BPPred: a Web-based computational tool for predicting biophysical parameters of proteins

We exploit the availability of recent experimental data on a variety of proteins to develop a Web-based prediction algorithm (BPPred) to calculate several biophysical parameters commonly used to describe the folding process. These parameters include the equilibrium m-values, the length of proteins, and the changes upon unfolding in the solvent-accessible surface area, in the heat capacity, and in the radius of gyration. We also show that the knowledge of any one of these quantities allows an estimate of the others to be obtained, and describe the confidence limits with which these estimations can be made. Furthermore, we discuss how the kinetic m-values, or the Beta Tanford values, may provide an estimate of the solvent-accessible surface area and the radius of gyration of the transition state for protein folding. Taken together, these results suggest that BPPred should represent a valuable tool for interpreting experimental measurements, as well as the results of molecular dynamics simulations.     

Effects of arterial wall models and measurement uncertainties on cardiovascular model predictions

We developed a methodology to assess and compare the prediction quality of cardiovascular models for patient-specific simulations calibrated with uncertainty-hampered measurements. The methodology was applied in a one-dimensional blood flow model to estimate the impact of measurement uncertainty in wall model parameters on the predictions of pressure and flow in an arterial network. We assessed the prediction quality of three wall models that have been widely used in one-dimensional blood flow simulations. A 37-artery network, previously used in one experimental and several simulation studies, was adapted to patient-specific conditions with a set of three clinically measurable inputs: carotid–femoral wave speed, mean arterial pressure and area in the brachial artery. We quantified the uncertainty of the predicted pressure and flow waves in eight locations in the network and assessed the sensitivity of the model prediction with respect to the measurements of wave speed, pressure and cross-sectional area. Furthermore, we developed novel time-averaged sensitivity indices to assess the contribution of model parameters to the uncertainty of time-varying quantities (e.g., pressure and flow). The results from our patient-specific network model demonstrated that our novel indices allowed for a more accurate sensitivity analysis of time-varying quantities compared to conventional Sobol sensitivity indices.     

Dynamics of the Hck-SH3 domain: comparison of experiment with multiple molecular dynamics simulations

Molecular dynamics calculations provide a method by which the dynamic properties of molecules can be explored over timescales and at a level of detail that cannot be obtained experimentally from NMR or X-ray analyses. Recent work (Philippopoulos M, Mandel AM, Palmer AG III, Lim C, 1997, Proteins 28:481-493) has indicated that the accuracy of these simulations is high, as measured by the correspondence of parameters extracted from these calculations to those determined through experimental means. Here, we investigate the dynamic behavior of the Src homology 3 (SH3) domain of hematopoietic cell kinase (Hck) via 5N backbone relaxation NMR studies and a set of four independent 4 ns solvated molecular dynamics calculations. We also find that molecular dynamics simulations accurately reproduce fast motion dynamics as estimated from generalized order parameter (S2) analysis for regions of the protein that have experimentally well-defined coordinates (i.e., stable secondary structural elements). However, for regions where the coordinates are not well defined, as indicated by high local root-mean-square deviations among NMR-determined structural family members or high B-factors/low electron density in X-ray crystallography determined structures, the parameters calculated from a short to moderate length (less than 5-10 ns) molecular dynamics trajectory are dependent on the particular coordinates chosen as a starting point for the simulation.     

A theory of protein dynamics to predict NMR relaxation

We present a theoretical, site-specific, approach to predict protein subunit correlation times, as measured by NMR experiments of ¹H-¹⁵N nuclear Overhauser effect, spin-lattice relaxation, and spin-spin relaxation. Molecular dynamics simulations are input to our equation of motion for protein dynamics, which is solved analytically to produce the eigenvalues and the eigenvectors that specify the NMR parameters. We directly compare our theoretical predictions to experiments and to simulation data for the signal transduction chemotaxis protein Y (CheY), which regulates the swimming response of motile bacteria. Our theoretical results are in good agreement with both simulations and experiments, without recourse to adjustable parameters. The theory is general, since it allows calculations of any dynamical property of interest. As an example, we present theoretical calculations of NMR order parameters and x-ray Debye-Waller temperature factors; both quantities show good agreement with experimental data.     

Motional timescale predictions by molecular dynamics simulations: Case study using proline and hydroxyproline sidechain dynamics

We propose a new approach for force field optimizations which aims at reproducing dynamics characteristics using biomolecular MD simulations, in addition to improved prediction of motionally averaged structural properties available from experiment. As the source of experimental data for dynamics fittings, we use ¹³C NMR spin‐lattice relaxation times T₁ of backbone and sidechain carbons, which allow to determine correlation times of both overall molecular and intramolecular motions. For structural fittings, we use motionally averaged experimental values of NMR J couplings. The proline residue and its derivative 4‐hydroxyproline with relatively simple cyclic structure and sidechain dynamics were chosen for the assessment of the new approach in this work. Initially, grid search and simplexed MD simulations identified large number of parameter sets which fit equally well experimental J couplings. Using the Arrhenius‐type relationship between the force constant and the correlation time, the available MD data for a series of parameter sets were analyzed to predict the value of the force constant that best reproduces experimental timescale of the sidechain dynamics. Verification of the new force‐field (termed as AMBER99SB‐ILDNP) against NMR J couplings and correlation times showed consistent and significant improvements compared to the original force field in reproducing both structural and dynamics properties. The results suggest that matching experimental timescales of motions together with motionally averaged characteristics is the valid approach for force field parameter optimization. Such a comprehensive approach is not restricted to cyclic residues and can be extended to other amino acid residues, as well as to the backbone. Proteins 2014; 82:195–215. © 2013 Wiley Periodicals, Inc.     

Evaluation of protein–ligand affinity prediction using steered molecular dynamics simulations

In computational drug design, ranking a series of compound analogs in a manner that is consistent with experimental affinities remains a challenge. In this study, we evaluated the prediction of protein–ligand binding affinities using steered molecular dynamics simulations. First, we investigated the appropriate conditions for accurate predictions in these simulations. A conic harmonic restraint was applied to the system for efficient sampling of work values on the ligand unbinding pathway. We found that pulling velocity significantly influenced affinity predictions, but that the number of collectable trajectories was less influential. We identified the appropriate pulling velocity and collectable trajectories for binding affinity predictions as 1.25 Å/ns and 100, respectively, and these parameters were used to evaluate three target proteins (FK506 binding protein, trypsin, and cyclin-dependent kinase 2). For these proteins using our parameters, the accuracy of affinity prediction was higher and more stable when Jarzynski’s equality was employed compared with the second-order cumulant expansion equation of Jarzynski’s equality. Our results showed that steered molecular dynamics simulations are effective for predicting the rank order of ligands; thus, they are a potential tool for compound selection in hit-to-lead and lead optimization processes.     

Structural Dynamics and Conformational Equilibria of SERCA Regulatory Proteins in Membranes by Solid-State NMR Restrained Simulations

Solid-state NMR spectroscopy is emerging as a powerful approach to determine structure, topology, and conformational dynamics of membrane proteins at the atomic level. Conformational dynamics are often inferred and quantified from the motional averaging of the NMR parameters. However, the nature of these motions is difficult to envision based only on spectroscopic data. Here, we utilized restrained molecular dynamics simulations to probe the structural dynamics, topology and conformational transitions of regulatory membrane proteins of the calcium ATPase SERCA, namely sarcolipin and phospholamban, in explicit lipid bilayers. Specifically, we employed oriented solid-state NMR data, such as dipolar couplings and chemical shift anisotropy measured in lipid bicelles, to refine the conformational ensemble of these proteins in lipid membranes. The samplings accurately reproduced the orientations of transmembrane helices and showed a significant degree of convergence with all of the NMR parameters. Unlike the unrestrained simulations, the resulting sarcolipin structures are in agreement with distances and angles for hydrogen bonds in ideal helices. In the case of phospholamban, the restrained ensemble sampled the conformational interconversion between T (helical) and R (unfolded) states for the cytoplasmic region that could not be observed using standard structural refinements with the same experimental data set. This study underscores the importance of implementing NMR data in molecular dynamics protocols to better describe the conformational landscapes of membrane proteins embedded in realistic lipid membranes.     

Structural Dynamics and Conformational Equilibria of SERCA Regulatory Proteins in Membranes by Solid-State NMR Restrained Simulations

Solid-state NMR spectroscopy is emerging as a powerful approach to determine structure, topology, and conformational dynamics of membrane proteins at the atomic level. Conformational dynamics are often inferred and quantified from the motional averaging of the NMR parameters. However, the nature of these motions is difficult to envision based only on spectroscopic data. Here, we utilized restrained molecular dynamics simulations to probe the structural dynamics, topology and conformational transitions of regulatory membrane proteins of the calcium ATPase SERCA, namely sarcolipin and phospholamban, in explicit lipid bilayers. Specifically, we employed oriented solid-state NMR data, such as dipolar couplings and chemical shift anisotropy measured in lipid bicelles, to refine the conformational ensemble of these proteins in lipid membranes. The samplings accurately reproduced the orientations of transmembrane helices and showed a significant degree of convergence with all of the NMR parameters. Unlike the unrestrained simulations, the resulting sarcolipin structures are in agreement with distances and angles for hydrogen bonds in ideal helices. In the case of phospholamban, the restrained ensemble sampled the conformational interconversion between T (helical) and R (unfolded) states for the cytoplasmic region that could not be observed using standard structural refinements with the same experimental data set. This study underscores the importance of implementing NMR data in molecular dynamics protocols to better describe the conformational landscapes of membrane proteins embedded in realistic lipid membranes.     

A glucose-insulin pharmacodynamic surface modeling validation and comparison of metabolic system models

Metabolic system modeling for model-based glycaemic control is becoming increasingly important. Few metabolic system models are clinically validated for both fit to the data and prediction ability. This research introduces a new additional form of pharmaco-dynamic (PD) surface comparison for model analysis and validation. These 3D surfaces are developed for 3 clinically validated models and 1 model with an added saturation dynamic. The models include the well-known Minimal Model. They are fit to two different data sets of clinical PD data from hyperinsulinaemic clamp studies at euglycaemia and/or hyperglycaemia. The models are fit to the first data set to determine an optimal set of population parameters. The second data set is used to test trend prediction of the surface modeling as it represents a lower insulin sensitivity cohort and should thus require only scaling in these (or related) parameters to match this data set. This particular approach clearly highlights differences in modeling methods, and the model dynamics utilized that may not appear as clearly in other fitting or prediction validation methods.Across all models saturation of insulin action is seen to be an important determinant of prediction and fit quality. In particular, the well-reported under-modeling of insulin sensitivity in the Minimal Model can be seen in this context to be a result of a lack of saturation dynamics, which in turn affects its ability to detect differences between cohorts. The overall approach of examining PD surfaces is seen to be an effective means of analyzing and thus validating a metabolic model's inherent dynamics and basic trend prediction on a population level, but is not a replacement for data driven, patient-specific fit and prediction validation for clinical use. The overall method presented could be readily generalized to similar PD systems and therapeutics.     

Molecular Dynamics Ensemble Refinement of Intrinsically Disordered Peptides According to Deconvoluted Spectra from Circular Dichroism

We have developed a computational method of atomistically refining the structural ensemble of intrinsically disordered peptides (IDPs) facilitated by experimental measurements using circular dichroism spectroscopy (CD). A major challenge surrounding this approach stems from the deconvolution of experimental CD spectra into secondary structure features of the IDP ensemble. Currently available algorithms for CD deconvolution were designed to analyze the spectra of proteins with stable secondary structures. Herein, our work aims to minimize any bias from the peptide deconvolution analysis by implementing a non-negative linear least-squares fitting algorithm in conjunction with a CD reference data set that contains soluble and denatured proteins (SDP48). The non-negative linear least-squares method yields the best results for deconvolution of proteins with higher disordered content than currently available methods, according to a validation analysis of a set of protein spectra with Protein Data Bank entries. We subsequently used this analysis to deconvolute our experimental CD data to refine our computational model of the peptide secondary structure ensemble produced by all-atom molecular dynamics simulations with implicit solvent. We applied this approach to determine the ensemble structures of a set of short IDPs, that mimic the calmodulin binding domain of calcium/calmodulin-dependent protein kinase II and its 1-amino-acid and 3-amino-acid mutants. Our study offers a, to our knowledge, novel way to solve the ensemble secondary structures of IDPs in solution, which is important to advance the understanding of their roles in regulating signaling pathways through the formation of complexes with multiple partners.     

Methods for molecular dynamics simulations of protein folding/unfolding in solution

All atom molecular dynamics simulations have become a standard method for mapping equilibrium protein dynamics and non-equilibrium events like folding and unfolding. Here, we present detailed methods for performing such simulations. Generic protocols for minimization, solvation, simulation, and analysis derived from previous studies are also presented. As a measure of validation, our water model is compared with experiment. An example of current applications of these methods, simulations of the ultrafast folding protein Engrailed Homeodomain are presented including the experimental evidence used to verify their results. Ultrafast folders are an invaluable tool for studying protein behavior as folding and unfolding events measured by experiment occur on timescales accessible with the high-resolution molecular dynamics methods we describe. Finally, to demonstrate the prospect of these methods for folding proteins, a temperature quench simulation of a thermal unfolding intermediate of the Engrailed Homeodomain is described.     

Reorientational contact-weighted elastic network model for the prediction of protein dynamics: comparison with NMR relaxation

A new model for the prediction of protein backbone motions is presented. The model, termed reorientational contact-weighted elastic network model, is based on a multidimensional reorientational harmonic potential of the backbone amide bond vector orientations and it is applied to the interpretation of dynamics parameters obtained from NMR relaxation data. The individual energy terms are weighted as a function of the intervector distances and by the contact strengths of each bond vector with respect to its local environment. Correlated reorientational motional properties of the bond vectors are obtained by means of normal mode analysis. Application to a set of proteins with known three-dimensional structures yields good to excellent agreement between predicted and experimental NMR order parameters presenting an improvement over the local contact model. The reorientational eigenmodes of the reorientational contact-weighted elastic network model method provide direct information on the collective nature of protein backbone motions. The dominant eigenmodes have a notably low collectivity, which is consistent with the behavior found for reorientational eigenmodes from molecular dynamics simulations.     

All-atom molecular dynamics simulations using orientational constraints from anisotropic NMR samples

Orientational constraints obtained from solid state NMR experiments on anisotropic samples are used here in molecular dynamics (MD) simulations for determining the structure and dynamics of several different membrane-bound molecules. The new MD technique is based on the inclusion of orientation dependent pseudo-forces in the COSMOS-NMR force field. These forces drive molecular rotations and re-orientations in the simulation, such that the motional time-averages of the tensorial NMR properties approach the experimentally measured parameters. The orientational-constraint-driven MD simulations are universally applicable to all NMR interaction tensors, such as chemical shifts, dipolar couplings and quadrupolar interactions. The strategy does not depend on the initial choice of coordinates, and is in principle suitable for any flexible molecule. To test the method on three systems of increasing complexity, we used as constraints some deuterium quadrupolar couplings from the literature on pyrene, cholesterol and an antimicrobial peptide embedded in oriented lipid bilayers. The MD simulations were able to reproduce the NMR parameters within experimental error. The alignment of the three membrane-bound molecules and some aspects of their conformation were thus derived from the NMR data, in good agreement with previous analyses. Furthermore, the new approach yielded for the first time the distribution of segmental orientations with respect to the membrane and the order parameter tensors of all three systems.     

On the ability of molecular dynamics force fields to recapitulate NMR derived protein side chain order parameters

Molecular dynamics (MD) simulations have become a central tool for investigating various biophysical questions with atomistic detail. While many different proxies are used to qualify MD force fields, most are based on largely structural parameters such as the root mean square deviation from experimental coordinates or nuclear magnetic resonance (NMR) chemical shifts and residual dipolar couplings. NMR derived Lipari–Szabo squared generalized order parameter (O²) values of amide N? H bond vectors of the polypeptide chain were also often employed for refinement and validation. However, with a few exceptions, side chain methyl symmetry axis order parameters have not been incorporated into experimental reference sets. Using a test set of five diverse proteins, the performance of several force fields implemented in the NAMDD simulation package was examined. It was found that simulations employing explicit water implemented using the TIP3 model generally performed significantly better than those using implicit water in reproducing experimental methyl symmetry axis O² values. Overall the CHARMM27 force field performs nominally better than two implementations of the Amber force field. It appeared that recent quantum mechanics modifications to side chain torsional angles of leucine and isoleucine in the Amber force field have significantly hindered proper motional modeling for these residues. There remained significant room for improvement as even the best correlations of experimental and simulated methyl group Lipari–Szabo generalized order parameters fall below an R² of 0.8.     

Refinement of the AMBER force field for nucleic acids: improving the description of alpha/gamma conformers

We present here the parmbsc0 force field, a refinement of the AMBER parm99 force field, where emphasis has been made on the correct representation of the alpha/gamma concerted rotation in nucleic acids (NAs). The modified force field corrects overpopulations of the alpha/gamma = (g+,t) backbone that were seen in long (more than 10 ns) simulations with previous AMBER parameter sets (parm94-99). The force field has been derived by fitting to high-level quantum mechanical data and verified by comparison with very high-level quantum mechanical calculations and by a very extensive comparison between simulations and experimental data. The set of validation simulations includes two of the longest trajectories published to date for the DNA duplex (200 ns each) and the largest variety of NA structures studied to date (15 different NA families and 97 individual structures). The total simulation time used to validate the force field includes near 1 mus of state-of-the-art molecular dynamics simulations in aqueous solution.     

Partial unfolding and refolding for structure refinement: A unified approach of geometric simulations and molecular dynamics

The most successful protein structure prediction methods to date have been template‐based modeling (TBM) or homology modeling, which predicts protein structure based on experimental structures. These high accuracy predictions sometimes retain structural errors due to incorrect templates or a lack of accurate templates in the case of low sequence similarity, making these structures inadequate in drug‐design studies or molecular dynamics simulations. We have developed a new physics based approach to the protein refinement problem by mimicking the mechanism of chaperons that rehabilitate misfolded proteins. The template structure is unfolded by selectively (targeted) pulling on different portions of the protein using the geometric based technique FRODA, and then refolded using hierarchically restrained replica exchange molecular dynamics simulations (hr‐REMD). FRODA unfolding is used to create a diverse set of topologies for surveying near native‐like structures from a template and to provide a set of persistent contacts to be employed during re‐folding. We have tested our approach on 13 previous CASP targets and observed that this method of folding an ensemble of partially unfolded structures, through the hierarchical addition of contact restraints (that is, first local and then nonlocal interactions), leads to a refolding of the structure along with refinement in most cases (12/13). Although this approach yields refined models through advancement in sampling, the task of blind selection of the best refined models still needs to be solved. Overall, the method can be useful for improved sampling for low resolution models where certain of the portions of the structure are incorrectly modeled. Proteins 2015; 83:2279–2292. © 2015 Wiley Periodicals, Inc.     

Helix-coil transition of alanine peptides in water: force field dependence on the folded and unfolded structures

The force fields used in classical modeling studies are semiempirical in nature and rely on their validation by comparison of simulations with experimental data. The all-atom replica-exchange molecular dynamics (REMD) methodology allows us to calculate the thermodynamics of folding/unfolding of peptides and small proteins, and provides a way of evaluating the reliability of force fields. We apply the REMD to obtain equilibrium folding/unfolding thermodynamics of a 21-residue peptide containing only alanine residues in explicit aqueous solution. The thermodynamics of this peptide is modeled with both the OPLS/AA/L and the A94/MOD force fields. We find that the helical content and the values for the helix propagation and nucleation parameters for this alanine peptide are consistent with measurements on similar peptides and with calculations using the modified AMBER force field (A94/MOD). The nature of conformations, both folded and unfolded, that contributes to the helix-coil transition profile, however, is quite different between these two force fields.     

Solutions for surrogacy validation with longitudinal outcomes for a gene therapy

Valid surrogate endpoints S can be used as a substitute for a true outcome of interest T to measure treatment efficacy in a clinical trial. We propose a causal inference approach to validate a surrogate by incorporating longitudinal measurements of the true outcomes using a mixed modeling approach, and we define models and quantities for validation that may vary across the study period using principal surrogacy criteria. We consider a surrogate-dependent treatment efficacy curve that allows us to validate the surrogate at different time points. We extend these methods to accommodate a delayed-start treatment design where all patients eventually receive the treatment. Not all parameters are identified in the general setting. We apply a Bayesian approach for estimation and inference, utilizing more informative prior distributions for selected parameters. We consider the sensitivity of these prior assumptions as well as assumptions of independence among certain counterfactual quantities conditional on pretreatment covariates to improve identifiability. We examine the frequentist properties (bias of point and variance estimates, credible interval coverage) of a Bayesian imputation method. Our work is motivated by a clinical trial of a gene therapy where the functional outcomes are measured repeatedly throughout the trial.     

Ab initio RNA folding by discrete molecular dynamics: from structure prediction to folding mechanisms

RNA molecules with novel functions have revived interest in the accurate prediction of RNA three-dimensional (3D) structure and folding dynamics. However, existing methods are inefficient in automated 3D structure prediction. Here, we report a robust computational approach for rapid folding of RNA molecules. We develop a simplified RNA model for discrete molecular dynamics (DMD) simulations, incorporating base-pairing and base-stacking interactions. We demonstrate correct folding of 150 structurally diverse RNA sequences. The majority of DMD-predicted 3D structures have <4 A deviations from experimental structures. The secondary structures corresponding to the predicted 3D structures consist of 94% native base-pair interactions. Folding thermodynamics and kinetics of tRNA(Phe), pseudoknots, and mRNA fragments in DMD simulations are in agreement with previous experimental findings. Folding of RNA molecules features transient, non-native conformations, suggesting non-hierarchical RNA folding. Our method allows rapid conformational sampling of RNA folding, with computational time increasing linearly with RNA length. We envision this approach as a promising tool for RNA structural and functional analyses.