Efficacy of independence sampling in replica exchange simulations of ordered and disordered proteins

Recasting temperature replica exchange (T‐RE) as a special case of Gibbs sampling has led to a simple and efficient scheme for enhanced mixing (Chodera and Shirts, J. Chem. Phys., 2011, 135, 194110). To critically examine if T‐RE with independence sampling (T‐REis) improves conformational sampling, we performed T‐RE and T‐REis simulations of ordered and disordered proteins using coarse‐grained and atomistic models. The results demonstrate that T‐REis effectively increase the replica mobility in temperatures space with minimal computational overhead, especially for folded proteins. However, enhanced mixing does not translate well into improved conformational sampling. The convergences of thermodynamic properties interested are similar, with slight improvements for T‐REis of ordered systems. The study re‐affirms the efficiency of T‐RE does not appear to be limited by temperature diffusion, but by the inherent rates of spontaneous large‐scale conformational re‐arrangements. Due to its simplicity and efficacy of enhanced mixing, T‐REis is expected to be more effective when incorporated with various Hamiltonian‐RE protocols. © 2017 Wiley Periodicals, Inc.     

Calculation of the relative free energy of oxidation of azurin at pH 5 and pH 9

Free energy calculations are described for the small copper‐containing redox protein Azurin from Pseudomonas aeruginosa. A thermodynamic cycle connecting the reduced and oxidized states at pH 5 and pH 9 is considered, allowing for an assessment of convergence in terms of hysteresis and cycle closure. Previously published thermodynamic integration (TI) data is compared to Hamiltonian replica exchange TI (RE‐TI) simulations using different simulation setups. The effects of varying simulation length, initial structure, position restraints on particular atoms, and the strength of temperature coupling are studied. Although the overall simulation times are too short to observe an experimentally described peptide plane rotation, it is found that RE‐TI simulations do stimulate the distribution of conformational changes over the relevant values of the TI coupling parameter λ. This results in significantly improved values for hysteresis and cycle closure when compared to regular TI. © 2012 Wiley Periodicals, Inc.     

Energy landscape analyses of disordered histone tails reveal special organization of their conformational dynamics

Histone tails are highly flexible N- or C-terminal protrusions of histone proteins which facilitate the compaction of DNA into dense superstructures known as chromatin. On a molecular scale histone tails are polyelectrolytes with high degree of conformational disorder which allows them to function as biomolecular "switches", regulating various genetic processes. Unfortunately, their intrinsically disordered nature creates obstacles for comprehensive experimental investigation of both the structural and dynamical aspects of histone tails, because of which their conformational behaviors are still not well understood. In this work we have carried out ～3 microsecond long all atom replica exchange molecular dynamics (REMD) simulations for each of four histone tails, H4, H3, H2B, and H2A, and probed their intrinsic conformational preferences. Our subsequent free energy landscape analysis demonstrated that most tails are not fully disordered, but show distinct conformational organization, containing specific flickering secondary structural elements. In particular, H4 forms β-hairpins, H3 and H2B adopt α-helical elements, while H2A is fully disordered. We rationalized observed patterns of conformational dynamics of various histone tails using ideas from physics of polyelectrolytes and disordered systems. We also discovered an intriguing re-entrant contraction-expansion of the tails upon heating, which is caused by subtle interplay between ionic screening and chain entropy.     

Disorder-to-order transition of an intrinsically disordered region of sortase revealed by multiscale enhanced sampling

Molecular functions of intrinsically disordered proteins (IDPs) or intrinsically disordered regions (IDRs), such as molecular recognition and cellular signaling, are ascribed to dynamic changes in the conformational space in response to binding of target molecules. Sortase, a transpeptitase in Gram-positive bacteria, has an IDR in a loop which undergoes a disordered-to-ordered transition (called "disordered loop"), accompanying a tilt of another loop ("dynamic loop"), upon binding of a signal peptide and a calcium ion. In this study, all-atom conformational ensembles of sortase were calculated for the four different binding states (with/without the peptide and with/without a calcium ion) by the multiscale enhanced sampling (MSES) simulation to examine how the binding of the peptide and/or calcium influences the conformational ensemble. The MSES is a multiscale and multicopy simulation method that allows an enhanced sampling of the all-atom model of large proteins including explicit solvent. A 100 ns MSES simulation of the ligand-free sortase using 20 replicas (in total 2 μs) demonstrated large flexibility in both the disordered and dynamic loops; however, their distributions were not random but had a clear preference which populates the N-terminal part of the disordered loop near the bound form. The MSES simulations of the three binding states clarified the allosteric mechanism of sortase: the N- and C-terminal parts of the disordered loop undergo a disorder-to-order transition independently of each other upon binding of the peptide and a calcium ion, respectively; however, upon binding of both ligands, the two parts work cooperatively to stabilize the bound peptide.     

Application of replica exchange umbrella sampling to protein structure refinement of nontemplate models

We provide an assessment of a computational strategy for protein structure refinement that combines self‐guided Langevin dynamics with umbrella‐potential biasing replica exchange using the radius of gyration as a coordinate (R_g‐ReX). Eight structurally nonredundant proteins and their decoys were examined by sampling conformational space at room temperature using the CHARMM22/GBMV2 force field to generate the ensemble of structures. Two atomic statistical potentials (RWplus and DFIRE) were analyzed for structure identification and compared to the simulation force‐field potential. The results show that, while the R_g‐ReX simulations were able to sample conformational basins that were more structurally similar to the X‐ray crystallographic structures than the starting first‐order ranked decoys, the potentials failed to detect these basins from refinement. Of the three potential functions, RWplus yielded the highest accuracy for recognition of structures that refined to an average of nearly 20% increase in native contacts relative to the starting decoys. The overall performance of R_g‐ReX is compared to an earlier study of applying temperature‐based replica exchange to refine the same decoy sets and highlights the general challenge of achieving consistently the sampling and detection threshold of 70% fraction of native contacts. © 2013 Wiley Periodicals, Inc.     

Simple continuous and discrete models for simulating replica exchange simulations of protein folding

The efficiency of temperature replica exchange (RE) simulations hinge on their ability to enhance conformational sampling at physiological temperatures by taking advantage of more rapid conformational interconversions at higher temperatures. While temperature RE is a parallel simulation technique that is relatively straightforward to implement, kinetics in the RE ensemble is complicated, and there is much to learn about how best to employ RE simulations in computational biophysics. Protein folding rates often slow down above a certain temperature due to entropic bottlenecks. This "anti-Arrhenius" behavior represents a challenge for RE. However, it is far from straightforward to systematically explore the impact of this on RE by brute force molecular simulations, since RE simulations of protein folding are very difficult to converge. To understand some of the basic mechanisms that determine the efficiency of RE, it is useful to study simplified low dimensionality systems that share some of the key characteristics of molecular systems. Results are presented concerning the efficiency of temperature RE on a continuous two-dimensional potential that contains an entropic bottleneck. Optimal efficiency was obtained when the temperatures of the replicas did not exceed the temperature at which the harmonic mean of the folding and unfolding rates is maximized. This confirms a result we previously obtained using a discrete network model of RE. Comparison of the efficiencies obtained using the continuous and discrete models makes it possible to identify non-Markovian effects, which slow down equilibration of the RE ensemble on the more complex continuous potential. In particular, the rate of temperature diffusion and also the efficiency of RE is limited by the time scale of conformational rearrangements within free energy basins.     

Bayesian inference of conformational state populations from computational models and sparse experimental observables

We present a Bayesian inference approach to estimating conformational state populations from a combination of molecular modeling and sparse experimental data. Unlike alternative approaches, our method is designed for use with small molecules and emphasizes high‐resolution structural models, using inferential structure determination with reference potentials, and Markov Chain Monte Carlo to sample the posterior distribution of conformational states. As an application of the method, we determine solution‐state conformational populations of the 14‐membered macrocycle cineromycin B, using a combination of previously published sparse Nuclear Magnetic Resonance (NMR) observables and replica‐exchange molecular dynamic/Quantum Mechanical (QM)‐refined conformational ensembles. Our results agree better with experimental data compared to previous modeling efforts. Bayes factors are calculated to quantify the consistency of computational modeling with experiment, and the relative importance of reference potentials and other model parameters. © 2014 Wiley Periodicals, Inc.     

Lattice models of peptide aggregation: evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.     

Helical Propensity in an Intrinsically Disordered Protein Accelerates Ligand Binding

Many intrinsically disordered proteins fold upon binding to other macromolecules. The secondary structure present in the well‐ordered complex is often formed transiently in the unbound state. The consequence of such transient structure for the binding process is, however, not clear. The activation domain of the activator for thyroid hormone and retinoid receptors (ACTR) is intrinsically disordered and folds upon binding to the nuclear coactivator binding domain (NCBD) of the CREB binding protein. A number of mutants was designed that selectively perturbs the amount of secondary structure in unbound ACTR without interfering with the intermolecular interactions between ACTR and NCBD. Using NMR spectroscopy and fluorescence‐monitored stopped‐flow kinetic measurements we show that the secondary structure content in helix 1 of ACTR indeed influences the binding kinetics. The results thus support the notion of preformed secondary structure as an important determinant for molecular recognition in intrinsically disordered proteins.     

Hamiltonian replica‐exchange simulations with adaptive biasing of peptide backbone and side chain dihedral angles

A Hamiltonian Replica‐Exchange Molecular Dynamics (REMD) simulation method has been developed that employs a two‐dimensional backbone and one‐dimensional side chain biasing potential specifically to promote conformational transitions in peptides. To exploit the replica framework optimally, the level of the biasing potential in each replica was appropriately adapted during the simulations. This resulted in both high exchange rates between neighboring replicas and improved occupancy/flow of all conformers in each replica. The performance of the approach was tested on several peptide and protein systems and compared with regular MD simulations and previous REMD studies. Improved sampling of relevant conformational states was observed for unrestrained protein and peptide folding simulations as well as for refinement of a loop structure with restricted mobility of loop flanking protein regions. © 2013 Wiley Periodicals, Inc.     

Hybrid Hamiltonian replica exchange molecular dynamics simulation method employing the Poisson-Boltzmann model

A hybrid Hamiltonian replica exchange molecular dynamics simulation scheme based on explicit water model hybrided with Poisson-Boltzmann model is brought out. In this method the motions of atoms are governed by potential energy obtained from explicit water model. However, the exchanges between different replicas under different temperatures are controlled by the solvation energies of the solute calculated using the Poisson-Boltzmann model. In order to get the correct canonical ensembles, the van der Waals radii, which are used to define the dielectric boundary, have to be optimized. The conformational spaces of three distinct pentapeptides, Met-enkephalin, alanine 5, and glycine 5, are explored. We find that with the optimized radii the structural ensembles are nearly identical to those obtained by standard replica exchange simulations while the number of replica needed is reduced greatly.     

Simulation studies of the fidelity of biomolecular structure ensemble recreation

We examine the ability of Bayesian methods to recreate structural ensembles for partially folded molecules from averaged data. Specifically we test the ability of various algorithms to recreate different transition state ensembles for folding proteins using a multiple replica simulation algorithm using input from "gold standard" reference ensembles that were first generated with a Go-like Hamiltonian having nonpairwise additive terms. A set of low resolution data, which function as the "experimental" phi values, were first constructed from this reference ensemble. The resulting phi values were then treated as one would treat laboratory experimental data and were used as input in the replica reconstruction algorithm. The resulting ensembles of structures obtained by the replica algorithm were compared to the gold standard reference ensemble, from which those "data" were, in fact, obtained. It is found that for a unimodal transition state ensemble with a low barrier, the multiple replica algorithm does recreate the reference ensemble fairly successfully when no experimental error is assumed. The Kolmogorov-Smirnov test as well as principal component analysis show that the overlap of the recovered and reference ensembles is significantly enhanced when multiple replicas are used. Reduction of the multiple replica ensembles by clustering successfully yields subensembles with close similarity to the reference ensembles. On the other hand, for a high barrier transition state with two distinct transition state ensembles, the single replica algorithm only samples a few structures of one of the reference ensemble basins. This is due to the fact that the phi values are intrinsically ensemble averaged quantities. The replica algorithm with multiple copies does sample both reference ensemble basins. In contrast to the single replica case, the multiple replicas are constrained to reproduce the average phi values, but allow fluctuations in phi for each individual copy. These fluctuations facilitate a more faithful sampling of the reference ensemble basins. Finally, we test how robustly the reconstruction algorithm can function by introducing errors in phi comparable in magnitude to those suggested by some authors. In this circumstance we observe that the chances of ensemble recovery with the replica algorithm are poor using a single replica, but are improved when multiple copies are used. A multimodal transition state ensemble, however, turns out to be more sensitive to large errors in phi (if appropriately gauged) and attempts at successful recreation of the reference ensemble with simple replica algorithms can fall short.     

Role of backbone-solvent interactions in determining conformational equilibria of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are functional proteins that do not fold into well-defined three-dimensional structures under physiological conditions. IDP sequences have low hydrophobicity, and hence, recent experiments have focused on quantitative studies of conformational ensembles of archetypal IDP sequences such as polyglutamine and glycine-serine block copolypeptides. Results from these experiments show that, despite the absence of hydrophobic residues, polar IDPs prefer ensembles of collapsed structures in aqueous milieus. Do these preferences originate in interactions that are unique to polar sidechains? The current study addresses this issue by analyzing conformational equilibria for polyglycine and a glycine-serine block copolypeptide in two environments, namely, water and 8 M urea. Polyglycine, a poly secondary-amide, has no sidechains and is a useful model system for generic polypeptide backbones. Results based on large-scale molecular dynamics simulations show that polyglycine forms compact, albeit disordered, globules in water and swollen, disordered coils in 8 M urea. There is minimal overlap between conformational ensembles in the two environments. Analysis of order parameters derived from theories for flexible polymers show that water at ambient temperatures is a poor solvent for generic polypeptide backbones. Therefore, the experimentally observed preferences for polyglutamine and glycine-serine block copolypeptides must originate, at least partially, in polypeptide backbones. A preliminary analysis of the driving forces that lead to distinct conformational preferences for polyglycine in two different environments is presented. Implications for describing conformational ensembles of generic IDP sequences are also discussed.     

Intrinsically Disordered Tardigrade Proteins Self-Assemble into Fibrous Gels in Response to Environmental Stress

Tardigrades are remarkable for their ability to survive harsh stress conditions as diverse as extreme temperature and desiccation. The molecular mechanisms that confer this unusual resistance to physical stress remain unknown. Recently, tardigrade-unique intrinsically disordered proteins have been shown to play an essential role in tardigrade anhydrobiosis. Here, we characterize the conformational and physical behaviour of CAHS-8 from Hypsibius exemplaris. NMR spectroscopy reveals that the protein comprises an extended central helical domain flanked by disordered termini. Upon concentration, the protein is shown to successively form oligomers, long fibres, and finally gels constituted of fibres in a strongly temperature-dependent manner. The helical domain forms the core of the fibrillar structure, with the disordered termini remaining highly dynamic within the gel. Soluble proteins can be encapsulated within cavities in the gel, maintaining their functional form. The ability to reversibly form fibrous gels may be associated with the enhanced protective properties of these proteins.     

Cross‐Linking/Mass Spectrometry for Studying Protein Structures and Protein–Protein Interactions: Where Are We Now and Where Should We Go from Here?

Structural mass spectrometry (MS) is gaining increasing importance for deriving valuable three‐dimensional structural information on proteins and protein complexes, and it complements existing techniques, such as NMR spectroscopy and X‐ray crystallography. Structural MS unites different MS‐based techniques, such as hydrogen/deuterium exchange, native MS, ion‐mobility MS, protein footprinting, and chemical cross‐linking/MS, and it allows fundamental questions in structural biology to be addressed. In this Minireview, I will focus on the cross‐linking/MS strategy. This method not only delivers tertiary structural information on proteins, but is also increasingly being used to decipher protein interaction networks, both in vitro and in vivo. Cross‐linking/MS is currently one of the most promising MS‐based approaches to derive structural information on very large and transient protein assemblies and intrinsically disordered proteins.     

Why does the silica-binding protein “Si-tag” bind strongly to silica surfaces? Implications of conformational adaptation of the intrinsically disordered polypeptide to solid surfaces

We recently reported that the bacterial 50S ribosomal protein L2 binds strongly to silica surfaces even in the presence of high salt concentrations, detergents, and denaturants such as 8 M urea. We designated L2 as Si-tag, a fusion tag for immobilizing functional proteins on silica materials. Here we discuss the remarkable properties of the Si-tag polypeptide in order to understand the mechanism underlying this binding. Experimental and theoretical studies have shown that the 60-aa N-terminal region and the 71-aa C-terminal region, both of which are rich in positively charged residues, lack a well-defined three-dimensional structure under physiological conditions. This lack of a stable tertiary structure suggests that Si-tag belongs to a family of intrinsically disordered (ID) proteins that exist as dynamic ensembles of rapidly fluctuating structures in aqueous solution. Because of its inherent flexibility, Si-tag could form a large intermolecular interface and optimize its structure for surface interactions by conformational adaptation at the binding interface. Such conformational adaptation occurring concomitantly with binding is common to many ID proteins and is called "coupled folding and binding". Through this conformational adaptation, Si-tag could optimize the interactions between its positively charged side chains and ionized surface silanol groups and between its apolar side chains and hydrophobic surface siloxane sites. The cumulative contribution of these contacts would significantly strengthen the binding of Si-tag, resulting in strong, virtually irreversible binding. Our study suggests that flexible ID proteins have tremendous potential for connecting biomolecules to inorganic materials.     

Conformational Ensemble of Disordered Proteins Probed by Solvent Paramagnetic Relaxation Enhancement (sPRE)

Characterization of the conformational ensemble of disordered proteins is highly important for understanding protein folding and aggregation mechanisms, but remains a computational and experimental challenge owing to the dynamic nature of these proteins. New observables that can provide unique insights into transient residual structures in disordered proteins are needed. Here using denatured ubiquitin as a model system, NMR solvent paramagnetic relaxation enhancement (sPRE) measurements provide an accurate and highly sensitive probe for detecting low populations of residual structure in a disordered protein. Furthermore, a new ensemble calculation approach based on sPRE restraints in conjunction with residual dipolar couplings (RDCs) and small‐angle X‐ray scattering (SAXS) is used to define the conformational ensemble of disordered proteins at atomic resolution. The approach presented should be applicable to a wide range of dynamic macromolecules.