Contact model for the prediction of NMR N-H order parameters in globular proteins

Parsing Dynamics of Protein Backbone NH and Side-Chain Methyl Groups using Molecular Dynamics Simulations

Experimental NMR spectroscopy and theoretical molecular dynamics (MD) simulations provide complementary insights into protein conformational dynamics and hence into biological function. The present work describes an extensive set of backbone NH and side-chain methyl group generalized order parameters for the Escherichia coli ribonuclease HI (RNH) enzyme derived from 2-μs microsecond MD simulations using the OPLS4 and AMBER-FF19SB force fields. The simulated generalized order parameters are compared with values derived from NMR 15N and 13CH2D spin relaxation measurements. The squares of the generalized order parameters, S2 for the N-H bond vector and Saxis2 for the methyl group symmetry axis, characterize the equilibrium distribution of vector orientations in a molecular frame of reference. Optimal agreement between simulated and experimental results was obtained by averaging S2 or Saxis2 calculated by dividing the simulated trajectories into 50 ns blocks (∼five times the rotational diffusion correlation time for RNH). With this procedure, the median absolute deviations (MAD) between experimental and simulated values of S2 and Saxis2 are 0.030 (NH) and 0.061 (CH3) for OPLS4 and 0.041 (NH) and 0.078 (CH3) for AMBER-FF19SB. The MAD between OPLS4 and AMBER-FF19SB are 0.021 (NH) and 0.072 (CH3). The generalized order parameters for the methyl group symmetry axis can be decomposed into contributions from backbone fluctuations, between-rotamer dihedral angle transitions, and within-rotamer dihedral angle fluctuations. Analysis of the simulation trajectories shows that (i) backbone and side chain conformational fluctuations exhibit little correlation and that (ii) fluctuations within rotamers are limited and highly uniform with values that depend on the number of dihedral angles considered. Low values of Saxis2, indicative of enhanced side-chain flexibility, result from between-rotamer transitions that can be enhanced by increased local backbone flexibility.

Prediction of order parameters based on protein NMR structure ensemble and machine learning

The fast motions of proteins at the picosecond to nanosecond timescale, known as fast dynamics, are closely related to protein conformational entropy and rearrangement, which in turn affect catalysis, ligand binding and protein allosteric effects. The most used NMR approach to study fast protein dynamics is the model free method, which uses order parameter S2 to describe the amplitude of the internal motion of local group. However, to obtain order parameter through NMR experiments is quite complex and lengthy. In this paper, we present a machine learning approach for predicting backbone 1H-15N order parameters based on protein NMR structure ensemble. A random forest model is used to learn the relationship between order parameters and structural features. Our method achieves high accuracy in predicting backbone 1H-15N order parameters for a test dataset of 10 proteins, with a Pearson correlation coefficient of 0.817 and a root-mean-square error of 0.131.

Validation of X-ray Crystal Structure Ensemble Representations of SARS-CoV-2 Main Protease by Solution NMR Residual Dipolar Couplings

Considerable debate has focused on whether sampling of molecular dynamics trajectories restrained by crystallographic data can be used to develop realistic ensemble models for proteins in their natural, solution state. For the SARS-CoV-2 main protease, Mpro, we evaluated agreement between solution residual dipolar couplings (RDCs) and various recently reported multi-conformer and dynamic-ensemble crystallographic models. Although Phenix-derived ensemble models showed only small improvements in crystallographic Rfree, substantially improved RDC agreement over fits to a conventionally refined 1.2-Å X-ray structure was observed, in particular for residues with above average disorder in the ensemble. For a set of six lower resolution (1.55-2.19 Å) Mpro X-ray ensembles, obtained at temperatures ranging from 100 to 310 K, no significant improvement over conventional two-conformer representations was found. At the residue level, large differences in motions were observed among these ensembles, suggesting high uncertainties in the X-ray derived dynamics. Indeed, combining the six ensembles from the temperature series with the two 1.2-Å X-ray ensembles into a single 381-member "super ensemble" averaged these uncertainties and substantially improved agreement with RDCs. However, all ensembles showed excursions that were too large for the most dynamic fraction of residues. Our results suggest that further improvements to X-ray ensemble refinement are feasible, and that RDCs provide a sensitive benchmark in such endeavors. Remarkably, a weighted ensemble of 350 PDB Mpro X-ray structures provided slightly better cross-validated agreement with RDCs than any individual ensemble refinement, implying that differences in lattice confinement also limit the fit of RDCs to X-ray coordinates.

Liquid-Liquid Phase Separation Modifies the Dynamic Properties of Intrinsically Disordered Proteins

Liquid-liquid phase separation of flexible biomolecules has been identified as a ubiquitous phenomenon underlying the formation of membraneless organelles that harbor a multitude of essential cellular processes. We use nuclear magnetic resonance (NMR) spectroscopy to compare the dynamic properties of an intrinsically disordered protein (measles virus N_TAIL) in the dilute and dense phases at atomic resolution. By measuring ¹⁵N NMR relaxation at different magnetic field strengths, we are able to characterize the dynamics of the protein in dilute and crowded conditions and to compare the amplitude and timescale of the different motional modes to those present in the membraneless organelle. Although the local backbone conformational sampling appears to be largely retained, dynamics occurring on all detectable timescales, including librational, backbone dihedral angle dynamics and segmental, chainlike motions, are considerably slowed down. Their relative amplitudes are also drastically modified, with slower, chain-like motions dominating the dynamic profile. In order to provide additional mechanistic insight, we performed extensive molecular dynamics simulations of the protein under self-crowding conditions at concentrations comparable to those found in the dense liquid phase. Simulation broadly reproduces the impact of formation of the condensed phase on both the free energy landscape and the kinetic interconversion between states. In particular, the experimentally observed reduction in the amplitude of the fastest component of backbone dynamics correlates with higher levels of intermolecular contacts or entanglement observed in simulations, reducing the conformational space available to this mode under strongly self-crowding conditions.

Parameterizing elastic network models to capture the dynamics of proteins

Coarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B-factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes.

Arginine Modulates Carbapenem Deactivation by OXA-24/40 in Acinetobacter baumannii

The resistance of Gram-negative bacteria to β-lactam antibiotics stems mainly from β-lactamase proteins that hydrolytically deactivate the β-lactams. Of particular concern are the β-lactamases that can deactivate a class of β-lactams known as carbapenems. Carbapenems are among the few anti-infectives that can treat multi-drug resistant bacterial infections. Revealing the mechanisms of their deactivation by β-lactamases is a necessary step for preserving their therapeutic value. Here, we present NMR investigations of OXA-24/40, a carbapenem-hydrolyzing Class D β-lactamase (CHDL) expressed in the gram-negative pathogen, Acinetobacter baumannii. Using rapid data acquisition methods, we were able to study the "real-time" deactivation of the carbapenem known as doripenem by OXA-24/40. Our results indicate that OXA-24/40 has two deactivation mechanisms: canonical hydrolytic cleavage, and a distinct mechanism that produces a β-lactone product that has weak affinity for the OXA-24/40 active site. The mechanisms issue from distinct active site environments poised either for hydrolysis or β-lactone formation. Mutagenesis reveals that R261, a conserved active site arginine, stabilizes the active site environment enabling β-lactone formation. Our results have implications not only for OXA-24/40, but the larger family of CHDLs now challenging clinical settings on a global scale.

Patterns in Protein Flexibility: A Comparison of NMR "Ensembles", MD Trajectories, and Crystallographic B-Factors

Proteins are molecular machines requiring flexibility to function. Crystallographic B-factors and Molecular Dynamics (MD) simulations both provide insights into protein flexibility on an atomic scale. Nuclear Magnetic Resonance (NMR) lacks a universally accepted analog of the B-factor. However, a lack of convergence in atomic coordinates in an NMR-based structure calculation also suggests atomic mobility. This paper describes a pattern in the coordinate uncertainties of backbone heavy atoms in NMR-derived structural “ensembles” first noted in the development of FindCore2 (previously called Expanded FindCore: DA Snyder, J Grullon, YJ Huang, R Tejero, GT Montelione, Proteins: Structure, Function, and Bioinformatics 82 (S2), 219–230) and demonstrates that this pattern exists in coordinate variances across MD trajectories but not in crystallographic B-factors. This either suggests that MD trajectories and NMR “ensembles” capture motional behavior of peptide bond units not captured by B-factors or indicates a deficiency common to force fields used in both NMR and MD calculations.

Weighted-persistent-homology-based machine learning for RNA flexibility analysis

With the great significance of biomolecular flexibility in biomolecular dynamics and functional analysis, various experimental and theoretical models are developed. Experimentally, Debye-Waller factor, also known as B-factor, measures atomic mean-square displacement and is usually considered as an important measurement for flexibility. Theoretically, elastic network models, Gaussian network model, flexibility-rigidity model, and other computational models have been proposed for flexibility analysis by shedding light on the biomolecular inner topological structures. Recently, a topology-based machine learning model has been proposed. By using the features from persistent homology, this model achieves a remarkable high Pearson correlation coefficient (PCC) in protein B-factor prediction. Motivated by its success, we propose weighted-persistent-homology (WPH)-based machine learning (WPHML) models for RNA flexibility analysis. Our WPH is a newly-proposed model, which incorporate physical, chemical and biological information into topological measurements using a weight function. In particular, we use local persistent homology (LPH) to focus on the topological information of local regions. Our WPHML model is validated on a well-established RNA dataset, and numerical experiments show that our model can achieve a PCC of up to 0.5822. The comparison with the previous sequence-information-based learning models shows that a consistent improvement in performance by at least 10% is achieved in our current model.

Accurate prediction of chemical shifts for aqueous protein structure on "Real World" data

Here we report a new machine learning algorithm for protein chemical shift prediction that outperforms existing chemical shift calculators on realistic data that is not heavily curated, nor eliminates test predictions ad hoc. Our UCBShift predictor implements two modules: a transfer prediction module that employs both sequence and structural alignment to select reference candidates for experimental chemical shift replication, and a redesigned machine learning module based on random forest regression which utilizes more, and more carefully curated, feature extracted data. When combined together, this new predictor achieves state-of-the-art accuracy for predicting chemical shifts on a randomly selected dataset without careful curation, with root-mean-square errors of 0.31 ppm for amide hydrogens, 0.19 ppm for Hα, 0.84 ppm for C', 0.81 ppm for Cα, 1.00 ppm for Cβ, and 1.81 ppm for N. When similar sequences or structurally related proteins are available, UCBShift shows superior native state selection from misfolded decoy sets compared to SPARTA+ and SHIFTX2, and even without homology we exceed current prediction accuracy of all other popular chemical shift predictors.

Cleavage, Downregulation, and Aggregation of Serum Amyloid A

Various diseases cause overexpression of the serum amyloid A (SAA) protein, which in some cases, but not in all cases, leads to amyloidosis as a secondary disease. Response to the overexpression involves dissociation of the SAA hexamer and subsequent cleavage of the released monomers, most commonly yielding fragments SAA_1-76 of the full-sized SAA_1-104. We report results from molecular dynamic simulations that probe the role of this cleavage for downregulating the activity and concentration of SAA. We propose a mechanism that relies on two elements. First, the probability to assemble into hexamers is lower for the fragments than it is for the full-sized protein. Second, unlike other fragments, SAA_1-76 can switch between two distinct configurations. The first kind is easy to proteolyse (allowing a fast reduction of the SAA concentration) but prone to aggregation, whereas the situation is opposite for the second kind. If the time scale for amyloid formation is longer than the one for proteolysis, the aggregation-prone species dominates. However, if environmental conditions such as low pH increases the risk of amyloid formation, the ensemble shifts toward the more protected form. We speculate that SAA amyloidosis is a failure of this switching mechanism leading to accumulation of the aggregation-prone species and subsequent amyloid formation.

Detection of chemical exchange in methyl groups of macromolecules

The zero- and double-quantum methyl TROSY Hahn-echo and the methyl ¹H-¹H dipole-dipole cross-correlation nuclear magnetic resonance experiments enable estimation of multiple quantum chemical exchange broadening in methyl groups in proteins. The two relaxation rate constants are established to be linearly dependent using molecular dynamics simulations and empirical analysis of experimental data. This relationship allows chemical exchange broadening to be recognized as an increase in the Hahn-echo relaxation rate constant. The approach is illustrated by analyzing relaxation data collected at three temperatures for E. coli ribonuclease HI and by analyzing relaxation data collected for different cofactor and substrate complexes of E. coli AlkB.

Conformational Entropy as Collective Variable for Proteins

Many enhanced sampling methods rely on the identification of appropriate collective variables. For proteins, even small ones, finding appropriate descriptors has proven challenging. Here we suggest that the NMR S² order parameter can be used to this effect. We trace the validity of this statement to the suggested relation between S² and conformational entropy. Using the S² order parameter and a surrogate for the protein enthalpy in conjunction with metadynamics or variationally enhanced sampling, we are able to reversibly fold and unfold a small protein and draw its free energy at a fraction of the time that is needed in unbiased simulations. We also use S² in combination with the free energy flooding method to compute the unfolding rate of this peptide. We repeat this calculation at different temperatures to obtain the unfolding activation energy.

Exploring the Sequence-based Prediction of Folding Initiation Sites in Proteins

Protein folding is a complex process that can lead to disease when it fails. Especially poorly understood are the very early stages of protein folding, which are likely defined by intrinsic local interactions between amino acids close to each other in the protein sequence. We here present EFoldMine, a method that predicts, from the primary amino acid sequence of a protein, which amino acids are likely involved in early folding events. The method is based on early folding data from hydrogen deuterium exchange (HDX) data from NMR pulsed labelling experiments, and uses backbone and sidechain dynamics as well as secondary structure propensities as features. The EFoldMine predictions give insights into the folding process, as illustrated by a qualitative comparison with independent experimental observations. Furthermore, on a quantitative proteome scale, the predicted early folding residues tend to become the residues that interact the most in the folded structure, and they are often residues that display evolutionary covariation. The connection of the EFoldMine predictions with both folding pathway data and the folded protein structure suggests that the initial statistical behavior of the protein chain with respect to local structure formation has a lasting effect on its subsequent states.

Predictions of Backbone Dynamics in Intrinsically Disordered Proteins Using De Novo Fragment-Based Protein Structure Predictions

Intrinsically disordaered proteins (IDPs) are a prevalent phenomenon with over 30% of human proteins estimated to have long disordered regions. Computational methods are widely used to study IDPs, however, nearly all treat disorder in a binary fashion, not accounting for the structural heterogeneity present in disordered regions. Here, we present a new de novo method, FRAGFOLD-IDP, which addresses this problem. Using 200 protein structural ensembles derived from NMR, we show that FRAGFOLD-IDP achieves superior results compared to methods which can predict related data (NMR order parameter, or crystallographic B-factor). FRAGFOLD-IDP produces very good predictions for 33.5% of cases and helps to get a better insight into the dynamics of the disordered ensembles. The results also show it is not necessary to predict the correct fold of the protein to reliably predict per-residue fluctuations. It implies that disorder is a local property and it does not depend on the fold. Our results are orthogonal to DynaMine, the only other method significantly better than the naïve prediction. We therefore combine these two using a neural network. FRAGFOLD-IDP enables better insight into backbone dynamics in IDPs and opens exciting possibilities for the design of disordered ensembles, disorder-to-order transitions, or design for protein dynamics.

The PipX Protein, When Not Bound to Its Targets, Has Its Signaling C-Terminal Helix in a Flexed Conformation

PipX, an 89-residue protein, acts as a coactivator of the global nitrogen regulator NtcA in cyanobacteria. NtcA-PipX interactions are regulated by 2-oxoglutarate (2-OG), an inverse indicator of the ammonia abundance, and by P_II, a protein that binds to PipX at low 2-OG concentrations. The structure of PipX, when bound to NtcA or P_II, consists of an N-terminal, five-stranded β-sheet (conforming a Tudor-like domain), and two long α-helices. These helices adopt either a flexed conformation, where they are in close contact and in an antiparallel mutual orientation, also packing against the β-sheet, or an open conformation (observed only in the P_II-PipX complex) where the last α-helix moves apart from the rest of the protein. The aim of this work was to study the structure and dynamics of isolated PipX in solution by NMR. The backbone chemical shifts, the hydrogen-exchange, and the NOE patterns indicated that the isolated, monomeric PipX structure was formed by an N-terminal five-stranded β-sheet and two C-terminal α-helices. Furthermore, the observed NOEs between the two helices, and of α-helix2 with β-strand2 suggested that PipX adopted a flexed conformation. The β-strands 1 and 5 were highly flexible, as shown by the lack of interstrand backbone-backbone NOEs; in addition, the ¹⁵N-dynamics indicated that the C terminus of β-strand4 and the following β-turn (Phe42-Thr47), and the C-cap of α-helix1 (Arg70-Asn71) were particularly mobile. These two regions could act as hinges, allowing PipX to interact with its partners, including PlmA in the newly recognized P_II-PipX-PlmA ternary complex.

Early Folding Events, Local Interactions, and Conservation of Protein Backbone Rigidity

Protein folding is in its early stages largely determined by the protein sequence and complex local interactions between amino acids, resulting in lower energy conformations that provide the context for further folding into the native state. We compiled a comprehensive data set of early folding residues based on pulsed labeling hydrogen deuterium exchange experiments. These early folding residues have corresponding higher backbone rigidity as predicted by DynaMine from sequence, an effect also present when accounting for the secondary structures in the folded protein. We then show that the amino acids involved in early folding events are not more conserved than others, but rather, early folding fragments and the secondary structure elements they are part of show a clear trend toward conserving a rigid backbone. We therefore propose that backbone rigidity is a fundamental physical feature conserved by proteins that can provide important insights into their folding mechanisms and stability.

Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM)

Gaussian network model (GNM) and anisotropic network model (ANM) are some of the most popular methods for the study of protein flexibility and related functions. In this work, we propose generalized GNM (gGNM) and ANM methods and show that the GNM Kirchhoff matrix can be built from the ideal low-pass filter, which is a special case of a wide class of correlation functions underpinning the linear scaling flexibility-rigidity index (FRI) method. Based on the mathematical structure of correlation functions, we propose a unified framework to construct generalized Kirchhoff matrices whose matrix inverse leads to gGNMs, whereas, the direct inverse of its diagonal elements gives rise to FRI method. With this connection, we further introduce two multiscale elastic network models, namely, multiscale GNM (mGNM) and multiscale ANM (mANM), which are able to incorporate different scales into the generalized Kirchhoff matrices or generalized Hessian matrices. We validate our new multiscale methods with extensive numerical experiments. We illustrate that gGNMs outperform the original GNM method in the B-factor prediction of a set of 364 proteins. We demonstrate that for a given correlation function, FRI and gGNM methods provide essentially identical B-factor predictions when the scale value in the correlation function is sufficiently large. More importantly, we reveal intrinsic multiscale behavior in protein structures. The proposed mGNM and mANM are able to capture this multiscale behavior and thus give rise to a significant improvement of more than 11% in B-factor predictions over the original GNM and ANM methods. We further demonstrate the benefits of our mGNM through the B-factor predictions of many proteins that fail the original GNM method. We show that the proposed mGNM can also be used to analyze protein domain separations. Finally, we showcase the ability of our mANM for the analysis of protein collective motions.

Decoding the Mobility and Time Scales of Protein Loops

The flexible nature of protein loops and the time scales of their dynamics are critical for many biologically important events at the molecular level, such as protein interaction and recognition processes. In order to obtain a predictive understanding of the dynamic properties of loops, 500 ns molecular dynamics (MD) computer simulations of 38 different proteins were performed and validated using NMR chemical shifts. A total of 169 loops were analyzed and classified into three types, namely fast loops with correlation times <10 ns, slow loops with correlation times between 10 and 500 ns, and loops that are static over the course of the whole trajectory. Chemical and biophysical loop descriptors, such as amino-acid sequence, average 3D structure, charge distribution, hydrophobicity, and local contacts were used to develop and parametrize the ToeLoop algorithm for the prediction of the flexibility and motional time scale of every protein loop, which is also implemented as a public Web server (http://spin.ccic.ohio-state.edu/index.php/loop). The results demonstrate that loop dynamics with their time scales can be predicted rapidly with reasonable accuracy, which will allow the screening of average protein structures to help better understand the various roles loops can play in the context of protein-protein interactions and binding.

Flexibility-rigidity index for protein-nucleic acid flexibility and fluctuation analysis

Protein-nucleic acid complexes are important for many cellular processes including the most essential functions such as transcription and translation. For many protein-nucleic acid complexes, flexibility of both macromolecules has been shown to be critical for specificity and/or function. The flexibility-rigidity index (FRI) has been proposed as an accurate and efficient approach for protein flexibility analysis. In this article, we introduce FRI for the flexibility analysis of protein-nucleic acid complexes. We demonstrate that a multiscale strategy, which incorporates multiple kernels to capture various length scales in biomolecular collective motions, is able to significantly improve the state of art in the flexibility analysis of protein-nucleic acid complexes. We take the advantage of the high accuracy and O(N) computational complexity of our multiscale FRI method to investigate the flexibility of ribosomal subunits, which are difficult to analyze by alternative approaches. An anisotropic FRI approach, which involves localized Hessian matrices, is utilized to study the translocation dynamics in an RNA polymerase.

Starting-Condition Dependence of Order Parameters Derived from Molecular Dynamics Simulations

We have studied how backbone N-H S(2) order parameters calculated from molecular dynamics simulations depend on the method used to calculate them, the starting conditions, and the length of the simulations. Using the carbohydrate binding domain of galectin-3 in the free and lactose-bound states as a test case, we compared the calculated order parameters with experimental data from NMR relaxation. The results indicate that the sampling can be improved by using several starting structures, taking into account conformational heterogeneity reported in crystal structures. However, the improvement is rather limited, and for 93% of the dihedrals that have alternative conformations in the crystal structures, the conformational space is well sampled even if a single conformation is used as the starting structure. Moreover, the agreement with experimental data is improved when using several short simulations, rather than a single long simulation. In the present case, we find that ∼10 independent simulations provide sufficient sampling, and the ideal length of the simulations is ∼10 ns, which is ∼25% longer than the global correlation time for rotational diffusion. On the other hand, the equilibration time appears to be less important, and our results suggest that an equilibration time of 0.25 ns is sufficient. We have also compared four different methods to extract the order parameters from the simulations, namely, the autocorrelation function and isotropic reorientational eigenmode dynamics using three different window sizes. Overall, the four methods yield comparable results, but large differences between the methods may serve to pinpoint cases for which the calculated parameters are unreliable.

PPM_One: a static protein structure based chemical shift predictor

We mined the most recent editions of the BioMagResDataBank and the protein data bank to parametrize a new empirical knowledge-based chemical shift predictor of protein backbone atoms using either a linear or an artificial neural network model. The resulting chemical shift predictor PPM_One accepts a single static 3D structure as input and emulates the effect of local protein dynamics via interatomic steric contacts. Furthermore, the chemical shift prediction was extended to most side-chain protons and it is found that the prediction accuracy is at a level allowing an independent assessment of stereospecific assignments. For a previously established set of test proteins some overall improvement was achieved over current top-performing chemical shift prediction programs.

From protein sequence to dynamics and disorder with DynaMine

Protein function and dynamics are closely related; however, accurate dynamics information is difficult to obtain. Here based on a carefully assembled data set derived from experimental data for proteins in solution, we quantify backbone dynamics properties on the amino-acid level and develop DynaMine--a fast, high-quality predictor of protein backbone dynamics. DynaMine uses only protein sequence information as input and shows great potential in distinguishing regions of different structural organization, such as folded domains, disordered linkers, molten globules and pre-structured binding motifs of different sizes. It also identifies disordered regions within proteins with an accuracy comparable to the most sophisticated existing predictors, without depending on prior disorder knowledge or three-dimensional structural information. DynaMine provides molecular biologists with an important new method that grasps the dynamical characteristics of any protein of interest, as we show here for human p53 and E1A from human adenovirus 5.

The DynaMine webserver: predicting protein dynamics from sequence

Protein dynamics are important for understanding protein function. Unfortunately, accurate protein dynamics information is difficult to obtain: here we present the DynaMine webserver, which provides predictions for the fast backbone movements of proteins directly from their amino-acid sequence. DynaMine rapidly produces a profile describing the statistical potential for such movements at residue-level resolution. The predicted values have meaning on an absolute scale and go beyond the traditional binary classification of residues as ordered or disordered, thus allowing for direct dynamics comparisons between protein regions. Through this webserver, we provide molecular biologists with an efficient and easy to use tool for predicting the dynamical characteristics of any protein of interest, even in the absence of experimental observations. The prediction results are visualized and can be directly downloaded. The DynaMine webserver, including instructive examples describing the meaning of the profiles, is available at http://dynamine.ibsquare.be.

Integrated description of protein dynamics from room-temperature X-ray crystallography and NMR

Detailed descriptions of atomic coordinates and motions are required for an understanding of protein dynamics and their relation to molecular recognition, catalytic function, and allostery. Historically, NMR relaxation measurements have played a dominant role in the determination of the amplitudes and timescales (picosecond-nanosecond) of bond vector fluctuations, whereas high-resolution X-ray diffraction experiments can reveal the presence of and provide atomic coordinates for multiple, weakly populated substates in the protein conformational ensemble. Here we report a hybrid NMR and X-ray crystallography analysis that provides a more complete dynamic picture and a more quantitative description of the timescale and amplitude of fluctuations in atomic coordinates than is obtainable from the individual methods alone. Order parameters (S(2)) were calculated from single-conformer and multiconformer models fitted to room temperature and cryogenic X-ray diffraction data for dihydrofolate reductase. Backbone and side-chain order parameters derived from NMR relaxation experiments are in excellent agreement with those calculated from the room-temperature single-conformer and multiconformer models, showing that the picosecond timescale motions observed in solution occur also in the crystalline state. These motions are quenched in the crystal at cryogenic temperatures. The combination of NMR and X-ray crystallography in iterative refinement promises to provide an atomic resolution description of the alternate conformational substates that are sampled through picosecond to nanosecond timescale fluctuations of the protein structure. The method also provides insights into the structural heterogeneity of nonmethyl side chains, aromatic residues, and ligands, which are less commonly analyzed by NMR relaxation measurements.

Buried and accessible surface area control intrinsic protein flexibility

Proteins experience a wide variety of conformational dynamics that can be crucial for facilitating their diverse functions. How is the intrinsic flexibility required for these motions encoded in their three-dimensional structures? Here, the overall flexibility of a protein is demonstrated to be tightly coupled to the total amount of surface area buried within its fold. A simple proxy for this, the relative solvent-accessible surface area (Arel), therefore shows excellent agreement with independent measures of global protein flexibility derived from various experimental and computational methods. Application of Arel on a large scale demonstrates its utility by revealing unique sequence and structural properties associated with intrinsic flexibility. In particular, flexibility as measured by Arel shows little correspondence with intrinsic disorder, but instead tends to be associated with multiple domains and increased α-helical structure. Furthermore, the apparent flexibility of monomeric proteins is found to be useful for identifying quaternary-structure errors in published crystal structures. There is also a strong tendency for the crystal structures of more flexible proteins to be solved to lower resolutions. Finally, local solvent accessibility is shown to be a primary determinant of local residue flexibility. Overall, this work provides both fundamental mechanistic insight into the origin of protein flexibility and a simple, practical method for predicting flexibility from protein structures.

Interchain hydrophobic clustering promotes rigidity in HIV-1 protease flap dynamics: new insights from molecular dynamics

The dynamics of HIV-1 protease (HIV-pr), a drug target for HIV infection, has been studied extensively by both computational and experimental methods. The flap dynamics of HIV-pr is considered to be more important for better ligand binding and enzymatic actions. Moreover, it has been demonstrated that the drug-induced mutations can change the flap dynamics of HIV-pr affecting the binding affinity of the ligands. Therefore, detailed understanding of flap dynamics is essential for designing better inhibitors. Previous computational investigations observed significant variation in the flap opening in nanosecond time scale indicating that the dynamics is highly sensitive to the simulation protocols. To understand the sensitivity of the flap dynamics on the force field and simulation protocol, molecular dynamics simulations of HIV-pr have been performed with two different AMBER force fields, ff99 and ff02. Two different trajectories (20 ns each) were obtained using the ff99 and ff02 force field. The results showed polarizable force field (ff02) make the flap tighter than the nonpolarizable force field (ff99). Some polar interactions and hydrogen bonds involving flap residues were found to be stronger with ff02 force field. The formation of interchain hydrophobic cluster (between flap tip of one chain and active site wall of another chain) was found to be dominant in the semi-open structures obtained from the simulations irrespective of the force field. It is proposed that an inhibitor, which will promote this interchain hydrophobic clustering, may make the flaps more rigid, and presumably the effect of mutation would be small on ligand binding.

PPM: a side-chain and backbone chemical shift predictor for the assessment of protein conformational ensembles

The combination of the wide availability of protein backbone and side-chain NMR chemical shifts with advances in understanding of their relationship to protein structure makes these parameters useful for the assessment of structural-dynamic protein models. A new chemical shift predictor (PPM) is introduced, which is solely based on physical-chemical contributions to the chemical shifts for both the protein backbone and methyl-bearing amino-acid side chains. To explicitly account for the effects of protein dynamics on chemical shifts, PPM was directly refined against 100 ns long molecular dynamics (MD) simulations of 35 proteins with known experimental NMR chemical shifts. It is found that the prediction of methyl-proton chemical shifts by PPM from MD ensembles is improved over other methods, while backbone Cα, Cβ, C', N, and H(N) chemical shifts are predicted at an accuracy comparable to the latest generation of chemical shift prediction programs. PPM is particularly suitable for the rapid evaluation of large protein conformational ensembles on their consistency with experimental NMR data and the possible improvement of protein force fields from chemical shifts.

Mapping molecular flexibility of proteins with site-directed spin labeling: a case study of myoglobin

Site-directed spin labeling (SDSL) has potential for mapping protein flexibility under physiological conditions. The purpose of the present study was to explore this potential using 38 singly spin-labeled mutants of myoglobin distributed throughout the sequence. Correlation of the EPR spectra with protein structure provides new evidence that the site-dependent variation in line shape, and hence motion of the spin label, is due largely to differences in mobility of the helical backbone in the ns time range. Fluctuations between conformational substates, typically in the μs-ms time range, are slow on the EPR time scale, and the spectra provide a snapshot of conformational equilibria frozen in time as revealed by multiple components in the spectra. A recent study showed that osmolyte perturbation can positively identify conformational exchange as the origin of multicomponent spectra (López et al. (2009), Protein Sci. 18, 1637). In the present study, this new strategy is employed in combination with line shape analysis and pulsed-EPR interspin distance measurements to investigate the conformation and flexibility of myoglobin in three folded and partially folded states. The regions identified to be in conformational exchange in the three forms agree remarkably well with those assigned by NMR, but the faster time scale of EPR allows characterization of localized states not detected in NMR. Collectively, the results suggest that SDSL-EPR and osmolyte perturbation provide a facile means for mapping the amplitude of fast backbone fluctuations and for detecting sequences in slow conformational exchange in folded and partially folded protein sequences.

Determination of structural fluctuations of proteins from structure-based calculations of residual dipolar couplings

Residual dipolar couplings (RDCs) have the potential of providing detailed information about the conformational fluctuations of proteins. It is very challenging, however, to extract such information because of the complex relationship between RDCs and protein structures. A promising approach to decode this relationship involves structure-based calculations of the alignment tensors of protein conformations. By implementing this strategy to generate structural restraints in molecular dynamics simulations we show that it is possible to extract effectively the information provided by RDCs about the conformational fluctuations in the native states of proteins. The approach that we present can be used in a wide range of alignment media, including Pf1, charged bicelles and gels. The accuracy of the method is demonstrated by the analysis of the Q factors for RDCs not used as restraints in the calculations, which are significantly lower than those corresponding to existing high-resolution structures and structural ensembles, hence showing that we capture effectively the contributions to RDCs from conformational fluctuations.

Structure and dynamics of an unfolded protein examined by molecular dynamics simulation

The accurate characterization of the structure and dynamics of proteins in disordered states is a difficult problem at the frontier of structural biology whose solution promises to further our understanding of protein folding and intrinsically disordered proteins. Molecular dynamics (MD) simulations have added considerably to our understanding of folded proteins, but the accuracy with which the force fields used in such simulations can describe disordered proteins is unclear. In this work, using a modern force field, we performed a 200 μs unrestrained MD simulation of the acid-unfolded state of an experimentally well-characterized protein, ACBP, to explore the extent to which state-of-the-art simulation can describe the structural and dynamical features of a disordered protein. By comparing the simulation results with the results of NMR experiments, we demonstrate that the simulation successfully captures important aspects of both the local and global structure. Our simulation was ~2 orders of magnitude longer than those in previous studies of unfolded proteins, a length sufficient to observe repeated formation and breaking of helical structure, which we found to occur on a multimicrosecond time scale. We observed one structural feature that formed but did not break during the simulation, highlighting the difficulty in sampling disordered states. Overall, however, our simulation results are in reasonable agreement with the experimental data, demonstrating that MD simulations can already be useful in describing disordered proteins. Finally, our direct calculation of certain NMR observables from the simulation provides new insight into the general relationship between structural features of disordered proteins and experimental NMR relaxation properties.

Ensemble modeling of protein disordered states: experimental restraint contributions and validation

Disordered states of proteins include the biologically functional intrinsically disordered proteins and the unfolded states of normally folded proteins. In recent years, ensemble-modeling strategies using various experimental measurements as restraints have emerged as powerful means for structurally characterizing disordered states. However, these methods are still in their infancy compared with the structural determination of folded proteins. Here, we have addressed several issues important to ensemble modeling using our ENSEMBLE methodology. First, we assessed how calculating ensembles containing different numbers of conformers affects their structural properties. We find that larger ensembles have very similar properties to smaller ensembles fit to the same experimental restraints, thus allowing a considerable speed improvement in our calculations. In addition, we analyzed the contributions of different experimental restraints to the structural properties of calculated ensembles, enabling us to make recommendations about the experimental measurements that should be made for optimal ensemble modeling. The effects of different restraints, most significantly from chemical shifts, paramagnetic relaxation enhancements and small-angle X-ray scattering, but also from other data, underscore the importance of utilizing multiple sources of experimental data. Finally, we validate our ENSEMBLE methodology using both cross-validation and synthetic experimental restraints calculated from simulated ensembles. Our results suggest that secondary structure and molecular size distribution can generally be modeled very accurately, whereas the accuracy of calculated tertiary structure is dependent on the number of distance restraints used.

Changes in dynamics upon oligomerization regulate substrate binding and allostery in amino acid kinase family members

Oligomerization is a functional requirement for many proteins. The interfacial interactions and the overall packing geometry of the individual monomers are viewed as important determinants of the thermodynamic stability and allosteric regulation of oligomers. The present study focuses on the role of the interfacial interactions and overall contact topology in the dynamic features acquired in the oligomeric state. To this aim, the collective dynamics of enzymes belonging to the amino acid kinase family both in dimeric and hexameric forms are examined by means of an elastic network model, and the softest collective motions (i.e., lowest frequency or global modes of motions) favored by the overall architecture are analyzed. Notably, the lowest-frequency modes accessible to the individual subunits in the absence of multimerization are conserved to a large extent in the oligomer, suggesting that the oligomer takes advantage of the intrinsic dynamics of the individual monomers. At the same time, oligomerization stiffens the interfacial regions of the monomers and confers new cooperative modes that exploit the rigid-body translational and rotational degrees of freedom of the intact monomers. The present study sheds light on the mechanism of cooperative inhibition of hexameric N-acetyl-L-glutamate kinase by arginine and on the allosteric regulation of UMP kinases. It also highlights the significance of the particular quaternary design in selectively determining the oligomer dynamics congruent with required ligand-binding and allosteric activities.

Protein function requires a three-dimensional structure with specific dynamic features for catalytic and binding events, and, in many cases, the structure results from the assembly of more than one polypeptide chain (also called monomer or subunit) to form an oligomer or multimer. Proteins such as hemoglobin or chaperonin GroEL are oligomers formed by 2 and 14 subunits, respectively, whereas virus capsids are multimers composed of hundreds of monomers. In these cases, the architecture of the interface between the subunits and the overall assembly geometry are essential in determining the functional motions that these sophisticated structures are able to perform under physiological conditions. Here we present results from our computational study of the large-amplitude motions of dimeric and hexameric proteins that belong to the Amino Acid Kinase family. Our study reveals that the monomers in these oligomeric proteins are arranged in such a way that the oligomer inherits the intrinsic dynamic features of its components. The packing geometry additionally confers the ability to perform highly cooperative conformational changes that involve all monomers and enable the biological activity of the multimer. The study highlights the significance of the quaternary design in favoring the oligomer dynamics that enables ligand-binding and allosteric regulation functions.

Interpretation of biomolecular NMR spin relaxation parameters

Biomolecular nuclear magnetic resonance (NMR) spin relaxation experiments provide exquisite information on the picosecond to nanosecond timescale motions of bond vectors. Spin-lattice (T1) and spin-spin (T2) relaxation times and the steady-state nuclear Overhauser effect (NOE) are the first set of parameters extracted from typical 15N or 13C NMR relaxation experiments. Therefore, verifying that T1, T2, and NOE are consistent with theoretical predictions is an important step before carrying out the more detailed model-free and reduced spectral density mapping analyses commonly employed. In this mini-review, we discuss the essential motional parameters used to describe biomolecular dynamics in the context of a variety of examples of folded and intrinsically disordered proteins and peptides in aqueous and membrane mimetic environments. Estimates of these parameters can be used as input for an online interface, introduced herein, allowing plotting of trends of T1, T2, and NOE with magnetic field strength. The plots may serve as a first-check to the spectroscopist preparing to embark on a detailed NMR relaxation analysis.

SPARTA+: a modest improvement in empirical NMR chemical shift prediction by means of an artificial neural network

NMR chemical shifts provide important local structural information for proteins and are key in recently described protein structure generation protocols. We describe a new chemical shift prediction program, SPARTA+, which is based on artificial neural networking. The neural network is trained on a large carefully pruned database, containing 580 proteins for which high-resolution X-ray structures and nearly complete backbone and (13)C(beta) chemical shifts are available. The neural network is trained to establish quantitative relations between chemical shifts and protein structures, including backbone and side-chain conformation, H-bonding, electric fields and ring-current effects. The trained neural network yields rapid chemical shift prediction for backbone and (13)C(beta) atoms, with standard deviations of 2.45, 1.09, 0.94, 1.14, 0.25 and 0.49 ppm for delta(15)N, delta(13)C', delta(13)C(alpha), delta(13)C(beta), delta(1)H(alpha) and delta(1)H(N), respectively, between the SPARTA+ predicted and experimental shifts for a set of eleven validation proteins. These results represent a modest but consistent improvement (2-10%) over the best programs available to date, and appear to be approaching the limit at which empirical approaches can predict chemical shifts.

The role of conformational entropy in molecular recognition by calmodulin

The physical basis for high affinity interactions involving proteins is complex and potentially involves a range of energetic contributions. Among these are changes in protein conformational entropy, which cannot yet be reliably computed from molecular structures. We have recently employed changes in conformational dynamics as a proxy for changes in conformational entropy of calmodulin upon association with domains from regulated proteins. The apparent change in conformational entropy was linearly related to the overall binding entropy. This view warrants a more quantitative foundation. Here we calibrate an “entropy meter” employing an experimental dynamical proxy based on NMR relaxation and show that changes in the conformational entropy of calmodulin are a significant component of the energetics of binding. Furthermore, the distribution of motion at the interface between the target domain and calmodulin are surprisingly non-complementary. These observations promote modification of our understanding of the energetics of protein-ligand interactions.

Dynamic activation of an allosteric regulatory protein

Allosteric regulation is used as a very efficient mechanism to control protein activity in most biological processes, including signal transduction, metabolism, catalysis and gene regulation. Allosteric proteins can exist in several conformational states with distinct binding or enzymatic activity. Effectors are considered to function in a purely structural manner by selectively stabilizing a specific conformational state, thereby regulating protein activity. Here we show that allosteric proteins can be regulated predominantly by changes in their structural dynamics. We have used NMR spectroscopy and isothermal titration calorimetry to characterize cyclic AMP (cAMP) binding to the catabolite activator protein (CAP), a transcriptional activator that has been a prototype for understanding effector-mediated allosteric control of protein activity. cAMP switches CAP from the 'off' state (inactive), which binds DNA weakly and non-specifically, to the 'on' state (active), which binds DNA strongly and specifically. In contrast, cAMP binding to a single CAP mutant, CAP-S62F, fails to elicit the active conformation; yet, cAMP binding to CAP-S62F strongly activates the protein for DNA binding. NMR and thermodynamic analyses show that despite the fact that CAP-S62F-cAMP(2) adopts the inactive conformation, its strong binding to DNA is driven by a large conformational entropy originating in enhanced protein motions induced by DNA binding. The results provide strong evidence that changes in protein motions may activate allosteric proteins that are otherwise structurally inactive.

Protein proton-proton dynamics from amide proton spin flip rates

Residue-specific amide proton spin-flip rates K were measured for peptide-free and peptide-bound calmodulin. K approximates the sum of NOE build-up rates between the amide proton and all other protons. This work outlines the theory of multi-proton relaxation, cross relaxation and cross correlation, and how to approximate it with a simple model based on a variable number of equidistant protons. This model is used to extract the sums of K-rates from the experimental data. Error in K is estimated using bootstrap methodology. We define a parameter Q as the ratio of experimental K-rates to theoretical K-rates, where the theoretical K-rates are computed from atomic coordinates. Q is 1 in the case of no local motion, but decreases to values as low as 0.5 with increasing domination of sidechain protons of the same residue to the amide proton flips. This establishes Q as a monotonous measure of local dynamics of the proton network surrounding the amide protons. The method is applied to the study of proton dynamics in Ca(2+)-saturated calmodulin, both free in solution and bound to smMLCK peptide. The mean Q is 0.81 +/- 0.02 for free calmodulin and 0.88 +/- 0.02 for peptide-bound calmodulin. This novel methodology thus reveals the presence of significant interproton disorder in this protein, while the increase in Q indicates rigidification of the proton network upon peptide binding, confirming the known high entropic cost of this process.

All-atom contact model for understanding protein dynamics from crystallographic B-factors

An all-atom local contact model is described that can be used to predict protein motions underlying isotropic crystallographic B-factors. It uses a mean-field approximation to represent the motion of an atom in a harmonic potential generated by the surrounding atoms resting at their equilibrium positions. Based on a 400-ns molecular dynamics simulation of ubiquitin in explicit water, it is found that each surrounding atom stiffens the spring constant by a term that on average scales exponentially with the interatomic distance. This model combines features of the local density model by Halle and the local contact model by Zhang and Brüschweiler. When applied to a nonredundant set of 98 ultra-high resolution protein structures, an average correlation coefficient of 0.75 is obtained for all atoms. The systematic inclusion of crystal contact contributions and fraying effects is found to enhance the performance substantially. Because the computational cost of the local contact model scales linearly with the number of protein atoms, it is applicable to proteins of any size for the prediction of B-factors of both backbone and side-chain atoms. The model performs as well as or better than several other models tested, such as rigid-body motional models, the local density model, and various forms of the elastic network model. It is concluded that at the currently achievable level of accuracy, collective intramolecular motions are not essential for the interpretation of B-factors.

An experimentally guided umbrella sampling protocol for biomolecules

We present a simple method for utilizing experimental data to improve the efficiency of numerical calculations of free energy profiles from molecular dynamics simulations. The method involves umbrella sampling simulations with restraining potentials based on a known approximate estimate of the free energy profile derived solely from experimental data. The use of the experimental data results in optimal restraining potentials, guides the simulation along relevant pathways, and decreases overall computational time. In demonstration of the method, two systems are showcased. First, guided, unguided (regular) umbrella sampling simulations and exhaustive sampling simulations are compared to each other in the calculation of the free energy profile for the distance between the ends of a pentapeptide. The guided simulation use restraints based on a simulated "experimental" potential of mean force of the end-to-end distance that would be measured by fluorescence resonance energy transfer (obtained from exhaustive sampling). Statistical analysis shows a dramatic improvement in efficiency for a 5 window guided umbrella sampling over 5 and 17 window unguided umbrella sampling simulations. Moreover, the form of the potential of mean force for the guided simulations evolves, as one approaches convergence, along the same milestones as the extensive simulations, but exponentially faster. Second, the method is further validated by replicating the forced unfolding pathway of the titin I27 domain using guiding umbrella sampling potentials determined from actual single molecule pulling data. Comparison with unguided umbrella sampling reveals that the use of guided sampling encourages unfolding simulations to converge faster to a forced unfolding pathway that agrees with previous results and produces a more accurate potential of mean force.

Structural biology by NMR: structure, dynamics, and interactions

The function of bio-macromolecules is determined by both their 3D structure and conformational dynamics. These molecules are inherently flexible systems displaying a broad range of dynamics on time-scales from picoseconds to seconds. Nuclear Magnetic Resonance (NMR) spectroscopy has emerged as the method of choice for studying both protein structure and dynamics in solution. Typically, NMR experiments are sensitive both to structural features and to dynamics, and hence the measured data contain information on both. Despite major progress in both experimental approaches and computational methods, obtaining a consistent view of structure and dynamics from experimental NMR data remains a challenge. Molecular dynamics simulations have emerged as an indispensable tool in the analysis of NMR data.

Hydrophobic core mutations in CI2 globally perturb fast side-chain dynamics similarly without regard to position

Protein dynamics is currently an area of intense research because of its importance as complementary information to the huge quantity of available data relating protein structure and function. Because it is usually the influence of dynamics on function that is studied, the physical determinants of the distribution of flexibility in proteins have not been explored as thoroughly. In the present NMR study, an expanded suite of five (2)H relaxation experiments was used to characterize the picosecond-to-nanosecond side-chain dynamics of chymotrypsin inhibitor 2 (CI2) and five hydrophobic core mutants, some of which are members of the folding nucleus. Because CI2 is a homologue of the serine protease inhibitor eglin c, which has already been extensively characterized in terms of its dynamics, it was possible to compare not only side-chain dynamics but also the responses of these dynamics to analogous mutations. Remarkably, each of the five core mutations in CI2 led to similar and reproducible increases in side-chain flexibility throughout the entire structure. Although the expanded suite of (2)H relaxation experiments does not affect model selection for the vast majority of residues, it did enable the detection of increasing levels of nanosecond-scale motions in CI2's reactive site binding loop as the L68 side chain was progressively shortened by mutation. Collectively, we observed that the CI2 mutants are more dynamically similar to each other than to the more rigid wild-type CI2, from which we propose that wild-type CI2 has been optimized to a specific level of rigidity which may aid in its function as a serine protease inhibitor. We also observed that the pattern of side-chain dynamics of CI2 is quantitatively similar to eglin c, but that this similarity is lost upon mutating both proteins at an equivalent position. Finally, (15)N relaxation was used to characterize the backbone dynamics of wild-type and mutant CI2. Interestingly, mutation at folding nucleus positions led to widespread increases in backbone flexibility, whereas non-folding-nucleus positions led to increases in flexibility in the C-terminal half of the protein only.