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The snake cube puzzle made of a linear array of 27 cubes and its modified and extended versions are used as theoretical models to study the mechanism of folding of proteins into their sequence-specific native three-dimensional structures. Each of the three versions is characterized by the respective set of characteristics attributed to each of its constituent cubes and an array is characterized by its specific sequence of the cube characteristics. The aim of the puzzles is to fold the cube array into a compact 3×3×3 cubic structure. In all three versions, out of all possible sequences, only a limited fraction of sequences are found foldable into the compact cube. Even among foldable sequences, the structures folded into the compact 3×3×3 cube are found often not uniquely determined from the sequence. By comparing the results obtained for the three versions of models, we conclude that the power of the hydrophobic interactions to make the folded structure unique to the sequence is much weaker than the geometrical varieties of constituent cubes as modelled in the original snake cube puzzle. However, when this weak cube attribute is compounded to that of the original snake cube puzzle, the power is enhanced very effectively. This is a strong manifestation of the consistency principle: The sequence-specific native structure of protein is realized as a result of consistency of various types of interactions working in protein.

A code with an algorithm for high-speed classification of X-ray diffraction patterns has been developed. Results obtained for a set of 1 × 106 simulated diffraction patterns are also reported., Single-particle coherent X-ray diffraction imaging using an X-ray free-electron laser has the potential to reveal the three-dimensional structure of a biological supra-molecule at sub-nanometer resolution. In order to realise this method, it is necessary to analyze as many as 1 × 106 noisy X-ray diffraction patterns, each for an unknown random target orientation. To cope with the severe quantum noise, patterns need to be classified according to their similarities and average similar patterns to improve the signal-to-noise ratio. A high-speed scalable scheme has been developed to carry out classification on the K computer, a 10PFLOPS supercomputer at RIKEN Advanced Institute for Computational Science. It is designed to work on the real-time basis with the experimental diffraction pattern collection at the X-ray free-electron laser facility SACLA so that the result of classification can be feedback for optimizing experimental parameters during the experiment. The present status of our effort developing the system and also a result of application to a set of simulated diffraction patterns is reported. About 1 × 106 diffraction patterns were successfully classificatied by running 255 separate 1 h jobs in 385-node mode.

A new algorithm is developed for reconstructing the high-resolution three-dimensional diffraction intensity function of a globular biological macromolecule from many quantum-noise-limited two-dimensional X-ray laser diffraction patterns, each for an unknown orientation. The structural resolution is expressed as a function of the incident X-ray intensity and quantities characterizing the target molecule., A new two-step algorithm is developed for reconstructing the three-dimensional diffraction intensity of a globular biological macromolecule from many experimentally measured quantum-noise-limited two-dimensional X-ray laser diffraction patterns, each for an unknown orientation. The first step is classification of the two-dimensional patterns into groups according to the similarity of direction of the incident X-rays with respect to the molecule and an averaging within each group to reduce the noise. The second step is detection of common intersecting circles between the signal-enhanced two-dimensional patterns to identify their mutual location in the three-dimensional wavenumber space. The newly developed algorithm enables one to detect a signal for classification in noisy experimental photon-count data with as low as ∼0.1 photons per effective pixel. The wavenumber of such a limiting pixel determines the attainable structural resolution. From this fact, the resolution limit due to the quantum noise attainable by this new method of analysis as well as two important experimental parameters, the number of two-dimensional patterns to be measured (the load for the detector) and the number of pairs of two-dimensional patterns to be analysed (the load for the computer), are derived as a function of the incident X-ray intensity and quantities characterizing the target molecule.

MutT distinguishes substrate 8-oxo-dGTP from dGTP and also 8-oxo-dGMP from dGMP despite small differences of chemical structures between them. In this paper we show by the method of molecular dynamics simulation that the transition between conformational substates of MutT is a key mechanism for a high-resolution molecular recognition of the differences between the very similar chemical compounds. (1) The native state MutT has two conformational substates with similar free energies, each characterized by either open or closed of two loops surrounding the substrate binding active site. Between the two substates, the open substate is more stable in free MutT and in dGMP–MutT complex, and the closed substate is more stable in 8-oxo-dGMP–MutT complex. (2) Conformational fluctuation of the open substate is much larger than that of the closed substate. An estimate of associated entropy difference was found to be consistent with the experimentally found difference of entropy contribution to the binding free energies of the two molecules. (3) A hydrogen bond between H7 atom of 8-oxo-dGMP and the sidechain of Asn119 plays a crucial role for maintaining the closed substate in 8-oxo-dGMP–MutT complex. When this hydrogen bond is absent in the H7-deficient dGMP–MutT complex, the closed substate is no more maintained and transition to the more entropically-favored open substate is induced. (4) Thus, this mechanism of the hydrogen bond controlling the relative stabilities of the drastically different two conformational substates enhances the resolution to recognize the small difference of the chemical structures between the two molecules, dGMP and 8-oxo-dGMP.

The theoretical model of proteins on the two-dimensional square lattice, introduced previously, is extended to include the specific short-range interactions. Attractive long-range interactions with various specificities and non-specific repulsive long-range interactions in the form of self-avoidance of the polymer chain are also operative in the model. Dynamics of the model protein is studied by a Monte Carlo method. The short-range interactions are found to accelerate the folding and unfolding transitions. Non-specific part of the attractive long-range interactions have a competing effect of decelerating the transitions. When the short-range interactions are weighted beyond a certain extent over the attractive long-range interactions are weighted beyond a certain extent over the attractive long-range interactions, the all-or-none character of the folding and unfolding transitions is destroyed. How the destruction proceeds is quantitatively expressed in terms of the S-H curves. The limiting case of dominance of the specific short-range interactions over the attractive long-range interactions is studied in detail. The lattice polymer in this limit does not behave like a globular protein at all. This observation leads to a reexamination of the currently popular notion of the dominance of the short-range interactions. A new concept of consistency is proposed to replace it. Possible mechanisms of the acceleration of the transitions by the specific short-range interactions are discussed.

The effect of ester bond on the conformation of peptide molecule was studied by designing and synthesizing a model tetradepsipeptide cyclo(-L-Ala-L-Hmb-)2 and by analyzing the conformation both theoretically and experimentally. Theoretical analysis showed that both ester and peptide bonds in the calculated low-energy conformations within 3 kcal/mol of the global minimum take a trans but distorted configuration. The distortion is larger in ester bonds than in peptide bonds. Further, the four carbonyls project from one side of the plane of the cyclic backbone, whereas the side chains project from the other side. These results are consistent with the experimental results obtained by NMR measurement; first, the coupling constant deduced from 1H-NMR species in DMSO-d6 is consistent with the dihedral angles of the calculated low-energy conformations; second, results of NOE measurement can reproduce the calculated configuration of the carbonyls and side chains. From the consistency between theoretical and experimental results, it is concluded that this model tetradepsipeptide takes an all-trans backbone conformation in solution and this backbone conformation is stabilized by large distortion in the ester bond, which compensates the strain resulted from the 12-membered cyclic backbone structure consisting only of L-residues.

For the purpose of calculating the crystal structure of polyglycine II, a system of three parallel chains are considered. The structure obtained by the energy minimization of this system agrees well with experimentally determined crystal structure. Hydrogen bonds of the type of Cα–H. O, which are discussed in literature as existing in the crystal structure, are neglected in the calculation. The fact that the crystal structure is well reproduced by this calculation indicates that hydrogen bonds of this type, if any, are weak in this crystal structure. The relative contributions of various energy terms to the stabilization of the structure are investigated. Interchain hydrogen bonds do not play a significant role in the determination of the crystal structure, but the interchain nonbonded interactions do. Mechanical properties are studied by calculating a response to a static external force applied to the system. Young's modulus E = 4.2 times 1011-dyncm-2 and Poisson's ratio s=0.25 are obtained. Relative contributions of various energy terms to elastic properties are discussed.

Proteins recognize specific DNA sequences not only through direct contact between amino acids and bases, but also indirectly based on the sequence-dependent conformation and deformability of the DNA (indirect readout). We used molecular dynamics simulations to analyze the sequence-dependent DNA conformations of all 136 possible tetrameric sequences sandwiched between CGCG sequences. The deformability of dimeric steps obtained by the simulations is consistent with that by the crystal structures. The simulation results further showed that the conformation and deformability of the tetramers can highly depend on the flanking base pairs. The conformations of xATx tetramers show the most rigidity and are not affected by the flanking base pairs and the xYRx show by contrast the greatest flexibility and change their conformations depending on the base pairs at both ends, suggesting tetramers with the same central dimer can show different deformabilities. These results suggest that analysis of dimeric steps alone may overlook some conformational features of DNA and provide insight into the mechanism of indirect readout during protein-DNA recognition. Moreover, the sequence dependence of DNA conformation and deformability may be used to estimate the contribution of indirect readout to the specificity of protein-DNA recognition as well as nucleosome positioning and large-scale behavior of nucleic acids.

DNA tetramer sequences AATT and TTAA are known to be conformationally more rigid and flexible, respectively. In this study, we carry out molecular dynamics (MD) simulations of these two sequences and investigate the characteristic hydration pattern. The rigid AATT is found to be more likely to construct the hydration spine in the minor groove, than the flexible TTAA. The result suggests that the hydration water molecules play a critical role, for determining the sequence dependent deformability of DNA conformation.

Protein–RNA interactions play essential roles in a number of regulatory mechanisms for gene expression such as RNA splicing, transport, translation and post-transcriptional control. As the number of available protein–RNA complex 3D structures has increased, it is now possible to statistically examine protein–RNA interactions based on 3D structures. We performed computational analyses of 86 representative protein–RNA complexes retrieved from the Protein Data Bank. Interface residue propensity, a measure of the relative importance of different amino acid residues in the RNA interface, was calculated for each amino acid residue type (residue singlet interface propensity). In addition to the residue singlet propensity, we introduce a new residue-based propensity, which gives a measure of residue pairing preferences in the RNA interface of a protein (residue doublet interface propensity). The residue doublet interface propensity contains much more information than the sum of two singlet propensities alone. The prediction of the RNA interface using the two types of propensities plus a position-specific multiple sequence profile can achieve a specificity of about 80%. The prediction method was then applied to the 3D structure of two mRNA export factors, TAP (Mex67) and UAP56 (Sub2). The prediction enables us to point out candidate RNA interfaces, part of which are consistent with previous experimental studies and may contribute to elucidation of atomic mechanisms of mRNA export.

Bacterial flagellar filament is a macromolecular assembly consisting of a single protein, flagellin. Bacterial swimming is controlled by the conformational transitions of this filament between left- and right-handed supercoils induced by the flagellar motor torque. We present a massive molecular dynamics simulation that was successful in constructing the atomic-level supercoil structures consistent with various experimental data and further in elucidating the detailed underlying molecular mechanisms of the polymorphic supercoiling. We have found that the following three types of interactions are keys to understanding the supercoiling mechanism. “Permanent” interactions are always maintained between subunits in the various supercoil structures. “Sliding” interactions are formed between variable hydrophilic or hydrophobic residue pairs, allowing intersubunit shear without large change in energy. The formation and breakage of “switch” interactions stabilize inter- and intrasubunit interactions, respectively. We conclude that polymorphic supercoiling is due to the energy frustration between them. The transition between supercoils is achieved by a “transform and relax” mechanism: the filament structure is geometrically transformed rapidly and then slowly relaxes to energetically metastable states by rearranging interactions.

The boson peak is a broad peak found in the low-frequency region of inelastic neutron and Raman scattering spectra in many glassy materials, including biopolymers below approximately 200 K. Here, we give a novel insight into the origins of the protein boson peak, which may also be valid for materials other than proteins. Molecular simulation reveals that the structured water molecules around a protein molecule increase the number of local minima in the protein energy landscape, which plays a key role in the origin of the boson peak. The peak appears when the protein dynamics are trapped within a local energy minimum at cryogenic temperatures. This trapping causes very low frequency collective motions to shift to higher frequencies. We demonstrate that the characteristic frequency of such systems shifts higher as the temperature decreases also in model one-dimensional energy surfaces with multiple minima.

The genetic code of nuclear genes in some ciliates was found to differ from that of other organisms in the assignment of UGA, UAG, and UAA codons, which are normally assigned as stop codons. In some ciliate species, the universal stop codons UAA and UAG instead encode glutamine. In some other ciliates, the universal stop codon UGA appears to be translated as cysteine or tryptophan. Eukaryotic release factor 1 (eRF1) is a key protein in stop codon recognition, thus, the protein is believed to play an important role in the stop codon reassignment in ciliates. We have cloned, sequenced, and analyzed the cDNA of eRF1 from four ciliate species of three different classes: Karyorelictea (Loxodes striatus), Heterotrichea (Blepharisma musculus), and Litostomatea (Didinium nasutum, Dileptus margaritifer). Phylogenetic analysis of these eRF1s supports the hypothesis that the genetic code in ciliates has deviated independently several times from the universal genetic code, and that different ciliate eRF1s may have undergone different processes to change the codon specificity. Using computational methods, we have also suggested areas on the surface of eRF1s that are important for stop codon recognition in ciliate eRF1s.

The motile mechanism of Mycoplasma mobile remains unknown but is believed to differ from any previously identified mechanism in bacteria. Gli349 of M. mobile is known to be responsible for both adhesion to glass surfaces and mobility. We therefore carried out sequence analyses of Gli349 and its homolog MYPU2110 from M. pulmonis to decipher their structures. We found that the motif “YxxxxxGF” appears 11 times in Gli349 and 16 times in MYPU2110. Further analysis of the sequences revealed that Gli349 contains 18 repeats of about 100 amino acid residues each, and MYPU2110 contains 22. No sequence homologous to any of the repeats was found in the NCBI RefSeq non-redundant sequence database, and no compatible fold structure was found among known protein structures, suggesting that the repeat found in Gli349 and MYPU2110 is novel and takes a new fold structure. Proteolysis of Gli349 using chymotrypsin revealed that cleavage positions were often located between the repeats, implying that regions connecting repeats are unstructured, flexible and exposed to the solvent. Assuming that each repeat folds into a structural domain, we constructed a model of Gli349 that fits well the shape and size of images obtained with electron microscopy.

Finding homologues for a given protein plays a major role in predicting the protein's structure and function. However, it is still difficult to find remote homologues with low sequence similarity, even with advanced sequence search methods. We propose a simple filtering method that uses predicted structural information, pertaining to secondary structures and solvent accessibilities. It filters the more promising homologues from the many candidate proteins obtained by PSI-BLAST with a less stringent threshold E-value. The final decision is made by a simple linear discrimination method, considering the E-value of PSI-BLAST and the statistical significance scores of structural matches. An in-house neural network program is used for the prediction of secondary structures and solvent accessibilities for both the query and library proteins. The performance of our filtering method was evaluated by the cross-validation method, using the SCOP superfamily relationship as the correct standard. Coverage-reliability plots show that our filtering method clearly improves the performance of PSI-BLAST. The secondary structure improves PSI-BLAST better than the solvent accessibilities, but the combination of these two features with PSI-BLAST leads to the best result. The advantage of our method is its easy implementation with fewer parameters to be tuned and faster computation. We also discuss its performance with predicted and observed secondary structures.

We have cloned, sequenced, and characterized cDNA of actins from five ciliate species of three different classes of the phylum Ciliophora: Karyorelictea (Loxodes striatus), Heterotrichea (Blepharisma japonicum, Blepharisma musculus), and Litostomatea (Didinium nasutum, Dileptus margaritifer). Loxodes striatus uses UGA as the stop codon and has numerous in-frame UAA and UAG, which are translated into glutamine. The other four species use UAA as the stop codon and have no in-frame UAG nor UGA. The putative amino acid sequences of the newly determined actin genes were found to be highly divergent as expected from previous findings of other ciliate actins. These sequences were also highly divergent from other ciliate actins, indicating that actin genes are highly diverse even within the phylum Ciliophora. Phylogenetic analysis showed high evolutionary rate of ciliate actins. Our results suggest that the evolutionary rate was accelerated because of the differences in molecular interactions.

We propose a new software framework, named "decoupling architecture", for all-to-all computation. In this framework, the user's kernel code and well-tuned parallel control code are clearly separated to allows users to move smoothly from running sequential programs on a single-node server to fully utilizing a powerful machine, such as the K computer. In an evaluation of our prototype, the proposed decoupling architecture introduced some overhead. However, we show that the overhead can be reduced.

The crystallographic normal mode refinements of myoglobin at a wide range of temperature from 40 K to 300 K were carried out to study the temperature dependence of the internal atomic fluctuations. The refinement method decomposes the mean square displacement from the average position, (deltar2), into the contributions from the internal degrees of freedom and those from the external degrees of freedom. The internal displacements show linear temperature dependence as (deltar2)=alphaT+beta, throughout the temperature range measured here, and exhibit no obvious change in the slope alpha at the dynamical transition temperature (Tc=ca. 180 K). The slope alpha is practically the same as the value predicted theoretically by normal mode analysis. Such linear dependence is considered to be due to the following reason. The crystallographic Debye-Waller factor represents the static distribution caused by convolution of temperature-dependent normal mode motions and a temperature-independent set of the conformational substates. In contrast, Mössbauer absorption spectroscopy shows a clear increase in the gradient alpha at Tc. This difference from X-ray diffraction originates from the incoherent nature of the Mössbauer effect together with its high-energy resolution, which yields the self-correlation, and the temporal behavior of individual Fe atoms in the myoglobin crystal.

Normal mode analysis in dihedral angle space is performed for a nucleic acid. In the analysis, the conformational change of a flexible sugar ring, so-called pseudo-rotational motion, is treated by a pseudo-rotation variable. This treatment in dihedral angle space allows the rings to be either flexible or rigid. Comparison of normal mode analyses with and without the pseudo-rotational motions has revealed a significant influence of the flexibility of the sugar rings on the static and dynamic conformation of nucleic acids. Assumed rigidity of sugar rings leads to a significant deviation of the minimum energy conformation and disappearance of some collective motions which are necessary to account for a high fraction of atomic fluctuations. Normal mode analysis in Cartesian coordinate space is also performed for the same nucleic acid. It is found that modes with frequencies below 20 cm−1 have 80% of the contribution of the total mean-square atomic fluctuation and are represented dominantly by motions caused by dihedral angles and pseudo-rotations only. This indicates that low-frequency modes from both analyses in dihedral angle space and in Cartesian coordinate space span the same subspace. Consequently, normal mode analysis in dihedral angle space, including pseudo-rotation variables, can be applied to nucleic acids in order to determine and characterize their dynamics.

A new formalism is developed that enables us to analyze reorganization energy of the protein electron transfer reaction from a classic molecular dynamics trajectory with special emphasis on structural and frequency signature. In particular, energy contributions are divided into those from interactions of donor or acceptor sites with surrounding protein or water environments. This formalism is applied to cytochrome c. The protein environment is found to be soft as the water environment and, therefore, contributes similarly to the reorganization energy.

In this paper we present a new approach to study the volume fluctuations of proteins. From a 1 ns molecular dynamics simulation, the volume fluctuation of human lysozyme has been calculated. We used two different ways for the calculation. In the first one, the volume fluctuation is extracted directly from the trajectory. For the second one, a newly developed formalism based on principal component analysis is used. The r.m.s. volume fluctuations obtained from the two analyses agree well with each other. The isothermal intrinsic compressibility was found to be larger than the one reported by experiment. The difference is discussed and suggested to exist in the assumed uncertainty of the compressibility of hydrated water to deduce the isothermal intrinsic compressibility from the experimental value. Spectral analysis shows that low-frequency dynamics dominate the total volume fluctuation. The same aspect is found in the study using principal component analysis. This low-frequency region is related to large and slow motions of proteins. Therefore a long time dynamics simulation is necessary to describe the volume fluctuations of proteins.

We have carried out normal mode analysis for four B-DNA molecules with different lengths and sequences. By focusing our attention on motions of the helical axes of the molecules and comparing them with those of the ideal rod obeying vibrational theory, we have shown that DNA molecules behave like isotropic and homogeneous elastic rods. Then, we have calculated dynamic constants representing their rigidities for bending and twisting. In the analysis of their twisting motions, we have shown that sliding and shifting motions between adjacent bases are important for the motions.

We carry out a systematic analysis of the correlation between similarity of protein three-dimensional structures and their evolutionary relationships. The structural similarity is quantitatively identified by an all-against-all comparison of the spatial arrangement of secondary structural elements in nonredundant 967 representative proteins, and the evolutionary relationship is judged according to the definition of superfamily in the SCOP database. We find the following symmetry rule: a protein pair that has similar folds but belong to different superfamilies has (with a very rare exception) certain internal symmetry in its common similar folds. Possible reasons behind the symmetry rule are discussed.

In order to search for a common structural motif in the phosphate-binding sites of protein-mononucleotide complexes, we investigated the structural variety of phosphate-binding schemes by an all-against-all comparison of 491 binding sites found in the Protein Data Bank. We found four frequently occurring structural motifs composed of protein atoms interacting with phosphate groups, each of which appears in different protein superfamilies with different folds. The most frequently occurring motif, which we call the structural P-loop, is shared by 13 superfamilies and is characterized by a four-residue fragment, GXXX, interacting with a phosphate group through the backbone atoms. Various sequence motifs, including Walker's A motif or the P-loop, turn out to be a structural P-loop found in a few specific superfamilies. The other three motifs are found in pairs of superfamilies: protein kinase and glutathione synthetase ATPase domain like, actin-like ATPase domain and nucleotidyltransferase, and FMN-linked oxidoreductase and PRTase.

Currently, collective coordinates are commonly employed in order to examine protein dynamics. In recent studies, they have been successfully applied to finding functionally relevant motions, to investigating the physical nature of protein dynamics, to sampling of the conformational space and to the analysis of experimental data. Collective coordinates also have other possible applications.

Pressure dependence of protein electron transfer rate constant is discussed. The rate constant is given as a product of two factors; electronic factor (electron tunneling matrix) and nuclear factor (Franck−Condon factor). Pressure affects the rate through both of these two factors. We analyzed effects of pressure on these two factors individually. The pressure dependence of the electronic factor is discussed by considering the dependence of through-space gaps in the tunneling pathway model. The effect of pressure on the nuclear factor is discussed in terms of the Marcus expression of the Franck−Condon factor and the pressure dependence of the two parameters, reorganization energy λ and reaction free energy ΔG, in it. We show that the dependence of λ is generally smaller than that of ΔG. To obtain a more quantitative picture, we carry out an analysis of pressure dependence of through-space gaps and ΔG by normal mode simulation on cytochrome c. In light of the results of these analyses, some experimental re...

We present an analytical model that describes the coupling of protein fluctuations to electron transfer. The model treats both the protein and the bulk solvent to couple to electron transfer. The protein is represented by a low-dielectric cavity containing explicit protein atoms, and the bulk solvent is represented by a highdielectric continuum surrounding the cavity. Protein fluctuations are modeled by collective normal modes with solvation energies incorporated through explicit reaction field energies. The shifts of the equilibrium normal mode variables upon electron transfer, related to the mode-specific couplings and reorganization energies, are calculated assuming the difference of the potential energy surfaces before and after electron transfer by a hyper plane in the normal mode vector space. This linear coupling assumption allows only one set of normal mode vectors to span both the reactant and product equilibrium conformations. The model is equivalent to a reduced spin-boson formalism (protein only); however, unlike previous work within this formalism, the bath modes are not spatially anonymous in our treatment. They are associated with unambiguous frequency and spatial signatures allowing a spectral analysis of protein reorganization energy with one-toone connection with actual protein fluctuation. This aspect of our model is very crucial since it allows, for the first time, to make a direct connection between actual protein motion and electron transfer, as demonstrated by a simulation presented in an accompanying paper (J. Phys. Chem. 1998, 102, XXX).

In an accompanying paper (part 1) we presented a model (NMRES) that describes the coupling of protein fluctuations to electron transfer. The NMRES model, employing normal mode analysis that incorpo...

The boson peak of a protein was examined in relation to hydration using staphylococcal nuclease. Although the boson peak is commonly observed in synthetic polymers, glassy materials and amorphous materials, the origin of the boson peak is not fully understood. The motions that contribute to the peak are harmonic vibrations. Upon hydration the peak frequency shifts to a higher frequency and the effective force constant of the vibration increases at low temperatures, suggesting that the protein energy surface is modified. Hydration of the protein leads to a more rugged surface and the vibrational motions are trapped within the local minimum at cryogenic temperatures. The origin of the protein boson peak may be related to this rugged energy surface.

The normal mode analysis in dihedral angle space is carried out on a famous double-stranded DNA dodecamer d(CGCGAATTCGCG) to reveal the dynamical characteristics and internal motion of this molecule. We have observed the coupled motion of sugar and base. We have also noted the dependence of internal motion in the dodecamer on location of the nucleotide relative to the helical ends, and the dependence of atomic fluctuations on distance from the helix axis. The similarity of atomic fluctuations between two strands suggests the presence of a twofold pseudosymmetry axis with its origin located at the center of the molecule. Our results show that the atomic fluctuations of duplex DNA are mainly determined by a small number of low-frequency normal modes, the normal modes with frequencies below 30 cm−1 make major contributions to the site-dependence of atomic fluctuations.

We have developed a method of searching for similar spatial arrangements of atoms around a given chemical moiety in proteins that bind a common ligand. The first step in this method is to consider a set of atoms that closely surround a given chemical moiety. Then, to compare the spatial arrangements of such surrounding atoms in different proteins, they are translated and rotated so that the chemical moieties are superposed on each other. Spatial arrangements of surrounding atoms in a pair of proteins are judged to be similar, when there are many corresponding atoms occupying similar spatial positions. Because the method focuses on the arrangements of surrounding atoms, it can detect structural similarities of binding sites in proteins that are dissimilar in their amino acid sequences or in their chain folds. We have applied this method to identify modes of nucleotide base recognition by proteins. An all-against-all comparison of the arrangements of atoms surrounding adenine moieties revealed an unexpected structural similarity between protein kinases, cAMP-dependent protein kinase (cAPK), and casein kinase-1 (CK1), and D-Ala:D-Ala ligase (DD-ligase) at their adenine-binding sites, despite a lack of similarity in their chain folds. The similar local structure consists of a four-residue segment and three sequentially separated residues. In particular the four-residue segments of these enzymes were found to have nearly identical conformations in their backbone parts, which are involved in the recognition of adenine. This common local structure was also found in substrate-free three-dimensional structures of other proteins that are similar to DD-ligase in the chain fold and of other protein kinases. As the proteins with different folds were found to share a common local structure, these proteins seem to constitute a remarkable example of convergent evolution for the same recognition mechanism.

The importance of collective motions in proteins, such as hinge-bending motions or motions involving domains, has been recognized. Occurrence of such motions and their experimental and theoretical studies are reviewed. Normal-mode analysis and principal component analysis are powerful theoretical tools for studying such motions. The former is based on the assumption of harmonicity of the dynamics, while the latter is valid even when the dynamics is highly anharmonic. The results of the latter analysis indicate that most important conformational events are taking place in a conformational subspace spanned by a rather small number of principal modes, and this important subspace is also spanned by a small number of normal modes. The normal-mode refinement method of protein X-ray crystallography, which is developed based on the concept of the above important subspace, is discussed.

An analytic formula is developed for calculating the generalized NMR order parameters in a protein from the normal mode analysis (NMA). The generalized order parameter, S2, is given as thermal ensemble average of a Taylor series in powers of Δ, the displacement of internuclear vector from its mean. Henry and Szabo developed a method to calculate the ensemble average based on the NMA carried out in the Cartesian coordinate space (CCS). However, atomic motions in each individual CCS normal modes are linear in the three‐dimensional space, which may cause interatomic distances even between covalently bonded atoms to change significantly. In this situation Henry and Szabo proposed to use a special formula for S2 which includes a trick to compensate such changes. We showed that by carrying out the NMA in the dihedral angle space (DAS) and by interpreting each DAS normal mode into curved atomic motions, S2 can be calculated reliably for spin pairs separated up to about 10 intervening covalent bonds by a natural formula without any trick.

The crystal structure of Escherichia coli B glutathione synthetase (GSHase) has been determined at the optimal catalytic condition pH 7.5. The most significant structural difference from the structure at pH 6.0 is the movement of the central domain towards the N-terminal domain almost as a rigid body. As a result of this movement, new interdomain and intersubunit polar interactions are formed which stabilize the dimeric structure further. The structure of GSHase at optimal pH was compared with 294 other known protein structures in terms of the spatial arrangements of secondary structural elements. Three enzymes (D-alanine: D-alanine ligase, succinyl-CoA synthetase and the biotin carboxylase subunit of acetyl-CoA carboxylase) were found to have structures similar to the ATP-binding site of GSHase, which extends across two domains. The ATP-binding sites in these four enzymes are composed of two antiparallel beta-sheets and are different from the classic mononucleotide-binding fold. Except for these proteins, no significant structural similarity was detected between GSHase and the other ATP-binding proteins. A structural motif in the N-terminal domain of GSHase has been found to be similar to the NAD-binding fold. This structural motif is shared by a number of other proteins that bind various negatively charged molecules.