TSAR,a new graph–theoretical approach to computational modeling of protein side‐chain flexibility: Modeling of ionization properties of proteins

A new graph–theoretical approach called thermodynamic sampling of amino acid residues (TSAR) has been elaborated to explicitly account for the protein side chain flexibility in modeling conformation‐dependent protein properties. In TSAR, a protein is viewed as a graph whose nodes correspond to structurally independent groups and whose edges connect the interacting groups. Each node has its set of states describing conformation and ionization of the group, and each edge is assigned an array of pairwise interaction potentials between the adjacent groups. By treating the obtained graph as a belief‐network—a well‐established mathematical abstraction—the partition function of each node is found. In the current work we used TSAR to calculate partition functions of the ionized forms of protein residues. A simplified version of a semi‐empirical molecular mechanical scoring function, borrowed from our Lead Finder docking software, was used for energy calculations. The accuracy of the resulting model was validated on a set of 486 experimentally determined pK_a values of protein residues. The average correlation coefficient (R) between calculated and experimental pK_a values was 0.80, ranging from 0.95 (for Tyr) to 0.61 (for Lys). It appeared that the hydrogen bond interactions and the exhaustiveness of side chain sampling made the most significant contribution to the accuracy of pK_a calculations. Proteins 2011; © 2011 Wiley‐Liss, Inc.     

Brownian dynamics simulations of molecular recognition in an antibody-antigen system.

The crystal structure for an antibody-antigen system, that of the anti-hen egg lysozyme monoclonal antibody HyHEL-5 complexed to lysozyme, is used as the starting point for computer simulations of diffusional encounters between the two proteins. The investigation consists of two parts: first, the linearized Poisson-Boltzmann equation is solved to determine the long-range electrostatic forces between antibody and antigen, and then, the relative motion as influenced by these forces is modeled within Brownian motion theory. The effects of various point mutations on the calculated reaction rate are considered. It is found that charged residues close to the binding site exert the greatest influence in steering the proteins into a configuration favorable for their binding, while more distant mutations are qualitatively described by the Smoluchowski model for the mutual diffusion of two uniformly charged spheres. The antibody residues involved in forming salt links with the lysozyme, Glu-H35 and Glu-H50, appear to be particularly important in electrostatic steering, as neutralization of both of them yields reaction rates that are two to three orders of magnitude below those of wild-type rates. The relative rates obtained from the simulations can be tested through kinetic measurements on mutant protein complexes. Kinetically efficient partners can also be designed and constructed through directed mutagenesis.     

Poisson-Boltzmann model studies of molecular electrostatic properties of the cAMP-dependent protein kinase

Protonation equilibria of residues important in the catalytic mechanism of a protein kinase were analyzed on the basis of the Poisson-Boltzmann electrostatic model along with a cluster-based treatment of the multiple titration state problem. Calculations were based upon crystallographic structures of the mammalian cAMP-dependent protein kinase, one representing the so called closed form of the enzyme and the other representing an open conformation. It was predicted that at pH 7 the preferred form of the phosphate group at the catalytically essential threonine 197 (P-Thr197) in the closed form is dianionic, whereas in the open form a monoanionic ionization state is preferred. This dianionic state of P-Thr197, in the closed form, is stabilized by interactions with ionizable residues His87, Arg165, and Lys189. Our calculations predict that the hydroxyl of the Ser residue in the peptide substrate is very difficult to ionize, both in the closed and open structures of the complex. Also, the supposed catalytic base, Asp166, does not seem to have a pK _a appropriate to remove the hydroxyl group proton of the peptide substrate. However, when Ser of the peptide substrate is forced to remain ionized, the predicted pK _a of Asp166 increases strongly, which suggests that the Asp residue is a likely candidate to attract the proton if the Ser residue becomes deprotonated, possibly during some structural change preceding formation of the transition state. Finally, in accord with suggestions made on the basis of the pH-dependence of kinase kinetics, our calculations predict that Glu230 and His87 are the residues responsible for the molecular pK _a values of 6.2 and 8.5, observed in the experiment. Received: 19 October 1998 / Revised version: 12 April 1999 / Accepted: 15 April 1999     

Simulation of protein conformational freedom as a function of pH: constant-pH molecular dynamics using implicit titration

Solution pH is a determinant parameter on protein function and stability, and its inclusion in molecular dynamics simulations is attractive for studies at the molecular level. Current molecular dynamics simulations can consider pH only in a very limited way, through a somewhat arbitrary choice of a set of fixed charges on the titrable sites. Conversely, continuum electrostatic methods that explicitly treat pH effects assume a single protein conformation whose choice is not clearly defined. In this paper we describe a general method that combines both titration and conformational freedom. The method is based on a potential of mean force for implicit titration and combines both usual molecular dynamics and pH-dependent calculations based on continuum methods. A simple implementation of the method, using a mean field approximation, is presented and applied to the bovine pancreatic trypsin inhibitor. We believe that this constant-pH molecular dynamics method, by correctly sampling both charges and conformation, can become a valuable help in the understanding of the dependence of protein function and stability on pH. © 1997 Wiley-Liss Inc.     

Assessing the acid-base and conformational properties of histidine residues in human prion protein (125-228) by means of pK(a) calculations and molecular dynamics simulations

A thorough study of the acid-base behavior of the four histidines and the other titratable residues of the structured domain of human prion protein (125-228) is presented. By using multi-tautomer electrostatic calculations, average titration curves have been built for all titratable residues, using the whole bundles of NMR structures determined at pH 4.5 and 7.0. According to our results, (1) only histidine residues are likely to be involved in the first steps of the pH-driven conformational transition of prion protein; (2) the pK(a)'s of His140 and His177 are approximately 7.0, whereas those of His155 and His187 are < 5.5. 10-ns long molecular dynamics simulations have been performed on five different models, corresponding to the most significant combinations of histidine protonation states. A critical comparison between the available NMR structures and our computational results (1) confirms that His155 and His187 are the residues whose protonation is involved in the conformational rearrangement of huPrP in mildly acidic condition, and (2) shows how their protonation leads to the destructuration of the C-terminal part of HB and to the loss of the last turn of HA that represent the crucial microscopic steps of the rearrangement.     

Folding of the villin headpiece subdomain from random structures. Analysis of the charge distribution as a function of pH

The structure of the 36 residue villin headpiece subdomain is investigated with the electrostatically driven Monte Carlo method. The ECEPP/3 (Empirical Conformational Energy Program for Peptides) force field, plus two different continuum solvation models, were used to describe the conformational energy of the chain with both blocked and unblocked N and C termini. A statistical analysis of an ensemble of ab initio generated conformations was carried out, based on a comparison with a set of ten native-like structures derived from published experimental data, by using rigid geometry and NMR-derived constraints obtained at pH 3.7. The ten native-like structures satisfy the NMR-derived constraints. The whole ensemble of conformations of the terminally unblocked villin headpiece sub-domain, generated by using ECEPP/3 with a continuum solvation model, were subsequently evaluated at pH 3.7 with a potential function that includes ECEPP/3 combined with a fast multigrid boundary element method. At pH 3.7, the lowest-energy conformation found during the conformational search satisfies approximately 70% of both the distance and the dihedral-angle constraints, and possesses the characteristic packing of three phenylalanine residues that constitute the main part of the hydrophobic core of the molecule. On the other hand, computations at pH 3.7 and pH 7.0 for the ten native-like structures satisfying the NMR-derived constraints indicate a substantial change in the charge distribution for each type of amino acid residue with the change in pH. The results of this study provide a basis to understand the effect of the interactions, such as hydrophobicity, charge-charge interaction and solvent polarization, on the stability of this small alpha-helical protein.     

Acidic range titration of HEWL using a constant-pH molecular dynamics method

In this work, we present the first application to a protein of the stochastic constant-pH molecular dynamics (MD) method with the inclusion of proton tautomerism. The acidic titration of HEWL was performed under different conditions. Both generalized reaction field (GRF) and particle mesh Ewald (PME) methods were used in the treatment of the long range electrostatics and, even though the PME simulations revealed to be more stable, the better results were obtained using GRF (pK(a) RMSD of 0.82 for GRF and 1.13 for PME). The results using PME at different dielectric constants (2, 4, and 8) also revealed that there was no significant improvement in pK(a)'s prediction upon increasing the dielectric constant. The secondary structure analysis of HEWL revealed a remarkably stable protein in the acidic pH range. The beta-sheet strands (unlike the alpha-helices) seem to be destabilized upon pH decrease, suggesting that the beta-domain is less stable than the alpha-domain. The four principal alpha-helices were also ordered according to their stability in the acidic pH range and the results (4 < 1 < 2 approximately = 3) were consistent with the ones obtained in thermal denaturation studies.     

Structure and internal dynamics of the bovine pancreatic trypsin inhibitor in aqueous solution from long-time molecular dynamics simulations

Structural and dynamic properties of bovine pancreatic trypsin inhibitor (BPTI) in aqueous solution are investigated using two molecular dynamics (MD) simulations: one of 1.4 ns length and one of 0.8 ns length in which atom-atom distance bounds derived from NMR spectroscopy are included in the potential energy function to make the trajectory satisfy these experimental data more closely. The simulated properties of BPTI are compared with crystal and solution structures of BPTI, and found to be in agreement with the available experimental data. The best agreement with experiment was obtained when atom-atom distance restraints were applied in a time-averaged manner in the simulation. The polypeptide segments found to be most flexible in the MD simulations coincide closely with those showing differences between the crystal and solution structures of BPTI. © 1995 Wiley-Liss, Inc.     

A detailed representation of electrostatic energy in prediction of sequence and pH dependence of protein stability

A molecular mechanics model, previously validated in applications to structure prediction, is shown to reproduce experiment in predictions of protein ionization state, and in predictions of sequence and pH dependence of protein stability. Over a large dataset, 1876 values of ΔΔG of folding, the RMSD is 1.34 kcal/mol. Using an alternative measure of accuracy, either the sign of the calculated ΔΔG agrees with experiment or the absolute value of the deviation is less than 1.0 kcal/mol, 1660 of 1876 data points (88.5%) pass the condition. Relative to models used previously in computer‐aided protein design, the concept, we propose, most responsible for the performance of our model, and for the extensibility to non‐neutral values of pH, is the treatment of electrostatic energy. The electronic structure of the protein is modeled using distributed atomic multipoles. The structured liquid state of the solvent is modeled using a dielectric continuum. A modification to the energetics of the reaction field, induced by the protein in the dielectric continuum, attempts to account for preformed multipoles of solvent water molecules and ions. An adjustable weight (with optimal value.141) applied to the total vacuum energy accounts implicitly for electronic polarization. A threshold distance, beyond which pairwise atomic interactions are neglected, is not used. In searches through subspaces of sequences and conformations, efficiency remains acceptable for useful applications. Proteins 2014; 82:2497–2511. © 2014 Wiley Periodicals, Inc.     

Fuzzy cluster analysis of molecular dynamics trajectories.

We propose fuzzy clustering as a method to analyze molecular dynamics (MD) trajectories, especially of proteins and polypeptides. A fuzzy cluster analysis locates classes of similar three-dimensional conformations explored during a molecular dynamics simulation. The method can be readily applied to results from both equilibrium and nonequilibrium simulations, with clustering on either global or local structural parameters. The potential of this technique is illustrated by results from fuzzy cluster analyses of trajectories from MD simulations of various fragments of human parathyroid hormone (PTH). For large molecules, it is more efficient to analyze the clustering of root-mean-square distances between conformations comprising the trajectory. We found that the results of the clustering analysis were unambiguous, in terms of the optimal number of clusters of conformations, for the majority of the trajectories examined. The conformation closest to the cluster center can be chosen as being representative of the class of structures making up the cluster, and can be further analyzed, for example, in terms of its secondary structure. The CPU time used by the cluster analysis was negligible compared to the MD simulation time.     

Refinement of homology-based protein structures by molecular dynamics simulation techniques

The use of classical molecular dynamics simulations, performed in explicit water, for the refinement of structural models of proteins generated ab initio or based on homology has been investigated. The study involved a test set of 15 proteins that were previously used by Baker and coworkers to assess the efficiency of the ROSETTA method for ab initio protein structure prediction. For each protein, four models generated using the ROSETTA procedure were simulated for periods of between 5 and 400 nsec in explicit solvent, under identical conditions. In addition, the experimentally determined structure and the experimentally derived structure in which the side chains of all residues had been deleted and then regenerated using the WHATIF program were simulated and used as controls. A significant improvement in the deviation of the model structures from the experimentally determined structures was observed in several cases. In addition, it was found that in certain cases in which the experimental structure deviated rapidly from the initial structure in the simulations, indicating internal strain, the structures were more stable after regenerating the side-chain positions. Overall, the results indicate that molecular dynamics simulations on a tens to hundreds of nanoseconds time scale are useful for the refinement of homology or ab initio models of small to medium-size proteins.     

X-ray crystal structures of a severely desiccated protein.

Unlike most protein crystals, form IX of bovine pancreatic ribonuclease A diffracts well when severely dehydrated. Crystal structures have been solved after 2.5 and 4 days of desiccation with CaSO4, at 1.9 and 2.0 A resolution, respectively. The two desiccated structures are very similar. An RMS displacement of 1.6 A is observed for main-chain atoms in each structure when compared to the hydrated crystal structure with some large rearrangements observed in loop regions. The structural changes are the result of intermolecular contacts formed by strong electrostatic interactions in the absence of a high dielectric medium. The electron density is very diffuse for some surface loops, consistent with a very disordered structure. This disorder is related to the conformational changes. These results help explain conformational changes during the lyophilization of protein and the associated phenomena of denaturation and molecular memory.     

Exploration of disorder in protein structures by X-ray restrained molecular dynamics

Conformational disorder in crystal structures of ribonuclease-A and crambin is studied by including two independent structures in least-squares optimizations against X-ray data. The optimizations are carried out by X-ray restrained molecular dynamics (simulated annealing refinement) and by conventional least-squares optimization. Starting from two identical structures, the optimizations against X-ray data lead to significant deviations between the two, with rms backbone displacements of 0.45 A for refinement of ribonuclease at 1.53 A resolution, and 0.31 A for crambin at 0.945 A. More than 15 independent X-ray restrained molecular dynamics runs have been carried out for ribonuclease, and the displacements between the resulting structures are highly reproducible for most atoms. These include residues with two or more conformations with significant dihedral angle differences and alternative hydrogen bonding, as well as groups of residues that undergo displacements that are suggestive of rigid-body librations. The crystallographic R-values obtained are approximately 13%, as compared to 15.3% for a comparable refinement with a single structure. Least-squares optimization without an intervening restrained molecular dynamics stage is sufficient to reproduce most of the observed displacements. Similar results are obtained for crambin, where the higher resolution of the X-ray data allows for refinement of unconstrained individual anisotropic temperature factors. These are shown to be correlated with the displacements in the two-structure refinements.     

Prediction of protein secondary structures from conformational biases

We use LINUS (the "Local Independently Nucleated Units of Structure"), a procedure developed by Srinivasan and Rose, to provide a physical interpretation of and predict the secondary structures of proteins. The secondary structure type at a given site is identified by the largest conformational bias during short simulations. We examine the rate of successful prediction as a function of temperature and the interaction window. At high temperatures, there is a large propensity for the establishment of beta-strands whereas alpha-helices appear only when the temperature is lower than a certain threshold value. It is found that there exists an optimal temperature at which the correct secondary structures are predicted most accurately. We find that this temperature is close to the peak temperature of the specific heat. Changing the interaction window or carrying out longer simulations approaching equilibrium lead to little change in the optimal success rate. Our findings are in accord with the observation by Srinivasan and Rose that the secondary structures are mainly determined by local interactions and appear in the early stage of folding.     

Visualizing global properties of a molecular dynamics trajectory

Molecular dynamics (MD) trajectories are very large data sets that contain substantial information about the dynamic behavior of a protein. Condensing these data into a form that can provide intuitively useful understanding of the molecular behavior during the trajectory is a substantial challenge that has received relatively little attention. Here, we introduce the sigma‐r plot, a plot of the standard deviation of intermolecular distances as a function of that distance. This representation of global dynamics contains within a single, one‐dimensional plot, the average range of motion between pairs of atoms within a macromolecule. Comparison of sigma‐r plots calculated from 10 ns trajectories of proteins representing the four major SCOP fold classes indicates diversity of dynamic behaviors which are recognizably different among the four classes. Differences in domain structure and molecular weight also produce recognizable features in sigma‐r plots, reflective of differences in global dynamics. Plots generated from trajectories with progressively increasing simulation time reflect the increased sampling of the structural ensemble as a function of time. Single amino acid replacements can give rise to changes in global dynamics detectable through comparison of sigma‐r plots. Dynamic behavior of substructures can be monitored by careful choice of interatomic vectors included in the calculation. These examples provide demonstrations of the utility of the sigma‐r plot to provide a simple measure of the global dynamics of a macromolecule. Proteins 2016; 84:82–91. © 2015 Wiley Periodicals, Inc.     

A molecular dynamics approach for the generation of complete protein structures from limited coordinate data

Generation of full protein coordinates from limited information, e.g., the Cα coordinates, is an important step in protein homology modeling and structure determination, and molecular dynamics (MD) simulations may prove to be important in this task. We describe a new method, in which the protein backbone is built quickly in a rather crude way and then refined by minimization techniques. Subsequently, the side chains are positioned using extensive MD calculations. The method is tested on two proteins, and results compared to proteins constructed using two other MD-based methods. In the first method, we supplemented an existing backbone building method with a new procedure to add side chains. The second one largely consists of available methodology. The constructed proteins are compared to the corresponding X-ray structures, which became available during this study, and they are in good agreement (backbone RMS values of 0.5–0.7 Å, and all-atom RMS values of 1.5–1.9 Å). This comparative study indicates that extensive MD simulations are able, to some extent, to generate details of the native protein structure, and may contribute to the development of a standardized methodology to predict reliably (parts of) protein structures when only partial coordinate data are available. © 1994 John Wiley & Sons, Inc.     

Prediction of transition metal-binding sites from apo protein structures

Metal ions are crucial for protein function. They participate in enzyme catalysis, play regulatory roles, and help maintain protein structure. Current tools for predicting metal-protein interactions are based on proteins crystallized with their metal ions present (holo forms). However, a majority of resolved structures are free of metal ions (apo forms). Moreover, metal binding is a dynamic process, often involving conformational rearrangement of the binding pocket. Thus, effective predictions need to be based on the structure of the apo state. Here, we report an approach that identifies transition metal-binding sites in apo forms with a resulting selectivity >95%. Applying the approach to apo forms in the Protein Data Bank and structural genomics initiative identifies a large number of previously unknown, putative metal-binding sites, and their amino acid residues, in some cases providing a first clue to the function of the protein.     

Prediction of protein oligomer structures using GALAXY in CASP13

Many proteins need to form oligomers to be functional, so oligomer structures provide important clues to biological roles of proteins. Prediction of oligomer structures therefore can be a useful tool in the absence of experimentally resolved structures. In this article, we describe the server and human methods that we used to predict oligomer structures in the CASP13 experiment. Performances of the methods on the 42 CASP13 oligomer targets consisting of 30 homo-oligomers and 12 hetero-oligomers are discussed. Our server method, Seok-assembly, generated models with interface contact similarity measure greater than 0.2 as model 1 for 11 homo-oligomer targets when proper templates existed in the database. Model refinement methods such as loop modeling and molecular dynamics (MD)-based overall refinement failed to improve model qualities when target proteins have domains not covered by templates or when chains have very small interfaces. In human predictions, additional experimental data such as low-resolution electron microscopy (EM) map were utilized. EM data could assist oligomer structure prediction by providing a global shape of the complex structure.     

Protein–protein structure prediction by scoring molecular dynamics trajectories of putative poses

The prediction of protein–protein interactions and their structural configuration remains a largely unsolved problem. Most of the algorithms aimed at finding the native conformation of a protein complex starting from the structure of its monomers are based on searching the structure corresponding to the global minimum of a suitable scoring function. However, protein complexes are often highly flexible, with mobile side chains and transient contacts due to thermal fluctuations. Flexibility can be neglected if one aims at finding quickly the approximate structure of the native complex, but may play a role in structure refinement, and in discriminating solutions characterized by similar scores. We here benchmark the capability of some state‐of‐the‐art scoring functions (BACH‐SixthSense, PIE/PISA and Rosetta) in discriminating finite‐temperature ensembles of structures corresponding to the native state and to non‐native configurations. We produce the ensembles by running thousands of molecular dynamics simulations in explicit solvent starting from poses generated by rigid docking and optimized in vacuum. We find that while Rosetta outperformed the other two scoring functions in scoring the structures in vacuum, BACH‐SixthSense and PIE/PISA perform better in distinguishing near‐native ensembles of structures generated by molecular dynamics in explicit solvent. Proteins 2016; 84:1312–1320. © 2016 Wiley Periodicals, Inc.