Kinetic modulation of a disordered protein domain by phosphorylation

Phosphorylation of disordered proteins tunes local and global intramolecular interactions

Protein post-translational modifications, such as phosphorylation, are important regulatory signals for diverse cellular functions. In particular, intrinsically disordered protein regions (IDRs) are subject to phosphorylation as a means to modulate their interactions and functions. Toward understanding the relationship between phosphorylation in IDRs and specific functional outcomes, we must consider how phosphorylation affects the IDR conformational ensemble. Various experimental techniques are suited to interrogate the features of IDR ensembles; molecular simulations can provide complementary insights and even illuminate ensemble features that may be experimentally inaccessible. Therefore, we sought to expand the tools available to study phosphorylated IDRs by all-atom Monte Carlo simulations. To this end, we implemented parameters for phosphoserine (pSer) and phosphothreonine (pThr) into the OPLS version of the continuum solvent model, ABSINTH, and assessed their performance in all-atom simulations compared to published findings. We simulated short (< 20 residues) and long (> 80 residues) phospho-IDRs that, collectively, survey both local and global phosphorylation-induced changes to the ensemble. Our simulations of four well-studied phospho-IDRs show near-quantitative agreement with published findings for these systems via metrics including changes to radius of gyration, transient helicity, and persistence length. We also leveraged the inherent advantage of sequence control in molecular simulations to explore the conformational effects of diverse combinations of phospho-sites in two multi-phosphorylated IDRs. Our results support and expand on prior observations that connect phosphorylation to changes in the IDR conformational ensemble. Herein, we describe phosphorylation as a means to alter sequence chemistry, net charge and charge patterning, and intramolecular interactions, which can collectively modulate the local and global IDR ensemble features.

Kinetic Ensemble of Tau Protein through the Markov State Model and Deep Learning Analysis

The ordered assembly of Tau protein into filaments characterizes Alzheimer's and other neurodegenerative diseases, and thus, stabilization of Tau protein is a promising avenue for tauopathies therapy. To dissect the underlying aggregation mechanisms on Tau, we employ a set of molecular simulations and the Markov state model to determine the kinetics of ensemble of K18. K18 is the microtubule-binding domain of Tau protein and plays a vital role in the microtubule assembly, recycling processes, and amyloid fibril formation. Here, we efficiently explore the conformation of K18 with about 150 μs lifetimes in silico. Our results observe that all four repeat regions (R1-R4) are very dynamic, featuring frequent conformational conversion and lacking stable conformations, and the R2 region is more flexible than the R1, R3, and R4 regions. Additionally, it is worth noting that residues 300-310 in R2-R3 and residues 319-336 in R3 tend to form sheet structures, indicating that K18 has a broader functional role than individual repeat monomers. Finally, the simulations combined with Markov state models and deep learning reveal 5 key conformational states along the transition pathway and provide the information on the microsecond time scale interstate transition rates. Overall, this study offers significant insights into the molecular mechanism of Tau pathological aggregation and develops novel strategies for both securing tauopathies and advancing drug discovery.

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

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

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.

A comprehensive review on preparation, structure-activities relationship, and calcium bioavailability of casein phosphopeptides

Calcium is one of the important elements for human health. Calcium deficiencies can lead to numerous diseases. Calcium chelating peptides have shown potential application in the management of calcium deficiencies. Casein phosphopeptides (CPP) are phosphoseryl-containing fragments of casein by enzymatic hydrolysis or fermentation during manufacture of milk products as well as during intestinal digestion. An increasing number of CPP with the ability to facilitate and enhance the bioavailability of calcium are being discovered and identified. In this review, 249 reported CPP derived from four types of bovine casein (αs1, αs2, β and κ) were collected, and the amino acid sequence and phosphoserine group information were sorted out. This review outlines the current enzyme hydrolysis, detection methods, purification, structure-activity relationship and mechanism of intestinal calcium absorption in vitro and in vivo as well as application of CPP.

Characterization of intrinsically disordered regions in proteins informed by human genetic diversity

All proteomes contain both proteins and polypeptide segments that don’t form a defined three-dimensional structure yet are biologically active—called intrinsically disordered proteins and regions (IDPs and IDRs). Most of these IDPs/IDRs lack useful functional annotation limiting our understanding of their importance for organism fitness. Here we characterized IDRs using protein sequence annotations of functional sites and regions available in the UniProt knowledgebase (“UniProt features”: active site, ligand-binding pocket, regions mediating protein-protein interactions, etc.). By measuring the statistical enrichment of twenty-five UniProt features in 981 IDRs of 561 human proteins, we identified eight features that are commonly located in IDRs. We then collected the genetic variant data from the general population and patient-based databases and evaluated the prevalence of population and pathogenic variations in IDPs/IDRs. We observed that some IDRs tolerate 2 to 12-times more single amino acid-substituting missense mutations than synonymous changes in the general population. However, we also found that 37% of all germline pathogenic mutations are located in disordered regions of 96 proteins. Based on the observed-to-expected frequency of mutations, we categorized 34 IDRs in 20 proteins (DDX3X, KIT, RB1, etc.) as intolerant to mutation. Finally, using statistical analysis and a machine learning approach, we demonstrate that mutation-intolerant IDRs carry a distinct signature of functional features. Our study presents a novel approach to assign functional importance to IDRs by leveraging the wealth of available genetic data, which will aid in a deeper understating of the role of IDRs in biological processes and disease mechanisms.

Molecular Simulations of Intrinsically Disordered Proteins and Their Binding Mechanisms

Intrinsically disordered proteins (IDPs) lack well-defined secondary or tertiary structures in solution but are found to be involved in a wide range of critical cellular processes that highlight their functional importance. IDPs usually undergo folding upon binding to their targets. Such binding coupled to folding behavior has widened our perspective on the protein structure-dynamics-function paradigm in molecular biology. However, characterizing the folding upon binding mechanism of IDPs experimentally remains quite challenging. Molecular simulations emerge as a potentially powerful tool that offers information complementary to experiments. Here we present a general computational framework for the molecular simulations of IDP folding upon binding processes that combines all-atom molecular dynamics (MD) and coarse-grained simulations. The classical all-atom molecular dynamics approach using GPU acceleration allows the researcher to explore the properties of the IDP conformational ensemble, whereas coarse-grained structure-based models implemented with parameters carefully calibrated to available experimental measurements can be used to simulate the entire folding upon binding process. We also discuss a set of tools for the analysis of MD trajectories and describe the details of the computational protocol to follow so that it can be adapted by the user to study any IDP in isolation and in complex with partners.

Unsupervised Learning Methods for Molecular Simulation Data

Unsupervised learning is becoming an essential tool to analyze the increasingly large amounts of data produced by atomistic and molecular simulations, in material science, solid state physics, biophysics, and biochemistry. In this Review, we provide a comprehensive overview of the methods of unsupervised learning that have been most commonly used to investigate simulation data and indicate likely directions for further developments in the field. In particular, we discuss feature representation of molecular systems and present state-of-the-art algorithms of dimensionality reduction, density estimation, and clustering, and kinetic models. We divide our discussion into self-contained sections, each discussing a specific method. In each section, we briefly touch upon the mathematical and algorithmic foundations of the method, highlight its strengths and limitations, and describe the specific ways in which it has been used-or can be used-to analyze molecular simulation data.

Markov models from the square root approximation of the Fokker-Planck equation: calculating the grid-dependent flux

Molecular dynamics (MD) are extremely complex, yet understanding the slow components of their dynamics is essential to understanding their macroscopic properties. To achieve this, one models the MD as a stochastic process and analyses the dominant eigenfunctions of the associated Fokker-Planck operator, or of closely related transfer operators. So far, the calculation of the discretized operators requires extensive MD simulations. The square-root approximation of the Fokker-Planck equation is a method to calculate transition rates as a ratio of the Boltzmann densities of neighboring grid cells times a flux, and can in principle be calculated without a simulation. In a previous work we still used MD simulations to determine the flux. Here, we propose several methods to calculate the exact or approximate flux for various grid types, and thus estimate the rate matrix without a simulation. Using model potentials we test computational efficiency of the methods, and the accuracy with which they reproduce the dominant eigenfunctions and eigenvalues. For these model potentials, rate matrices with up to [Formula: see text] states can be obtained within seconds on a single high-performance compute server if regular grids are used.

Intrinsic disorder in protein domains contributes to both organism complexity and clade-specific functions

Interestingly, some protein domains are intrinsically disordered (abbreviated as IDD), and the disorder degree of same domains may differ in different contexts. However, the evolutionary causes and biological significance of these phenomena are unclear. Here, we address these issues by genome-wide analyses of the evolutionary and functional features of IDDs in 1,870 species across the three superkingdoms. As the result, there is a significant positive correlation between the proportion of IDDs and organism complexity with some interesting exceptions. These phenomena may be due to the high disorder of clade-specific domains and the different disorder degrees of the domains shared in different clades. The functions of IDDs are clade-specific and the higher proportion of post-translational modification sites may contribute to their complex functions. Compared with metazoans, fungi have more IDDs with a consecutive disorder region but a low disorder ratio, which reflects their different functional requirements. As for disorder variation, it’s greater for domains among different proteins than those within the same proteins. Some clade-specific ‘no-variation’ or ‘high-variation’ domains are involved in clade-specific functions. In sum, intrinsic domain disorder is related to both the organism complexity and clade-specific functions. These results deepen the understanding of the evolution and function of IDDs.

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.

Gradual compaction of the nascent peptide during cotranslational folding on the ribosome

Nascent polypeptides begin to fold in the constrained space of the ribosomal peptide exit tunnel. Here we use force-profile analysis (FPA) and photo-induced energy-transfer fluorescence correlation spectroscopy (PET-FCS) to show how a small α-helical domain, the N-terminal domain of HemK, folds cotranslationally. Compaction starts vectorially as soon as the first α-helical segments are synthesized. As nascent chain grows, emerging helical segments dock onto each other and continue to rearrange at the vicinity of the ribosome. Inside or in the proximity of the ribosome, the nascent peptide undergoes structural fluctuations on the µs time scale. The fluctuations slow down as the domain moves away from the ribosome. Mutations that destabilize the packing of the domain's hydrophobic core have little effect on folding within the exit tunnel, but abolish the final domain stabilization. The results show the power of FPA and PET-FCS in solving the trajectory of cotranslational protein folding and in characterizing the dynamic properties of folding intermediates.

Characterization of partially ordered states in the intrinsically disordered N-terminal domain of p53 using millisecond molecular dynamics simulations

The exploration of intrinsically disordered proteins in isolation is a crucial step to understand their complex dynamical behavior. In particular, the emergence of partially ordered states has not been explored in depth. The experimental characterization of such partially ordered states remains elusive due to their transient nature. Molecular dynamics mitigates this limitation thanks to its capability to explore biologically relevant timescales while retaining atomistic resolution. Here, millisecond unbiased molecular dynamics simulations were performed in the exemplar N-terminal region of p53. In combination with state-of-the-art Markov state models, simulations revealed the existence of several partially ordered states accounting for [Formula: see text] 40% of the equilibrium population. Some of the most relevant states feature helical conformations similar to the bound structure of p53 to Mdm2, as well as novel [Formula: see text]-sheet elements. This highlights the potential complexity underlying the energy surface of intrinsically disordered proteins.

Combining Monte Carlo and Molecular Dynamics Simulations for Enhanced Binding Free Energy Estimation through Markov State Models

We present a multistep protocol, combining Monte Carlo and molecular dynamics simulations, for the estimation of absolute binding free energies, one of the most significant challenges in computer-aided drug design. The protocol is based on an initial short enhanced Monte Carlo simulation, followed by clustering of the ligand positions, which serve to identify the most relevant states of the unbinding process. From these states, extensive molecular dynamics simulations are run to estimate an equilibrium probability distribution obtained with Markov State Models, which is subsequently used to estimate the binding free energy. We tested the procedure on two different protein systems, the Plasminogen kringle domain 1 and Urokinase, each with multiple ligands, for an aggregated molecular dynamics length of 760 μs. Our results indicate that the initial sampling of the unbinding events largely facilitates the convergence of the subsequent molecular dynamics exploration. Moreover, the protocol is capable to properly rank the set of ligands examined, albeit with a significant computational cost for the, more realistic, Urokinase complexes. Overall, this work demonstrates the usefulness of combining enhanced sampling methods with regular simulation techniques as a way to obtain more reliable binding affinity estimates.

Dynamical matrix propagator scheme for large-scale proton dynamics simulations

We derive a matrix formalism for the simulation of long range proton dynamics for extended systems and timescales. On the basis of an ab initio molecular dynamics simulation, we construct a Markov chain, which allows us to store the entire proton dynamics in an M × M transition matrix (where M is the number of oxygen atoms). In this article, we start from common topology features of the hydrogen bond network of good proton conductors and utilize them as constituent constraints of our dynamic model. We present a thorough mathematical derivation of our approach and verify its uniqueness and correct asymptotic behavior. We propagate the proton distribution by means of transition matrices, which contain kinetic data from both ultra-short (sub-ps) and intermediate (ps) timescales. This concept allows us to keep the most relevant features from the microscopic level while effectively reaching larger time and length scales. We demonstrate the applicability of the transition matrices for the description of proton conduction trends in proton exchange membrane materials.

Phosphorylation of a Disordered Peptide-Structural Effects and Force Field Inconsistencies

Phosphorylation is one of the most abundant types of post-translational modifications of intrinsically disordered proteins (IDPs). This study examines the conformational changes in the 15-residue-long N-terminal fragment of the IDP statherin upon phosphorylation, using computer simulations with two different force fields: AMBER ff99SB-ILDN and CHARMM36m. The results from the simulations are compared with experimental small-angle X-ray scattering (SAXS) and circular dichroism data. In the unphosphorylated state, the two force fields are in excellent agreement regarding global structural properties such as size and shape. However, they exhibit some differences in the extent and type of the secondary structure. In the phosphorylated state, neither of the force fields performs well compared to the experimental data. Both force fields show a compaction of the peptide upon phosphorylation, greater than what is seen in SAXS experiments, although they differ in the local structure. While the CHARMM force field increases the fraction of bends in the peptide as a response to strong interactions between the phosphorylated residues and arginines, the AMBER force field shows an increase of the helical content in the N-terminal part of the peptide, where the phosphorylated residues reside, in better agreement with circular dichroism results.

Explicit Characterization of the Free Energy Landscape of pKID-KIX Coupled Folding and Binding

The most fundamental aspect of the free energy landscape of proteins is that it is globally funneled such that protein folding is energetically biased. Then, what are the distinctive characteristics of the landscape of intrinsically disordered proteins, apparently lacking such energetic bias, that nevertheless fold upon binding? Here, we address this fundamental issue through the explicit characterization of the free energy landscape of the paradigmatic pKID-KIX system (pKID, phosphorylated kinase-inducible domain; KIX, kinase interacting domain). This is done based on unguided, fully atomistic, explicit-water molecular dynamics simulations with an aggregated simulation time of >30 μs and on the computation of the free energy that defines the landscape. We find that, while the landscape of pKID before binding is considerably shallower than the one for a protein that autonomously folds, it becomes progressively more funneled as the binding of pKID with KIX proceeds. This explains why pKID is disordered in a free state, and the binding of pKID with KIX is a prerequisite for pKID's folding. In addition, we observe that the key event in completing the pKID-KIX coupled folding and binding is the directed self-assembly where pKID is docked upon the KIX surface to maximize the surface electrostatic complementarity, which, in turn, require pKID to adopt the correct folded structure. This key process shows up as the free energy barrier in the pKID landscape separating the intermediate nonspecific complex state and the specific complex state. The present work not only provides a detailed molecular picture of the coupled folding and binding of pKID but also expands the funneled landscape perspective to intrinsically disordered proteins.

Recent Advances in Computational Protocols Addressing Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDP) are abundant in the human genome and have recently emerged as major therapeutic targets for various diseases. Unlike traditional proteins that adopt a definitive structure, IDPs in free solution are disordered and exist as an ensemble of conformations. This enables the IDPs to signal through multiple signaling pathways and serve as scaffolds for multi-protein complexes. The challenge in studying IDPs experimentally stems from their disordered nature. Nuclear magnetic resonance (NMR), circular dichroism, small angle X-ray scattering, and single molecule Förster resonance energy transfer (FRET) can give the local structural information and overall dimension of IDPs, but seldom provide a unified picture of the whole protein. To understand the conformational dynamics of IDPs and how their structural ensembles recognize multiple binding partners and small molecule inhibitors, knowledge-based and physics-based sampling techniques are utilized in-silico, guided by experimental structural data. However, efficient sampling of the IDP conformational ensemble requires traversing the numerous degrees of freedom in the IDP energy landscape, as well as force-fields that accurately model the protein and solvent interactions. In this review, we have provided an overview of the current state of computational methods for studying IDP structure and dynamics and discussed the major challenges faced in this field.

Estimation of the infinitesimal generator by square-root approximation

In recent years, for the analysis of molecular processes, the estimation of time-scales and transition rates has become fundamental. Estimating the transition rates between molecular conformations is-from a mathematical point of view-an invariant subspace projection problem. We present a method to project the infinitesimal generator acting on function space to a low-dimensional rate matrix. This projection can be performed in two steps. First, we discretize the conformational space in a Voronoi tessellation, then the transition rates between adjacent cells is approximated by the geometric average of the Boltzmann weights of the Voronoi cells. This method demonstrates that there is a direct relation between the potential energy surface of molecular structures and the transition rates of conformational changes. We will show also that this approximation is correct and converges to the generator of the Smoluchowski equation in the limit of infinitely small Voronoi cells. We present results for a two dimensional diffusion process and alanine dipeptide as a high-dimensional system.

From Levinthal's Paradox to the Effects of Cell Environmental Perturbation on Protein Folding

BACKGROUND

The rapidly increasing number of known protein sequences calls for more efficient methods to predict the Three-Dimensional (3D) structures of proteins, thus providing basic knowledge for rational drug design. Understanding the folding mechanism of proteins is valuable for predicting their 3D structures and for designing proteins with new functions and medicinal applications. Levinthal's paradox is that although the astronomical number of conformations possible even for proteins as small as 100 residues cannot be fully sampled, proteins in nature normally fold into the native state within timescales ranging from microseconds to hours. These conflicting results reveal that there are factors in organisms that can assist in protein folding.

METHODS

In this paper, we selected a crowded cell-like environment and temperature, and the top three Posttranslational Modifications (PTMs) as examples to show that Levinthal's paradox does not reflect the folding mechanism of proteins. We then revealed the effects of these factors on protein folding.

RESULTS

The results summarized in this review indicate that a crowded cell-like environment, temperature, and the top three PTMs reshape the Free Energy Landscapes (FELs) of proteins, thereby regulating the folding process. The balance between entropy and enthalpy is the key to understanding the effect of the crowded cell-like environment and PTMs on protein folding. In addition, the stability/flexibility of proteins is regulated by temperature.

CONCLUSION

This paper concludes that the cellular environment could directly intervene in protein folding. The long-term interactions of the cellular environment and sequence evolution may enable proteins to fold efficiently. Therefore, to correctly understand the folding mechanism of proteins, the effect of the cellular environment on protein folding should be considered.

Selecting for Fast Protein-Protein Association As Demonstrated on a Random TEM1 Yeast Library Binding BLIP

Protein-protein interactions mediate the vast majority of cellular processes. Though protein interactions obey basic chemical principles also within the cell, the in vivo physiological environment may not allow for equilibrium to be reached. Thus, in vitro measured thermodynamic affinity may not provide a complete picture of protein interactions in the biological context. Binding kinetics composed of the association and dissociation rate constants are relevant and important in the cell. Therefore, changes in protein-protein interaction kinetics have a significant impact on the in vivo activity of the proteins. The common protocol for the selection of tighter binders from a mutant library selects for protein complexes with slower dissociation rate constants. Here we describe a method to specifically select for variants with faster association rate constants by using pre-equilibrium selection, starting from a large random library. Toward this end, we refine the selection conditions of a TEM1-β-lactamase library against its natural nanomolar affinity binder β-lactamase inhibitor protein (BLIP). The optimal selection conditions depend on the ligand concentration and on the incubation time. In addition, we show that a second sort of the library helps to separate signal from noise, resulting in a higher percent of faster binders in the selected library. Fast associating protein variants are of particular interest for drug development and other biotechnological applications.

MELD-Path Efficiently Computes Conformational Transitions, Including Multiple and Diverse Paths

The molecular actions of proteins occur along reaction coordinates. Current computer methods have limited ability to explore them. We describe a fast protocol called MELD-path that (1) efficiently samples relevant conformational states via MELD, an accelerator of Molecular Dynamics (MD), (2) seeds multiple short MD trajectories from MELD states, and then (3) constructs Markov State Models (MSM) that give the routes and kinetics. We tested the method against extensive (multi μs) MD simulations of the right-handed- to left-handed-helix transition of a 9-mer peptide of AIB, the symmetry of which allows us to establish convergence. MELD-path finds all the metastable states, their correct relative populations, and the full ensemble of routes, not just a single assumed route. For this transition, we find a very broad route structure. MELD-path is highly parallelizable and efficient, yielding the full route map in a few days of computation. We believe MELD-path could be a general and rapid way to explore mechanistic processes in biomolecules on the computer.

Simulations meet machine learning in structural biology

Classical molecular dynamics (MD) simulations will be able to reach sampling in the second timescale within five years, producing petabytes of simulation data at current force field accuracy. Notwithstanding this, MD will still be in the regime of low-throughput, high-latency predictions with average accuracy. We envisage that machine learning (ML) will be able to solve both the accuracy and time-to-prediction problem by learning predictive models using expensive simulation data. The synergies between classical, quantum simulations and ML methods, such as artificial neural networks, have the potential to drastically reshape the way we make predictions in computational structural biology and drug discovery.

Dynamic control of RSK complexes by phosphoswitch-based regulation

Assembly and disassembly of protein-protein complexes needs to be dynamically controlled and phosphoswitches based on linear motifs are crucial in this process. Extracellular signal-regulated kinase 2 (ERK2) recognizes a linear-binding motif at the C-terminal tail (CTT) of ribosomal S6 kinase 1 (RSK1), leading to phosphorylation and subsequent activation of RSK1. The CTT also contains a classical PDZ domain-binding motif which binds RSK substrates (e.g. MAGI-1). We show that autophosphorylation of the disordered CTT promotes the formation of an intramolecular charge clamp, which efficiently masks critical residues and indirectly hinders ERK binding. Thus, RSK1 CTT operates as an autoregulated phosphoswitch: its phosphorylation at specific sites affects its protein-binding capacity and its conformational dynamics. These biochemical feedbacks, which form the structural basis for the rapid dissociation of ERK2-RSK1 and RSK1-PDZ substrate complexes under sustained epidermal growth factor (EGF) stimulation, were structurally characterized and validated in living cells. Overall, conformational changes induced by phosphorylation in disordered regions of protein kinases, coupled to allosteric events occurring in the kinase domain cores, may provide mechanisms that contribute to the emergence of complex signaling activities. In addition, we show that phosphoswitches based on linear motifs can be functionally classified as ON and OFF protein-protein interaction switches or dimmers, depending on the specific positioning of phosphorylation target sites in relation to functional linear-binding motifs. Moreover, interaction of phosphorylated residues with positively charged residues in disordered regions is likely to be a common mechanism of phosphoregulation.

DATABASE

Structural data are available in the PDB database under the accession numbers 5N7D, 5N7F and 5N7G. NMR spectral assignation data are available in the BMRB database under the accession numbers 27213 and 27214.

The liquid structure of elastin

The protein elastin imparts extensibility, elastic recoil, and resilience to tissues including arterial walls, skin, lung alveoli, and the uterus. Elastin and elastin-like peptides are hydrophobic, disordered, and undergo liquid-liquid phase separation upon self-assembly. Despite extensive study, the structure of elastin remains controversial. We use molecular dynamics simulations on a massive scale to elucidate the structural ensemble of aggregated elastin-like peptides. Consistent with the entropic nature of elastic recoil, the aggregated state is stabilized by the hydrophobic effect. However, self-assembly does not entail formation of a hydrophobic core. The polypeptide backbone forms transient, sparse hydrogen-bonded turns and remains significantly hydrated even as self-assembly triples the extent of non-polar side chain contacts. Individual chains in the assembly approach a maximally-disordered, melt-like state which may be called the liquid state of proteins. These findings resolve long-standing controversies regarding elastin structure and function and afford insight into the phase separation of disordered proteins.

Protein-peptide association kinetics beyond the seconds timescale from atomistic simulations

Understanding and control of structures and rates involved in protein ligand binding are essential for drug design. Unfortunately, atomistic molecular dynamics (MD) simulations cannot directly sample the excessively long residence and rearrangement times of tightly binding complexes. Here we exploit the recently developed multi-ensemble Markov model framework to compute full protein-peptide kinetics of the oncoprotein fragment 25-109Mdm2 and the nano-molar inhibitor peptide PMI. Using this system, we report, for the first time, direct estimates of kinetics beyond the seconds timescale using simulations of an all-atom MD model, with high accuracy and precision. These results only require explicit simulations on the sub-milliseconds timescale and are tested against existing mutagenesis data and our own experimental measurements of the dissociation and association rates. The full kinetic model reveals an overall downhill but rugged binding funnel with multiple pathways. The overall strong binding arises from a variety of conformations with different hydrophobic contact surfaces that interconvert on the milliseconds timescale.

On the role of residue phosphorylation in 14-3-3 partners: AANAT as a case study

Twenty years ago, a novel concept in protein structural biology was discovered: the intrinsically disordered regions (IDRs). These regions remain largely unstructured under native conditions and the more are studied, more properties are attributed to them. Possibly, one of the most important is their ability to conform a new type of protein-protein interaction. Besides the classical domain-to-domain interactions, IDRs follow a 'fly-casting' model including 'induced folding'. Unfortunately, it is only possible to experimentally explore initial and final states. However, the complete movie of conformational changes of protein regions and their characterization can be addressed by in silico experiments. Here, we simulate the binding of two proteins to describe how the phosphorylation of a single residue modulates the entire process. 14-3-3 protein family is considered a master regulator of phosphorylated proteins and from a modern point-of-view, protein phosphorylation is a three component system, with writers (kinases), erasers (phosphatases) and readers. This later biological role is attributed to the 14-3-3 protein family. Our molecular dynamics results show that phosphorylation of the key residue Thr31 in a partner of 14-3-3, the aralkylamine N-acetyltransferase, releases the fly-casting mechanism during binding. On the other hand, the non-phosphorylation of the same residue traps the proteins, systematically and repeatedly driving the simulations into wrong protein-protein conformations.

Collective variables for the study of long-time kinetics from molecular trajectories: theory and methods

Collective variables are an important concept to study high-dimensional dynamical systems, such as molecular dynamics of macromolecules, liquids, or polymers, in particular to define relevant metastable states and state-transition or phase-transition. Over the past decade, a rigorous mathematical theory has been formulated to define optimal collective variables to characterize slow dynamical processes. Here we review recent developments, including a variational principle to find optimal approximations to slow collective variables from simulation data, and algorithms such as the time-lagged independent component analysis. Using these concepts, a distance metric can be defined that quantifies how slowly molecular conformations interconvert. Extensions and open questions are discussed.

Optimized parameter selection reveals trends in Markov state models for protein folding

As molecular dynamics simulations access increasingly longer time scales, complementary advances in the analysis of biomolecular time-series data are necessary. Markov state models offer a powerful framework for this analysis by describing a system's states and the transitions between them. A recently established variational theorem for Markov state models now enables modelers to systematically determine the best way to describe a system's dynamics. In the context of the variational theorem, we analyze ultra-long folding simulations for a canonical set of twelve proteins [K. Lindorff-Larsen et al., Science 334, 517 (2011)] by creating and evaluating many types of Markov state models. We present a set of guidelines for constructing Markov state models of protein folding; namely, we recommend the use of cross-validation and a kinetically motivated dimensionality reduction step for improved descriptions of folding dynamics. We also warn that precise kinetics predictions rely on the features chosen to describe the system and pose the description of kinetic uncertainty across ensembles of models as an open issue.

Evaluation of the Coupled Two-Dimensional Main Chain Torsional Potential in Modeling Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) carry out crucial biological functions in essential biological processes of life. Because of the highly dynamic and conformationally heterogeneous nature of the disordered states of IDPs, molecular dynamics simulations are becoming an indispensable tool for the investigation of the conformational ensembles and dynamic properties of IDPs. Nevertheless, there is still no consensus on the most reliable force field in molecular dynamics simulations for IDPs hitherto. In this work, the recently proposed AMBER99SB^2D force field is evaluated in modeling some disordered polypeptides and proteins by checking its ability to reproduce experimental NMR data. The results highlight that when the ildn side-chain corrections are included, AMBER99SB^2D-ildn exhibits reliable results that agree with experiments compared with its predecessors, the AMBER14SB, AMBER99SB, AMBER99SB-ildn, and AMBER99SB^2D force fields, and that decreasing the overall magnitude of protein-protein interactions in favor of protein-water interactions is a key ingredient behind the improvement.

Exploring the dark foldable proteome by considering hydrophobic amino acids topology

The protein universe corresponds to the set of all proteins found in all organisms. A way to explore it is by taking into account the domain content of the proteins. However, some part of sequences and many entire sequences remain un-annotated despite a converging number of domain families. The un-annotated part of the protein universe is referred to as the dark proteome and remains poorly characterized. In this study, we quantify the amount of foldable domains within the dark proteome by using the hydrophobic cluster analysis methodology. These un-annotated foldable domains were grouped using a combination of remote homology searches and domain annotations, leading to define different levels of darkness. The dark foldable domains were analyzed to understand what make them different from domains stored in databases and thus difficult to annotate. The un-annotated domains of the dark proteome universe display specific features relative to database domains: shorter length, non-canonical content and particular topology in hydrophobic residues, higher propensity for disorder, and a higher energy. These features make them hard to relate to known families. Based on these observations, we emphasize that domain annotation methodologies can still be improved to fully apprehend and decipher the molecular evolution of the protein universe.

Mechanism of Phosphorylation-Induced Folding of 4E-BP2 Revealed by Molecular Dynamics Simulations

Site-specific phosphorylation of an intrinsically disordered protein, eIF4E-binding protein isoform 2 (4E-BP2), can suppress its native function by folding it into a four-stranded β-sheet, but the mechanism of this phosphorylation-induced folding is unclear. In this work, we use all-atom molecular dynamics simulations to investigate both the folded and unfolded states of 4E-BP2 under different phosphorylation states of T37 and T46. The results show that the phosphorylated forms of both T37 and T46 play important roles in stabilizing the folded structure, especially for the β-turns and the sequestered binding motif. The phosphorylated residues not only guide the folding of the protein through several intermediate states but also affect the conformational distribution of the unfolded ensemble. Significantly, the phosphorylated residues can function as nucleation sites for the folding of the protein by forming certain local structures that are stabilized by hydrogen bonding involving the phosphate group. The region around phosphorylated T46 appears to fold before that around phosphorylated T37. These findings provide new insight into the intricate effects of protein phosphorylation.

Analytical methods for structural ensembles and dynamics of intrinsically disordered proteins

Intrinsically disordered proteins, proteins that do not have a well-defined three-dimensional structure, make up a significant proportion of our proteome and are particularly prevalent in signaling and regulation. Although their importance has been realized for two decades, there is a lack of high-resolution experimental data. Molecular dynamics simulations have been crucial in reaching our current understanding of the dynamical structural ensemble sampled by intrinsically disordered proteins. In this review, we discuss enhanced sampling simulation methods that are particularly suitable to characterize the structural ensemble, along with examples of applications and limitations. The dynamics within the ensemble can be rigorously analyzed using Markov state models. We discuss recent developments that make Markov state modeling a viable approach for studying intrinsically disordered proteins. Finally, we briefly discuss challenges and future directions when applying molecular dynamics simulations to study intrinsically disordered proteins.

MHC class II complexes sample intermediate states along the peptide exchange pathway

The presentation of peptide-MHCII complexes (pMHCIIs) for surveillance by T cells is a well-known immunological concept in vertebrates, yet the conformational dynamics of antigen exchange remain elusive. By combining NMR-detected H/D exchange with Markov modelling analysis of an aggregate of 275 microseconds molecular dynamics simulations, we reveal that a stable pMHCII spontaneously samples intermediate conformations relevant for peptide exchange. More specifically, we observe two major peptide exchange pathways: the kinetic stability of a pMHCII's ground state defines its propensity for intrinsic peptide exchange, while the population of a rare, intermediate conformation correlates with the propensity of the HLA-DM-catalysed pathway. Helix-destabilizing mutants designed based on our model shift the exchange behaviour towards the HLA-DM-catalysed pathway and further allow us to conceptualize how allelic variation can shape an individual's MHC restricted immune response.

MHCII proteins bind and present both foreign and self-antigens to potentially activate CD4+ T cells via cognate T cell receptors (TCRs) during the adaptive immune response. Here, the authors combine NMR-detected H/D exchange with Markov modelling analysis to shed light on the dynamics of MHCII peptide exchange.

Efficient Atomistic Simulation of Pathways and Calculation of Rate Constants for a Protein-Peptide Binding Process: Application to the MDM2 Protein and an Intrinsically Disordered p53 Peptide

The characterization of protein binding processes - with all of the key conformational changes - has been a grand challenge in the field of biophysics. Here, we have used the weighted ensemble path sampling strategy to orchestrate molecular dynamics simulations, yielding atomistic views of protein-peptide binding pathways involving the MDM2 oncoprotein and an intrinsically disordered p53 peptide. A total of 182 independent, continuous binding pathways were generated, yielding a kon that is in good agreement with experiment. These pathways were generated in 15 days using 3500 cores of a supercomputer, substantially faster than would be possible with "brute force" simulations. Many of these pathways involve the anchoring of p53 residue F19 into the MDM2 binding cleft when forming the metastable encounter complex, indicating that F19 may be a kinetically important residue. Our study demonstrates that it is now practical to generate pathways and calculate rate constants for protein binding processes using atomistic simulation on typical computing resources.

Multibody cofactor and substrate molecular recognition in the myo-inositol monophosphatase enzyme

Molecular recognition is rarely a two-body protein-ligand problem, as it often involves the dynamic interplay of multiple molecules that together control the binding process. Myo-inositol monophosphatase (IMPase), a drug target for bipolar disorder, depends on 3 Mg(2+) ions as cofactor for its catalytic activity. Although the crystallographic pose of the pre-catalytic complex is well characterized, the binding process by which substrate, cofactor and protein cooperate is essentially unknown. Here, we have characterized cofactor and substrate cooperative binding by means of large-scale molecular dynamics. Our study showed the first and second Mg(2+) ions identify the binding pocket with fast kinetics whereas the third ion presents a much higher energy barrier. Substrate binding can occur in cooperation with cofactor, or alone to a binary or ternary cofactor-IMPase complex, although the last scenario occurs several orders of magnitude faster. Our atomic description of the three-body mechanism offers a particularly challenging example of pathway reconstruction, and may prove particularly useful in realistic contexts where water, ions, cofactors or other entities cooperate and modulate the binding process.

Claws, Disorder, and Conformational Dynamics of the C-Terminal Region of Human Desmoplakin

Multicellular organisms consist of cells that interact via elaborate adhesion complexes. Desmosomes are membrane-associated adhesion complexes that mechanically tether the cytoskeletal intermediate filaments (IFs) between two adjacent cells, creating a network of tough connections in tissues such as skin and heart. Desmoplakin (DP) is the key desmosomal protein that binds IFs, and the DP·IF association poses a quandary: desmoplakin must stably and tightly bind IFs to maintain the structural integrity of the desmosome. Yet, newly synthesized DP must traffic along the cytoskeleton to the site of nascent desmosome assembly without "sticking" to the IF network, implying weak or transient DP···IF contacts. Recent work reveals that these contacts are modulated by post-translational modifications (PTMs) in DP's C-terminal tail (DPCTT). Using molecular dynamics simulations, we have elucidated the structural basis of these PTM-induced effects. Our simulations, nearing 2 μs in aggregate, indicate that phosphorylation of S2849 induces an "arginine claw" in desmoplakin's C-terminal tail. If a key arginine, R2834, is methylated, the DPCTT preferentially samples conformations that are geometrically well-suited as substrates for processive phosphorylation by the cognate kinase GSK3. We suggest that DPCTT is a molecular switch that modulates, via its conformational dynamics, DP's overall efficacy as a substrate for GSK3. Finally, we show that the fluctuating DPCTT can contact other parts of DP, suggesting a competitive binding mechanism for the modulation of DP···IF interactions.

The pathway of ligand entry from the membrane bilayer to a lipid G protein-coupled receptor

The binding process through the membrane bilayer of lipid-like ligands to a protein target is an important but poorly explored recognition process at the atomic level. In this work we succeeded in resolving the binding of the lipid inhibitor ML056 to the sphingosine-1-phosphate receptor 1 (S1P1R) using unbiased molecular dynamics simulations with an aggregate sampling of over 800 μs. The binding pathway is a multi-stage process consisting of the ligand diffusing in the bilayer leaflet to contact a "membrane vestibule" at the top of TM 7, subsequently moving from this lipid-facing vestibule to the orthosteric binding cavity through a channel formed by TMs 1 and 7 and the N-terminal of the receptor. Unfolding of the N-terminal alpha-helix increases the volume of the channel upon ligand entry, helping to reach the crystallographic pose that also corresponds to the predicted favorable pose. The relaxation timescales of the binding process show that the binding of the ligand to the "membrane vestibule" is the rate-limiting step in the multi microseconds timescale. We comment on the significance and parallels of the binding process in the context of other binding studies.

Structural Ensembles of Intrinsically Disordered Proteins Depend Strongly on Force Field: A Comparison to Experiment

Intrinsically disordered proteins (IDPs) are notoriously challenging to study both experimentally and computationally. The structure of IDPs cannot be described by a single conformation but must instead be described as an ensemble of interconverting conformations. Atomistic simulations are increasingly used to obtain such IDP conformational ensembles. Here, we have compared the IDP ensembles generated by eight all-atom empirical force fields against primary small-angle X-ray scattering (SAXS) and NMR data. Ensembles obtained with different force fields exhibit marked differences in chain dimensions, hydrogen bonding, and secondary structure content. These differences are unexpectedly large: changing the force field is found to have a stronger effect on secondary structure content than changing the entire peptide sequence. The CHARMM 22* ensemble performs best in this force field comparison: it has the lowest error in chemical shifts and J-couplings and agrees well with the SAXS data. A high population of left-handed α-helix is present in the CHARMM 36 ensemble, which is inconsistent with measured scalar couplings. To eliminate inadequate sampling as a reason for differences between force fields, extensive simulations were carried out (0.964 ms in total); the remaining small sampling uncertainty is shown to be much smaller than the observed differences. Our findings highlight how IDPs, with their rugged energy landscapes, are highly sensitive test systems that are capable of revealing force field deficiencies and, therefore, contributing to force field development.

PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models

Markov (state) models (MSMs) and related models of molecular kinetics have recently received a surge of interest as they can systematically reconcile simulation data from either a few long or many short simulations and allow us to analyze the essential metastable structures, thermodynamics, and kinetics of the molecular system under investigation. However, the estimation, validation, and analysis of such models is far from trivial and involves sophisticated and often numerically sensitive methods. In this work we present the open-source Python package PyEMMA ( http://pyemma.org ) that provides accurate and efficient algorithms for kinetic model construction. PyEMMA can read all common molecular dynamics data formats, helps in the selection of input features, provides easy access to dimension reduction algorithms such as principal component analysis (PCA) and time-lagged independent component analysis (TICA) and clustering algorithms such as k-means, and contains estimators for MSMs, hidden Markov models, and several other models. Systematic model validation and error calculation methods are provided. PyEMMA offers a wealth of analysis functions such that the user can conveniently compute molecular observables of interest. We have derived a systematic and accurate way to coarse-grain MSMs to few states and to illustrate the structures of the metastable states of the system. Plotting functions to produce a manuscript-ready presentation of the results are available. In this work, we demonstrate the features of the software and show new methodological concepts and results produced by PyEMMA.