AWSEM-IDP: A Coarse-Grained Force Field for Intrinsically Disordered Proteins

Wild-Type α-Synuclein Structure and Aggregation: A Comprehensive Coarse-Grained and All-Atom Molecular Dynamics Study

α-Synuclein (α-syn) is a 140 amino acid intrinsically disordered protein (IDP) and the primary component of cytotoxic oligomers implicated in the etiology of Parkinson's disease (PD). While IDPs lack a stable three-dimensional structure, they sample a heterogeneous ensemble of conformations that can, in principle, be assessed through molecular dynamics simulations. However, describing the structure and aggregation of large IDPs is challenging due to force field (FF) accuracy and sampling limitations. To cope with the latter, coarse-grained (CG) FFs emerge as a potential alternative at the expense of atomic detail loss. Whereas CG models can accurately describe the structure of the monomer, less is known about aggregation. The latter is key for assessing aggregation pathways and designing aggregation inhibitor drugs. Herein, we investigate the structure and dynamics of α-syn using different resolution CG (Martini3 and Sirah2) and all-atom (Amber99sb and Charmm36m) FFs to gain insight into the differences and resemblances between these models. The dependence of the magnitude of protein-water interactions and the putative need for enhanced sampling (replica exchange) methods in CG simulations are analyzed to distinguish between force field accuracy and sampling limitations. The stability of the CG models of an α-syn fibril was also investigated. Additionally, α-syn aggregation was studied through umbrella sampling for the CG models and CG/all-atom models for an 11-mer peptide (NACore) from an amyloidogenic domain of α-syn. Our results show that despite the α-syn structures of Martini3 and Sirah2 with enhanced protein-water interactions being similar, major differences exist concerning aggregation. The Martini3 fibril is not stable, and the binding free energy of α-syn and NACore is positive, opposite to Sirah2. Sirah2 peptides in a zwitterionic form, in turn, display termini interactions that are too strong, resulting in end-to-end orientation. Sirah2, with enhanced protein-water interactions and neutral termini, provides, however, a peptide aggregation free energy profile similar to that found with all-atom models. Overall, we find that Sirah2 with enhanced protein-water interactions is suitable for studying protein-protein and protein-drug aggregation.

A Practical Guide to All-Atom and Coarse-Grained Molecular Dynamics Simulations Using Amber and Gromacs: A Case Study of Disulfide-Bond Impact on the Intrinsically Disordered Amyloid Beta

Intrinsically disordered proteins (IDPs) pose challenges to conventional experimental techniques due to their large-scale conformational fluctuations and transient structural elements. This work presents computational methods for studying IDPs at various resolutions using the Amber and Gromacs packages with both all-atom (Amber ff19SB with the OPC water model) and coarse-grained (Martini 3 and SIRAH) approaches. The effectiveness of these methodologies is demonstrated by examining the monomeric form of amyloid-β (Aβ42), an IDP, with and without disulfide bonds at different resolutions. Our results clearly show that the addition of a disulfide bond decreases the β-content of Aβ42; however, it increases the tendency of the monomeric Aβ42 to form fibril-like conformations, explaining the various aggregation rates observed in experiments. Moreover, analysis of the monomeric Aβ42 compactness, secondary structure content, and comparison between calculated and experimental chemical shifts demonstrates that all three methods provide a reasonable choice to study IDPs; however, coarse-grained approaches may lack some atomistic details, such as secondary structure recognition, due to the simplifications used. In general, this study not only explains the role of disulfide bonds in Aβ42 but also provides a step-by-step protocol for setting up, conducting, and analyzing molecular dynamics (MD) simulations, which is adaptable for studying other biomacromolecules, including folded and disordered proteins and peptides.

Molecular Dynamics Simulations of Polyelectrolyte Complexes

Polyelectrolyte complexes (PECs) are currently of great interest due to their applications toward developing new adaptive materials and their relevance in membraneless organelles. These complexes emerge during phase separation when oppositely charged polymers are mixed in aqueous media. Peptide-based PECs are particularly useful toward developing new drug delivery methods due to their inherent biocompatibility. The underlying peptide sequence can be tuned to optimize specific material properties of the complex, such as interfacial tension and viscosity. Given their applicability, it would be advantageous to understand the underlying sequence-dependent phase behavior of oppositely charged peptides. Here, we report microsecond molecular dynamic simulations to characterize the effect of hydrophobicity on the sequence-dependent peptide conformation for model polypeptide sequences that were previously reported by Tabandeh et al. These sequences are designed with alternating chirality of the peptide backbone. We present microsecond simulations of six oppositely charged peptide pairs, characterizing the sequence-dependent effect on peptide size, degree of hydrogen bonding, secondary structure, and conformation. This analysis recapitulates sensible trends in peptide conformation and degree of hydrogen bonding, consistent with experimentally reported results. Ramachandran plots reveal that backbone conformation at the single amino acid level is highly influenced by the neighboring sequence in the chain. These results give insight into how subtle changes in hydrophobic side chain size and chirality influence the strength of hydrogen bonding between the chains and, ultimately, the secondary structure. Furthermore, principal component analysis reveals that the minimum energy structures may be subtly modulated by the underlying sequence.

Direct prediction of intrinsically disordered protein conformational properties from sequence

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

Toward Accurate Simulation of Coupling between Protein Secondary Structure and Phase Separation

Intrinsically disordered proteins (IDPs) frequently mediate phase separation that underlies the formation of a biomolecular condensate. Together with theory and experiment, efficient coarse-grained (CG) simulations have been instrumental in understanding the sequence-specific phase separation of IDPs. However, the widely used Cα-only models are limited in capturing the peptide nature of IDPs, particularly backbone-mediated interactions and effects of secondary structures, in phase separation. Here, we describe a hybrid resolution (HyRes) protein model toward a more accurate description of the backbone and transient secondary structures in phase separation. With an atomistic backbone and coarse-grained side chains, HyRes can semiquantitatively capture the residue helical propensity and overall chain dimension of monomeric IDPs. Using GY-23 as a model system, we show that HyRes is efficient enough for the direct simulation of spontaneous phase separation and, at the same time, appears accurate enough to resolve the effects of single His to Lys mutations. HyRes simulations also successfully predict increased β-structure formation in the condensate, consistent with available experimental CD data. We further utilize HyRes to study the phase separation of TPD-43, where several disease-related mutants in the conserved region (CR) have been shown to affect residual helicities and modulate the phase separation propensity as measured by the saturation concentration. The simulations successfully recapitulate the effect of these mutants on the helicity and phase separation propensity of TDP-43 CR. Analyses reveal that the balance between backbone and side chain-mediated interactions, but not helicity itself, actually determines phase separation propensity. These results support that HyRes represents an effective protein model for molecular simulation of IDP phase separation and will help to elucidate the coupling between transient secondary structures and phase separation.

RNA regulates cohesiveness and porosity of a biological condensate

Biological condensates have emerged as key elements of a biological cell function, concentrating disparate biomolecules to accomplish specific biological tasks. RNA was identified as a key ingredient of such condensates, however, its effect on the physical properties of the condensate was found to depend on the condensate's composition while its effect on the microstructure has remained elusive. Here, we characterize the physical properties and the microstructure of a protein-RNA condensate by means of large-scale coarse-grained (CG) molecular dynamics simulations. By developing a custom CG model of RNA compatible with a popular CG model of proteins, we systematically investigate the structural, thermodynamic, and kinetic properties of condensate droplets containing thousands of individual protein and RNA molecules over a range of temperatures. While we find RNA to increase the condensate's cohesiveness, its effect on the condensate's fluidity is more nuanced with longer molecules compacting the condensate and making it less fluid. We show that a biological condensate has a sponge-like morphology of interconnected channels of size that increases with temperature and decreases in the presence of RNA. Our results suggest that longer RNA form a dynamic scaffold within a condensate, regulating not only its fluidity but also permeability to intruder molecules.

Molecular Docking of Intrinsically Disordered Proteins: Challenges and Strategies

Intrinsically disordered proteins (IDPs) are a novel class of proteins that have established a significant importance and attention within a very short period of time. These proteins are essentially characterized by their inherent structural disorder, encoded mainly by their amino acid sequences. The profound abundance of IDPs and intrinsically disordered regions (IDRs) in the biological world delineates their deep-rooted functionality. IDPs and IDRs convey such extensive functionality through their unique dynamic nature, which enables them to carry out huge number of multifaceted biomolecular interactions and make them "interaction hub" of the cellular systems. Additionally, with such widespread functions, their misfunctioning is also intimately associated with multiple diseases. Thus, understanding the dynamic heterogeneity of various IDPs along with their interactions with respective binding partners is an important field with immense potentials in biomolecular research. In this context, molecular docking-based computational approaches have proven to be remarkable in case of ordered proteins. Molecular docking methods essentially model the biomolecular interactions in both structural and energetic terms and use this information to characterize the putative interactions between the two participant molecules. However, direct applications of the conventional docking methods to study IDPs are largely limited by their structural heterogeneity and demands for unique IDP-centric strategies. Thus, in this chapter, we have presented an overview of current methodologies for successful docking operations involving IDPs and IDRs. These specialized methods majorly include the ensemble-based and fragment-based approaches with their own benefits and limitations. More recently, artificial intelligence and machine learning-assisted approaches are also used to significantly reduce the complexity and computational burden associated with various docking applications. Thus, this chapter aims to provide a comprehensive summary of major challenges and recent advancements of molecular docking approaches in the IDP field for their better utilization and greater applicability.Asp (D).

The role of cryptic ancestral symmetry in histone folding mechanisms across Eukarya and Archaea

Histones compact and store DNA in both Eukarya and Archaea, forming heterodimers in Eukarya and homodimers in Archaea. Despite this, the folding mechanism of histones across species remains unclear. Our study addresses this gap by investigating 11 types of histone and histone-like proteins across humans, Drosophila, and Archaea through multiscale molecular dynamics (MD) simulations, complemented by NMR and circular dichroism experiments. We confirm and elaborate on the widely applied "folding upon binding" mechanism of histone dimeric proteins and report a new alternative conformation, namely, the inverted non-native dimer, which may be a thermodynamically metastable configuration. Protein sequence analysis indicated that the inverted conformation arises from the hidden ancestral head-tail sequence symmetry underlying all histone proteins, which is congruent with the previously proposed histone evolution hypotheses. Finally, to explore the potential formations of homodimers in Eukarya, we utilized MD-based AWSEM and AI-based AlphaFold-Multimer models to predict their structures and conducted extensive all-atom MD simulations to examine their respective structural stabilities. Our results suggest that eukaryotic histones may also form stable homodimers, whereas their disordered tails bring significant structural asymmetry and tip the balance towards the formation of commonly observed heterotypic dimers.

Transferable Implicit Solvation via Contrastive Learning of Graph Neural Networks

Implicit solvent models are essential for molecular dynamics simulations of biomolecules, striking a balance between computational efficiency and biological realism. Efforts are underway to develop accurate and transferable implicit solvent models and coarse-grained (CG) force fields in general, guided by a bottom-up approach that matches the CG energy function with the potential of mean force (PMF) defined by the finer system. However, practical challenges arise due to the lack of analytical expressions for the PMF and algorithmic limitations in parameterizing CG force fields. To address these challenges, a machine learning-based approach is proposed, utilizing graph neural networks (GNNs) to represent the solvation free energy and potential contrasting for parameter optimization. We demonstrate the effectiveness of the approach by deriving a transferable GNN implicit solvent model using 600,000 atomistic configurations of six proteins obtained from explicit solvent simulations. The GNN model provides solvation free energy estimations much more accurately than state-of-the-art implicit solvent models, reproducing configurational distributions of explicit solvent simulations. We also demonstrate the reasonable transferability of the GNN model outside of the training data. Our study offers valuable insights for deriving systematically improvable implicit solvent models and CG force fields from a bottom-up perspective.

"Boundary residues" between the folded RNA recognition motif and disordered RGG domains are critical for FUS-RNA binding

Fused in sarcoma (FUS) is an abundant RNA-binding protein, which drives phase separation of cellular condensates and plays multiple roles in RNA regulation. The RNA-binding ability of FUS protein is crucial to its cellular function. Here, our molecular simulation study on the FUS-RNA complex provides atomic resolution insights into the observations from biochemical studies and also illuminates our understanding of molecular driving forces that mediate the structure, stability, and interaction of the RNA recognition motif (RRM) and RGG domains of FUS with a stem-loop junction RNA. We observe clear cooperativity and division of labor among the ordered (RRM) and disordered domains (RGG1 and RGG2) of FUS that leads to an organized and tighter RNA binding. Irrespective of the length of RGG2, the RGG2-RNA interaction is confined to the stem-loop junction and the proximal stem regions. On the other hand, the RGG1 interactions are primarily with the longer RNA stem. We find that the C terminus of RRM, which make up the "boundary residues" that connect the folded RRM with the long disordered RGG2 stretch of the protein, plays a critical role in FUS-RNA binding. Our study provides high-resolution molecular insights into the FUS-RNA interactions and forms the basis for understanding the molecular origins of full-length FUS interaction with RNA.

Pragmatic Coarse-Graining of Proteins: Models and Applications

The molecular details involved in the folding, dynamics, organization, and interaction of proteins with other molecules are often difficult to assess by experimental techniques. Consequently, computational models play an ever-increasing role in the field. However, biological processes involving large-scale protein assemblies or long time scale dynamics are still computationally expensive to study in atomistic detail. For these applications, employing coarse-grained (CG) modeling approaches has become a key strategy. In this Review, we provide an overview of what we call pragmatic CG protein models, which are strategies combining, at least in part, a physics-based implementation and a top-down experimental approach to their parametrization. In particular, we focus on CG models in which most protein residues are represented by at least two beads, allowing these models to retain some degree of chemical specificity. A description of the main modern pragmatic protein CG models is provided, including a review of the most recent applications and an outlook on future perspectives in the field.

Transferable Coarse Graining via Contrastive Learning of Graph Neural Networks

Coarse-grained (CG) force fields are essential for molecular dynamics simulations of biomolecules, striking a balance between computational efficiency and biological realism. These simulations employ simplified models grouping atoms into interaction sites, enabling the study of complex biomolecular systems over biologically relevant timescales. Efforts are underway to develop accurate and transferable CG force fields, guided by a bottom-up approach that matches the CG energy function with the potential of mean force (PMF) defined by the finer system. However, practical challenges arise due to many-body effects, lack of analytical expressions for the PMF, and limitations in parameterizing CG force fields. To address these challenges, a machine learning-based approach is proposed, utilizing graph neural networks (GNNs) to represent CG force fields and potential contrasting for parameterization from atomistic simulation data. We demonstrate the effectiveness of the approach by deriving a transferable GNN implicit solvent model using 600,000 atomistic configurations of six proteins obtained from explicit solvent simulations. The GNN model provides solvation free energy estimations much more accurately than state-of-the-art implicit solvent models, reproducing configurational distributions of explicit solvent simulations. We also demonstrate the reasonable transferability of the GNN model outside the training data. Our study offers valuable insights for building accurate coarse-grained models bottom-up.

Not Only Expansion: Proline Content and Density Also Induce Disordered Protein Conformation Compaction

Intrinsically disordered proteins (IDPs) adopt a wide array of different conformations that can be constrained by the presence of proline residues, which are frequently found in IDPs. To assess the effects of proline, we designed a series of peptides that differ with respect to the number of prolines in the sequence and their organization. Using high-resolution atomistic molecular dynamics simulations, we found that accounting for whether the proline residues are clustered or isolated contributed significantly to explaining deviations in the experimentally-determined gyration radii of IDPs from the values expected based on the Flory scaling-law. By contrast, total proline content makes smaller contribution to explaining the effect of prolines on IDP conformation. Proline residues exhibit opposing effects depending on their organizational pattern in the IDP sequence. Clustered prolines (i.e., prolines with ≤2 intervening non-proline residues) result in expanded peptide conformations whereas isolated prolines (i.e., prolines with >2 intervening non-proline residues) impose compacted conformations. Clustered prolines were estimated to induce an expansion of ∼20% in IDP dimension (via formation of PPII structural elements) whereas isolated prolines were estimated to induce a compaction of ∼10% in IDP dimension (via the formation of backbone turns). This dual role of prolines provides a mechanism for conformational switching that does not rely on the kinetically much slower isomerization of cis proline to the trans form. Bioinformatic analysis demonstrates high populations of both isolated and clustered prolines and implementing them in coarse-grained molecular dynamics models illustrates that they improve the characterization of the conformational ensembles of IDPs.

Accurate Simulation of Coupling between Protein Secondary Structure and Liquid-Liquid Phase Separation

Intrinsically disordered proteins (IDPs) frequently mediate liquid-liquid phase separation (LLPS) that underlies the formation of membraneless organelles. Together with theory and experiment, efficient coarse-grained (CG) simulations have been instrumental in understanding sequence-specific phase separation of IDPs. However, the widely-used Cα-only models are severely limited in capturing the peptide nature of IDPs, including backbone-mediated interactions and effects of secondary structures, in LLPS. Here, we describe a hybrid resolution (HyRes) protein model for accurate description of the backbone and transient secondary structures in LLPS. With an atomistic backbone and coarse-grained side chains, HyRes accurately predicts the residue helical propensity and chain dimension of monomeric IDPs. Using GY-23 as a model system, we show that HyRes is efficient enough for direct simulation of spontaneous phase separation, and at the same time accurate enough to resolve the effects of single mutations. HyRes simulations also successfully predict increased beta-sheet formation in the condensate, consistent with available experimental data. We further utilize HyRes to study the phase separation of TPD-43, where several disease-related mutants in the conserved region (CR) have been shown to affect residual helicities and modulate LLPS propensity. The simulations successfully recapitulate the effect of these mutants on the helicity and LLPS propensity of TDP-43 CR. Analyses reveal that the balance between backbone and sidechain-mediated interactions, but not helicity itself, actually determines LLPS propensity. We believe that the HyRes model represents an important advance in the molecular simulation of LLPS and will help elucidate the coupling between IDP transient secondary structures and phase separation.

New Insights into the Cooperativity and Dynamics of Dimeric Enzymes

A survey of protein databases indicates that the majority of enzymes exist in oligomeric forms, with about half of those found in the UniProt database being homodimeric. Understanding why many enzymes are in their dimeric form is imperative. Recent developments in experimental and computational techniques have allowed for a deeper comprehension of the cooperative interactions between the subunits of dimeric enzymes. This review aims to succinctly summarize these recent advancements by providing an overview of experimental and theoretical methods, as well as an understanding of cooperativity in substrate binding and the molecular mechanisms of cooperative catalysis within homodimeric enzymes. Focus is set upon the beneficial effects of dimerization and cooperative catalysis. These advancements not only provide essential case studies and theoretical support for comprehending dimeric enzyme catalysis but also serve as a foundation for designing highly efficient catalysts, such as dimeric organic catalysts. Moreover, these developments have significant implications for drug design, as exemplified by Paxlovid, which was designed for the homodimeric main protease of SARS-CoV-2.

Clustering Heterogeneous Conformational Ensembles of Intrinsically Disordered Proteins with t-Distributed Stochastic Neighbor Embedding

Intrinsically disordered proteins (IDPs) populate a range of conformations that are best described by a heterogeneous ensemble. Grouping an IDP ensemble into "structurally similar" clusters for visualization, interpretation, and analysis purposes is a much-desired but formidable task, as the conformational space of IDPs is inherently high-dimensional and reduction techniques often result in ambiguous classifications. Here, we employ the t-distributed stochastic neighbor embedding (t-SNE) technique to generate homogeneous clusters of IDP conformations from the full heterogeneous ensemble. We illustrate the utility of t-SNE by clustering conformations of two disordered proteins, Aβ42, and α-synuclein, in their APO states and when bound to small molecule ligands. Our results shed light on ordered substates within disordered ensembles and provide structural and mechanistic insights into binding modes that confer specificity and affinity in IDP ligand binding. t-SNE projections preserve the local neighborhood information, provide interpretable visualizations of the conformational heterogeneity within each ensemble, and enable the quantification of cluster populations and their relative shifts upon ligand binding. Our approach provides a new framework for detailed investigations of the thermodynamics and kinetics of IDP ligand binding and will aid rational drug design for IDPs.

Toward a general neural network force field for protein simulations: Refining the intramolecular interaction in protein

Molecular dynamics (MD) is an extremely powerful, highly effective, and widely used approach to understanding the nature of chemical processes in atomic details for proteins. The accuracy of results from MD simulations is highly dependent on force fields. Currently, molecular mechanical (MM) force fields are mainly utilized in MD simulations because of their low computational cost. Quantum mechanical (QM) calculation has high accuracy, but it is exceedingly time consuming for protein simulations. Machine learning (ML) provides the capability for generating accurate potential at the QM level without increasing much computational effort for specific systems that can be studied at the QM level. However, the construction of general machine learned force fields, needed for broad applications and large and complex systems, is still challenging. Here, general and transferable neural network (NN) force fields based on CHARMM force fields, named CHARMM-NN, are constructed for proteins by training NN models on 27 fragments partitioned from the residue-based systematic molecular fragmentation (rSMF) method. The NN for each fragment is based on atom types and uses new input features that are similar to MM inputs, including bonds, angles, dihedrals, and non-bonded terms, which enhance the compatibility of CHARMM-NN to MM MD and enable the implementation of CHARMM-NN force fields in different MD programs. While the main part of the energy of the protein is based on rSMF and NN, the nonbonded interactions between the fragments and with water are taken from the CHARMM force field through mechanical embedding. The validations of the method for dipeptides on geometric data, relative potential energies, and structural reorganization energies demonstrate that the CHARMM-NN local minima on the potential energy surface are very accurate approximations to QM, showing the success of CHARMM-NN for bonded interactions. However, the MD simulations on peptides and proteins indicate that more accurate methods to represent protein-water interactions in fragments and non-bonded interactions between fragments should be considered in the future improvement of CHARMM-NN, which can increase the accuracy of approximation beyond the current mechanical embedding QM/MM level.

Evolution of Sequence and Structure of SARS-CoV-2 Spike Protein: A Dynamic Perspective

Novel coronavirus (SARS-CoV-2) enters its host cell through a surface spike protein. The viral spike protein has undergone several modifications/mutations at the genomic level, through which it modulated its structure-function and passed through several variants of concern. Recent advances in high-resolution structure determination and multiscale imaging techniques, cost-effective next-generation sequencing, and development of new computational methods (including information theory, statistical methods, machine learning, and many other artificial intelligence-based techniques) have hugely contributed to the characterization of sequence, structure, function of spike proteins, and its different variants to understand viral pathogenesis, evolutions, and transmission. Laying on the foundation of the sequence-structure-function paradigm, this review summarizes not only the important findings on structure/function but also the structural dynamics of different spike components, highlighting the effects of mutations on them. As dynamic fluctuations of three-dimensional spike structure often provide important clues for functional modulation, quantifying time-dependent fluctuations of mutational events over spike structure and its genetic/amino acidic sequence helps identify alarming functional transitions having implications for enhanced fusogenicity and pathogenicity of the virus. Although these dynamic events are more difficult to capture than quantifying a static, average property, this review encompasses those challenging aspects of characterizing the evolutionary dynamics of spike sequence and structure and their implications for functions.

Benchmarking Molecular Dynamics Force Fields for All-Atom Simulations of Biological Condensates

Proteins containing intrinsically disordered regions are integral parts of the cellular signaling pathways and common components of biological condensates. Point mutations in the protein sequence, genetic at birth or acquired through aging, can alter the properties of the condensates, marking the onset of neurodegenerative diseases such as ALS and dementia. While the all-atom molecular dynamics method can, in principle, elucidate the conformational changes that arise from point mutations, the applications of this method to protein condensate systems is conditioned upon the availability of molecular force fields that can accurately describe both structured and disordered regions of such proteins. Using the special-purpose Anton 2 supercomputer, we benchmarked the efficacy of nine presently available molecular force fields in describing the structure and dynamics of a Fused in sarcoma (FUS) protein. Five-microsecond simulations of the full-length FUS protein characterized the effect of the force field on the global conformation of the protein, self-interactions among its side chains, solvent accessible surface area, and the diffusion constant. Using the results of dynamic light scattering as a benchmark for the FUS radius of gyration, we identified several force fields that produced FUS conformations within the experimental range. Next, we used these force fields to perform ten-microsecond simulations of two structured RNA binding domains of FUS bound to their respective RNA targets, finding the choice of the force field to affect stability of the RNA-FUS complex. Taken together, our data suggest that a combination of protein and RNA force fields sharing a common four-point water model provides an optimal description of proteins containing both disordered and structured regions and RNA-protein interactions. To make simulations of such systems available beyond the Anton 2 machines, we describe and validate implementation of the best performing force fields in a publicly available molecular dynamics program NAMD. Our NAMD implementation enables simulations of large (tens of millions of atoms) biological condensate systems and makes such simulations accessible to a broader scientific community.

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

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

Benchmarking Molecular Dynamics Force Fields for All-Atom Simulations of Biological Condensates

Proteins containing intrinsically disordered regions are integral components of the cellular signaling pathways and common components of biological condensates. Point mutations in the protein sequence, genetic at birth or acquired through aging, can alter the properties of the condensates, marking the onset of neurodegenerative diseases such as ALS and dementia. While all-atom molecular dynamics method can, in principle, elucidate the conformational changes responsible for the aging of the condensate, the applications of this method to protein condensate systems is conditioned by the availability of molecular force fields that can accurately describe both structured and disordered regions of such proteins. Using the special-purpose Anton 2 supercomputer, we benchmarked the efficacy of nine presently available molecular force fields in describing the structure and dynamics of a Fused in sarcoma (FUS) protein. Five-microsecond simulations of the full-length FUS protein characterized the effect of the force field on the global conformation of the protein, self-interactions among its side chains, solvent accessible surface area and the diffusion constant. Using the results of dynamic light scattering as a benchmark for the FUS radius of gyration, we identified several force field that produced FUS conformations within the experimental range. Next, we used these force fields to perform ten-microsecond simulations of two structured RNA binding domains of FUS bound to their respective RNA targets, finding the choice of the force field to affect stability of the RNA-FUS complex. Taken together, our data suggest that a combination of protein and RNA force fields sharing a common four-point water model provides an optimal description of proteins containing both disordered and structured regions and RNA-protein interactions. To make simulations of such systems available beyond the Anton 2 machines, we describe and validate implementation of the best performing force fields in a publicly available molecular dynamics program NAMD. Our NAMD implementation enables simulations of large (tens of millions of atoms) biological condensate systems and makes such simulations accessible to a broader scientific community.

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Coupled binding and folding of disordered SPIN N-terminal region in myeloperoxidase inhibition

Gram-positive pathogenic bacteria Staphylococcus express and secret staphylococcal peroxidase inhibitor (SPIN) proteins to help evade neutrophil-mediated immunity by inhibiting the activity of the main oxidative-defense player myeloperoxidase (MPO) enzyme. SPIN contains a structured 3-helix bundle C-terminal domain, which can specifically bind to MPO with high affinity, and an intrinsically disordered N-terminal domain (NTD), which folds into a structured β-hairpin and inserts itself into the active site of MPO for inhibition. Mechanistic insights of the coupled folding and binding process are needed in order to better understand how residual structures and/or conformational flexibility of NTD contribute to the different strengths of inhibition of SPIN homologs. In this work, we applied atomistic molecular dynamics simulations on two SPIN homologs, from S. aureus and S. delphini, respectively, which share high sequence identity and similarity, to explore the possible mechanistic basis for their different inhibition efficacies on human MPO. Direct simulations of the unfolding and unbinding processes at 450 K reveal that these two SPIN/MPO complexes systems follow surprisingly different mechanisms of coupled binding and folding. While coupled binding and folding of SPIN-aureus NTD is highly cooperative, SPIN-delphini NTD appears to mainly utilize a conformational selection-like mechanism. These observations are in contrast to an overwhelming prevalence of induced folding-like mechanisms for intrinsically disordered proteins that fold into helical structures upon binding. Further simulations of unbound SPIN NTDs at room temperature reveal that SPIN-delphini NTD has a much stronger propensity of forming β-hairpin like structures, consistent with its preference to fold and then bind. These may help explain why the inhibition strength is not well correlated with binding affinity for different SPIN homologs. Altogether, our work establishes the relationship between the residual conformational stability of SPIN-NTD and their inhibitory function, which can help us develop new strategies towards treating Staphylococcal infections.

Early-Stage Oligomerization of Prion-like Polypeptides Reveals the Molecular Mechanism of Amyloid-Disrupting Capacity by Proline Residues

Proline cis/trans isomerization governs protein local conformational changes via its local mechanical rigidity. The amyloid-disrupting capacity of proline is widely acknowledged; however, the molecular mechanism is still not clear. To understand how proline residues in polypeptide chains influence amyloid propensity, we study several truncated sequences of the TDP-43 C-terminal region (287-322) and their triple proline variants (308PPP310). We use coarse-grained molecular simulation to study the time evolution of the process of aggregation in the early stages in an effective high-concentration condition (∼25 mM). This ensures the long time scales for protein association at laboratory concentrations. We use several experimentally determined structure templates as initial structures of monomer conformations. We carry out oligomer size analysis and cluster analysis, along with several structural measures, to characterize the size distributions of oligomers and their morphological/structural properties. We show that average oligomer size is not a good indicator of amyloid propensity. Structural order and/or morphological properties are better alternatives. We show that proline variants can efficiently maintain the formation of large "ordered" oligomers of shorter truncated sequences, i.e., 307-322. This "order" maintenance is weakened when using longer truncated sequences (i.e., 287-322), leading to the formation of "disordered" oligomers. From an energy trade-off perspective, if the entropic effect is weak (short sequence length), the shape-complementarity of proline variants effectively guides the oligomerization process to form "ordered" oligomer intermediates. This leads to a distinct aggregation pathway that promotes amyloid formation (on-pathway). Strong entropic effects (long sequence length), however, would cause the formation of "disordered" oligomers. This in turn will suppress amyloid formation (off-pathway). The proline shape-complementary effects provide a guided morphological restraint to facilitate the pathways of amyloid formation. Our study supports the importance of structure-based kinetic heterogeneity of prion-like sequence fragments in driving different aggregation pathways. This work sheds light on the role of morphological and structural order of early-stage oligomeric species in regulating amyloid-disrupting capacity by prolines.

Modeling Concentration-dependent Phase Separation Processes Involving Peptides and RNA via Residue-Based Coarse-Graining

Biomolecular condensation, especially liquid-liquid phase separation, is an important physical process with relevance for a number of different aspects of biological functions. Key questions of what drives such condensation, especially in terms of molecular composition, can be addressed via computer simulations, but the development of computationally efficient yet physically realistic models has been challenging. Here, the coarse-grained model COCOMO is introduced that balances the polymer behavior of peptides and RNA chains with their propensity to phase separate as a function of composition and concentration. COCOMO is a residue-based model that combines bonded terms with short- and long-range terms, including a Debye-Hückel solvation term. The model is highly predictive of experimental data on phase-separating model systems. It is also computationally efficient and can reach the spatial and temporal scales on which biomolecular condensation is observed with moderate computational resources.

pH Induced Switch in the Conformational Ensemble of Intrinsically Disordered Protein Prothymosin-α and Its Implications for Amyloid Fibril Formation

Aggregation of intrinsically disordered proteins (IDPs) can lead to neurodegenerative diseases. Although there is experimental evidence that acidic pH promotes IDP monomer compaction leading to aggregation, the general mechanism is unclear. We studied the pH effect on the conformational ensemble of prothymosin-α (proTα), which is involved in multiple essential functions, and probed its role in aggregation using computer simulations. We show that compaction in the proTα dimension at low pH is due to the protein's collapse in the intermediate region (E41-D80) rich in glutamic acid residues, enhancing its β-sheet content. We observed by performing dimer simulations that the conformations with high β-sheet content could act as aggregation-prone (N*) states and nucleate the aggregation process. The simulations initiated using N* states form dimers within a microsecond time scale, whereas the non-N* states do not form dimers within this time scale. This study contributes to understanding the general principles of pH-induced IDP aggregation.

Contrastive Learning of Coarse-Grained Force Fields

Coarse-grained models have proven helpful for simulating complex systems over long time scales to provide molecular insights into various processes. Methodologies for systematic parametrization of the underlying energy function or force field that describes the interactions among different components of the system are of great interest for ensuring simulation accuracy. We present a new method, potential contrasting, to enable efficient learning of force fields that can accurately reproduce the conformational distribution produced with all-atom simulations. Potential contrasting generalizes the noise contrastive estimation method with umbrella sampling to better learn the complex energy landscape of molecular systems. When applied to the Trp-cage protein, we found that the technique produces force fields that thoroughly capture the thermodynamics of the folding process despite the use of only α-carbons in the coarse-grained model. We further showed that potential contrasting could be applied over large data sets that combine the conformational ensembles of many proteins to improve force field transferability. We anticipate potential contrasting as a powerful tool for building general-purpose coarse-grained force fields.

Developing Bonded Potentials for a Coarse-Grained Model of Intrinsically Disordered Proteins

Recent advances in residue-level coarse-grained (CG) computational models have enabled molecular-level insights into biological condensates of intrinsically disordered proteins (IDPs), shedding light on the sequence determinants of their phase separation. The existing CG models that treat protein chains as flexible molecules connected via harmonic bonds cannot populate common secondary-structure elements. Here, we present a CG dihedral angle potential between four neighboring beads centered at Cα atoms to faithfully capture the transient helical structures of IDPs. In order to parameterize and validate our new model, we propose Cα-based helix assignment rules based on dihedral angles that succeed in reproducing the atomistic helicity results of a polyalanine peptide and folded proteins. We then introduce sequence-dependent dihedral angle potential parameters (εd) and use experimentally available helical propensities of naturally occurring 20 amino acids to find their optimal values. The single-chain helical propensities from the CG simulations for commonly studied prion-like IDPs are in excellent agreement with the NMR-based α-helix fraction, demonstrating that the new HPS-SS model can accurately produce structural features of IDPs. Furthermore, this model can be easily implemented for large-scale assembly simulations due to its simplicity.

Toward Accurate Coarse-Grained Simulations of Disordered Proteins and Their Dynamic Interactions

Intrinsically disordered proteins (IDPs) play crucial roles in cellular regulatory networks and are now recognized to often remain highly dynamic even in specific interactions and assemblies. Accurate description of these dynamic interactions is extremely challenging using atomistic simulations because of the prohibitive computational cost. Efficient coarse-grained approaches could offer an effective solution to overcome this bottleneck if they could provide an accurate description of key local and global properties of IDPs in both unbound and bound states. The recently developed hybrid-resolution (HyRes) protein model has been shown to be capable of providing a semiquantitative description of the secondary structure propensities of IDPs. Here, we show that greatly improved description of global structures and transient interactions can be achieved by introducing a solvent-accessible surface area-based implicit solvent term followed by reoptimization of effective interaction strengths. The new model, termed HyRes II, can semiquantitatively reproduce a wide range of local and global structural properties of a set of IDPs of various lengths and complexities. It can also distinguish the level of compaction between folded proteins and IDPs. In particular, applied to the disordered N-terminal transactivation domain (TAD) of tumor suppressor p53, HyRes II is able to recapitulate various nontrivial structural properties compared to experimental results, some of them to a level of accuracy that is almost comparable to results from atomistic explicit solvent simulations. Furthermore, we demonstrate that HyRes II can be used to simulate the dynamic interactions of TAD with the DNA-binding domain of p53, generating structural ensembles that are highly consistent with existing NMR data. We anticipate that HyRes II will provide an efficient and relatively reliable tool toward accurate coarse-grained simulations of dynamic protein interactions.

Salt-Induced Transitions in the Conformational Ensembles of Intrinsically Disordered Proteins

Salts modulate the behavior of intrinsically disordered proteins (IDPs) and influence the formation of membraneless organelles through liquid-liquid phase separation (LLPS). In low ionic strength solutions, IDP conformations are perturbed by the screening of electrostatic interactions, independent of the salt identity. In this regime, insight into the IDP behavior can be obtained using the theory for salt-induced transitions in charged polymers. However, salt-specific interactions with the charged and uncharged residues, known as the Hofmeister effect, influence IDP behavior in high ionic strength solutions. There is a lack of reliable theoretical models in high salt concentration regimes to predict the salt effect on IDPs. We propose a simulation methodology using a coarse-grained IDP model and experimentally measured water to salt solution transfer free energies of various chemical groups that allowed us to study the salt-specific transitions induced in the IDPs conformational ensemble. We probed the effect of three different monovalent salts on five IDPs belonging to various polymer classes based on charged residue content. We demonstrate that all of the IDPs of different polymer classes behave as self-avoiding walks (SAWs) at physiological salt concentration. In high salt concentrations, the transitions observed in the IDP conformational ensembles are dependent on the salt used and the IDP sequence and composition. Changing the anion with the cation fixed can result in the IDP transition from a SAW-like behavior to a collapsed globule. An important implication of these results is that a suitable salt can be identified to induce condensation of an IDP through LLPS.

Affinity of disordered protein complexes is modulated by entropy-energy reinforcement

Intrinsically disordered proteins (IDPs), which are very common and essential to many biological activities, sometimes function via interaction with another IDP and form a fuzzy complex, which can be highly stable. It is unclear what the biophysical forces are that govern their thermodynamics and specificity, which are essential for de novo fuzzy complex design. Here, we explored the fuzzy complex formed between ProTα and H1, which are oppositely charged IDPs, by swapping the charges between them, generating variants that have either greater polyampholytic or polyelectrolytic nature as well as different charge patterns. Charge swapping and shuffling dramatically change the affinity of the fuzzy complex, which is contributed to by both enthalpy and entropy, where the latter is dominated by counterion release.

The association between two intrinsically disordered proteins (IDPs) may produce a fuzzy complex characterized by a high binding affinity, similar to that found in the ultrastable complexes formed between two well-structured proteins. Here, using coarse-grained simulations, we quantified the biophysical forces driving the formation of such fuzzy complexes. We found that the high-affinity complex formed between the highly and oppositely charged H1 and ProTα proteins is sensitive to electrostatic interactions. We investigated 52 variants of the complex by swapping charges between the two oppositely charged proteins to produce sequences whose negatively or positively charged residue content was more homogeneous or heterogenous (i.e., polyelectrolytic or polyampholytic, having higher or lower absolute net charges, respectively) than the wild type. We also changed the distributions of oppositely charged residues within each participating sequence to produce variants in which the charges were segregated or well mixed. Both types of changes significantly affect binding affinity in fuzzy complexes, which is governed by both enthalpy and entropy. The formation of H1–ProTa is supported by an increase in configurational entropy and by entropy due to counterion release. The latter can be twice as large as the former, illustrating the dominance of counterion entropy in modulating the binding thermodynamics. Complexes formed between proteins with greater absolute net charges are more stable, both enthalpically and entropically, indicating that enthalpy and entropy have a mutually reinforcing effect. The sensitivity of the thermodynamics of the complex to net charge and the charge pattern within each of the binding constituents may provide a means to achieve binding specificity between IDPs.

Automated Protein Secondary Structure Assignment from Cα Positions Using Neural Networks

The assignment of secondary structure elements in protein conformations is necessary to interpret a protein model that has been established by computational methods. The process essentially involves labeling the amino acid residues with H (Helix), E (Strand), or C (Coil, also known as Loop). When particular atoms are absent from an input protein structure, the procedure becomes more complicated, especially when only the alpha carbon locations are known. Various techniques have been tested and applied to this problem during the last forty years. The application of machine learning techniques is the most recent trend. This contribution presents the HECA classifier, which uses neural networks to assign protein secondary structure types. The technique exclusively employs Cα coordinates. The Keras (TensorFlow) library was used to implement and train the neural network model. The BioShell toolkit was used to calculate the neural network input features from raw coordinates. The study’s findings show that neural network-based methods may be successfully used to take on structure assignment challenges when only Cα trace is available. Thanks to the careful selection of input features, our approach’s accuracy (above 97%) exceeded that of the existing methods.

Single-molecule biophysics experiments in silico: Toward a physical model of a replisome

The interpretation of single-molecule experiments is frequently aided by computational modeling of biomolecular dynamics. The growth of computing power and ongoing validation of computational models suggest that it soon may be possible to replace some experiments outright with computational mimics. Here, we offer a blueprint for performing single-molecule studies in silico using a DNA-binding protein as a test bed. We demonstrate how atomistic simulations, typically limited to sub-millisecond durations and zeptoliter volumes, can guide development of a coarse-grained model for use in simulations that mimic single-molecule experiments. We apply the model to recapitulate, in silico, force-extension characterization of protein binding to single-stranded DNA and protein and DNA replacement assays, providing a detailed portrait of the underlying mechanics. Finally, we use the model to simulate the trombone loop of a replication fork, a large complex of proteins and DNA.

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Coarse-grained model derived from all-atom simulation recapitulates experiments

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Model reproduces the elastic response to force and exchange dynamics

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Model reveals structure of intermediate states usually inaccessible to experiment

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Model applied to viral replisome with trombone loop containing tens of SSB proteins

Global Structure of the Intrinsically Disordered Protein Tau Emerges from Its Local Structure

The paradigmatic disordered protein tau plays an important role in neuronal function and neurodegenerative diseases. To disentangle the factors controlling the balance between functional and disease-associated conformational states, we build a structural ensemble of the tau K18 fragment containing the four pseudorepeat domains involved in both microtubule binding and amyloid fibril formation. We assemble 129-residue-long tau K18 chains with atomic detail from an extensive fragment library constructed with molecular dynamics simulations. We introduce a reweighted hierarchical chain growth (RHCG) algorithm that integrates experimental data reporting on the local structure into the assembly process in a systematic manner. By combining Bayesian ensemble refinement with importance sampling, we obtain well-defined ensembles and overcome the problem of exponentially varying weights in the integrative modeling of long-chain polymeric molecules. The resulting tau K18 ensembles capture nuclear magnetic resonance (NMR) chemical shift and J-coupling measurements. Without further fitting, we achieve very good agreement with measurements of NMR residual dipolar couplings. The good agreement with experimental measures of global structure such as single-molecule Förster resonance energy transfer (FRET) efficiencies is improved further by ensemble refinement. By comparing wild-type and mutant ensembles, we show that pathogenic single-point P301L, P301S, and P301T mutations shift the population from the turn-like conformations of the functional microtubule-bound state to the extended conformations of disease-associated tau fibrils. RHCG thus provides us with an atomically detailed view of the population equilibrium between functional and aggregation-prone states of tau K18, and demonstrates that global structural characteristics of this intrinsically disordered protein emerge from its local structure.

Tuning Formation of Protein-DNA Coacervates by Sequence and Environment

The high concentration of nucleic acids and positively charged proteins in the cell nucleus provides many possibilities for complex coacervation. We consider a prototypical mixture of nucleic acids together with the polycationic C-terminus of histone H1 (CH1). Using a minimal coarse-grained model that captures the shape, flexibility, and charge distributions of the molecules, we find that coacervates are readily formed at physiological ionic strengths, in agreement with experiment, with a progressive increase in local ordering at low ionic strength. Variation of the positions of charged residues in the protein tunes phase separation: for well-mixed or only moderately blocky distributions of charge, there is a modest increase of local ordering with increasing blockiness that is also associated with an increased propensity to phase separate. This ordering is also associated with a slowdown of rotational and translational diffusion in the dense phase. However, for more extreme blockiness (and consequently higher local charge density), we see a qualitative change in the condensed phase to become a segregated structure with a dramatically increased ordering of the DNA. Naturally occurring proteins with these sequence properties, such as protamines in sperm cells, are found to be associated with very dense packing of nucleic acids.

Conformational Dynamics of Intrinsically Disordered Proteins Regulate Biomolecular Condensate Chemistry

Motions in biomolecules are critical for biochemical reactions. In cells, many biochemical reactions are executed inside of biomolecular condensates formed by ultradynamic intrinsically disordered proteins. A deep understanding of the conformational dynamics of intrinsically disordered proteins in biomolecular condensates is therefore of utmost importance but is complicated by diverse obstacles. Here we review emerging data on the motions of intrinsically disordered proteins inside of liquidlike condensates. We discuss how liquid–liquid phase separation modulates internal motions across a wide range of time and length scales. We further highlight the importance of intermolecular interactions that not only drive liquid–liquid phase separation but appear as key determinants for changes in biomolecular motions and the aging of condensates in human diseases. The review provides a framework for future studies to reveal the conformational dynamics of intrinsically disordered proteins in the regulation of biomolecular condensate chemistry.

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.

Unifying coarse-grained force fields for folded and disordered proteins

Liquid-liquid phase separation drives the formation of biological condensates that play essential roles in transcriptional regulation and signal sensing. Computational modeling could provide high-resolution structural characterizations of these condensates and help uncover physicochemical interactions that dictate their stability. However, many protein molecules involved in phase separation often contain multiple ordered domains connected with flexible, structureless linkers. Simulating such proteins necessitates force fields with consistent accuracy for both folded and disordered proteins. We provide a critical review of existing coarse-grained force fields for disordered proteins and highlight the challenges in their application to folded proteins. After discussing existing algorithms for force field parameterization, we propose an optimization strategy that should lead to computer models with improved transferability across protein types.

Computational Models for the Study of Protein Aggregation

Protein aggregation has been studied by many groups around the world for many years because it can be the cause of a number of neurodegenerative diseases that have no effective treatment. Obtaining the structure of related fibrils and toxic oligomers, as well as describing the pathways and main factors that govern the self-organization process, is of paramount importance, but it is also very difficult. To solve this problem, experimental and computational methods are often combined to get the most out of each method. The effectiveness of the computational approach largely depends on the construction of a reasonable molecular model. Here we discussed different versions of the four most popular all-atom force fields AMBER, CHARMM, GROMOS, and OPLS, which have been developed for folded and intrinsically disordered proteins, or both. Continuous and discrete coarse-grained models, which were mainly used to study the kinetics of aggregation, are also summarized.

When Order Meets Disorder: Modeling and Function of the Protein Interface in Fuzzy Complexes

The degree of proteins structural organization ranges from highly structured, compact folding to intrinsic disorder, where each degree of self-organization corresponds to specific functions: well-organized structural motifs in enzymes offer a proper environment for precisely positioned functional groups to participate in catalytic reactions; at the other end of the self-organization spectrum, intrinsically disordered proteins act as binding hubs via the formation of multiple, transient and often non-specific interactions. This review focusses on cases where structurally organized proteins or domains associate with highly disordered protein chains, leading to the formation of interfaces with varying degrees of fuzziness. We present a review of the computational methods developed to provide us with information on such fuzzy interfaces, and how they integrate experimental information. The discussion focusses on two specific cases, microtubules and homologous recombination nucleoprotein filaments, where a network of intrinsically disordered tails exerts regulatory function in recruiting partner macromolecules, proteins or DNA and tuning the atomic level association. Notably, we show how computational approaches such as molecular dynamics simulations can bring new knowledge to help bridging the gap between experimental analysis, that mostly concerns ensemble properties, and the behavior of individual disordered protein chains that contribute to regulation functions.

Advanced Sampling Methods for Multiscale Simulation of Disordered Proteins and Dynamic Interactions

Intrinsically disordered proteins (IDPs) are highly prevalent and play important roles in biology and human diseases. It is now also recognized that many IDPs remain dynamic even in specific complexes and functional assemblies. Computer simulations are essential for deriving a molecular description of the disordered protein ensembles and dynamic interactions for a mechanistic understanding of IDPs in biology, diseases, and therapeutics. Here, we provide an in-depth review of recent advances in the multi-scale simulation of disordered protein states, with a particular emphasis on the development and application of advanced sampling techniques for studying IDPs. These techniques are critical for adequate sampling of the manifold functionally relevant conformational spaces of IDPs. Together with dramatically improved protein force fields, these advanced simulation approaches have achieved substantial success and demonstrated significant promise towards the quantitative and predictive modeling of IDPs and their dynamic interactions. We will also discuss important challenges remaining in the atomistic simulation of larger systems and how various coarse-grained approaches may help to bridge the remaining gaps in the accessible time- and length-scales of IDP simulations.

Coarse-Grained Modeling and Molecular Dynamics Simulations of Ca2+-Calmodulin

Calmodulin (CaM) is a calcium-binding protein that transduces signals to downstream proteins through target binding upon calcium binding in a time-dependent manner. Understanding the target binding process that tunes CaM’s affinity for the calcium ions (Ca²⁺), or vice versa, may provide insight into how Ca²⁺-CaM selects its target binding proteins. However, modeling of Ca²⁺-CaM in molecular simulations is challenging because of the gross structural changes in its central linker regions while the two lobes are relatively rigid due to tight binding of the Ca²⁺ to the calcium-binding loops where the loop forms a pentagonal bipyramidal coordination geometry with Ca²⁺. This feature that underlies the reciprocal relation between Ca²⁺ binding and target binding of CaM, however, has yet to be considered in the structural modeling. Here, we presented a coarse-grained model based on the Associative memory, Water mediated, Structure, and Energy Model (AWSEM) protein force field, to investigate the salient features of CaM. Particularly, we optimized the force field of CaM and that of Ca²⁺ ions by using its coordination chemistry in the calcium-binding loops to match with experimental observations. We presented a “community model” of CaM that is capable of sampling various conformations of CaM, incorporating various calcium-binding states, and carrying the memory of binding with various targets, which sets the foundation of the reciprocal relation of target binding and Ca²⁺ binding in future studies.

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

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

Multiscale modeling of genome organization with maximum entropy optimization

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.

The diversity of molecular interactions involving intrinsically disordered proteins: A molecular modeling perspective

Intrinsically Disordered Proteins and Regions (IDPs/IDRs) are key components of a multitude of biological processes. Conformational malleability enables IDPs/IDRs to perform very specialized functions that cannot be accomplished by globular proteins. The functional role for most of these proteins is related to the recognition of other biomolecules to regulate biological processes or as a part of signaling pathways. Depending on the extent of disorder, the number of interacting sites and the type of partner, very different architectures for the resulting assemblies are possible. More recently, molecular condensates with liquid-like properties composed of multiple copies of IDPs and nucleic acids have been proven to regulate key processes in eukaryotic cells. The structural and kinetic details of disordered biomolecular complexes are difficult to unveil experimentally due to their inherent conformational heterogeneity. Computational approaches, alone or in combination with experimental data, have emerged as unavoidable tools to understand the functional mechanisms of this elusive type of assemblies. The level of description used, all-atom or coarse-grained, strongly depends on the size of the molecular systems and on the timescale of the investigated mechanism. In this mini-review, we describe the most relevant architectures found for molecular interactions involving IDPs/IDRs and the computational strategies applied for their investigation.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

Improved coarse-grained model for studying sequence dependent phase separation of disordered proteins

We present improvements to the hydropathy scale (HPS) coarse-grained (CG) model for simulating sequence-specific behavior of intrinsically disordered proteins (IDPs), including their liquid-liquid phase separation (LLPS). The previous model based on an atomistic hydropathy scale by Kapcha and Rossky (KR scale) is not able to capture some well-known LLPS trends such as reduced phase separation propensity upon mutations (R-to-K and Y-to-F). Here, we propose to use the Urry hydropathy scale instead, which was derived from the inverse temperature transitions in a model polypeptide with guest residues X. We introduce two free parameters to shift (Δ) and scale (µ) the overall interaction strengths for the new model (HPS-Urry) and use the experimental radius of gyration for a diverse group of IDPs to find their optimal values. Interestingly, many possible (Δ, µ) combinations can be used for typical IDPs, but the phase behavior of a low-complexity (LC) sequence FUS is only well described by one of these models, which highlights the need for a careful validation strategy based on multiple proteins. The CG HPS-Urry model should enable accurate simulations of protein LLPS and provide a microscopically detailed view of molecular interactions.

Consistent Force Field Captures Homologue-Resolved HP1 Phase Separation

Many proteins have been shown to function via liquid-liquid phase separation. Computational modeling could offer much needed structural details of protein condensates and reveal the set of molecular interactions that dictate their stability. However, the presence of both ordered and disordered domains in these proteins places a high demand on the model accuracy. Here, we present an algorithm to derive a coarse-grained force field, MOFF, which can model both ordered and disordered proteins with consistent accuracy. It combines maximum entropy biasing, least-squares fitting, and basic principles of energy landscape theory to ensure that MOFF recreates experimental radii of gyration while predicting the folded structures for globular proteins with lower energy. The theta temperature determined from MOFF separates ordered and disordered proteins at 300 K and exhibits a strikingly linear relationship with amino acid sequence composition. We further applied MOFF to study the phase behavior of HP1, an essential protein for post-translational modification and spatial organization of chromatin. The force field successfully resolved the structural difference of two HP1 homologues despite their high sequence similarity. We carried out large-scale simulations with hundreds of proteins to determine the critical temperature of phase separation and uncover multivalent interactions that stabilize higher-order assemblies. In all, our work makes significant methodological strides to connect theories of ordered and disordered proteins and provides a powerful tool for studying liquid-liquid phase separation with near-atomistic details.

Exploring Energy Landscapes of Intrinsically Disordered Proteins: Insights into Functional Mechanisms

Intrinsically disordered proteins (IDPs) lack a rigid three-dimensional structure and populate a polymorphic ensemble of conformations. Because of the lack of a reference conformation, their energy landscape representation in terms of reaction coordinates presents a daunting challenge. Here, our newly developed energy landscape visualization method (ELViM), a reaction coordinate-free approach, shows its prime application to explore frustrated energy landscapes of an intrinsically disordered protein, prostate-associated gene 4 (PAGE4). PAGE4 is a transcriptional coactivator that potentiates the oncogene c-Jun. Two kinases, namely, HIPK1 and CLK2, phosphorylate PAGE4, generating variants phosphorylated at different serine/threonine residues (HIPK1-PAGE4 and CLK2-PAGE4, respectively) with opposing functions. While HIPK1-PAGE4 predominantly phosphorylates Thr51 and potentiates c-Jun, CLK2-PAGE4 hyperphosphorylates PAGE4 and attenuates transactivation. To understand the underlying mechanisms of conformational diversity among different phosphoforms, we have analyzed their atomistic trajectories simulated using AWSEM forcefield, and the energy landscapes were elucidated using ELViM. This method allows us to identify and compare the population distributions of different conformational ensembles of PAGE4 phosphoforms using the same effective phase space. The results reveal a predominant conformational ensemble with an extended C-terminal segment of WT PAGE4, which exposes a functional residue Thr51, implying its potential of undertaking a fly-casting mechanism while binding to its cognate partner. In contrast, for HIPK1-PAGE4, a compact conformational ensemble enhances its population sequestering phosphorylated-Thr51. This clearly explains the experimentally observed weaker affinity of HIPK1-PAGE4 for c-Jun. ELViM appears as a powerful tool, especially to analyze the highly frustrated energy landscape representation of IDPs where appropriate reaction coordinates are hard to apprehend.

Physics-based computational and theoretical approaches to intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are an important class of proteins that do not fold to a well-defined three-dimensional shape but rather adopt an ensemble of inter-converting conformations. This feature makes their experimental characterization challenging and invites a theoretical and computational approach to complement experimental studies. In this review, we highlight the recent progress in developing new computational and theoretical approaches to study the structure and dynamics of monomeric and order higher assemblies of IDPs, with a particular emphasis on their phase separation into protein-rich condensates.

Molecular Transfer Model for pH Effects on Intrinsically Disordered Proteins: Theory and Applications

We present a theoretical method to study how changes in pH shape the heterogeneous conformational ensemble explored by intrinsically disordered proteins (IDPs). The theory is developed in the context of coarse-grained models, which enable a fast, accurate, and extensive exploration of conformational space at a given protonation state. In order to account for pH effects, we generalize the molecular transfer model (MTM), in which conformations are re-weighted using the transfer free energy, which is the free energy necessary for bringing to equilibrium in a new environment a "frozen" conformation of the system. Using the semi-grand ensemble, we derive an exact expression of the transfer free energy, which amounts to the appropriate summation over all the protonation states. Because the exact result is computationally too demanding to be useful for large polyelectrolytes or IDPs, we introduce a mean-field (MF) approximation of the transfer free energy. Using a lattice model, we compare the exact and MF results for the transfer free energy and a variety of observables associated with the model IDP. We find that the precise location of the charged groups (the sequence), and not merely the net charge, determines the structural properties. We demonstrate that some of the limitations previously noted for MF theory in the context of globular proteins are mitigated when disordered polymers are studied. The excellent agreement between the exact and MF results poises us to use the method presented here as a computational tool to study the properties of IDPs and other biological systems as a function of pH.