Normal mode analysis calculation for a full-atom model with a smaller number of degrees of freedom for huge protein molecules.

The number of degrees of freedom (DOF), N, in normal mode analysis (NMA) calculations of proteins is a crucial problem in huge systems because the eigenvalue problem of an N-by-N matrix must be solved. If it were possible to perform the analysis with a smaller number of DOF for the same system with minimal deterioration in accuracy, this would make a significant impact on the computational study of protein dynamics. We examined two models in which the number of DOF was reduced. Both of them adopted a full-atom model with dihedral angles as independent variables. In one model, side-chain dihedral angles, χ's, and a main-chain dihedral angle, ω, were fixed and only the main-chain dihedral angles, ϕ and ψ, were variable. In another model, the dihedral angles around virtual bonds that connect neighboring Cα atoms were tested. The number of DOFs for the two models was two and one per residue, respectively. The residue-by-residue fluctuation profiles for atoms and dihedral angles were well reproduced in both models. The motion of atoms in the individual lowest-frequency normal modes of the two models was also very similar to those of the original model in which all rotatable dihedral angles were variable. Consequently, these models could predict large-amplitude concerted motion. These results also imply that proteins in a full-atom model can undergo only limited large-scale conformational changes around the native conformation, and consequently, NMA results do not strongly depend on the independent variables adopted.

Dynamic properties of oligomers that characterize low-frequency normal modes.

Dynamics of oligomeric proteins (one trimer, two tetramers, and one hexamer) were studied by elastic network model-based normal mode analysis to characterize their large-scale concerted motions. First, the oligomer motions were simplified by considering rigid-body motions of individual subunits. The subunit motions were resolved into three components in a cylindrical coordinate system: radial, tangential, and axial ones. Single component is dominant in certain normal modes. However, more than one component is mixed in others. The subunits move symmetrically in certain normal modes and as a standing wave with several wave nodes in others. Secondly, special attention was paid to atoms on inter-subunit interfaces. Their displacement vectors were decomposed into intra-subunit deformative (internal) and rigid-body (external) motions in individual subunits. The fact that most of the cosines of the internal and external motion vectors were negative for the atoms on the inter-subunit interfaces, indicated their opposing movements. Finally, a structural network of residues defined for each normal mode was investigated; the network was constructed by connecting two residues in contact and moving coherently. The centrality measure "betweenness" of each residue was calculated for the networks. Several residues with significantly high betweenness were observed on the inter-subunit interfaces. The results indicate that these residues are responsible for oligomer dynamics. It was also observed that amino acid residues with significantly high betweenness were more conservative. This supports that the betweenness is an effective characteristic for identifying an important residue in protein dynamics.

A study of CDR3 loop dynamics reveals distinct mechanisms of peptide recognition by T-cell receptors exhibiting different levels of cross-reactivity.

T-cell receptors (TCRs) can productively interact with many different peptides bound within the MHC binding groove. This property varies with the level of cross-reactivity of TCRs; some TCRs are particularly hyper cross-reactive while others exhibit greater specificity. To elucidate the mechanism behind these differences, we studied five TCRs in complex with the same class II MHC (1Ab )-peptide (3K), that are known to exhibit different levels of cross-reactivity. Although these complexes have similar binding affinities, the interface areas between the TCR and the peptide-MHC (pMHC) differ significantly. We investigated static and dynamic structural features of the TCR-pMHC complexes and of TCRs in a free state, as well as the relationship between binding affinity and interface area. It was found that the TCRs known to exhibit lower levels of cross-reactivity bound to pMHC using an induced-fitting mechanism, forming large and tight interfaces rich in specific hydrogen bonds. In contrast, TCRs known to exhibit high levels of cross-reactivity used a more rigid binding mechanism where non-specific π-interactions involving the bulky Trp residue in CDR3ß dominated. As entropy loss upon binding in these highly degenerate and rigid TCRs is smaller than that in less degenerate TCRs, they can better tolerate changes in residues distal from the major contacts with MHC-bound peptide. Hence, our dynamics study revealed that differences in the peptide recognition mechanisms by TCRs appear to correlate with the levels of T-cell cross-reactivity.

New tools and functions in data-out activities at Protein Data Bank Japan (PDBj).

The Protein Data Bank Japan (PDBj), a member of the worldwide Protein Data Bank (wwPDB), accepts and processes the deposited data of experimentally determined biological macromolecular structures. In addition to archiving the PDB data in collaboration with the other wwPDB partners, PDBj also provides a wide range of original and unique services and tools, which are continuously improved and updated. Here, we report the new RDB PDBj Mine 2, the WebGL molecular viewer Molmil, the ProMode-Elastic server for normal mode analysis, a virtual reality system for the eF-site protein electrostatic molecular surfaces, the extensions of the Omokage search for molecular shape similarity, and the integration of PDBj and BMRB searches.

Normal mode analysis as a method to derive protein dynamics information from the Protein Data Bank.

Normal mode analysis (NMA) can facilitate quick and systematic investigation of protein dynamics using data from the Protein Data Bank (PDB). We developed an elastic network model-based NMA program using dihedral angles as independent variables. Compared to the NMA programs that use Cartesian coordinates as independent variables, key attributes of the proposed program are as follows: (1) chain connectivity related to the folding pattern of a polypeptide chain is naturally embedded in the model; (2) the full-atom system is acceptable, and owing to a considerably smaller number of independent variables, the PDB data can be used without further manipulation; (3) the number of variables can be easily reduced by some of the rotatable dihedral angles; (4) the PDB data for any molecule besides proteins can be considered without coarse-graining; and (5) individual motions of constituent subunits and ligand molecules can be easily decomposed into external and internal motions to examine their mutual and intrinsic motions. Its performance is illustrated with an example of a DNA-binding allosteric protein, a catabolite activator protein. In particular, the focus is on the conformational change upon cAMP and DNA binding, and on the communication between their binding sites remotely located from each other. In this illustration, NMA creates a vivid picture of the protein dynamics at various levels of the structures, i.e., atoms, residues, secondary structures, domains, subunits, and the complete system, including DNA and cAMP. Comparative studies of the specific protein in different states, e.g., apo- and holo-conformations, and free and complexed configurations, provide useful information for studying structurally and functionally important aspects of the protein.

Characterization of protein folding by a Φ-value calculation with a statistical-mechanical model.

The Φ-value analysis approach provides information about transition-state structures along the folding pathway of a protein by measuring the effects of an amino acid mutation on folding kinetics. Here we compared the theoretically calculated Φ values of 27 proteins with their experimentally observed Φ values; the theoretical values were calculated using a simple statistical-mechanical model of protein folding. The theoretically calculated Φ values reflected the corresponding experimentally observed Φ values with reasonable accuracy for many of the proteins, but not for all. The correlation between the theoretically calculated and experimentally observed Φ values strongly depends on whether the protein-folding mechanism assumed in the model holds true in real proteins. In other words, the correlation coefficient can be expected to illuminate the folding mechanisms of proteins, providing the answer to the question of which model more accurately describes protein folding: the framework model or the nucleation-condensation model. In addition, we tried to characterize protein folding with respect to various properties of each protein apart from the size and fold class, such as the free-energy profile, contact-order profile, and sensitivity to the parameters used in the Φ-value calculation. The results showed that any one of these properties alone was not enough to explain protein folding, although each one played a significant role in it. We have confirmed the importance of characterizing protein folding from various perspectives. Our findings have also highlighted that protein folding is highly variable and unique across different proteins, and this should be considered while pursuing a unified theory of protein folding.

Normal mode analysis based on an elastic network model for biomolecules in the Protein Data Bank, which uses dihedral angles as independent variables.

We have developed a computer program, named PDBETA, that performs normal mode analysis (NMA) based on an elastic network model that uses dihedral angles as independent variables. Taking advantage of the relatively small number of degrees of freedom required to describe a molecular structure in dihedral angle space and a simple potential-energy function independent of atom types, we aimed to develop a program applicable to a full-atom system of any molecule in the Protein Data Bank (PDB). The algorithm for NMA used in PDBETA is the same as the computer program FEDER/2, developed previously. Therefore, the main challenge in developing PDBETA was to find a method that can automatically convert PDB data into molecular structure information in dihedral angle space. Here, we illustrate the performance of PDBETA with a protein-DNA complex, a protein-tRNA complex, and some non-protein small molecules, and show that the atomic fluctuations calculated by PDBETA reproduce the temperature factor data of these molecules in the PDB. A comparison was also made with elastic-network-model based NMA in a Cartesian-coordinate system.

Dynamic features of homodimer interfaces calculated by normal-mode analysis.

Knowledge of the dynamic features of protein interfaces is necessary for a deeper understanding of protein-protein interactions. We performed normal-mode analysis (NMA) of 517 nonredundant homodimers and their protomers to characterize dimer interfaces from a dynamic perspective. The motion vector calculated by NMA for each atom of a dimer was decomposed into internal and external motion vectors in individual component subunits, followed by the averaging of time-averaged correlations between these vectors over atom pairs in the interface. This averaged correlation coefficient (ACC) was defined for various combinations of vectors and investigated in detail. ACCs decrease exponentially with an increasing interface area and r-value, that is, interface area divided by the entire subunit surface area. As the r-value reflects the nature of dimer formation, the result suggests that both the interface area and the nature of dimer formation are responsible for the dynamic properties of dimer interfaces. For interfaces with small or medium r-values and without intersubunit entanglements, ACCs are found to increase on dimer formation when compared with those in the protomer state. In contrast, ACCs do not increase on dimer formation for interfaces with large r-values and intersubunit entanglements such as in interwinding dimers. Furthermore, relationships between ACCs for intrasubunit atom pairs and for intersubunit atom pairs are found to significantly differ between interwinding and noninterwinding dimers for external motions. External motions are considered as an important factor for characterizing dimer interfaces.

Ligand-induced conformational change of a protein reproduced by a linear combination of displacement vectors obtained from normal mode analysis.

The conformational change of a protein upon ligand binding was examined by normal mode analysis (NMA) based on an elastic-network model (ENM) for a full-atom system using dihedral angles as independent variables. Specifically, we investigated the extent to which conformational change vectors of atoms from an apo form to a holo form of a protein can be represented by a linear combination of the displacement vectors of atoms in the apo form calculated for the lowest-frequency m normal modes (m=1, 2,…, 20). In this analysis, the latter vectors were best fitted to the former ones by the least-squares method. Twenty-two paired proteins in the holo and apo forms, including three dimer pairs, were examined. The results showed that, in most cases, the conformational change vectors were reproduced well by a linear combination of the displacement vectors of a small number of low-frequency normal modes. The conformational change around an active site was reproduced as well as the entire conformational change, except for some proteins that only undergo significant conformational changes around active sites. The weighting factors for 20 normal modes optimized by the least-squares fitting characterize the conformational changes upon ligand binding for these proteins. The conformational changes sampled around the apo form of a protein by the linear combination of the displacement vectors obtained by ENM-based NMA may help solve the flexible-docking problem of a protein with another molecule because the results presented herein suggest that they have a relatively high probability of being involved in an actual conformational change.

Prediction of protein motions from amino acid sequence and its application to protein-protein interaction.

BACKGROUND: Structural flexibility is an important characteristic of proteins because it is often associated with their function. The movement of a polypeptide segment in a protein can be broken down into two types of motions: internal and external ones. The former is deformation of the segment itself, but the latter involves only rotational and translational motions as a rigid body. Normal Model Analysis (NMA) can derive these two motions, but its application remains limited because it necessitates the gathering of complete structural information. RESULTS: In this work, we present a novel method for predicting two kinds of protein motions in ordered structures. The prediction uses only information from the amino acid sequence. We prepared a dataset of the internal and external motions of segments in many proteins by application of NMA. Subsequently, we analyzed the relation between thermal motion assessed from X-ray crystallographic B-factor and internal/external motions calculated by NMA. Results show that attributes of amino acids related to the internal motion have different features from those related to the B-factors, although those related to the external motion are correlated strongly with the B-factors. Next, we developed a method to predict internal and external motions from amino acid sequences based on the Random Forest algorithm. The proposed method uses information associated with adjacent amino acid residues and secondary structures predicted from the amino acid sequence. The proposed method exhibited moderate correlation between predicted internal and external motions with those calculated by NMA. It has the highest prediction accuracy compared to a naïve model and three published predictors. CONCLUSIONS: Finally, we applied the proposed method predicting the internal motion to a set of 20 proteins that undergo large conformational change upon protein-protein interaction. Results show significant overlaps between the predicted high internal motion regions and the observed conformational change regions.

ProMode: a database of normal mode analyses on protein molecules with a full-atom model.

MOTIVATION: Although information from protein dynamics simulation is important to understand principles of architecture of a protein structure and its function, simulations such as molecular dynamics and Monte Carlo are very CPU-intensive. Although the ability of normal mode analysis (NMA) is limited because of the need for a harmonic approximation on which NMA is based, NMA is adequate to carry out routine analyses on many proteins to compute aspects of the collective motions essential to protein dynamics and function. Furthermore, it is hoped that realistic animations of the protein dynamics can be observed easily without expensive software and hardware, and that the dynamic properties for various proteins can be compared with each other. RESULTS: ProMode, a database collecting NMA results on protein molecules, was constructed. The NMA calculations are performed with a full-atom model, by using dihedral angles as independent variables, faster and more efficiently than the calculations using Cartesian coordinates. In ProMode, an animation of the normal mode vibration is played with a free plug-in, Chime (MDL Information Systems, Inc.). With the full-atom model, the realistic three-dimensional motions at an atomic level are displayed with Chime. The dynamic domains and their mutual screw motions defined from the NMA results are also displayed. Properties for each normal mode vibration and their time averages, e.g. fluctuations of atom positions, fluctuations of dihedral angles and correlations between the atomic motions, are also presented graphically for characterizing the collective motions in more detail. AVAILABILITY: http://promode.socs.waseda.ac.jp