Hiroshi Wako

Statistical Mechanical Theory of the Protein Conformation. II. Folding Pathway for Protein

The theory of a one-dimensional lattice gas with long-range many-body interactions is applied to the folding pathways of proteins. This model presents the quantitative informations about the order of inter-residue interactions, the location of nucleation and so on. Three typical proteins are cited as examples and their folding pathways are traced according to the computation of some useful properties.

Statistical mechanical theory of the protein conformation. I. General considerations and the application to homopolymers

A one-dimensional lattice gas with long-range many-body interactions is studied by a matrix method for the model of the transition between native and denatured states of globular proteins. The interactions in our model have the nature that two particles situated on two different sites can interact with each other only when all sites between them are occupied by other particles, or in other words, only when they are in a same island which is formed by particles situated side by side. In this system a phase transition occurs in the limit of the infinite long-range interaction and under certain potential functions. The sharpness and the all-or-none type property of the transitions are discussed from the nature of interaction.

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

FEDER/2: program for static and dynamic conformational energy analysis of macro-molecules in dihedral angle space

Abstract The computer program, FEDER/2, has been developed to carry out static and dynamic conformational energy analysis of macromolecules by treating dihedral angles as independent variables. The original program, FEDER (H. Wako and N. Gō, J. Comput. Chem. 8 (1987) 625), developed to rapidly calculate first and second derivatives of a conformational energy function with respect to dihedral angles for a single one protein molecule, has been extended by generalizing the tree representation and by revising the program. The tree topology of a molecular system, which is essential to this program, is defined in terms of rigid ‘unit’ and rotatable ‘bond’. Then, algorithms and formulae based on the tree topology are developed to calculate the first and second derivatives. In this revised version of the program we have constructed a library of units, from which a set of data required for a given specific system of molecules is generated. By separating such parts of the program that take care of specifics of various molecular systems into a form of data in the library of units, the main part of the program to calculate the first and second derivatives has become general enough to be applicable to wider types of molecules.

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.

Sampling efficiency of molecular dynamics and Monte Carlo method in protein simulation

Molecular dynamics (MD) and Monte Carlo (MC) method were compared in terms of the sampling efficiency in protein simulations. In the comparison, both methods use torsion angles as the degrees of freedom and the same force field, ECEPP/2. The MC method used here is the force-bias scaled-collective-variable Monte Carlo (SCV MC) [A. Kidera, Int. J. Quant. Chem. 75 (1999) 207], which corresponds to a finite step size extension to Brownian dynamics. It is shown that MD has about 1.5 times larger sampling efficiency. This difference is attributed to the inertia force term in MD, which does not exist in MC.

Significance of a Two-Domain Structure in Subunits of Phycobiliproteins Revealed by the Normal Mode Analysis

Phycobiliproteins are basic building blocks of phycobilisomes, a supra-molecular assembly for the light-capturing function of photosynthesis in cyanobacteria and red algae. One functional form of phycobiliproteins is a trimeric form consisting of three identical units having C(3) symmetry, with each unit composed of two kinds of subunits, the alpha-subunit and beta-subunit. These subunits have similar chain folds and can be divided into either globin-like or X-Y helices domains. We studied the significance of this two-domain structure for their assembled structures and biological function (light-absorption) using a normal mode analysis to investigate dynamic aspects of their three-dimensional structures. We used C-phycocyanin (C-PC) as an example, and focused on the interactions between the two domains. The normal mode analysis was carried out for the following two cases: 1) the whole subunit, including the two domains; and 2) the globin-like domain alone. By comparing the dynamic properties, such as correlative movements between residues and the fluctuations of individual residues, we found that the X-Y helices domain plays an important role not only in the C(3) symmetry assemblies of the subunits in phycobiliproteins, but also in stabilizing the light absorption property by suppressing the fluctuation of the specific Asp residues near the chromophore. Interestingly, the conformation of the X-Y helices domain corresponds to that of a module in pyruvate phosphate dikinase (PPDK). The module in PPDK is involved in the interactions of two domains, just as the X-Y helices domain is involved in the interactions of two subunits. Finally, we discuss the mechanical construction of the C-PC subunits based on the normal mode analysis.

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

BackgroundStructural 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.ResultsIn 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.ConclusionsFinally, 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.

Secondary structure prediction of β-subunits of the gonadotropin-thyrotropin family from its aligned sequences using environment-dependent amino-acid substitution tables and conformational propensities

The secondary structures of beta-subunits of the glycoprotein hormone family, LH (luteinizing hormone), CG (chorionic gonadotropin), FSH (follicle stimulating hormone), TSH (thyroid stimulating hormone), and GTH I/GTH II (two types of fish gonadotropins), are predicted by comparing an amino-acid substitution pattern at equivalent sites in their aligned sequences with environment-dependent amino-acid substitution tables and conformational propensities calculated from other protein families whose three-dimensional structures are known. According to the prediction results, together with other structural information obtained from experiments, the following points come up as important structural features of the beta-subunits of this family; The regions assigned to regular secondary structures (one alpha-helix and three beta-strands) are considered to constitute a core of the beta-subunits. They involve interaction sites with carbohydrate and alpha-subunit. Out of the six disulfide bonds formed in the beta-subunit, four are located together on one side of the core, and the other two on the opposite side. The two regions assumed to be a receptor binding region from experiments (therefore, species-specific regions) are predicted as loops located on the same side of the beta-subunit in this study. Some of the predicted loops are rich in proline residues. While the positions of proline residues are conserved in the family generally, there are hormone- or species-specific ones in the loop that is assumed to take part in receptor binding. The possible importance of proline residues in hormone or species specificity is discussed. (After submitting the manuscript the X-ray crystal structure of human CG was published. In order to evaluate the prediction, the original manuscript is kept intact and a comparison has been made between the prediction results and the crystal structure in an appendix).

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.