Normal-mode refinement of anisotropic thermal parameters for potassium channel KcsA at 3.2 A crystallographic resolution

We report a normal-mode method for anisotropic refinement of membrane-protein structures, based on a hypothesis that the global near-native-state disordering of membrane proteins in crystals follows low-frequency normal modes. Thus, a small set of modes is sufficient to represent the anisotropic thermal motions in X-ray crystallographic refinement. By applying the method to potassium channel KcsA at 3.2 A, we obtained a structural model with an improved fit with the diffraction data. Moreover, the improved electron density maps allowed for large structural adjustments for 12 residues in each subunit, including the rebuilding of 3 missing side chains. Overall, the anisotropic KcsA structure at 3.2 A was systematically closer to a 2.0 A KcsA structure, especially in the selectivity filter. Furthermore, the anisotropic thermal ellipsoids from the refinement revealed functionally relevant structural flexibility. We expect this method to be a valuable tool for structural refinement of many membrane proteins with moderate-resolution diffraction data.     

Comparison of energy-minimized crystal structures of 2,3-dilauroyl-D-glycerol, 3-palmitoyl-DL-glycerol-1-phosphorylethanolamine and 1,2-dilauroyl-DL-phosphatidylethanolamine:acetic acid

Computational procedures have been developed by which the total energy of a lipid multibilayer can be calculated and minimized. The energy is expressed as a sum of non-bonded, electrostatic, hydrogen bonded and torsional energy terms and includes intramolecular and intermolecular components. Calculations were carried out on three lipid crystals for which structural data are available from X-ray diffraction analysis. For each crystal, the energy was minimized as a function of all bond rotations, molecular rotations and translations and the lattice constants. The minimized structures differed by only small amounts from the experimental structures, which confirms the validity of the current set of energy functions and parameters for use with lipids. The intermolecular energy of each crystal is analyzed in terms of lateral interactions, interactions between the two monolayers of the same bilayer and interactions between bilayers. The intermolecular non-bonded energy per CH2 or CH3 group in the acyl chains is also given.     

Normal mode refinement: crystallographic refinement of protein dynamic structure applied to human lysozyme.

A new method of dynamic structure refinement of protein x-ray crystallography, normal mode refinement, is developed. In this method the Debye-Waller factor is expanded in terms of the low-frequency normal modes and external normal modes, whose amplitudes and couplings are optimized in the process of crystallographic refinement. By this method, internal and external contributions to the atomic fluctuations can be separated. Also, anisotropic atomic fluctuations and their interatomic correlations can be determined experimentally even with a relatively small number of adjustable parameters. The method is applied to the analysis of experimental data of human lysozyme to reveal its dynamic structure.     

Large-scale characteristics of the energy landscape in protein-protein interactions

Characterization of intermolecular energy landscapes in protein-protein interactions is important for understanding the mechanisms of these interactions as well as for designing better protein docking methods. A simplified representation of the landscape was used for a systematic study of its large-scale characteristics in a large nonredundant dataset of protein complexes. The focus of the study is on the basic features of the low-resolution energy basins and their distribution on the landscape. The results clearly show that, in general, the number of such basins is small, these basins are well formed, correlated with actual binding modes, and the pattern of basins distribution depends on the type of the complex. For docking studies, the results suggest that adequate starting points for the structural refinement are detectable by low-resolution procedures and the number of such starting points is relatively small.     

Normal mode refinement: crystallographic refinement of protein dynamic structure. I. Theory and test by simulated diffraction data.

A dynamic structure refinement method for X-ray crystallography, referred to as the normal mode refinement, is proposed. The Debye-Waller factor is expanded in terms of the low-frequency normal modes whose amplitudes and eigenvectors are experimentally optimized in the process of the crystallographic refinement. In this model, the atomic fluctuations are treated as anisotropic and concerted. The normal modes of the external motion (TLS model) are also introduced to cover the factors other than the internal fluctuations, such as the lattice disorder and diffusion. A program for the normal mode refinement (NM-REF) has been developed. The method has first been tested against simulated diffraction data for human lysozyme calculated by a Monte Carlo simulation. Applications of the method have demonstrated that the normal mode refinement has: (1) improved the fitting to the diffraction data, even with fewer adjustable parameters; (2) distinguished internal fluctuations from external ones; (3) determined anisotropic thermal factors; and (4) identified concerted fluctuations in the protein molecule.     

Elastic network normal mode dynamics reveal the GPCR activation mechanism

G‐protein‐coupled receptors (GPCR) are a family of membrane‐embedded metabotropic receptors which translate extracellular ligand binding into an intracellular response. Here, we calculate the motion of several GPCR family members such as the M2 and M3 muscarinic acetylcholine receptors, the A_2A adenosine receptor, the β₂‐adrenergic receptor, and the CXCR4 chemokine receptor using elastic network normal modes. The normal modes reveal a dilation and a contraction of the GPCR vestibule associated with ligand passage, and activation, respectively. Contraction of the vestibule on the extracellular side is correlated with cavity formation of the G‐protein binding pocket on the intracellular side, which initiates intracellular signaling. Interestingly, the normal modes of rhodopsin do not correlate well with the motion of other GPCR family members. Electrostatic potential calculation of the GPCRs reveal a negatively charged field around the ligand binding site acting as a siphon to draw‐in positively charged ligands on the membrane surface. Altogether, these results expose the GPCR activation mechanism and show how conformational changes on the cell surface side of the receptor are allosterically translated into structural changes on the inside. Proteins 2014; 82:579–586. © 2013 Wiley Periodicals, Inc.     

Sequence,Structure and Ligand Binding Evolution of Rhodopsin-Like G Protein-Coupled Receptors: A Crystal Structure-Based Phylogenetic Analysis

G protein-coupled receptors (GPCRs) form the largest family of membrane receptors in the human genome. Advances in membrane protein crystallization so far resulted in the determination of 24 receptors available as high-resolution atomic structures. We performed the first phylogenetic analysis of GPCRs based on the available set of GPCR structures. We present a new phylogenetic tree of known human rhodopsin-like GPCR sequences based on this structure set. We can distinguish the three separate classes of small-ligand binding GPCRs, peptide binding GPCRs, and olfactory receptors. Analyzing different structural subdomains, we found that small molecule binding receptors most likely have evolved from peptide receptor precursors, with a rhodopsin/S1PR1 ancestor, most likely an ancestral opsin, forming the link between both classes. A light-activated receptor therefore seems to be the origin of the small molecule hormone receptors of the central nervous system. We find hints for a common evolutionary path of both ligand binding site and central sodium/water binding site. Surprisingly, opioid receptors exhibit both a binding cavity and a central sodium/water binding site similar to the one of biogenic amine receptors instead of peptide receptors, making them seemingly prone to bind small molecule ligands, e.g. opiates. Our results give new insights into the relationship and the pharmacological properties of rhodopsin-like GPCRs.     

Refinement of F-Actin Model against Fiber Diffraction Data by Long-Range Normal Modes

The atomic model of F-actin was refined against fiber diffraction data using long-range normal modes as adjustable parameters to account for the collective long-range filamentous deformations. To determine the effect of long-range deformations on the refinement, each of the four domains of G-actin was treated as a rigid body. It was found that among all modes, the bending modes make the most significant contributions to the improvement of the refinement. Inclusion of only 7–9 bending modes as adjustable parameters yielded a lowest R-factor of 6.3%. These results demonstrate that employing normal modes as refinement parameters has the advantage of using a small number of adjustable parameters to achieve a good fitting efficiency. Such a refinement procedure may therefore prevent the refinement from overfitting the structural model. More importantly, the results of this study demonstrate that, for any fiber diffraction data, a substantial amount of refinement error is due to long-range deformations, especially the bending, of the filaments. The effects of these intrinsic deformations cannot be easily compensated for by adjusting local structural parameters, and must be properly accounted for in the refinement to achieve improved fit of refined models with experimental diffraction data.     

Toward better refinement of comparative models: predicting loops in inexact environments

Achieving atomic-level accuracy in comparative protein models is limited by our ability to refine the initial, homolog-derived model closer to the native state. Despite considerable effort, progress in developing a generalized refinement method has been limited. In contrast, methods have been described that can accurately reconstruct loop conformations in native protein structures. We hypothesize that loop refinement in homology models is much more difficult than loop reconstruction in crystal structures, in part, because side-chain, backbone, and other structural inaccuracies surrounding the loop create a challenging sampling problem; the loop cannot be refined without simultaneously refining adjacent portions. In this work, we single out one sampling issue in an artificial but useful test set and examine how loop refinement accuracy is affected by errors in surrounding side-chains. In 80 high-resolution crystal structures, we first perturbed 6-12 residue loops away from the crystal conformation, and placed all protein side chains in non-native but low energy conformations. Even these relatively small perturbations in the surroundings made the loop prediction problem much more challenging. Using a previously published loop prediction method, median backbone (N-Calpha-C-O) RMSD's for groups of 6, 8, 10, and 12 residue loops are 0.3/0.6/0.4/0.6 A, respectively, on native structures and increase to 1.1/2.2/1.5/2.3 A on the perturbed cases. We then augmented our previous loop prediction method to simultaneously optimize the rotamer states of side chains surrounding the loop. Our results show that this augmented loop prediction method can recover the native state in many perturbed structures where the previous method failed; the median RMSD's for the 6, 8, 10, and 12 residue perturbed loops improve to 0.4/0.8/1.1/1.2 A. Finally, we highlight three comparative models from blind tests, in which our new method predicted loops closer to the native conformation than first modeled using the homolog template, a task generally understood to be difficult. Although many challenges remain in refining full comparative models to high accuracy, this work offers a methodical step toward that goal.     

Protein purification and preliminary crystallographic analysis of human Lyn tyrosine kinase

Lyn is a member of the Src family of non-receptor protein kinase. As well as all members of the Src family, Lyn is thought to participate in signal transduction from cell surface receptors. The crystal structure of Lyn would have a better understanding of Lyn function in various cells. For the purpose of crystallization, C-terminal catalytic segment of human Lyn kinase conjugating hexahistidine purification tag (His-tag) was expressed in Sf21 insect cells. After first step purification utilizing His-tag, an anion-exchange chromatogram yielded four major peaks which had distinguishable phosphorylation manner as judged by Western blot analysis, Native-PAGE analysis and kinase activity measurements. The fractioned samples were separately examined for crystallization screening using a commercial available screening kit. The mono-phosphorylated protein was crystallized with a small rod-shaped and needle clusters. The higher phosphorylated samples corresponding to the other three fractions on the anion-exchange chromatogram were aggregated or precipitated under the above conditions. A crystal of the mono-phosphorylated sample was diffracted to 3.2 Å with synchrotron source at Photon Factory and a complete X-ray diffraction data set was collected. The coarse structure was solved by a molecular replacement method and further structural refinement is currently underway.     

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.     

Assisted assignment of ligands corresponding to unknown electron density

A semi-automated computational procedure to assist in the identification of bound ligands from unknown electron density has been developed. The atomic surface surrounding the density blob is compared to a library of three-dimensional ligand binding surfaces extracted from the Protein Data Bank (PDB). Ligands corresponding to surfaces which share physicochemical texture and geometric shape similarities are considered for assignment. The method is benchmarked against a set of well represented ligands from the PDB, in which we show that we can identify the correct ligand based on the corresponding binding surface. Finally, we apply the method during model building and refinement stages from structural genomics targets in which unknown density blobs were discovered. A semi-automated computational method is described which aims to assist crystallographers with assigning the identity of a ligand corresponding to unknown electron density. Using shape and physicochemical similarity assessments between the protein surface surrounding the density and a database of known ligand binding surfaces, a plausible list of candidate ligands are identified for consideration. The method is validated against highly observed ligands from the Protein Data Bank and results are shown from its use in a high-throughput structural genomics pipeline.     

Development, validation, and application of adapted PEOE charges to estimate pKa values of functional groups in protein-ligand complexes

For routine pK(a) calculations of protein-ligand complexes in drug design, the PEOE method to compute partial charges was modified. The new method is applicable to a large scope of proteins and ligands. The adapted charges were parameterized using experimental free energies of solvation of amino acids and small organic ligands. For a data set of 80 small organic molecules, a correlation coefficient of r(2) = 0.78 between calculated and experimental solvation free energies was obtained. Continuum electrostatics pK(a) calculations based on the Poisson-Boltzmann equation were carried out on a validation set of nine proteins for which 132 experimental pK(a) values are known. In total, an overall RMSD of 0.88 log units between calculated and experimentally determined data is achieved. In particular, the predictions of significantly shifted pK(a) values are satisfactory, and reasonable estimates of protonation states in the active sites of lysozyme and xylanase could be obtained. Application of the charge-assignment and pK(a)-calculation procedure to protein-ligand complexes provides clear structural interpretations of experimentally observed changes of protonation states of functional groups upon complex formation. This information is essential for the interpretation of thermodynamic data of protein-ligand complex formation and provides the basis for the reliable factorization of the free energy of binding in enthalpic and entropic contributions. The modified charge-assignment procedure forms the basis for future automated pK(a) calculations of protein-ligand complexes.     

A new approach for determining low-frequency normal modes in macromolecules

A new method for calculating a set of low-frequency normal modes in macromolecules is proposed and applied to the case of proteins. In a first step, the protein chain is partitioned into blocks of one or more residues and the low-frequency modes are evaluated at a low-resolution level by combining the local translations and rotations of each block. In a second step, these low-resolution modes are perturbed by high-frequency modes explicitly calculated in each block, thus leading to the exact low-frequency modes. The procedure is tested for three cases–decaalanine, icosaleucin, and crambin–using a perturbation-iteration scheme in the second step. Convergence properties and numerical accuracy are assessed and tested for various partitions. The low-resolution modes obtained in the first step are always found to be good starting approximations. Potential advantages of the method include a central processing unit time roughly N² dependent on the size of the problem (N being the number of degrees of freedom), the possibility of using parallel processing, the nonrequirement for loading the complete mass-weighted second-derivative input matrix into central memory, and the possibility of introducing in the procedure further structural hierarchy, such as secondary structures or motifs. In addition, any improvement or refinement of the algorithm benefits from the efficient formalism of the effective Hamiltonian theory. © 1994 John Wiley & Sons, Inc.     

SuperStar: comparison of CSD and PDB-based interaction fields as a basis for the prediction of protein-ligand interactions.

SuperStar is an empirical method for identifying interaction sites in proteins, based entirely on the experimental information about non-bonded interactions, present in the IsoStar database. The interaction information in IsoStar is contained in scatterplots, which show the distribution of a chosen probe around structure fragments. SuperStar breaks a template molecule (e.g. a protein binding site) into structural fragments which correspond to those in the scatterplots. The scatterplots are then superimposed on the corresponding parts of the template and converted into a composite propensity map.The original version of SuperStar was based entirely on scatterplots from the CSD. Here, scatterplots based on protein-ligand interactions are implemented in SuperStar, and validated on a test set of 122 X-ray structures of protein-ligand complexes. In this validation, propensity maps are compared with the experimentally observed positions of ligand atoms of comparable types. Although non-bonded interaction geometries in small molecule structures are similar to those found in protein-ligand complexes, their relative frequencies of occurrence are different. Polar interactions are more common in the first class of structures, while interactions between hydrophobic groups are more common in protein crystals. In general, PDB and CSD-based SuperStar maps appear equally successful in the prediction of protein-ligand interactions. PDB-based maps are more suitable to identify hydrophobic pockets, and inherently take into account the experimental uncertainties of protein atomic positions. If the protonation state of a histidine, aspartate or glutamate protein side-chain is known, specific CSD-based maps for that protonation state are preferred over PDB-based maps which represent an ensemble of protonation states.     

Identification of substrate binding sites in enzymes by computational solvent mapping

Enzyme structures determined in organic solvents show that most organic molecules cluster in the active site, delineating the binding pocket. We have developed algorithms to perform solvent mapping computationally, rather than experimentally, by placing molecular probes (small molecules or functional groups) on a protein surface, and finding the regions with the most favorable binding free energy. The method then finds the consensus site that binds the highest number of different probes. The probe-protein interactions at this site are compared to the intermolecular interactions seen in the known complexes of the enzyme with various ligands (substrate analogs, products, and inhibitors). We have mapped thermolysin, for which experimental mapping results are also available, and six further enzymes that have no experimental mapping data, but whose binding sites are well characterized. With the exception of haloalkane dehalogenase, which binds very small substrates in a narrow channel, the consensus site found by the mapping is always a major subsite of the substrate-binding site. Furthermore, the probes at this location form hydrogen bonds and non-bonded interactions with the same residues that interact with the specific ligands of the enzyme. Thus, once the structure of an enzyme is known, computational solvent mapping can provide detailed and reliable information on its substrate-binding site. Calculations on ligand-bound and apo structures of enzymes show that the mapping results are not very sensitive to moderate variations in the protein coordinates.     

An analysis of core deformations in protein superfamilies

An analysis is presented on how structural cores modify their shape across homologous proteins, and whether or not a relationship exists between these structural changes and the vibrational normal modes that proteins experience as a result of the topological constraints imposed by the fold. A set of 35 representative, well-populated protein families is studied. The evolutionary directions of deformation are obtained by using multiple structural alignments to superimpose the structures and extract a conserved core, together with principal components analysis to extract the main deformation modes from the three-dimensional superimposition. In parallel, a low-resolution normal mode analysis technique is employed to study the properties of the mechanical core plasticity of these same families. We show that the evolutionary deformations span a low dimensional space of 4-5 dimensions on average. A statistically significant correspondence exists between these principal deformations and the approximately 20 slowest vibrational modes accessible to a particular topology. We conclude that, to a significant extent, the structural response of a protein topology to sequence changes takes place by means of collective deformations along combinations of a small number of low-frequency modes. The findings have implications in structure prediction by homology modeling.     

The free energy landscape of small molecule unbinding

The spontaneous dissociation of six small ligands from the active site of FKBP (the FK506 binding protein) is investigated by explicit water molecular dynamics simulations and network analysis. The ligands have between four (dimethylsulphoxide) and eleven (5-diethylamino-2-pentanone) non-hydrogen atoms, and an affinity for FKBP ranging from 20 to 0.2 mM. The conformations of the FKBP/ligand complex saved along multiple trajectories (50 runs at 310 K for each ligand) are grouped according to a set of intermolecular distances into nodes of a network, and the direct transitions between them are the links. The network analysis reveals that the bound state consists of several subbasins, i.e., binding modes characterized by distinct intermolecular hydrogen bonds and hydrophobic contacts. The dissociation kinetics show a simple (i.e., single-exponential) time dependence because the unbinding barrier is much higher than the barriers between subbasins in the bound state. The unbinding transition state is made up of heterogeneous positions and orientations of the ligand in the FKBP active site, which correspond to multiple pathways of dissociation. For the six small ligands of FKBP, the weaker the binding affinity the closer to the bound state (along the intermolecular distance) are the transition state structures, which is a new manifestation of Hammond behavior. Experimental approaches to the study of fragment binding to proteins have limitations in temporal and spatial resolution. Our network analysis of the unbinding simulations of small inhibitors from an enzyme paints a clear picture of the free energy landscape (both thermodynamics and kinetics) of ligand unbinding.     

Normal mode calculations of icosahedral viruses with full dihedral flexibility by use of molecular symmetry

The study of the dynamics and thermodynamics of small icosahedral virus capsids is an active field of research. Normal mode analysis is one of the computational tools that can provide important insights into the conformational changes of the virus associated with cell entry or caused by changing of the physicochemical environment. Normal mode analysis of virus capsids has been limited due to the size of these systems, which often exceed 50,000 residues. Here we present the first normal mode calculation with full dihedral flexibility of several virus capsids, including poliovirus, rhinovirus, and cowpea chlorotic mottle virus. The calculations were made possible by applying group theoretical methods, which greatly simplified the calculations without any approximation beyond the all-atom force field representations in general use for smaller protein systems. Since a full Cartesian basis set was too large to be handled by the available computer memory, we used a basis set that includes all internal dihedral angles of the system with the exception of the peptide bonds, which were assumed rigid. The fluctuations of the normal modes are shown to correlate well with crystallographic temperature factors. The motions of the first several normal modes of each symmetry type are described. A hinge bending motion in poliovirus was found that may be involved in the mechanism by which bound small molecules inhibit conformational changes of the capsid. Fully flexible normal mode calculations of virus capsids are expected to increase our understanding of virus dynamics and thermodynamics, and can be useful in the refinement of cryo-electron microscopy structures of viruses.