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1.  Paramagnetism-Based NMR Restraints Lift Residual Dipolar Coupling Degeneracy in Multidomain Detergent-Solubilized Membrane Proteins 
Residual dipolar couplings (RDCs) give orientational dependent NMR restraints that improve the resolution of NMR conformational ensembles and define the relative orientation of multidomain proteins and protein complexes. The interpretation of RDCs is complicated by protein dynamics and the intrinsic degeneracy of solutions that lead to ill-defined orientations of the structural domains (ghost orientations). Here, we illustrate how paramagnetic-based restraints can remove the orientational ambiguity of multidomain membrane proteins solubilized in detergent micelles. We tested this approach for the monomeric form of phospholamban (PLN), a 52-residue membrane protein, which is composed of two helical domains connected by a relatively flexible loop. We show that the combination of classical solution NMR restraints (NOEs and dihedral angles) with RDCs and PREs resolve topological ambiguities, improving the convergence of the PLN structural ensemble and giving the depth of insertion of the protein within the micelle. This combined approach will be necessary for membrane proteins, whose three-dimensional structure is strongly influenced by interactions with the membrane-mimicking environment rather than compact tertiary folds common in soluble proteins.
PMCID: PMC3328396  PMID: 21287984
Structure Determination; NMR; Membrane Protein Topology; Paramagnetic Relaxation Enhancement; Residual Dipolar Couplings; Detergent Micelles; Phospholamban
2.  Molecular dynamics re-refinement of two different small RNA loop structures using the original NMR data suggest a common structure 
Journal of Biomolecular Nmr  2012;53(4):321-339.
Restrained molecular dynamics simulations are a robust, though perhaps underused, tool for the end-stage refinement of biomolecular structures. We demonstrate their utility—using modern simulation protocols, optimized force fields, and inclusion of explicit solvent and mobile counterions—by re-investigating the solution structures of two RNA hairpins that had previously been refined using conventional techniques. The structures, both domain 5 group II intron ribozymes from yeast ai5γ and Pylaiella littoralis, share a nearly identical primary sequence yet the published 3D structures appear quite different. Relatively long restrained MD simulations using the original NMR restraint data identified the presence of a small set of violated distance restraints in one structure and a possibly incorrect trapped bulge nucleotide conformation in the other structure. The removal of problematic distance restraints and the addition of a heating step yielded representative ensembles with very similar 3D structures and much lower pairwise RMSD values. Analysis of ion density during the restrained simulations helped to explain chemical shift perturbation data published previously. These results suggest that restrained MD simulations, with proper caution, can be used to “update” older structures or aid in the refinement of new structures that lack sufficient experimental data to produce a high quality result. Notable cautions include the need for sufficient sampling, awareness of potential force field bias (such as small angle deviations with the current AMBER force fields), and a proper balance between the various restraint weights.
Electronic supplementary material
The online version of this article (doi:10.1007/s10858-012-9642-5) contains supplementary material, which is available to authorized users.
PMCID: PMC3405240  PMID: 22714631
RNA structure; Molecular dynamics; Residual dipolar coupling restraints; Bulge structure; Force fields; Ion binding
3.  Prediction, Refinement and Persistency of Transmembrane Helix Dimers in Lipid Bilayers using Implicit and Explicit Solvent/Lipid Representations: Microsecond Molecular Dynamics Simulations of ErbB1/B2 and EphA1 
Proteins  2012;81(3):365-376.
All-atom simulations are carried out on ErbB1/B2 and EphA1 transmembrane helix dimers in lipid bilayers starting from their solution/DMPC bicelle NMR structures. Over the course of microsecond trajectories, the structures remain in close proximity to the initial configuration and satisfy the great majority of experimental tertiary contact restraints. These results further validate CHARMM protein/lipid force fields and simulation protocols on Anton. Separately, dimer conformations are generated using replica exchange in conjunction with an implicit solvent and lipid representation. The implicit model requires further improvement, and this study investigates whether lengthy all-atom molecular dynamics simulations can alleviate the shortcomings of the initial conditions. The simulations correct many of the deficiencies. For example excessive helix twisting is eliminated over a period of hundreds of nanoseconds. The helix tilt, crossing angles and dimer contacts approximate those of the NMR derived structure, although the detailed contact surface remains off-set for one of two helices in both systems. Hence, even microsecond simulations are not long enough for extensive helix rotations. The alternate structures can be rationalized with reference to interaction motifs and may represent still sought after receptor states that are important in ErbB1/B2 and EphA1 signaling.
PMCID: PMC3557542  PMID: 23042146
structure prediction; implicit solvent and lipid; Generalized Born model; replica exchange; receptor tyrosine kinases; solution NMR
4.  Reduced native state stability in crowded cellular environment due to protein-protein interactions 
The effect of cellular crowding environments on protein structure and stability is a key issue in molecular and cellular biology. The classical view of crowding emphasizes the volume exclusion effect that generally favors compact, native states. Here, results from molecular dynamics simulations and NMR experiments show that protein crowders may destabilize native states via protein-protein interactions. In the model system considered here, mixtures of villin head piece and protein G at high concentrations, villin structures become increasingly destabilized upon increasing crowder concentrations. The denatured states observed in the simulation involve partial unfolding as well as more subtle conformational shifts. The unfolded states remain overall compact and only partially overlap with unfolded ensembles at high temperature and in the presence of urea. NMR measurements on the same systems confirm structural changes upon crowding based on changes of chemical shifts relative to dilute conditions. An analysis of protein-protein interactions and energetic aspects suggests the importance of enthalpic and solvation contributions to the crowding free energies that challenge an entropic-centered view of crowding effects.
PMCID: PMC3601481  PMID: 23402619
Molecular dynamics simulation; folding; villin; protein-protein interactions
5.  Multi-Timescale Conformational Dynamics of CD2AP SH3C using NMR and Accelerated Molecular Dynamics** 
A complete understanding of the relationship between biological activity and molecular conformation requires an understanding of the thermally accessible potential energy landscape. An extensive set of experimental NMR residual dipolar couplings (RDCs) has been used to determine the conformational behavior of CD2AP SH3C on multiple timescales, using the Gaussian Axial Fluctuation model, and comparison to restraint-free accelerated molecular dynamics simulation. These robust analyses provide a comprehensive description of conformational fluctuations on picosecond to millisecond timescales. While the β-sheets show negligible slow motions, larger amplitude slow dynamics are found in the n-SRC and RT loops that mediate physiological interactions.
PMCID: PMC3541011  PMID: 22565613
NMR; Protein Dynamics; RDC; Molecular Dynamics; Molecular recognition; spin relaxation
6.  Simultaneous use of solution, solid-state NMR and X-ray crystallography to study the conformational landscape of the Crh protein during oligomerization and crystallization 
We explore, using the Crh protein dimer as a model, how information from solution NMR, solid-state NMR and X-ray crystallography can be combined using structural bioinformatics methods, in order to get insights into the transition from solution to crystal. Using solid-state NMR chemical shifts, we filtered intra-monomer NMR distance restraints in order to keep only the restraints valid in the solid state. These filtered restraints were added to solid-state NMR restraints recorded on the dimer state to sample the conformational landscape explored during the oligomerization process. The use of non-crystallographic symmetries then permitted the extraction of converged conformers subsets. Ensembles of NMR and crystallographic conformers calculated independently display similar variability in monomer orientation, which supports a funnel shape for the conformational space explored during the solution-crystal transition. Insights into alternative conformations possibly sampled during oligomerization were obtained by analyzing the relative orientation of the two monomers, according to the restraint precision. Molecular dynamics simulations of Crh confirmed the tendencies observed in NMR conformers, as a paradoxical increase of the distance between the two β1a strands, when the structure gets closer to the crystallographic structure, and the role of water bridges in this context.
PMCID: PMC3170007  PMID: 21918624
structural bioinformatics; NMR structure calculation; ARIA; non-crystallographic symmetry; crystallographic ensemble refinement; molecular dynamics simulation
7.  Like-charged residues at the ends of oligoalanine sequences might induce a chain reversal 
Biopolymers  2011;97(4):240-249.
We have examined the effect of like-charged residues on the conformation of an oligoalanine sequence. This was facilitated by CD and NMR spectroscopic and differential scanning calorimetric (DSC) measurements, and molecular dynamics calculations, of the following three alanine-based peptides: Ac-K-(A)5-K-NH2 (KAK5), Ac-K-(A)4-K-NH2 (KAK4), Ac-K-(A)3-K-NH2 (KAK3), where A and K denote alanine and lysine residues, respectively. Our earlier studies suggested that the presence of like-charged residues at the end of a short polypeptide chain composed of nonpolar residues can induce a chain reversal. For all three peptides, canonical MD simulations with NMR-derived restraints demonstrate the presence of ensembles of structures with a tendency to form a chain reversal. The KAK3 peptide exhibits a bent shape with its ends close to each other, while KAK4 and KAK5 are more extended. In the KAK5 peptide, the lysine residues do not have any influence on each other and are very mobile. Nevertheless, the tendency to form a more or less pronounced chain reversal is observed and it seems to be stable in all three peptides. This chain reversal seems to be caused by screening of the nonpolar core from the solvent by the hydrated charged residues
PMCID: PMC3371584  PMID: 22161955
alanine-based peptides; NMR spectroscopy; molecular dynamics; conformational studies; bent-like structure
8.  Application of Solid-State NMR Restraint Potentials in Membrane Protein Modeling 
We have developed a set of orientational restraint potentials for solid-state NMR observables including 15N chemical shift and 15N-1H dipolar coupling. Torsion angle molecular dynamics simulations with available experimental 15N chemical shift and 15N-1H dipolar coupling as target values have been performed to determine orientational information of four membrane proteins and to model the structures of some of these systems in oligomer states. The results suggest that incorporation of the orientational restraint potentials into molecular dynamics provides an efficient means to the determination of structures that optimally satisfy the experimental observables without an extensive geometrical search.
PMCID: PMC2546517  PMID: 18462966
molecular dynamics; transmembrane helices; orientational restraint; 15N chemical shift; 15N-1H dipolar coupling
9.  Folding intermediate in the villin headpiece domain arises from disruption of a N-terminal hydrogen-bonded network 
The critical role of partially folded intermediates in protein misfolding and amyloid formation has sparked interest in exploring factors that control the formation of these meta-stable species. Recent NMR experiments reported a sparsely populated intermediate of the villin headpiece domain, in which the N-terminal subdomain is random coil like under native conditions. Here we use continuous constant pH molecular dynamics simulations with replica-exchange sampling protocol to test the hypothesis that the conformational state obtained by simulations derived from a solution NMR structure represents a putative intermediate in which the N-terminal subdomain is partially unfolded. Based on the unique titration behavior of His41 as well as the structural and dynamic properties of this state, we propose that the loss of a hydrogen bond between Nδ of His41 and the backbone carbonyl oxygen of E14 in the NMR structure leads to the loss of inter-subdomain contacts as well as partial disruption of the N-terminal hydrophobic cluster. Thus, the loss of the hydrogen-bonded network and not the protonation of His41 is a prerequisite for unfolding.
PMCID: PMC2546516  PMID: 17311386
10.  Impact of 15N R2/R1 Relaxation Restraints on Molecular Size, Shape and Bond Vector Orientation for NMR Protein Structure Determination with Sparse Distance Restraints 
15N-R2/R1 relaxation data contain information on molecular shape and size as well as on bond vector orientations relative to the diffusion tensor. Since the diffusion tensor can be directly calculated from the molecular coordinates, direct inclusion of 15N-R2/R1 restraints in NMR structure calculations without any a priori assumptions is possible. Here we show that 15N-R2/R1 restraints are particularly valuable when only sparse distance restraints are available. Using three examples of proteins of varying size, namely GB3 (56 residues), ubiquitin (76 residues) and the N-terminal domain of enzyme I (EIN, 249 residues), we show that incorporation of 15N-R2/R1 restraints results in large and significant increases in coordinate accuracy that can make the difference between being able or not being able to determine an approximate global fold. For GB3 and ubiquitin, good coordinate accuracy is obtained using only backbone hydrogen bond restraints supplemented by 15N-R2/R1 relaxation restraints. For EIN, the global fold can be determined using sparse NOE distance restraints, involving only NH and methyl groups, in conjunction with 15N-R2/R1 restraints. These results are of practical significance in the study of larger and more complex systems where increasing spectral complexity and chemical shift degeneracies reduce the number of unambiguous NOE asssignments that can be readily obtained, resulting in progressively reduced NOE coverage as the size of the protein increases.
PMCID: PMC3095518  PMID: 21462982
11.  Solid-state NMR characterization of conformational plasticity within the transmembrane domain of the influenza A M2 proton channel 
Biochimica et biophysica acta  2007;1768(12):3162-3170.
Membrane protein function within the membrane interstices is achieved by mechanisms that are not typically available to water-soluble proteins. The whole balance of molecular interactions that stabilize three-dimensional structure in the membrane environment is different from that in an aqueous environment. As a result interhelical interactions are often dominated by non-specific van der Waals interactions permitting dynamics and conformational heterogeneity in these interfaces. Here, solid-state NMR data of the transmembrane domain of the M2 protein from influenza A virus are used to exemplify such conformational plasticity in a tetrameric helical bundle. Such data lead to very high resolution structural restraints that can identify both subtle and substantial structural differences associated with various states of the protein. Spectra from samples using two different preparation protocols, samples prepared in the presence and absence of amantadine, and spectra as a function of pH are used to illustrate conformational plasticity.
PMCID: PMC2258276  PMID: 17936720
M2 channel; Influenza A virus; Conformational plasticity; PISEMA; Solid-state NMR; Membrane protein
12.  What Can Solid State NMR Contribute To Our Understanding of Protein Folding? 
Biophysical chemistry  2010;151(1-2):10-21.
Complete understanding of the folding process that connects a structurally disordered state of a protein to an ordered, biochemically functional state requires detailed characterization of intermediate structural states with high resolution and site specificity. While the intrinsically inhomogeneous and dynamic nature of unfolded and partially folded states limits the efficacy of traditional x-ray diffraction and solution NMR in structural studies, solid state NMR methods applied to frozen solutions can circumvent the complications due to molecular motions and conformational exchange encountered in unfolded and partially folded states. Moreover, solid state NMR methods can provide both qualitative and quantitative structural information at the site-specific level, even in the presence of structural inhomogeneity. This article reviews relevant solid state NMR methods and their initial applications to protein folding studies. Using either chemical denaturation to prepare unfolded states at equilibrium or a rapid freezing apparatus to trap non-equilibrium, transient structural states on a sub-millisecond time scale, recent results demonstrate that solid state NMR can contribute essential information about folding processes that is not available from more familiar biophysical methods.
PMCID: PMC2906680  PMID: 20542371
protein folding; freeze-trapping; chemical denaturation; conformational ensembles; solid state NMR; villin; HP35
13.  Characterisation of transition state structures for protein folding using ‘high’, ‘medium’ and ‘low’ Φ-values 
It has been suggested that Φ-values, which allow structural information about transition states (TSs) for protein folding to be obtained, are most reliably interpreted when divided into three classes (high, medium and low). High Φ-values indicate almost completely folded regions in the TS, intermediate Φ-values regions with a detectable amount of structure and low Φ-values indicate mostly unstructured regions. To explore the extent to which this classification can be used to characterise in detail the structure of TSs for protein folding, we used Φ-values divided into these classes as restraints in molecular dynamics simulations. This type of procedure is related to that used in NMR spectroscopy to define the structure of native proteins from the measurement of inter-proton distances derived from nuclear Overhauser effects. We illustrate this approach by determining the TS ensembles of five proteins and by showing that the results are similar to those obtained by using as restraints the actual numerical Φ-values measured experimentally. Our results indicate that the simultaneous consideration of a set of low-resolution Φ-values can provide sufficient information for characterising the architecture of a TS for folding of a protein.
PMCID: PMC2397543  PMID: 18299294
CI2; Φ-values; protein folding; restrained molecular dynamics simulations
14.  Toward a Unified Representation of Protein Structural Dynamics in Solution 
Journal of the American Chemical Society  2009;131(46):16968-16975.
An atomic resolution description of protein flexibility is essential for understanding the role that structural dynamics play in biological processes. Despite the unique dependence of nuclear magnetic resonance (NMR) to motional averaging on different time scales, NMR-based protein structure determination often ignores the presence of dynamics, representing rapidly exchanging conformational equilibria in terms of a single static structure. In this study, we use the rich dynamic information encoded in experimental NMR parameters to develop a molecular and statistical mechanical characterization of the conformational behavior of proteins in solution. Critically, and in contrast to previously proposed techniques, we do not use empirical energy terms to restrain a conformational search, a procedure that can strongly perturb simulated dynamics in a nonpredictable way. Rather, we use accelerated molecular dynamic simulation to gradually increase the level of conformational sampling and to identify the appropriate level of sampling via direct comparison of unrestrained simulation with experimental data. This constraint-free approach thereby provides an atomic resolution free-energy weighted Boltzmann description of protein dynamics occurring on time scales over many orders of magnitude in the protein ubiquitin.
PMCID: PMC2779067  PMID: 19919148
15.  Solution NMR Structure of a Designed Metalloprotein and Complementary Molecular Dynamics Refinement 
Structure (London, England : 1993)  2008;16(2):10.1016/j.str.2007.11.011.
We report the solution NMR structure of a designed dimetal-binding protein, di-Zn(II) DFsc, along with a secondary refinement step employing molecular dynamics techniques. Calculation of the initial NMR structural ensemble by standard methods led to distortions in the metal-ligand geometries at the active site. Unrestrained molecular dynamics using a non-bonded force field for the metal shell, followed by quantum mechanical/molecular mechanical dynamics of DFsc, were used to relax local frustrations at the dimetal site that were apparent in the initial NMR structure and provide a more realistic description of the structure. The MD model is consistent with NMR restraints, and in good agreement with the structural and functional properties expected for DF proteins. This work demonstrates that NMR structures of metalloproteins can be further refined using classical and first-principles molecular dynamics methods in the presence of explicit solvent to provide otherwise unavailable insight into the geometry of the metal center.
PMCID: PMC3814030  PMID: 18275812
16.  Molecular Dynamics Simulation of Phosphorylated KID Post-Translational Modification 
PLoS ONE  2009;4(8):e6516.
Kinase-inducible domain (KID) as transcriptional activator can stimulate target gene expression in signal transduction by associating with KID interacting domain (KIX). NMR spectra suggest that apo-KID is an unstructured protein. After post-translational modification by phosphorylation, KID undergoes a transition from disordered to well folded protein upon binding to KIX. However, the mechanism of folding coupled to binding is poorly understood.
To get an insight into the mechanism, we have performed ten trajectories of explicit-solvent molecular dynamics (MD) for both bound and apo phosphorylated KID (pKID). Ten MD simulations are sufficient to capture the average properties in the protein folding and unfolding.
Room-temperature MD simulations suggest that pKID becomes more rigid and stable upon the KIX-binding. Kinetic analysis of high-temperature MD simulations shows that bound pKID and apo-pKID unfold via a three-state and a two-state process, respectively. Both kinetics and free energy landscape analyses indicate that bound pKID folds in the order of KIX access, initiation of pKID tertiary folding, folding of helix αB, folding of helix αA, completion of pKID tertiary folding, and finalization of pKID-KIX binding. Our data show that the folding pathways of apo-pKID are different from the bound state: the foldings of helices αA and αB are swapped. Here we also show that Asn139, Asp140 and Leu141 with large Φ-values are key residues in the folding of bound pKID. Our results are in good agreement with NMR experimental observations and provide significant insight into the general mechanisms of binding induced protein folding and other conformational adjustment in post-translational modification.
PMCID: PMC2717803  PMID: 19654879
17.  Improving NMR Protein Structure Quality by Rosetta Refinement: A Molecular Replacement Study 
Proteins  2009;75(1):147-167.
The structure of human protein HSPC034 has been determined by both solution NMR spectroscopy and X-ray crystallography. Refinement of the NMR structure ensemble, using a Rosetta protocol in the absence of NMR restraints, resulted in significant improvements not only in structure quality, but also in molecular replacement (MR) performance with the raw X-ray diffraction data using MOLREP and Phaser. This method has recently been shown to be generally applicable with improved MR performance demonstrated for eight NMR structures refined using Rosetta.1 Additionally, NMR structures of HSPC034 calculated by standard methods that include NMR restraints, have improvements in the RMSD to the crystal structure and MR performance in the order DYANA, CYANA, XPLOR-NIH, and CNS with explicit water refinement (CNSw). Further Rosetta refinement of the CNSw structures, perhaps due to more thorough conformational sampling and/or a superior force field, was capable of finding alternative low energy protein conformations that were equally consistent with the NMR data according to the RPF scores. Upon further examination, the additional MR-performance shortfall for NMR refined structures as compared to the X-ray structure MR performance were attributed, in part, to crystal-packing effects, real structural differences, and inferior hydrogen bonding in the NMR structures. A good correlation between a decrease in the number of buried unsatisfied hydrogen-bond donors and improved MR performance demonstrates the importance of hydrogen-bond terms in the force field for improving NMR structures. The superior hydrogen-bond network in Rosetta-refined structures, demonstrates that correct identification of hydrogen bonds should be a critical goal of NMR structure refinement. Inclusion of non-bivalent hydrogen bonds identified from Rosetta structures as additional restraints in the structure calculation results in NMR structures with improved MR performance
PMCID: PMC2878636  PMID: 18816799
NMR; X-ray; HSPC034; PP25; C1orf41; Northeast Structural Genomics Consortium; structural genomics; comparison of NMR and X-ray structures; Rosetta; NMR force field refinement; molecular replacement; hydrogen bonding; X-ray crystallography; refinement methods
18.  Graphical analysis of NMR structural quality and interactive contact map of NOE assignments in ARIA 
The Ambiguous Restraints for Iterative Assignment (ARIA) approach is widely used for NMR structure determination. It is based on simultaneously calculating structures and assigning NOE through an iterative protocol. The final solution consists of a set of conformers and a list of most probable assignments for the input NOE peak list.
ARIA was extended with a series of graphical tools to facilitate a detailed analysis of the intermediate and final results of the ARIA protocol. These additional features provide (i) an interactive contact map, serving as a tool for the analysis of assignments, and (ii) graphical representations of structure quality scores and restraint statistics. The interactive contact map between residues can be clicked to obtain information about the restraints and their contributions. Profiles of quality scores are plotted along the protein sequence, and contact maps provide information of the agreement with the data on a residue pair level.
The graphical tools and outputs described here significantly extend the validation and analysis possibilities of NOE assignments given by ARIA as well as the analysis of the quality of the final structure ensemble. These tools are included in the latest version of ARIA, which is available at . The Web site also contains an installation guide, a user manual and example calculations.
PMCID: PMC2432060  PMID: 18533992
19.  Determination of the Structures of Symmetric Protein Oligomers from NMR Chemical Shifts and Residual Dipolar Couplings 
Symmetric protein dimers, trimers, and higher-order cyclic oligomers play key roles in many biological processes. However, structural studies of oligomeric systems by solution NMR can be difficult due to slow tumbling of the system and the difficulty in identifying NOE interactions across protein interfaces. Here, we present an automated method (RosettaOligomers) for determining the solution structures of oligomeric systems using only chemical shifts, sparse NOEs, and domain orientation restraints from residual dipolar couplings (RDCs) without a need for a previously determined structure of the monomeric subunit. The method integrates previously developed Rosetta protocols for solving the structures of monomeric proteins using sparse NMR data and for predicting the structures of both nonintertwined and intertwined symmetric oligomers. We illustrated the performance of the method using a benchmark set of nine protein dimers, one trimer, and one tetramer with available experimental data and various interface topologies. The final converged structures are found to be in good agreement with both experimental data and previously published high-resolution structures. The new approach is more readily applicable to large oligomeric systems than conventional structure-determination protocols, which often require a large number of NOEs, and will likely become increasingly relevant as more high-molecular weight systems are studied by NMR.
PMCID: PMC3080108  PMID: 21466200
20.  DNA structures from phosphate chemical shifts 
Nucleic Acids Research  2009;38(3):e18.
For B-DNA, the strong linear correlation observed by nuclear magnetic resonance (NMR) between the 31P chemical shifts (δP) and three recurrent internucleotide distances demonstrates the tight coupling between phosphate motions and helicoidal parameters. It allows to translate δP into distance restraints directly exploitable in structural refinement. It even provides a new method for refining DNA oligomers with restraints exclusively inferred from δP. Combined with molecular dynamics in explicit solvent, these restraints lead to a structural and dynamical view of the DNA as detailed as that obtained with conventional and more extensive restraints. Tests with the Jun-Fos oligomer show that this δP-based strategy can provide a simple and straightforward method to capture DNA properties in solution, from routine NMR experiments on unlabeled samples.
PMCID: PMC2817473  PMID: 19942687
21.  Extended Model Free Approach to Analyze Correlation Functions of Multi-domain Proteins in the Presence of Motional Coupling 
Journal of the American Chemical Society  2008;130(38):12745-12751.
Inter-domain motion in proteins plays an important role in biomolecular interaction. Its presence also complicates interpretation of many spectroscopy measurements. Nuclear Magnetic Resonance (NMR) study of domain dynamics relies on knowledge of its rotational correlation function. The Extended Model Free (EMF) approach has been implemented to analyze coupled domain and overall motions for calmodulin, a dual-domain protein; however, the validity of EMF treatment in coupled motion has not been tested. We performed stochastic simulations on a dual-vector system employing two simple restraints to drive hydrodynamics and domain coupling: 1. both unitary vectors diffuse randomly on the surface of a sphere, 2. vectors are correlated through user-defined inter-vector potential. The resulting correlation curve can be adequately fit with either a single- or double-exponential decay function. The latter is consistent with the EMF treatment. The derived order parameters S2 range from about 0.4 to 1, while the motion separation, the ratio of overall and domain motion time scales (τm/τs), ranges from 1 to 4. A complete overlap between time scales occurs when S2 is less than 0.4, and the correlation function effectively behaves as a single-exponential. The S2 values are consistent with theoretical predictions from the given potential function, differing by no more than 0.03, suggesting EMF to be a generally valid approach. In addition, from the dependence of S2 on τm/τs obtained from simulation, we found out a cosine potential, favoring extended conformers, as opposed to the normally assumed cone potential, reached a better agreement to experimental data.
PMCID: PMC2596624  PMID: 18761455
22.  Structure of the Disulfide Bond Generating Membrane Protein DsbB in the Lipid Bilayer 
Journal of molecular biology  2013;425(10):1670-1682.
The integral membrane protein DsbB in Escherichia coli is responsible for oxidizing the periplasmic protein DsbA, which forms disulfide bonds in substrate proteins. We have developed a high-resolution structural model by combining experimental X-ray and solid-state NMR with molecular dynamics (MD) simulations. We embedded the high-resolution DsbB structure, derived from the joint calculation with X-ray reflections and solid-state NMR restraints, into the lipid bilayer and performed MD simulations to provide a mechanistic view of DsbB function in the membrane. Further, we revealed the membrane topology of DsbB by selective proton spin diffusion experiments, which directly probe the correlations of DsbB with water and lipid acyl chains. NMR data also support the model of a flexible periplasmic loop and an interhelical hydrogen bond between Glu26 and Tyr153.
PMCID: PMC3670690  PMID: 23416557
disulfide bond generation; DsbB; membrane protein; solid-state NMR; molecular dynamics simulation
23.  Structured Pathway across the Transition State for Peptide Folding Revealed by Molecular Dynamics Simulations 
PLoS Computational Biology  2011;7(9):e1002137.
Small globular proteins and peptides commonly exhibit two-state folding kinetics in which the rate limiting step of folding is the surmounting of a single free energy barrier at the transition state (TS) separating the folded and the unfolded states. An intriguing question is whether the polypeptide chain reaches, and leaves, the TS by completely random fluctuations, or whether there is a directed, stepwise process. Here, the folding TS of a 15-residue β-hairpin peptide, Peptide 1, is characterized using independent 2.5 μs-long unbiased atomistic molecular dynamics (MD) simulations (a total of 15 μs). The trajectories were started from fully unfolded structures. Multiple (spontaneous) folding events to the NMR-derived conformation are observed, allowing both structural and dynamical characterization of the folding TS. A common loop-like topology is observed in all the TS structures with native end-to-end and turn contacts, while the central segments of the strands are not in contact. Non-native sidechain contacts are present in the TS between the only tryptophan (W11) and the turn region (P7-G9). Prior to the TS the turn is found to be already locked by the W11 sidechain, while the ends are apart. Once the ends have also come into contact, the TS is reached. Finally, along the reactive folding paths the cooperative loss of the W11 non-native contacts and the formation of the central inter-strand native contacts lead to the peptide rapidly proceeding from the TS to the native state. The present results indicate a directed stepwise process to folding the peptide.
Author Summary
The folding dynamics of many small protein/peptides investigated recently are in terms of simple two-state model in which only two populations exist (folded and unfolded), separated by a single free energy barrier with only one kinetically important transition state (TS). However, dynamical characterization of the folding TS is challenging. We have used independent unbiased atomistic molecular dynamics simulations with clear folding-unfolding transitions to characterize structural and dynamical features of transition state ensemble of Peptide 1. A common loop-like topology is observed in all TS structures extracted from multiple simulations. The trajectories were used to examine the mechanism by which the TS is reached and subsequent events in folding pathways. The folding TS is reached and crossed in a directed stagewise process rather than through random fluctuations. Specific structures are formed before, during, and after the transition state, indicating a clear structured folding pathway.
PMCID: PMC3169518  PMID: 21931542
24.  On the use of orientational restraints and symmetry corrections in alchemical free energy calculations 
The Journal of chemical physics  2006;125(8):084902.
Alchemical free energy calculations are becoming a useful tool for calculating absolute binding free energies of small molecule ligands to proteins. Here, we find that the presence of multiple metastable ligand orientations can cause convergence problems when distance restraints alone are used. We demonstrate that the use of orientational restraints can greatly accelerate the convergence of these calculations. However, even with this acceleration, we find that sufficient sampling requires substantially longer simulations than are used in many published protocols. To further accelerate convergence, we introduce a new method of configuration space decomposition by orientation which reduces required simulation lengths by at least a factor of 5 in the cases examined. Our method is easily parallelizable, well suited for cases where a ligand cocrystal structure is not available, and can utilize initial orientations generated by docking packages.
PMCID: PMC3583553  PMID: 16965052
25.  Using Enhanced Sampling and Structural Restraints to Refine Atomic Structures into Low-resolution Electron Microscopy Maps 
Structure (London, England : 1993)  2012;20(9):1453-1462.
For a variety of problems in structural biology, low-resolution maps generated by electron microscopy (EM) imaging are often interpreted with the help of various flexible-fitting computational algorithms. In this work, we systematically analyze the quality of final models of various proteins obtained via molecular dynamics flexible fitting (MDFF) by varying the map-resolution, strength of structural restraints, and the steering forces. We find that MDFF can be extended to understand conformational changes in lower-resolution maps if larger structural restraints and lower steering forces are used to prevent overfitting. We further show that the capabilities of MDFF can be extended by combining it with an enhanced conformational sampling method, temperature-accelerated molecular dynamics (TAMD). Specifically, TAMD can be either used to generate better starting configurations for MDFF fitting, or TAMD-assisted MDFF (TAMDFF) can be performed to accelerate conformational search in atomistic simulations.
PMCID: PMC3438525  PMID: 22958641
molecular dynamics; molecular dynamics flexible fitting; temperature-accelerated molecular dynamics; electron microscopy

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