Force field development and simulations of intrinsically disordered proteins

Molecular Dynamics Simulations of Phosphorylated Intrinsically Disordered Proteins: A Force Field Comparison

Phosphorylation is a common post-translational modification among intrinsically disordered proteins and regions, which helps regulate function by changing the protein conformations, dynamics, and interactions with binding partners. To fully comprehend the effects of phosphorylation, computer simulations are a helpful tool, although they are dependent on the accuracy of the force field used. Here, we compared the conformational ensembles produced by Amber ff99SB-ILDN+TIP4P-D and CHARMM36m, for four phosphorylated disordered peptides ranging in length from 14-43 residues. CHARMM36m consistently produced more compact conformations with a higher content of bends, mainly due to more stable salt bridges. Based on comparisons with experimental size estimates for the shortest and longest peptide, CHARMM36m appeared to overestimate the compactness. The difference between the force fields was largest for the peptide showing the greatest separation between positively charged and phosphorylated residues, in line with the importance of charge distribution. For this peptide, the conformational ensemble did not change significantly upon increasing the ionic strength from 0 mM to 150 mM, despite a reduction of the salt-bridging probability in the CHARMM36m simulations, implying that salt concentration has negligible effects in this study.

Molecular dynamics study of conformation transition from helix to sheet of Aβ42 peptide

Aβ42 peptides can form helix and sheet structure under different conditions. The conformational conversion is closely associated with Aβ peptides aggregation and their neurotoxicity. But the transition from helix to sheet is not be clearly understood. In this study we performed microsecond timescale MD simulations of Aβ42 peptide to investigate the conformation transition from α-helix to β-sheet. Markov state model (MSM) was built to facilitate identification of crucial intermediate states and possible transition pathway. Based on the analysis, we found that the region Y10-A21 in the middle of Aβ42 peptide plays an initial role in this transition. MSM model revealed that the collapse of helical structure in this region might trigger the formation of sheet structure. Moreover, we further simulated the aggregation of Aβ42 peptides with different conformations. We found that the Aβ42 peptides forming sheet structure have higher aggregation potential compared with peptides with helix structure. These results demonstrate that we can prevent the aggregation of Aβ42 peptides by stabilizing the helix structure in the region of Y10-A21. In addition, this study provides new insight into better understanding the conformational transition and aggregation of Aβ42 peptides.

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.

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

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

Structural and Dynamical Differences in the Spike Protein RBD in the SARS-CoV-2 Variants B.1.1.7 and B.1.351

The novel coronavirus (SARS-CoV-2) pandemic that started in late 2019 is responsible for hundreds of millions of cases worldwide and millions of fatalities. Though vaccines are available, the virus is mutating to form new strains among which are the variants B.1.1.7 and B.1.351 that demonstrate increased transmissivity and infectivity. In this study, we performed molecular dynamics simulations to explore the role of the mutations in the interaction of the virus spike protein receptor binding domain (RBD) with the host receptor ACE2. We find that the hydrogen bond networks are rearranged in the variants and also that new hydrogen bonds are established between the RBD and ACE2 as a result of mutations. We investigated three variants: the wild-type (WT), B.1.1.7, and B.1.351. We find that the B.1.351 variant (also known as 501Y.V2) shows larger flexibility in the RBD loop segment involving residue K484, yet the RBD-ACE2 complex shows higher stability. Mutations that allow a more flexible interface that can result in a more stable complex may be a factor contributing to the increased infectivity of the mutated variants.

Force Field Benchmark of Amino Acids. 3. Hydration with Scaled Lennard-Jones Interactions

Classical protein force fields were reported with too weak protein-water interactions relative to protein-protein interactions, leading to more compact structures and artificial protein aggregation. Here we investigated the impacts of scaled Lennard-Jones (LJ) interactions on the hydration of amino acids and the simulation of folded and intrinsically disordered proteins (IDPs). The obtained optimal scaling parameters reproduce accurately hydration free energies of neutral amino acid side chain analogues and do not affect the compactness and structural stability of folded proteins significantly. The scaling leads to less compact IDPs and varies from case to case. Strengthening the interactions between protein and water oxygen or hydrogen atoms by increasing the interacting LJ well depth (ε) appears more effective than weakening protein-protein interactions by reducing the interacting dispersion coefficients (C₆). We demonstrate that weakening water-water interactions is a solution as well to obtaining more favorable protein-water interactions in an indirect way, although modern force fields like Amber ff19SB and a99SB-disp tend to use water models with strong water-water interactions. This is likely a compromise between strong protein-protein interactions and strong water-water interactions. Independent optimization of protein force fields and water models is therefore needed to make both interactions more close to reality, leading to good accuracy without bias or scaling.

Ubiquitin Interacting Motifs: Duality Between Structured and Disordered Motifs

Ubiquitin is a small protein at the heart of many cellular processes, and several different protein domains are known to recognize and bind ubiquitin. A common motif for interaction with ubiquitin is the Ubiquitin Interacting Motif (UIM), characterized by a conserved sequence signature and often found in multi-domain proteins. Multi-domain proteins with intrinsically disordered regions mediate interactions with multiple partners, orchestrating diverse pathways. Short linear motifs for binding are often embedded in these disordered regions and play crucial roles in modulating protein function. In this work, we investigated the structural propensities of UIMs using molecular dynamics simulations and NMR chemical shifts. Despite the structural portrait depicted by X-crystallography of stable helical structures, we show that UIMs feature both helical and intrinsically disordered conformations. Our results shed light on a new class of disordered UIMs. This group is here exemplified by the C-terminal domain of one isoform of ataxin-3 and a group of ubiquitin-specific proteases. Intriguingly, UIMs not only bind ubiquitin. They can be a recruitment point for other interactors, such as parkin and the heat shock protein Hsc70-4. Disordered UIMs can provide versatility and new functions to the client proteins, opening new directions for research on their interactome.

Simultaneous Identification of Multiple Binding Sites in Proteins: A Statistical Mechanics Approach

We present an extension of the Poisson-Boltzmann model in which the solute of interest is immersed in an assembly of self-orienting Langevin water dipoles, anions, cations, and hydrophobic molecules, all of variable densities. Interactions between charges are controlled by electrostatics, while hydrophobic interactions are modeled with a Yukawa potential. We impose steric constraints by assuming that the system is represented on a cubic lattice. We also assume incompressibility; i.e., all sites of the lattice are occupied. This model, which we refer to as the Hydrophobic Dipolar Poisson-Boltzmann Langevin (HDPBL) model, leads to a system of two equations whose solutions give the water dipole, salt, and hydrophobic molecule densities, all of them in the presence of the others in a self-consistent way. We use those to study the organization of the ions, cosolvent, and solvent molecules around proteins. In particular, peaks of densities are expected to reveal, simultaneously, the presence of compatible binding sites of different kinds on a protein. We have tested and validated the ability of HDPBL to detect pockets in proteins that bind to hydrophobic ligands, polar ligands, and charged small probes as well as to characterize the binding sites of lipids for membrane proteins.

Computational IR Spectroscopy of Insulin Dimer Structure and Conformational Heterogeneity

We have investigated the structure and conformational dynamics of insulin dimer using a Markov state model (MSM) built from extensive unbiased atomistic molecular dynamics simulations and performed infrared spectral simulations of the insulin MSM to describe how structural variation within the dimer can be experimentally resolved. Our model reveals two significant conformations to the dimer: a dominant native state consistent with other experimental structures of the dimer and a twisted state with a structure that appears to reflect a ∼55° clockwise rotation of the native dimer interface. The twisted state primarily influences the contacts involving the C-terminus of insulin's B chain, shifting the registry of its intermolecular hydrogen bonds and reorganizing its side-chain packing. The MSM kinetics predict that these configurations exchange on a 14 μs time scale, largely passing through two Markov states with a solvated dimer interface. Computational amide I spectroscopy of site-specifically ¹³C¹⁸O labeled amides indicates that the native and twisted conformation can be distinguished through a series of single and dual labels involving the B24F, B25F, and B26Y residues. Additional structural heterogeneity and disorder is observed within the native and twisted states, and amide I spectroscopy can also be used to gain insight into this variation. This study will provide important interpretive tools for IR spectroscopic investigations of insulin structure and transient IR kinetics experiments studying the conformational dynamics of insulin dimer.

Assessment of transferable forcefields for protein simulations attests improved description of disordered states and secondary structure propensities, and hints at multi-protein systems as the next challenge for optimization

Continuous assessment of transferable forcefields for molecular simulations is essential to identify their weaknesses and direct improvement efforts. The latest efforts focused on better describing disordered proteins while retaining proper description of folded domains, important because forcefields of the previous generations produce overly compact disordered states. Such improvements should additionally alleviate the related problem of over-stabilized protein–protein interactions, which has been largely overlooked. Here we evaluated three state-of-the-art forcefields, current flagships of their respective developers, optimized for ordered and disordered proteins: CHARMM36m with its recommended corrected TIP3P* water, ff19SB with the recommended OPC water, and the 2019 a99SBdisp forcefield by D. E. Shaw Research with its modified TIP4P water; plus ff14SB with TIP3P as an example of the former generation of forcefields. Our evaluation entailed simulations of (i) multiple copies of a protein that is highly soluble yet undergoes weak dimerization, (ii) a disordered peptide with low, well-characterized alpha helical propensity, and (iii) a peptide known to form insoluble β-aggregates. Our results recapitulate ff14SB-TIP3P over-stabilizing aggregates and secondary structures and place a99SBdisp-TIP4PD at the other end i.e. predicting overly weak intermolecular interactions despite reasonably predicting secondary structure propensities. In-between, CHARMM36m-TIP3P* still over-stabilizes aggregates but predicts residue-wise alpha helical propensities in solution slightly better than ff19SB-OPC, while ff19SB-OPC poses the best prediction of weak dimerization of the soluble protein still predicting aggregation of the β-peptides. This independent assessment shows that the claimed forcefield improvements are real, but also that a right balance between noncovalent attraction and repulsion has not yet been reached. We thus propose developers to consider systems like those tested here in their forcefield tuning protocols. Last, the good performance of CHARMM36m-TIP3P* further shows that tuning 3-point water models might still be an alternative to the more costly 4-point models like OPC and TIP4PD.

How to assess the structural dynamics of transcription factors by integrating sparse NMR and EPR constraints with molecular dynamics simulations

We review recent advances in modeling structural ensembles of transcription factors from nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) spectroscopic data, integrated with molecular dynamics (MD) simulations. We focus on approaches that confirm computed conformational ensembles by sparse constraints obtained from magnetic resonance. This combination enables the deduction of functional and structural protein models even if nuclear Overhauser effects (NOEs) are too scarce for conventional structure determination. We highlight recent insights into the folding-upon-DNA binding transitions of intrinsically disordered transcription factors that could be assessed using such integrative approaches.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Philosophy and Development of KBFF20

A new classical nonpolarizable force field, KBFF20, for the simulation of peptides and proteins is presented. The force field relies heavily on the use of Kirkwood-Buff theory to provide a comparison of simulated and experimental Kirkwood-Buff integrals for solutes containing the functional groups common in proteins, thus ensuring intermolecular interactions that provide a good balance between the peptide-peptide, peptide-solvent, and solvent-solvent distributions observed in solution mixtures. In this way, it differs significantly from other biomolecular force fields. Further development and testing of the intermolecular potentials are presented here. Subsequently, rotational potentials for the ϕ/ψ and χ dihedral degrees of freedom are obtained by analysis of the Protein Data Bank, followed by small modifications to provide a reasonable balance between simulated and observed α and β percentages for small peptides. This, the first of two articles, describes in detail the philosophy and development behind KBFF20.

Full structural ensembles of intrinsically disordered proteins from unbiased molecular dynamics simulations

Molecular dynamics (MD) simulation is widely used to complement ensemble-averaged experiments of intrinsically disordered proteins (IDPs). However, MD often suffers from limitations of inaccuracy. Here, we show that enhancing the sampling using Hamiltonian replica-exchange MD (HREMD) led to unbiased and accurate ensembles, reproducing small-angle scattering and NMR chemical shift experiments, for three IDPs of varying sequence properties using two recently optimized force fields, indicating the general applicability of HREMD for IDPs. We further demonstrate that, unlike HREMD, standard MD can reproduce experimental NMR chemical shifts, but not small-angle scattering data, suggesting chemical shifts are insufficient for testing the validity of IDP ensembles. Surprisingly, we reveal that despite differences in their sequence, the inter-chain statistics of all three IDPs are similar for short contour lengths (< 10 residues). The results suggest that the major hurdle of generating an accurate unbiased ensemble for IDPs has now been largely overcome.

Recent Force Field Strategies for Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are widely distributed across eukaryotic cells, playing important roles in molecular recognition, molecular assembly, post-translational modification, and other biological processes. IDPs are also associated with many diseases such as cancers, cardiovascular diseases, and neurodegenerative diseases. Due to their structural flexibility, conventional experimental methods cannot reliably capture their heterogeneous structures. Molecular dynamics simulation becomes an important complementary tool to quantify IDP structures. This review covers recent force field strategies proposed for more accurate molecular dynamics simulations of IDPs. The strategies include adjusting dihedral parameters, adding grid-based energy correction map (CMAP) parameters, refining protein-water interactions, and others. Different force fields were found to perform well on specific observables of specific IDPs but also are limited in reproducing all available experimental observables consistently for all tested IDPs. We conclude the review with perspective areas for improvements for future force fields for IDPs.

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.

A practical guide to biologically relevant molecular simulations with charge scaling for electronic polarization

Molecular simulations can elucidate atomistic-level mechanisms of key biological processes, which are often hardly accessible to experiment. However, the results of the simulations can only be as trustworthy as the underlying simulation model. In many of these processes, interactions between charged moieties play a critical role. Current empirical force fields tend to overestimate such interactions, often in a dramatic way, when polyvalent ions are involved. The source of this shortcoming is the missing electronic polarization in these models. Given the importance of such biomolecular systems, there is great interest in fixing this deficiency in a computationally inexpensive way without employing explicitly polarizable force fields. Here, we review the electronic continuum correction approach, which accounts for electronic polarization in a mean-field way, focusing on its charge scaling variant. We show that by pragmatically scaling only the charged molecular groups, we qualitatively improve the charge-charge interactions without extra computational costs and benefit from decades of force field development on biomolecular force fields.

Recent advances in atomic molecular dynamics simulation of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) play important roles in cellular functions. The inherent structural heterogeneity of IDPs makes the high-resolution experimental characterization of IDPs extremely difficult. Molecular dynamics (MD) simulation could provide the atomic-level description of the structural and dynamic properties of IDPs. This perspective reviews the recent progress in atomic MD simulation studies of IDPs, including the development of force fields and sampling methods, as well as applications in IDP-involved protein-protein interactions. The employment of large-scale simulations and advanced sampling techniques allows more accurate estimation of the thermodynamics and kinetics of IDP-mediated protein interactions, and the holistic landscape of the binding process of IDPs is emerging.

Heterogeneous dynamics in partially disordered proteins

Importance of disordered protein regions is increasingly recognized in biology, but their characterization remains challenging due to the lack of suitable experimental and theoretical methods. NMR experiments can detect multiple timescale dynamics and structural details of disordered protein regions, but their detailed interpretation is often difficult. Here we combine protein backbone 15N spin relaxation data with molecular dynamics (MD) simulations to detect not only heterogeneous dynamics of large partially disordered proteins but also their conformational ensembles. We observed that the rotational dynamics of folded regions in partially disordered proteins is dominated by similar rigid body rotation as in globular proteins, thereby being largely independent of flexible disordered linkers. Disordered regions, on the other hand, exhibit complex rotational motions with multiple timescales below ∼30 ns which are difficult to detect from experimental data alone, but can be captured by MD simulations. Combining MD simulations and backbone 15N spin relaxation data, measured applying segmental isotopic labeling with salt-inducible split intein, we resolved the conformational ensemble and dynamics of partially disordered periplasmic domain of TonB protein from Helicobacter pylori containing 250 residues. To demonstrate the universality of our approach, it was applied also to the partially disordered region of chicken Engrailed 2. Our results pave the way in understanding how TonB transfers energy from inner membrane to the outer membrane receptors in Gram-negative bacteria, as well as the function of other proteins with disordered domains.

Conformational Preferences of an Intrinsically Disordered Protein Domain: A Case Study for Modern Force Fields

Molecular simulations of intrinsically disordered proteins (IDPs) are challenging because they require sampling a very large number of relevant conformations, corresponding to a multitude of shallow minima in a flat free energy landscape. However, in the presence of a binding partner, the free energy landscape of an IDP can be dominated by few deep minima. This characteristic imposes high demands on the accuracy of the force field used to describe the molecular interactions. Here, as a model system for an IDP that is unstructured in solution but folds upon binding to a structured interaction partner, the transactivation domain of c-Myb was studied both in the unbound (free) form and when bound to the KIX domain. Six modern biomolecular force fields were systematically tested and compared in terms of their ability to describe the structural ensemble of the IDP. The protein force field/water model combinations included in this study are AMBER ff99SB-disp with its corresponding water model that was derived from TIP4P-D, CHARMM36m with TIP3P, ff15ipq with SPC/E_b, ff99SB*-ILDNP with TIP3P and TIP4P-D, and FB15 with TIP3P-FB water. Comparing the results from REST2-enhanced sampling simulations with experimental CD spectra and secondary chemical shifts reveals that the ff99SB-disp force field can realistically capture the broad and mildly helical structural ensemble of free c-Myb. The structural ensembles yielded by CHARMM36m, ff99SB*-ILDNP together with TIP4P-D water, and FB15 are also mildly helical; however, each of these force fields can be assigned a specific subset of c-Myb residues for which the simulations could not reproduce the experimental secondary chemical shifts. In addition, microsecond-timescale MD simulations of the KIX/c-Myb complex show that most force fields used preserve a stable helix fold of c-Myb in the complex. Still, all force fields predict a KIX/c-Myb complex interface that differs slightly from the structures provided by NMR because several NOE-derived distances between KIX and c-Myb were exceeded in the simulations. Taken together, the ff99SB-disp force field in the first place but also CHARMM36m, ff99SB*-ILDNP together with TIP4P-D water, and FB15 can be suitable choices for future simulation studies of the coupled folding and binding mechanism of the KIX/c-Myb complex and potentially also other IDPs.

Computational modeling suggests binding-induced expansion of Epsin disordered regions upon association with AP2

Intrinsically disordered regions (IDRs) are prevalent in the eukaryotic proteome. Common functional roles of IDRs include forming flexible linkers or undergoing allosteric folding-upon-binding. Recent studies have suggested an additional functional role for IDRs: generating steric pressure on the plasma membrane during endocytosis, via molecular crowding. However, in order to accomplish useful functions, such crowding needs to be regulated in space (e.g., endocytic hotspots) and time (e.g., during vesicle formation). In this work, we explore binding-induced regulation of IDR steric volume. We simulate the IDRs of two proteins from Clathrin-mediated endocytosis (CME) to see if their conformational spaces are regulated via binding-induced expansion. Using Monte-Carlo computational modeling of excluded volumes, we generate large conformational ensembles (3 million) for the IDRs of Epsin and Eps15 and dock the conformers to the alpha subunit of Adaptor Protein 2 (AP2α), their CME binding partner. Our results show that as more molecules of AP2α are bound, the Epsin-derived ensemble shows a significant increase in global dimensions, measured as the radius of Gyration (R_G) and the end-to-end distance (EED). Unlike Epsin, Eps15-derived conformers that permit AP2α binding at one motif were found to be more likely to accommodate binding of AP2α at other motifs, suggesting a tendency toward co-accessibility of binding motifs. Co-accessibility was not observed for any pair of binding motifs in Epsin. Thus, we speculate that the disordered regions of Epsin and Eps15 perform different roles during CME, with accessibility in Eps15 allowing it to act as a recruiter of AP2α molecules, while binding-induced expansion of the Epsin disordered region could impose steric pressure and remodel the plasma membrane during vesicle formation.

Protein functions were originally believed to arise from ordered protein structures. This dogma was later challenged by the identification of intrinsically disordered proteins that lack specific structure. The functional roles of such proteins usually fell in two categories–exploiting the disorder for flexibility (like floppy connector), or imposing order upon binding to an external partner. In this study we explore the possibility of an alternative mechanism that harnesses disorder for function through regulated molecular crowding. Specifically, we use modeling to study two proteins involved in reshaping the cell membrane, Epsin and Eps15. We ask if they undergo binding-induced expansion, where binding of an external partner AP2 causes not a transition toward order, but rather an energetically favorable increase in propensity to occupy larger volumes. Our results show that Epsin tends to occupy a larger volume when bound to AP2, consistent with increased molecular crowding, which could help reshape the cell membrane. Such regulation of disorder via binding (without folding) opens hitherto unexplored avenues that cells might employ to harness disorder.

Molecular simulations of IDPs: From ensemble generation to IDP interactions leading to disorder-to-order transitions

Intrinsically disordered proteins (IDPs) lack a well-defined three-dimensional structure but do exhibit some dynamical and structural ordering. The structural plasticity of IDPs indicates that entropy-driven motions are crucial for their function. Many IDPs undergo function-related disorder-to-order transitions upon by their interaction with specific binding partners. Approaches that are based on both experimental and theoretical tools enable the biophysical characterization of IDPs. Molecular simulations provide insights into IDP structural ensembles and disorder-to-order transition mechanisms. However, such studies depend strongly on the chosen force field parameters and simulation techniques. In this chapter, we provide an overview of IDP characteristics, review all-atom force fields recently developed for IDPs, and present molecular dynamics-based simulation methods that allow IDP ensemble generation as well as the characterization of disorder-to-order transitions. In particular, we introduce metadynamics, replica exchange molecular dynamics simulations, and also kinetic models resulting from Markov State modeling, and provide various examples for the successful application of these simulation methods to IDPs.

Computational modelling of flavivirus dynamics: The ins and outs

Enveloped viruses such as the flaviviruses represent a significant burden to human health around the world, with hundreds of millions of people each year affected by dengue alone. In an effort to improve our understanding of the molecular basis for the infective mechanisms of these viruses, extensive computational modelling approaches have been applied to elucidate their conformational dynamics. Multiscale protocols have been developed to simulate flavivirus envelopes in close accordance with biophysical data, in particular derived from cryo-electron microscopy, enabling high-resolution refinement of their structures and elucidation of the conformational changes associated with adaptation both to host environments and to immunological factors such as antibodies. Likewise, integrative modelling efforts combining data from biophysical experiments and from genome sequencing with chemical modification are providing unparalleled insights into the architecture of the previously unresolved nucleocapsid complex. Collectively, this work provides the basis for the future rational design of new antiviral therapeutics and vaccine development strategies targeting enveloped viruses.

Unraveling the NaCl Concentration Effect on the First Stages of α-Synuclein Aggregation

Intraneuronal aggregation of the intrinsically disordered protein α-synuclein is at the core of Parkinson's disease and related neurodegenerative disorders. Several reports show that the concentration of salts in the medium heavily affects its aggregation rate and fibril morphology, but a characterization of the individual monomeric conformations underlying these effects is still lacking. In this work, we have applied our α-synuclein-optimized coarse-grained molecular dynamics approach to decipher the structural features of the protein monomer under a range of NaCl concentrations (0.0-1.0 M). The results show that key intramolecular contacts between the terminal domains are lost at intermediate concentrations (leading to extended conformations likely to fibrillate), but recovered at high concentrations (leading to compact conformations likely to evolve toward amorphous aggregates). The pattern of direct interactions of the terminal α-synuclein domains with Na⁺ and Cl^- ions plays a key role in explaining this effect. Our results are consistent with a recent study reporting a fibrillation enhancement at moderate NaCl concentrations but an inhibition at higher concentrations. The present work will contribute to improving our understanding of the structural features of monomeric α-synuclein, determining its NaCl-induced fibrillation propensity and the molecular basis of synucleinopathies, necessary for the future development of disease-halting therapies.

Significant compaction of H4 histone tail upon charge neutralization by acetylation and its mimics, possible effects on chromatin structure

The intrinsically disordered, positively charged H4 histone tail is important for chromatin structure and function. We have explored conformational ensembles of human H4 tail in solution, with varying levels of charge neutralization via acetylation or amino-acid substitutions such as K→Q. We have employed an explicit water model shown recently to be well suited for simulations of intrinsically disordered proteins. Upon progressive neutralization of the H4, its radius of gyration decreases linearly with the tail charge q, the trend is explained using a simple polymer model. While the wild type state (q=+8) is essentially a random coil, hyper-acetylated H4 (q=+3) is virtually as compact and stable as a globular protein of the same number of amino-acids. Conformational ensembles of acetylated H4 match the corresponding K→X substitutions only approximately: based on the ensemble similarity, we propose K→M as a possible alternative to the commonly used K→Q. Possible effects of the H4 tail compaction on chromatin structure are discussed within a qualitative model in which the chromatin is highly heterogeneous, easily inter-converting between various structural forms. We predict that upon progressive charge neutralization of the H4 tail, the least compact sub-states of chromatin de-condense first, followed by de-condensation of more compact structures, e.g. those that harbor a high fraction of stacked di-nucleosomes. The predicted hierarchy of DNA accessibility increase upon progressive acetylation of H4 might be utilized by the cell for selective DNA accessibility control.

Refining All-Atom Protein Force Fields for Polar-Rich, Prion-like, Low-Complexity Intrinsically Disordered Proteins

Significant efforts in the past decade have given us highly accurate all-atom protein force fields for molecular dynamics (MD) simulations of folded and disordered proteins. These simulations, complemented with experimental data, provide new insights into molecular interactions that underlie the physical properties of proteins, especially for intrinsically disordered proteins (IDPs) for which defining the heterogeneous structural ensemble is hugely challenging by experiments alone. Consequently, the accuracy of these protein force fields is of utmost importance to ensure reliable simulated conformational data. Here, we first assess the accuracy of current state-of-the-art force fields for IDPs (ff99SBws and ff03ws) applied to disordered proteins of low amino acid sequence complexity that can undergo liquid-liquid phase separation. On the basis of a detailed comparison of NMR chemical shifts between simulation and experiment on several IDPs, we find that regions surrounding specific polar residues result in simulated ensembles with exaggerated helicity when compared to experiment. To resolve this discrepancy, we introduce residue-specific modifications to the backbone torsion potential of three residues (Ser, Thr, and Gln) in the ff99SBws force field. The modified force field, ff99SBws-STQ, provides a more accurate representation of helical structure propensity in these LC domains without compromising faithful representation of helicity in a region with distinct sequence composition. Our refinement strategy also suggests a path forward for integrating experimental data in the assessment of residue-specific deficiencies in the current physics-based force fields and improves these force fields further for their broader applicability.

Large-Scale Assessment of Binding Free Energy Calculations in Active Drug Discovery Projects

Accurate ranking of compounds with regards to their binding affinity to a protein using computational methods is of great interest to pharmaceutical research. Physics-based free energy calculations are regarded as the most rigorous way to estimate binding affinity. In recent years, many retrospective studies carried out both in academia and industry have demonstrated its potential. Here, we present the results of large-scale prospective application of the FEP+ method in active drug discovery projects in an industry setting at Merck KGaA, Darmstadt, Germany. We compare these prospective data to results obtained on a new diverse, public benchmark of eight pharmaceutically relevant targets. Our results offer insights into the challenges faced when using free energy calculations in real-life drug discovery projects and identify limitations that could be tackled by future method development. The new public data set we provide to the community can support further method development and comparative benchmarking of free energy calculations.

Molecular dynamics simulations of DNA-DNA and DNA-protein interactions

The all-atom molecular dynamics method can characterize the molecular-level interactions in DNA and DNA-protein systems with unprecedented resolution. Recent advances in computational technologies have allowed the method to reveal the unbiased behavior of such systems at the microseconds time scale, whereas enhanced sampling approaches have matured enough to characterize the interaction free energy with quantitative precision. Here, we describe recent progress toward increasing the realism of such simulations by refining the accuracy of the molecular dynamics force field, and we highlight recent application of the method to systems of outstanding biological interest.

The accuracy of force fields on the simulation of intrinsically disordered proteins: A benchmark test on the human p53 tumor suppressor

Intrinsically disordered proteins (IDPs) are a class of proteins without stable three-dimensional structures under physiological conditions. IDPs exhibit high dynamic nature and could be described by structural ensembles. As one of the most widely used tools, molecular dynamics (MD) simulation could provide the atomic descriptions of the structural ensemble of IDPs. However, the accuracy of the MD simulation largely depends on the accuracy of the force field. In this paper, we compared the structural ensembles of the activation domain 1 (AD1) in p53 tumor suppressor obtained from the widely used force fields, AMBER99SB-ILDN, CHARMM27, CHARMM36m with different water models. The results show that CHARMM36m generates more extended conformations than other force fields, while CHARMM27 prefers to sample the [Formula: see text]-helical structure. Moreover, the chemical shifts obtained by CHARMM36m are the closest to the experimental measurements. These results indicate that the CHARMM36m force field performs best in characterizing the structure properties of p53 AD1. Water models are also critical to describe the structural ensemble of IDPs. TIP4P water model can obtain more extended conformations and produce more local helical conformations than the TIP3P model in our simulation. In addition, we also compare the chemical shifts predicted by different chemical shift predicting programs with experimental measurements, the results show that SHIFTX2 obtains the best performance in the chemical shifts prediction.

Amyloid assembly is dominated by misregistered kinetic traps on an unbiased energy landscape

Atomistic description of protein fibril formation has been elusive due to the complexity and long time scales of the conformational search. Here, we develop a multiscale approach combining numerous atomistic simulations in explicit solvent to construct Markov State Models (MSMs) of fibril growth. The search for the in-register fully bound fibril state is modeled as a random walk on a rugged two-dimensional energy landscape defined by β-sheet alignment and hydrogen-bonding states, whereas transitions involving states without hydrogen bonds are derived from kinetic clustering. The reversible association/dissociation of an incoming peptide and overall growth kinetics are then computed from MSM simulations. This approach is applied to derive a parameter-free, comprehensive description of fibril elongation of Aβ_16-22 and how it is modulated by phenylalanine-to-cyclohexylalanine (CHA) mutations. The trajectories show an aggregation mechanism in which the peptide spends most of its time trapped in misregistered β-sheet states connected by weakly bound states twith short lifetimes. Our results recapitulate the experimental observation that mutants CHA19 and CHA1920 accelerate fibril elongation but have a relatively minor effect on the critical concentration for fibril growth. Importantly, the kinetic consequences of mutations arise from cumulative effects of perturbing the network of productive and nonproductive pathways of fibril growth. This is consistent with the expectation that nonfunctional states will not have evolved efficient folding pathways and, therefore, will require a random search of configuration space. This study highlights the importance of describing the complete energy landscape when studying the elongation mechanism and kinetics of protein fibrils.

Understanding and modelling the interactions of peptides with membranes: from partitioning to self-assembly

Atomic detail simulations are starting to reveal how flexible polypeptides interact with fluid lipid bilayers. These insights are transforming our understanding of one of the fundamental processes in biology: membrane protein folding and assembly. Advanced molecular dynamics (MD) simulation techniques enable accurate prediction of protein structure, folding pathways and assembly in microsecond-timescales. Such simulations show how membrane-active peptides self-assemble in cell membranes, revealing their binding, folding, insertion, and aggregation, while at the same time providing atomic resolution details of peptide-lipid interactions. Essential to the impact of simulations are experimental approaches that enable calibration and validation of the computational models and techniques. In this review, we summarize the current development of applying unbiased atomic detail MD simulations and the relation to experimental techniques, to study peptide folding and provide our perspective of the field.

The Mechanism of Cholesterol Modification of Hedgehog Ligand

Hedgehog (Hh) proteins are important components of signal transduction pathways involved in animal development, and their defects are implicated in carcinogenesis. Their N-terminal domain (HhN) acts as a signaling ligand, and their C-terminal domain (HhC) performs an autocatalytic function of cleaving itself away, while adding a cholesterol moiety to HhN. HhC has two sub-domains: a hedgehog/intein (hint) domain that primarily performs the autocatalytic activity, and a sterol-recognition region (SRR) that binds to cholesterol and properly positions it with respect to HhN. The three-dimensional details of this autocatalytic mechanism remain unknown, as does the structure of the precursor Hh protein. In this study, a complete cholesterol-bound precursor form of the drosophila Hh precursor is modeled using known crystal structures of HhN and the hint domain, and a hypothesized similarity of SRR to an unrelated but similar-sized cholesterol binding protein. The restrained geometries and topology switching (RGATS) strategy is then used to predict atomic-detail pathways for the full autocatalytic reaction starting from the precursor and ending in a cholesterol-linked HhN domain and a cleaved HhC domain. The RGATS explicit solvent simulations indicate the roles of individual HhC residues in facilitating the reaction, which can be confirmed through mutational experiments. These simulations also provide plausible structural models for the N/S acyl transfer intermediate and the product states of this reaction. This study thus provides a good framework for future computational and experimental studies to develop a full structural and dynamic understanding of Hh autoprocessing. © 2019 Wiley Periodicals, Inc.

Polarisable force fields: what do they add in biomolecular simulations?

The quality of biomolecular simulations critically depends on the accuracy of the force field used to calculate the potential energy of the molecular configurations. Currently, most simulations employ non-polarisable force fields, which describe electrostatic interactions as the sum of Coulombic interactions between fixed atomic charges. Polarisation of these charge distributions is incorporated only in a mean-field manner. In the past decade, extensive efforts have been devoted to developing simple, efficient, and yet generally applicable polarisable force fields for biomolecular simulations. In this review, we summarise the latest developments in accounting for key biomolecular interactions with polarisable force fields and applications to address challenging biological questions. In the end, we provide an outlook for future development in polarisable force fields.

Predicting partition coefficients of drug-like molecules in the SAMPL6 challenge with Drude polarizable force fields

The water-octanol partition coefficient is an important physicochemical property for small molecule drug design. Here, we report our participation in the SAMPL6 logP prediction challenge with free energy perturbation (FEP) calculations in the water phase and in the 1-octanol phase using Drude polarizable force fields. Root mean square error (RMSE) and mean absolute error (MAE) of our prediction are equal to 1.85 and 1.25 logP units. The errors are not evenly distributed. Out of eleven SAMPL6 solutes, FEP/Drude performed very badly on three molecules (deviations all larger than 2 logP units) but good on the remaining eight (deviations all less than 1 logP unit). We find while FEP converges well within one nanosecond in water, simulations in 1-octanol need much longer simulation time and possibly more independent runs for sampling. We also find out that 1-octanol, albeit being a non-polar solvent, still polarizes solute molecules and forms stable hydrogen bonds with them. At the end, we attempt to reweight FEP trajectories with QM/Drude calculations and discuss possible caveats in our simulation setup.

Combining molecular dynamics simulations and experimental analyses in protein misfolding

The fold of a protein determines its function and its misfolding can result in loss-of-function defects. In addition, for certain proteins their misfolding can lead to gain-of-function toxicities resulting in protein misfolding diseases such as Alzheimer's, Parkinson's, or the prion diseases. In all of these diseases one or more proteins misfold and aggregate into disease-specific assemblies, often in the form of fibrillar amyloid deposits. Most, if not all, protein misfolding diseases share a fundamental molecular mechanism that governs the misfolding and subsequent aggregation. A wide variety of experimental methods have contributed to our knowledge about misfolded protein aggregates, some of which are briefly described in this review. The misfolding mechanism itself is difficult to investigate, as the necessary timescale and resolution of the misfolding events often lie outside of the observable parameter space. Molecular dynamics simulations fill this gap by virtue of their intrinsic, molecular perspective and the step-by-step iterative process that forms the basis of the simulations. This review focuses on molecular dynamics simulations and how they combine with experimental analyses to provide detailed insights into protein misfolding and the ensuing diseases.

Enhanced Molecular Dynamics Simulations of Intrinsically Disordered Proteins

Molecular dynamics simulations represent a powerful tool to gain insights into structural and dynamical features of biomolecular systems. Nevertheless, their recognized limitation in terms of achievable timescales becomes particularly severe when dealing with slow processes. In such cases, the employment of enhanced sampling methods, which allow accelerating the characterization of rare events in a timeframe consistent with conventional computational resources, results as crucial. In particular, such advanced techniques have proven highly valuable in the context of protein folding and, specifically, to explore the conformational ensemble spanned by intrinsically disordered proteins (IDPs). Here, we describe how to set up molecular dynamics simulations with one of these enhanced sampling approaches (namely, Parallel Tempering Metadynamics in the Well-Tempered Ensemble) using the N_TAIL peptide as a test case.

Binding without folding - the biomolecular function of disordered polyelectrolyte complexes

Recent evidence shows that oppositely charged intrinsically disordered proteins (IDPs) can form high-affinity complexes that involve neither the formation of secondary or tertiary structure nor site-specific interactions between individual residues. Similar electrostatically dominated interactions have also been identified for positively charged IDPs binding to nucleic acids. These highly disordered polyelectrolyte complexes constitute an extreme case within the spectrum of biomolecular interactions involving disorder. Such interactions are likely to be widespread, since sequence analysis predicts proteins with highly charged disordered regions to be surprisingly numerous. Here, we summarize the insights that have emerged from the highly disordered polyelectrolyte complexes identified so far, and we highlight recent developments and future challenges in (i) establishing models for the underlying highly dynamic structural ensembles, (ii) understanding the novel binding mechanisms associated with them, and (iii) identifying the functional consequences.

Conformational Flexibility of the Protein-Protein Interfaces of the Ebola Virus VP40 Structural Matrix Filament

The Ebola virus (EBOV) is a virulent pathogen that causes severe hemorrhagic fever with a high fatality rate in humans. The EBOV transformer protein VP40 plays crucial roles in viral assembly and budding at the plasma membrane of infected cells. One of VP40's roles is to form the long, flexible, pleomorphic filamentous structural matrix for the virus. Each filament contains three unique interfaces: monomer NTD-NTD to form a dimer, dimer-to-dimer NTD-NTD oligomerization to form a hexamer, and end-to-end hexamer CTD-CTD to build the filament. However, the atomic-level details of conformational flexibility of the VP40 filament are still elusive. In this study, we have performed explicit-solvent, all-atom molecular dynamic simulations to explore the conformational flexibility of the three different interface structures of the filament. Using dynamic network analysis and other calculational methods, we find that the CTD-CTD hexamer interface with weak interdomain amino acid communities is the most flexible, and the NTD-NTD oligomer interface with strong interdomain communities is the least flexible. Our study suggests that the high flexibility of the CTD-CTD interface may be essential for the supple bending of the Ebola filovirus, and such flexibility may present a target for molecular interventions to disrupt the Ebola virus functioning.

An intrinsically disordered proteins community for ELIXIR

Intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs) are now recognised as major determinants in cellular regulation. This white paper presents a roadmap for future e-infrastructure developments in the field of IDP research within the ELIXIR framework. The goal of these developments is to drive the creation of high-quality tools and resources to support the identification, analysis and functional characterisation of IDPs. The roadmap is the result of a workshop titled “An intrinsically disordered protein user community proposal for ELIXIR” held at the University of Padua. The workshop, and further consultation with the members of the wider IDP community, identified the key priority areas for the roadmap including the development of standards for data annotation, storage and dissemination; integration of IDP data into the ELIXIR Core Data Resources; and the creation of benchmarking criteria for IDP-related software. Here, we discuss these areas of priority, how they can be implemented in cooperation with the ELIXIR platforms, and their connections to existing ELIXIR Communities and international consortia. The article provides a preliminary blueprint for an IDP Community in ELIXIR and is an appeal to identify and involve new stakeholders.

Generation of the configurational ensemble of an intrinsically disordered protein from unbiased molecular dynamics simulation

Intrinsically disordered proteins (IDPs) are abundant in eukaryotic proteomes, play a major role in cell signaling, and are associated with human diseases. To understand IDP function it is critical to determine their configurational ensemble, i.e., the collection of 3-dimensional structures they adopt, and this remains an immense challenge in structural biology. Attempts to determine this ensemble computationally have been hitherto hampered by the necessity of reweighting molecular dynamics (MD) results or biasing simulation in order to match ensemble-averaged experimental observables, operations that reduce the precision of the generated model because different structural ensembles may yield the same experimental observable. Here, by employing enhanced sampling MD we reproduce the experimental small-angle neutron and X-ray scattering profiles and the NMR chemical shifts of the disordered N terminal (SH4UD) of c-Src kinase without reweighting or constraining the simulations. The unbiased simulation results reveal a weakly funneled and rugged free energy landscape of SH4UD, which gives rise to a heterogeneous ensemble of structures that cannot be described by simple polymer theory. SH4UD adopts transient helices, which are found away from known phosphorylation sites and could play a key role in the stabilization of structural regions necessary for phosphorylation. Our findings indicate that adequately sampled molecular simulations can be performed to provide accurate physical models of flexible biosystems, thus rationalizing their biological function.

Drude Polarizable Force Field Parametrization of Carboxylate and N-Acetyl Amine Carbohydrate Derivatives

In this work, we report the development of Drude polarizable force field parameters for the carboxylate and N-acetyl amine derivatives, extending the functionality of the existing Drude polarizable carbohydrate force field. The force field parameters have been developed in a hierarchical manner, reproducing the quantum mechanical gas-phase properties of small model compounds representing the key functional group in the carbohydrate derivatives, including optimization of the electrostatic and bonded parameters. The optimized parameters were then used to generate the models for carboxylate and N-acetyl amine carbohydrate derivatives. The transferred parameters were further tested and optimized to reproduce crystal geometries and J-coupling data from nuclear magnetic resonance experiments. The parameter development resulted in the incorporation of d-glucuronate, l-iduronate, N-acetyl-d-glucosamine (GlcNAc), and N-acetyl-d-galactosamine (GalNAc) sugars into the Drude polarizable force field. The parameters developed in this study were then applied to study the conformational properties of glycosaminoglycan polymer hyaluronan, composed of d-glucuronate and N-acetyl-d-glucosamine, in aqueous solution. Upon comparing the results from the additive and polarizable simulations, it was found that the inclusion of polarization improved the description of the electrostatic interactions observed in hyaluronan, resulting in enhanced conformational flexibility. The developed Drude polarizable force field parameters in conjunction with the remainder of the Drude polarizable force field parameters can be used for future studies involving carbohydrates and their conjugates in complex, heterogeneous systems.

Thermodynamics of Conformational Transitions in a Disordered Protein Backbone Model

Conformational entropy is expected to contribute significantly to the thermodynamics of structural transitions in intrinsically disordered proteins or regions in response to protein/ligand binding, posttranslational modifications, and environmental changes. We calculated the backbone (dihedral) conformational entropy of oligoglycine (Gly_N), a protein backbone mimic and model intrinsically disordered region, as a function of chain length (N=3, 4, 5, 10, and 15) from simulations using three different approaches. The backbone conformational entropy scales linearly with chain length with a slope consistent with the entropy of folding of well-structured proteins. The entropic contributions of second-order dihedral correlations are predominantly through intraresidue ϕ-ψ pairs, suggesting that oligoglycine may be thermodynamically modeled as a system of independent glycine residues. We find the backbone conformational entropy to be largely independent of global structural parameters, like the end-to-end distance and radius of gyration. We introduce a framework referred to herein as "ensemble confinement" to estimate the loss (gain) of conformational free energy and its entropic component when individual residues are constrained to (released from) particular regions of the ϕ-ψ map. Quantitatively, we show that our protein backbone model resists ordering/folding with a significant, unfavorable ensemble confinement free energy because of the loss of a substantial portion of the absolute backbone entropy. Proteins can couple this free-energy reservoir to distal binding events as a regulatory mechanism to promote or suppress binding.

Refinement of Peptide Conformational Ensembles by 2D IR Spectroscopy: Application to Ala‒Ala‒Ala

Characterizing ensembles of intrinsically disordered proteins is experimentally challenging because of the ill-conditioned nature of ensemble determination with limited data and the intrinsic fast dynamics of the conformational ensemble. Amide I two-dimensional infrared (2D IR) spectroscopy has picosecond time resolution to freeze structural ensembles as needed for probing disordered-protein ensembles and conformational dynamics. Also, developments in amide I computational spectroscopy now allow a quantitative and direct prediction of amide I spectra based on conformational distributions drawn from molecular dynamics simulations, providing a route to ensemble refinement against experimental spectra. We performed a Bayesian ensemble refinement method on Ala-Ala-Ala against isotope-edited Fourier-transform infrared spectroscopy and 2D IR spectroscopy and tested potential factors affecting the quality of ensemble refinements. We found that isotope-edited 2D IR spectroscopy provides a stringent constraint on Ala-Ala-Ala conformations and returns consistent conformational ensembles with the dominant ppII conformer across varying prior distributions from many molecular dynamics force fields and water models. The dominant factor influencing ensemble refinements is the systematic frequency uncertainty from spectroscopic maps. However, the uncertainty of conformer populations can be significantly reduced by incorporating 2D IR spectra in addition to traditional Fourier-transform infrared spectra. Bayesian ensemble refinement against isotope-edited 2D IR spectroscopy thus provides a route to probe equilibrium-complex protein ensembles and potentially nonequilibrium conformational dynamics.

Using Small-Angle Scattering Data and Parametric Machine Learning to Optimize Force Field Parameters for Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) and proteins with intrinsically disordered regions (IDRs) play important roles in many aspects of normal cell physiology, such as signal transduction and transcription, as well as pathological states, including Alzheimer's, Parkinson's, and Huntington's disease. Unlike their globular counterparts that are defined by a few structures and free energy minima, IDP/IDR comprise a large ensemble of rapidly interconverting structures and a corresponding free energy landscape characterized by multiple minima. This aspect has precluded the use of structural biological techniques, such as X-ray crystallography and nuclear magnetic resonance (NMR) for resolving their structures. Instead, low-resolution techniques, such as small-angle X-ray or neutron scattering (SAXS/SANS), have become a mainstay in characterizing coarse features of the ensemble of structures. These are typically complemented with NMR data if possible or computational techniques, such as atomistic molecular dynamics, to further resolve the underlying ensemble of structures. However, over the past 10–15 years, it has become evident that the classical, pairwise-additive force fields that have enjoyed a high degree of success for globular proteins have been somewhat limited in modeling IDP/IDR structures that agree with experiment. There has thus been a significant effort to rehabilitate these models to obtain better agreement with experiment, typically done by optimizing parameters in a piecewise fashion. In this work, we take a different approach by optimizing a set of force field parameters simultaneously, using machine learning to adapt force field parameters to experimental SAXS scattering profiles. We demonstrate our approach in modeling three biologically IDP ensembles based on experimental SAXS profiles and show that our optimization approach significantly improve force field parameters that generate ensembles in better agreement with experiment.