disordered proteins and folded proteins

Intrinsically disordered proteins (IDPs) have received increasing attention in recent studies due to their structural heterogeneity and critical biological functions. To fully understand the structural properties and determine accurate ensembles of IDPs, molecular dynamics (MD) simulation was widely used to sample diverse conformations and reveal the structural dynamics. However, the classical state-of-the-art force fields perform well for folded proteins while being unsatisfactory for the simulations of disordered proteins reported in many previous studies. Thus, improved force fields were developed to precisely describe both folded proteins and disordered proteins. Preliminary tests show that our newly developed CHARMM36IDPSFF (C36IDPSFF) force field can well reproduce the experimental observables of several disordered proteins, but more tests on different types of proteins are needed to further evaluate the performance of C36IDPSFF. Here, we extensively simulate short peptides, disordered proteins, and fast-folding proteins as well as folded proteins, and compare the simulated results with the experimental observables. The simulation results show that C36IDPSFF could substantially reproduce the experimental observables for most of the tested proteins but some limitations are also found in the radius of gyration of large disordered proteins and the stability of fast-folding proteins. This force field will facilitate large scale studies of protein structural dynamics and functions using MD simulations.

Specific metallo-protein interactions and antimicrobial activity in Histatin-5, an intrinsically disordered salivary peptide

Histatin-5 (Hst-5) is an antimicrobial, salivary protein that is involved in the host defense system. Hst-5 has been proposed to bind functionally relevant zinc and copper but presents challenges in structural studies due to its disordered conformation in aqueous solution. Here, we used circular dichroism (CD) and UV resonance Raman (UVRR) spectroscopy to define metallo-Hst-5 interactions in aqueous solution. A zinc-containing Hst-5 sample exhibits shifted Raman bands, relative to bands observed in the absence of zinc. Based on comparison to model compounds and to a family of designed, zinc-binding beta hairpins, the alterations in the Hst-5 UVRR spectrum are attributed to zinc coordination by imidazole side chains. Zinc addition also shifted a tyrosine aromatic ring UVRR band through an electrostatic interaction. Copper addition did not have these effects. A sequence variant, H18A/H19A, was employed; this mutant has less potent antifungal activity, when compared to Hst-5. Zinc addition had only a small effect on the thermal stability of this mutant. Interestingly, both zinc and copper addition shifted histidine UVRR bands in a manner diagnostic for metal coordination. Results obtained with a K13E/R22G mutant were similar to those obtained with wildtype. These experiments show that H18 and H19 contribute to a zinc binding site. In the H18A/H19A mutant the specificity of the copper/zinc binding sites is lost. The experiments implicate specific zinc binding to be important in the antimicrobial activity of Hst-5.

Dynamical Oligomerisation of Histidine Rich Intrinsically Disordered ProteinS Is Regulated through Zinc-Histidine Interactions

Intrinsically disordered proteins (IDPs) can form functional oligomers and in some cases, insoluble disease related aggregates. It is therefore vital to understand processes and mechanisms that control pathway distribution. Divalent cations including Zn²⁺ can initiate IDP oligomerisation through the interaction with histidine residues but the mechanisms of doing so are far from understood. Here we apply a multi-disciplinary approach using small angle X-ray scattering, nuclear magnetic resonance spectroscopy, calorimetry and computations to show that that saliva protein Histatin 5 forms highly dynamic oligomers in the presence of Zn²⁺. The process is critically dependent upon interaction between Zn²⁺ ions and distinct histidine rich binding motifs which allows for thermodynamic switching between states. We propose a molecular mechanism of oligomerisation, which may be generally applicable to other histidine rich IDPs. Finally, as Histatin 5 is an important saliva component, we suggest that Zn²⁺ induced oligomerisation may be crucial for maintaining saliva homeostasis.

Sequence Effects on Size, Shape, and Structural Heterogeneity in Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) lack well-defined three-dimensional structures, thus challenging the archetypal notion of structure-function relationships. Determining the ensemble of conformations that IDPs explore under physiological conditions is the first step toward understanding their diverse cellular functions. Here, we quantitatively characterize the structural features of IDPs as a function of sequence and length using coarse-grained simulations. For diverse IDP sequences, with the number of residues ( NT) ranging from 20 to 441, our simulations not only reproduce the radii of gyration ( Rg) obtained from experiments, but also predict the full scattering intensity profiles in excellent agreement with small-angle X-ray scattering experiments. The Rg values are well-described by the standard Flory scaling law, Rg = Rg0 NTν, with ν ≈ 0.588, making it tempting to assert that IDPs behave as polymers in a good solvent. However, clustering analysis reveals that the menagerie of structures explored by IDPs is diverse, with the extent of heterogeneity being highly sequence-dependent, even though ensemble-averaged properties, such as the dependence of Rg on chain length, may suggest synthetic polymer-like behavior in a good solvent. For example, we show that for the highly charged Prothymosin-α, a substantial fraction of conformations is highly compact. Even if the sequence compositions are similar, as is the case for α-Synuclein and a truncated construct from the Tau protein, there are substantial differences in the conformational heterogeneity. Taken together, these observations imply that metrics based on net charge or related quantities alone cannot be used to anticipate the phases of IDPs, either in isolation or in complex with partner IDPs or RNA. Our work sets the stage for probing the interactions of IDPs with each other, with folded protein domains, or with partner RNAs, which are critical for describing the structures of stress granules and biomolecular condensates with important cellular functions.

An Extended Guinier Analysis for Intrinsically Disordered Proteins

Guinier analysis allows model-free determination of the radius of gyration (R_g) of a biomolecule from X-ray or neutron scattering data, in the limit of very small scattering angles. Its range of validity is well understood for globular proteins, but is known to be more restricted for unfolded or intrinsically disordered proteins (IDPs). We have used ensembles of disordered structures from molecular dynamics simulations to investigate which structural properties cause deviations from the Guinier approximation at small scattering angles. We find that the deviation from the Guinier approximation is correlated with the polymer scaling exponent ν describing the unfolded ensemble. We therefore introduce an empirical, ν-dependent, higher-order correction term, to augment the standard Guinier analysis. We test the new fitting scheme using all-atom simulation data for several IDPs and experimental data for both an IDP and a destabilized mutant of a folded protein. In all cases tested, we achieve an accuracy of the inferred R_g within ∼3% of the true R_g. The method is straightforward to implement and extends the range of validity to a maximum qR_g of ∼2 versus ∼1.1 for Guinier analysis. Compared with the Guinier or Debye approaches, our method allows data from wider angles with lower noise to be used to analyze scattering data accurately. In addition to R_g, our fitting scheme also yields estimates of the scaling exponent ν in excellent agreement with the reference ν determined from the underlying molecular ensemble.

On the Calculation of SAXS Profiles of Folded and Intrinsically Disordered Proteins from Computer Simulations

Solution techniques such as small-angle X-ray scattering (SAXS) play a central role in structural studies of intrinsically disordered proteins (IDPs); yet, due to low resolution, it is generally necessary to combine SAXS with additional experimental sources of data and to use molecular simulations. Computational methods for the calculation of theoretical SAXS intensity profiles can be separated into two groups, depending on whether the solvent is modeled implicitly as continuous electron density or considered explicitly. The former offers reduced computational cost but requires the definition of a number of free parameters to account for, for example, the excess density of the solvation layer. Overfitting can thus be an issue, particularly when the structural ensemble is unknown. Here, we investigate and show how small variations of the contrast of the hydration shell, δρ, severely affect the outcome, analysis and interpretation of computed SAXS profiles for folded and disordered proteins. For both the folded and disordered proteins studied here, using a default δρ may, in some cases, result in the calculation of non-representative SAXS profiles, leading to an overestimation of their size and a misinterpretation of their structural nature. The solvation layer of the different IDP simulations also impacts their size estimates differently, depending on the protein force field used. The same is not true for the folded protein simulations, suggesting differences in the solvation of the two classes of proteins, and indicating that different force fields optimized for IDPs may cause expansion of the polypeptide chain through different physical mechanisms.

Characterization of the structural ensembles of p53 TAD2 by molecular dynamics simulations with different force fields

The conformations of p53 TAD2 in complexes and sampled in simulations with five force fields.

Structural Characterization of Histatin 5-Spermidine Conjugates: A Combined Experimental and Theoretical Study

Histatin 5 (Hst5) is a naturally occurring antimicrobial peptide that acts as the first line of defense against oral candidiasis. It has been shown that conjugation of the active Hst5 fragment, Hst5_4-15, and the polyamine spermidine (Spd) improves the candidacidal effect. Knowledge about the structure of these conjugates is, however, very limited. Thus, the aim of this study was to characterize the structural properties of the Hst5_4-15-Spd conjugates by performing atomistic molecular dynamics simulations in combination with small-angle X-ray scattering. It was shown that the Hst5_4-15-Spd conjugates adopt extended and slightly rigid random coil conformations without any secondary structure in aqueous solution. It is hypothesized that the increased fungal killing potential of Hst5_4-15-Spd, in comparison with the Spd-Hst5_4-15 conjugate, is due to the more extended conformations of the former, which cause the bonded Spd molecule to be more accessible for recognition by polyamine transporters in the cell.

Determining Atomistic SAXS Models of Tri-Ubiquitin Chains from Bayesian Analysis of Accelerated Molecular Dynamics Simulations

Small-angle X-ray scattering (SAXS) has become an increasingly popular technique for characterizing the solution ensemble of flexible biomolecules. However, data resulting from SAXS is typically low-dimensional and is therefore difficult to interpret without additional structural knowledge. In theory, molecular dynamics (MD) trajectories can provide this information, but conventional simulations rarely sample the complete ensemble. Here, we demonstrate that accelerated MD simulations can be used to produce higher quality models in shorter time scales than standard simulations, and we present an iterative Bayesian Monte Carlo method that is able to identify multistate ensembles without overfitting. This methodology is applied to several ubiquitin trimers to demonstrate the effect of linkage type on the solution states of the signaling protein. We observe that the linkage site directly affects the solution flexibility of the trimer and theorize that this difference in plasticity contributes to their disparate roles in vivo.

Molecular Dynamics Simulations of Intrinsically Disordered Proteins: On the Accuracy of the TIP4P-D Water Model and the Representativeness of Protein Disorder Models

Here, we first present a follow-up to a previous work by our group on the problematic of molecular dynamics simulations of intrinsically disordered proteins (IDPs) [ Henriques et al. J. Chem. Theory Comput. 2015 , 11 , 3420 - 3431 ], using the recently developed TIP4P-D water model. When used in conjunction with the standard AMBER ff99SB-ILDN force field and applied to the simulation of Histatin 5, our IDP model, we obtain results which are in excellent agreement with the best performing IDP-suitable force field from the earlier study and with experiment. We then assess the representativeness of the IDP models used in these and similar studies, finding that most are too short in comparison to the average IDP and contain a bias toward hydrophilic amino acid residues. Moreover, several key order- and disorder-promoting residues are also found to be misrepresented. It seems appropriate for future studies to address these issues.