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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.

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.

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.

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 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.

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.

We have developed a new method of protein structure comparison based on spatial arrangements of secondary structural elements (SSEs). Each SSE is represented by a single vector, and common spatial arrangements of vectors in a pair of proteins are detected. The method allows not only insertions and deletions of SSEs, but also topological permutations. It has a flexible target function that can be adjusted depending upon particular levels or definitions of structural similarity, and it is fast enough to allow structural comparisons for many pairs of proteins. The parameters for the target function are determined based on distributions of the geometrical variables for the spatial arrangements of the equivalent SSEs in well-known structural motifs. The obtained parameter set is tuned for detecting relatively strong structural similarity. We report several tests on examples including comparisons of known structural similarity and database searches for a target structure, and examine the results when this parameter set is used for the comparison of distantly related structures.

A comparison of a normal mode analysis and principal component analysis of a 200-ps molecular dynamics trajectory of bovine pancreatic trypsin inhibitor in vacuum has been made in order to further elucidate the harmonic and anharmonic aspects in the dynamics of proteins. An anharmonicity factor is defined which measures the degree of anharmonicity in the modes, be they principal modes or normal modes, and it is shown that the principal mode system naturally divides into anharmonic modes with peak frequencies below 80 cm-1, and harmonic modes with frequencies above this value. In general the larger the mean-square fluctuation of a principal mode, the greater the degree of anharmonicity in its motion. The anharmonic modes represent only 12% of the total number of variables, but account for 98% of the total mean-square fluctuation. The transitional nature of the anharmonic motion is demonstrated. The results strongly suggest that in a large subspace, the free energy surface, as probed by the simulation, is approximated by a multi-dimensional parabola which is just a rescaled version of the parabola corresponding to the harmonic approximation to the conformational energy surface at a single minimum. After 200 ps, the rescaling factor, termed the "normal mode rescaling factor," has apparently converged to a value whereby the mean-square fluctuation within the subspace is about twice that predicted by the normal mode analysis.

X-ray crystallography provides a wealth of information about the dynamic as well as static protein structure. A new method of dynamic structure refinement of protein X-ray crystallography, normal mode refinement, is proposed. In this method, the Debye-Waller factor is expanded in terms of the low-frequency internal normal modes and external normal modes, whose amplitudes and couplings are optimized in the process of crystallographic refinement. The internal and external contributions to the atomic fluctuations can be separated. Also, anisotropic atomic fluctuations and their inter-atomic correlations can be determined experimentally even with a relatively small number of adjustable parameters. The method is applied to the analyses of experimental data of human lysozyme and its mutant, C77A/C95A, to reveal its dynamic structure.

Normal mode analyses on the protein, bovine pancreatic trypsin inhibitor, in dihedral angle space and Cartesian coordinate space are compared. In Cartesian coordinate space it is found that modes of frequencies lower than 30 cm−1 contribute 80% of the total mean-square fluctuation and are represented almost completely by motions in the dihedral angles. Bond angle and length fluctuations dominate in modes above 200 cm−1, but contribute less than 2% to the total mean-square fluctuation. In the low-frequency modes a good correspondence between patterns of atomic displacements was found, but on average the root-mean-square fluctuations of the Cartesian coordinate modes are 13% greater than their dihedral angle counterparts. The main effect of fluctuations in the bond angles and lengths, therefore, is to allow the dihedral angles to become more flexible. As the important subspaces determined from the two methods overlap considerably, dihedral angle space analysis can be applied to proteins too large for Cartesian coordinate space analysis

Normal mode analysis of mouse epidermal growth factor (mEGF) has been carried out at room temperature. The value of the lowest frequency is 4.1 cm-1. This mode corresponds to hinge-bending motion between the N-terminal and C-terminal domains of mEGF. This hinge-bending motion corresponds to the "mitten mode." In this motion, the N-terminal domain is almost rigid. However, the C-terminal domain is found to consist of three rigid segments. Two segments, C33-D46 and G51-R53, are observed moving in the same direction, but L47-W50 moves in the opposite direction. For this mode, the effective Young's modulus turned out to be 1.1 x 10(9) dyn.cm-2. This value is a little larger than that of the mode with the lowest frequency 4.4 cm-1 of BPTI. The difference may be related to the fraction of residues involved in beta-sheets in the molecule. Similar analyses are carried out for other low frequency modes.

Pressure effect on the equilibrium conformation in sperm whale deoxymyoglobin and its volume fluctuation are studied by the normal mode analysis and strain tensor analysis. The pressure-induced deformation of interhelix regions are found to be remarkably more compressed than the other parts of the molecule. The intrahelix compressibility is shown to be relatively small. We also calculate the compressibility of the three hydrophobic clusters, located at the bottom, distal, and proximal side of the heme. Its value is found to decrease in the indicated order. The average compressibility of these hydrophobic clusters is less than the average interhelix compressibility, even though there are large cavities in these clusters. In order to study overall deformation, we define a linear compressibility and calculate it for all pairs of C alpha atoms. The pressure-induced deformation is observed to be heterogeneous also in this analysis. The calculated root-mean-square displacement of the constituent atoms in the equilibrium conformation at 1,000 atm from those at 0 atm is 0.12 A, which is much smaller in magnitude than the average value of the atomic fluctuations at room temperature. In the water solvent, the volume excluded by the protein molecule in the equilibrium conformation is reduced by 0.9%, when the pressure is raised from 0 to 1,000 atm. The calculated magnitude of the root-mean-square volume fluctuation is 0.3% of the excluded volume at room temperature. The square of the volume fluctuation is given as a sum of contributions from individual normal modes. Contributions from low frequency normal modes are found to dominate over those from higher frequency normal modes. The estimated value of the isothermal compressibility of deoxymyoglobin is 9.37 x 10(-12) cm2/dyn.

A normal mode analysis of human lysozyme has been carried out at room temperature. Human lysozyme is an enzyme constituted of two domains separated by an active site cleft, the motion of which is thought to be relevant for biological function. This motion has been described as a hinge bending motion. McCammon et al. have determined the characteristics of the hinge bending motion but they assumed a prior knowledge of the hinge axis. In this work we propose a method which is free from this assumption and determines the hinge axis and root mean square (rms) rotation angle which give the best agreement with the pattern of changes in all the distances between nonhydrogen atoms in the two domains, obtained by the normal mode analysis. The hinge axis we found is notably different from the one previously determined and goes, roughly, through the C alpha 55 and C alpha 76, i.e., it is located at the base of the beta-sheet of the second domain. The rms value for the rotation angle is also twice as large as the previous one: 3.37 degrees. It is shown that this hinge bending motion provides a fairly good approximation of the dynamics of human lysozyme and that the normal mode with the lowest frequency has a dominating contribution to this hinge bending motion. A study of the accessible surface area of the residues within the cleft reveals that the motion does not result in a better exposure to the solvent of these residues. A characterization of the thermally excited state (under the hypothesis of the harmonicity of the potential energy surface) has been done using the concept of topology of atom packing. Under this hypothesis the thermal fluctuations result only in a small change of the topology of atom packing, leading therefore to nearly elastic deformations of the protein.

One of the simplest ways to predict ligand binding sites is to identify pocket-shaped regions on the protein surface. Many programs have already been proposed to identify these pocket regions. Examination of their algorithms revealed that a pocket intrinsically has two arbitrary properties, "size" and "depth". We proposed a new definition for pockets using two explicit adjustable parameters that correspond to these two arbitrary properties. A pocket region is defined as a space into which a small probe can enter, but a large probe cannot. The radii of small and large probe spheres are the two parameters that correspond to the "size" and "depth" of the pockets, respectively. These values can be adjusted individual putative ligand molecule. To determine the optimal value of the large probe spheres radius, we generated pockets for thousands of protein structures in the database, using several size of large probe spheres, examined the correspondence of these pockets with known binding site positions. A new measure of shallowness, a minimum inaccessible radius, R(inaccess), indicated that binding sites of coenzymes are very deep, while those for adenine/guanine mononucleotide have only medium shallowness and those for short peptides and oligosaccharides are shallow. The optimal radius of large probe spheres was 3-4 A for the coenzymes, 4 A for adenine/guanine mononucleotides, and 5 A or more for peptides/oligosaccharides. Comparison of our program with two other popular pocket-finding programs showed that our program had a higher performance of detecting binding pockets, although it required more computational time.

Multicopper blue proteins (MCBPs) are multidomain proteins that utilize the distinctive redox ability of copper ions. There are a variety of MCBPs that have been roughly classified into three different groups, based on their domain organization and functions: (i) nitrite reductase-type with two domains, (ii) laccase-type with three domains, and (iii) ceruloplasmin-type with six domains. Together, the second and third group are often commonly called multicopper oxidases (MCOs). The rapid accumulation of genome sequence information in recent years has revealed several new types of proteins containing MCBP domains, mainly from bacteria. In this review, the recent research on the functions and structures of MCBPs is summarized, mainly focusing on the new types. The latter half of this review focusses on the two domain MCBPs, which we propose as the evolutionary intermediate of the MCBP family.

Superfamily classifications are based variably on similarity of sequences, global folds, local structures, or functions. We have examined the possibility of defining superfamilies purely from the viewpoint of the global fold/function relationship. For this purpose, we first classified protein domains according to the beta-sheet topology. We then introduced the concept of kinship relations among the classified beta-sheet topology by assuming that the major elementary event leading to creation of a new beta-sheet topology is either an addition or deletion of one beta-strand at the edge of an existing beta-sheet during the molecular evolution. Based on this kinship relation, a network of protein domains was constructed so that the distance between a pair of domains represents the number of evolutionary events that lead one from the other domain. We then mapped on it all known domains with a specific core chemical function (here taken, as an example, that involving ATP or its analogs). Careful analyses revealed that the domains are found distributed on the network as20 mutually disjointed clusters. The proteins in each cluster are defined to form a fold-based superfamily. The results indicate that20 ATP-binding protein superfamilies have been invented independently in the process of molecular evolution, and the conservative evolutionary diffusion of global folds and functions is the origin of the relationship between them.

We have investigated energy landscape of human lysozyme in its native state by using principal component analysis and a model, jumping-among-minima (JAM) model. These analyses are applied to 1 nsec molecular dynamics trajectory of the protein in water. An assumption embodied in the JAM model allows us to divide protein motions into intra-substate and inter-substate motions. By examining intra-substate motions, it is shown that energy surfaces of individual conformational substates are nearly harmonic and mutually similar. As a result of principal component analysis and JAM model analysis, protein motions are shown to consist of three types of collective modes, multiply hierarchical modes, singly hierarchical modes, and harmonic modes. Multiply hierarchical modes, the number of which accounts only for 0.5% of all modes, dominate contributions to total mean-square atomic fluctuation. Inter-substate motions are observed only in a small-dimensional subspace spanned by the axes of multiplyhierarchical and singly hierarchical modes. Inter-substate motions have two notable time components: faster component seen within 200 psec and slower component. The former involves transitions among the conformational substates of the low-level hierarchy, whereas the latter involves transitions of the higher level substates observed along the first four multiply hierarchical modes. We also discuss dependence of the subspace, which contains conformational substates, on time duration of simulation.

Molecular dynamics simulations were carried out to study what happens in a photoreceptor protein, photoactive yellow protein (PYP), immediately after the vertical transition of the chromophore from the ground to the excited state. A photon absorption simulation was performed to investigate the movement of amino acid residues upon photoexcitation. To calculate the excited state of the chromophore, SCF-CI calculation was carried out with INDO/S Hamiltonian. We observed that some amino acid residues have strong interactions with the chromophore. Most of these amino acid residues are conserved in PYPs from three different species of bacteria. This observation indicates the biological importance of these residues.

Background : Free energy calculations are carried out to study the change of thermal stability caused by Ile23→Val, Ile56→Val, Ile89→Val and Ile106→Val mutations in human lysozyme. In order to examine the dependence of the free energy difference, ΔΔ G, on the denatured-state structure, extended and native-like conformations are employed as initial conformations in the denatured-state simulations. Results : Calculated values of ΔΔ G for the mutations, Ile56→Val, Ile89→Val and Ile106→Val, were in good agreement with experimental values when the native-like structure was employed in the respective denatured-state simulations. In the case of Ile23→Val, a considerable difference between the calculated and experimental values of ΔΔ G was observed. Conclusions : The physical nature of Ile56→Val, Ile89→Val and Ile106→Val mutations was rationally characterized by a free energy component analysis. It is suggested that the α domain in which Ile23 is included is considerably structured even in the denatured state.

The mechanical response of a TIM-barrel protein to an applied pressure has been studied. We generated structures under an applied pressure by assuming the volume change to be a linear function of normal mode variables. By Delaunay tessellation, the space occupied by protein atoms is divided uniquely into tetrahedra, whose four vertices correspond to atomic positions. Based on the atoms that define them, the resulting Delaunay tetrahedra are classified as belonging to various secondary structures in the protein. The compressibility of various regions identified with respect to secondary structural elements in this protein is obtained from volume changes of respective regions in two structures with and without an applied pressure. We found that the beta barrel region located at the core of the protein is quite soft. The interior of the beta barrel, occupied by side chains of beta strands, is the softest. The helix, strand, and loop segments themselves are extremely rigid, while the regions existing between these secondary structural elements are soft. These results suggest that the regions between secondary structural elements play an important role in protein dynamics. Another aspect of tetrahedra, referred to as bond distance, is introduced to account for rigidities of the tetrahedra. Bond distance is a measure of separation of the atoms of a tetrahedron in terms of number of bonds along the polypeptide chain or side chains. Tetrahedra with longer bond distances are found to be softer on average. From this behavior, we derive a simple empirical equation, which well describes the compressibilities of various regions.

In our previous paper we reported the conformation of melittin bound to perdeuterated dodecylphosphocholine micelles as studied by {sup 1}H NMR experiment and distance geometry calculation. No hydrogen bonds were taken into consideration explicitly in the calculation. However, mostly alpha-helical conformations were obtained as results of the calculation even with no explicitly assumed hydrogen bonds. In the present paper we refined the distance geometry calculation by incorporating hydrogen bonds suggested by the previous calculation. As a result, we obtained the conformation of melittin, which was consistent with both NMR data and the additional hydrogen bonding data. The alpha-helical rod in the refined conformation also has a kink at Thr-11 and Gly-12, but its bent angle is now a bit narrowly distributed in 135 degrees +/- 15 degrees. In the present study another distortion at Trp-19 and IIe-20 becomes conspicuous. The average root-mean-square displacement of atoms is now much smaller and is 1.5 A for all backbone atoms. In the present paper side chain conformations are also analyzed.

The differences in conformation between alpha-human atrial natriuretic polypeptide (alpha-hANP) and its inactive analog, Met(O)-alpha-hANP, have been analyzed by nuclear magnetic resonance spectroscopy. All proton resonances for both peptides were assigned by means of the sequential assignment procedure. The three-dimensional structure of alpha-hANP in solution had previously been determined by distance geometry calculation using distance constraints derived from nuclear Overhauser effects (NOEs). Here, the three-dimensional structure of Met(O)-alpha-hANP was determined. The conformational differences between these two molecules were as follows: three segments of alpha-hANP, Ser1-Cys7, Arg11-Ala17 and Gln18-Tyr28, have some ordered structures. In Met(O)-alpha-hANP the Gln18-Tyr28 region has a similar conformation, while the remaining two regions do not have the ordered structure found in alpha-hANP. It is suggested that the conserved conformation of the Gln18-Tyr28 region is required for binding to the ANP receptor and that the slight biological activity of Met(O)-alpha-hANP is due to loss of the ordered structures evoked in the Ser1-Cys7 and Arg11-Ala17 regions of alpha-hANP.

An exact theorem is proved and its implication is discussed. The theorem states that, if a large molecule, typically biological macromolecules such as proteins, undergoes small-amplitude conformational fluctuations around its native conformation in such a way that within the range of conformational fluctuations at thermal equilibrium the conformational energy surface can be approximated by a multidimensional parabola, then the mass-weighted mean-square displacement of constituent atoms is given by the sum of the contributions from each normal mode of conformational vibration, which in turn is proportional to the inverse of the square of its frequency. This theorem provides a firm theoretical basis for the fact hitherto empirically recognized in the conformational dynamics of, for instance, native proteins that very-low-frequency normal modes make dominant contributions to the conformational fluctuations at thermal equilibrium. Discussion is given on the implication of this theorem, especially on the importance of the concept of the low-frequency normal modes, even in the case where the basic assumption of the harmonicity of the energy surface does not hold.

The conformation of the hydrogen-bonded complex of a trinucleoside diphosphate (anticodon bases), a nucleic acid base (discriminator base), and an amino acid is investigated. This complex has been named C4N (complex of the four nucleotides) by one of the authors. Concerning the aminoacylation of tRNA and the genetic code, it has been proposed that C4N accepts the cognate protein amino acid by the lock-and-key relationship. The purpose of the calculation is to investigate the conformational and energetic properties of C4N from the energy minimum principle. The calculation is carried out by using the empirical potential functions. Glycine, glutamine, and valine are taken as typical cases. The formation energies are estimated. It is shown that some conformational changes are induced in the anticodon trinucleoside diphosphate by the binding of the discriminator base. Conformational changes of C4N and the amino acid are also by the binding of the amino acid to C4N.

A computer experiment of protein dynamics is carried out, which consists of two steps: (1) A Monte Carlo simulation of thermal fluctuations in the native state of a globular protein, bovinepancreatic trypsin inhibitor; and (2) a simulation of the quick freezingof fluctuating conformations into energy minima by minimization of the energy of a number of conformations sampled in the Monte Carlo simulations sampled in the Monte Carlo simulation. From the analysis of results of the computer experiment is obtained the following picture of protein dynamics:multiple energy minima exist in the native state, and they are distributedin clusters in the conformational space. The dynamics has a hierarchical structure which has at least two levels. In the first level, dynamics is restricted within one of the clusters of minima. In the second, transitions occur among the clusters. Local parts of a protein molecule, side chains and local main chain segments, can take multiple locally stable conformations in the native state. Many minima result from combinations of these multiple local conformations. The hierarchical structure in the dynamics comes from interactions among the local parts. Protein moleculeshave two types of flexibility, each associated with elastic and plastic deformations, respectively.

The {sup 1}H NMR spectrum of melittin bound to perdeuterated dodecylphosphocholine micelles was analyzed completely by the sequential assignment method with use of two-dimensional NMR techniques. On the basis of the complete sequence-specific resonance assignments, the three-dimensional structure of melittin bound to micelles was determined by distance geometry calculation. Melittin forms an {alpha}-helical rod with a kink of 120-160{degree} at Thr11 and Gly12. This rod binds to the micelles with the {alpha}-helical axis parallel to the lipid-water interface. The present result is consistent with the wedge model, where melittin binds to the outer surface of membranes and destabilizes the membrane organization, leading lysis. However, the above parallel arrangement does not exclude the possibility that melittin is reoriented to a transmembrane position to form a pore when a membrane potential is applied.

Protein-folding and -unfolding transitions were studied by the method of computer simulation. The protein was modeled as a two-dimensional lattice polymer. Various energy terms were assumed to be operative between units composing the polymer. But hydrophobic interactions were neglected explicitly. Both thermodynamic and kinetic quantities were obtained from the simulation, and from their temperature dependence in the transition zone characteristics of the conformational transition of proteins were discussed. Two amino acid substituted models, differing in the location of substitution, were studied and compared with the original in order to clarify the effect of substitution on conformational transition of proteins. The following conclusions were reached in this study: (1) The relaxation time of the slow mode, which reflects the overall folding and unfolding processes, shows a peak near the transition temperature, while that of the fast mode is almost independent of temperature. The peak of the slow mode occurs at a slightly lower temperature than the transition temperature. (2) The dependence of the logarithm of the rate constants on the inverse of temperature (Arrhenius plot) is linear. Therefore, the plot of the free energy of activation vs temperature is linear. (3) The values of kinetic parameters obtained suggest that in the activated state the intramolecular interactions are half broken, while the state is close to the native state on the entropy axis. (4) The amino acid substitution, which is modeled as having slightly unfavorable short-range interactions, causes the substituted ones to be slightly unstable. Moreover, it causes the folding transition to slow. From the analysis of the way slowing down is observed in the two substituted models, we conclude that a structure, designed to model a β-sheet, is formed before it gets assembled with other structures, which are designed to model α-helices. The process of assembly occurs nearly at the activated state of the folding and unfolding transition. (5) It is suggested from this study that the maximum of folding rate constant in the Arrhenius plot that has been observed experimentally in real proteins is likely due to hydrophobic interactions.

Conformational fluctuations in a globular protein, bovine pancreatic trypsin inhibitor, in the time range between picoseconds and nanoseconds are studied by a Monte Carlo simulation method. Multiple energy minima are derived from sampled conformations by minimizing their energy. They are distributed in clusters in the conformational space. A hierarchical structure is observed in the simulated dynamics. In the time range between 10(-14) and 10(-10) seconds dynamics is well represented by a superposition of vibrational motions within an energy well with transitions among minima within each cluster. Transitions among clusters take place in the time range of nanoseconds or longer.

An analysis is carried out of differences in the minimum energy conformations obtained in the previous paper by energy minimization starting from conformations sampled by a Monte Carlo simulation of conformational fluctuations in the native state of a globular protein, bovine pancreatic trypsin inhibitor. Main conformational differences in each pair of energy minima are found usually localized in several side chains and in a few local main chain segments. Such side chains and local main chain segments are found to take a few distinct local conformations in the minimum energy conformations. Energy minimum conformations can thus be described in terms of combinations of these multiple local conformations.

Differences in atom packing are studied in the minimum energy conformations derived from the record of the Monte Carlo simulation of conformational fluctuation in the native state of a globular protein, bovine pancreatic trypsin inhibitor. It is found that local deformations observed among the minima which are found in the previous paper are accompanied by rearrangement of atom packing. Spatial locations of the local deformations in the three-dimensional folded structure are also studied. It is found that the local deformations are distributed in space in several clusters in the folded structure. The size and location of the clusters characterize the respective fluctuations of the first and the second levels observed in the simulation. In the fluctuations of the first level local deformations, each of which usually involves a few side chains and one main chain local segment, are thermally exited independently of each other near the surface of the molecule. The observed fluctuation of the second level involves a cooperative deformation involving many side chains and local main chain segments all in one cluster, which goes though the core of the molecule. The collective local deformations observed both in the first and second levels are plastic in the sense that they are accompanied with rearrangement of atom packing.

Conformational analyses on four cyclic model peptides of the β-bend, chicle( l - or d -Phe- l -Pro-ϵ-aminocaproyl(Aca)) and cyclo( l -Pro- l - or d -Phe-Aca), were carried out both experimentally and theoretically. Chicle( d -Phe- l -Pro- Aca) was shown to exist as a single conformer taking the type II′ β-bend. The comparison of its CD spectra with those of chicle ( l -Ala- l -Ala-Aca) revealed that type I and II′ β-bends, both with α-helix-like CD spectra, can be distinguished. Chicle ( l -Phe- l -Pro-Aca) was shown to exist as a single conformer with a cis l -Phe- l -Pro peptide bond, taking the type VI β-bend. Its CD spectrum has thus been observed for the first time for the bend containing a cis peptide bond. Chicle( l -Pro- l -Phe-Aca) was shown to exist as a mixture of two conformers, the major one taking the type I β-bend with a trans Aca- l -Pro peptide bond and the minor one with a cis Aca- l -Pro peptide bond. Chicle( l -Pro- d -Phe-Aca) was suggested to exist as a mixture of two conformers, the major one taking the type II β-bend with a trans Aca- l -Pro peptide bond and the minor one with a cis Aca- l -Pro peptide bond.

Conformational analysis of conotoxin GI, one of the neurotoxic peptides produced by a marine snail, genus Conus, was performed by a combination of nuclear magnetic resonance spectroscopy (NMR) and distance geometry calculations. The resulting conformers on minimization of the target function were classified into two groups. The difference in the structures of the conformers is mainly due to the difference in the orientation of the side chain of the tyrosyl residue. The results show that the solution structure of conotoxin GI satisfies the conformational requirements for the biological activity of an antagonist toward nicotinic cholinergic receptors elucidated in a series of studies on alkaloids. The structure is discussed on the basis of the results of comparison of the atomic arrangements of the active sites of snake venom peptides and molecular models based on the results of secondary structure prediction.

The three-dimensional structure of alpha-human ANP in solution was determined through the combined use of nuclear magnetic resonance spectroscopy and distance geometry. The results are based on distance constraints determined by nuclear Overhauser effect measurements and one disulfide bond. The structure is as follows. Three separate regions, which are Ser1-Cys7, Arg11-Ile15, and Gln18-Tyr28 each have some ordered structure. The remaining parts in the sequences of Gly9-Gly10 and Gly16-Ala17 act as hinges. And the C-terminal part is folded back toward the cyclic moiety. The conformation of alpha-hANP reported here is expected to give a better understanding of the relationships between its biological activities and three-dimensional structure.

An analysis of the genome sequence database revealed novel types of two-domain multi-copper oxidases. The two-domain proteins have the conspicuous combination of blue-copper and inter-domain trinuclear copper binding residues, which is common in ceruloplasmin and ascorbate oxidase but not in nitrite reductase, and therefore are considered to retain the characteristics of the plausible ancestral form of ceruloplasmin and ascorbate oxidase. A possible evolutionary relationship of these proteins is proposed.

The melting-profile method consists of a continuous observation of a structural parameter while the temperature of the sample is raised at a constant rate [Fugita, S. C., & Imahori, K. (1974) IN Peptides, Polypeptides and Proteins (Blout, E. R., Bovey, F. A., Goodman, M., & Lotan, N., Eds.) p 217, Wiley, New York, N.Y.]. An analytical solution to the melting profile was formulated for the two-state irreversible process and called temperature-scanning kinetics. The theory was tested with thermolysin with consistent results, and the thermodynamic parameters of thermal denaturation were calculated: deltaH identical to = 80.3 kcal/mol, deltaS identical to = 153 eu. These values agreed with the corresponding values obtained from the classical constant-temperature relaxation kinetics. The possibilities of temperature-scanning kinetics are discussed.

A theory is developed about large-amplitude conformational fluctuations in globular proteins in their native or predenaturational state. A model is introduced, an independent fluctuating site model, in which we assume that there is more than one independent fluctuating site, each one localized in some part of a protein molecule. Without assuming any further details for each fluctuating site, the entropy S versus enthalpy H curve of this model is shown to be convex. From this fact the predenaturational excess heat capacity can be derived, as observed in recent experimental studies of a few systems of a protein in solution.

Distances between centers of gravity of individual residues are compared among the minimum energy conformations derived from the record of the Monte Carlo simulation of conformational fluctuations in the native state of a globular protein, bovine pancreatic trypsin inhibitor. It is found that local deformations originating from the multiplicity of local conformations cause deformations of the whole structure of the molecule in various ways, which can be classified into two types. Type 1: When a local deformation occurs in a region consisting of a few residues near the surface of the molecule, the whole shape of the molecule responds by deforming elastically. The magnitude of this deformation is in the range of thermal fluctuations calculated by the harmonic approximation around a single minimum. Type 2: We have observed one case belonging to the second type in which local deformations occur cooperatively in an extended region. This region goes across the whole molecule and divide the remaining parts into two. Atom packing changes in and around the extended region of local deformations. For this reason deformation in this region is plastic. Relative location and orientation between the divided two parts change very much. Deformation of the whole shape in this case, associated with the plastic deformation in an extended region, demonstrates that protein molecules have a flexibility beyond the harmonic limit.

A long record of computer simulation of folding-unfolding transition in a two-dimensional lattice model of protein as monitored by one conformational order parameter was studied to see if it could be approximated by a markoffian process. For this purpose the normalized time correlation functions of the order parameter were calculated (i) directly from the record of simulation and (ii) by assuming the markoffian behavior of the record. Both of them can be well approximated by a sum of two simple exponential terms. The relaxation time of the slow relaxing term, which corresponds to the overall folding-unfolding transition, becomes very short when the markoffian assumption is made. From this observation we conclude that intermediate states defined by one more-or-less arbitrarily chosen conformational parameter are, in general, collections of very heterogeneous conformations and therefore transitions between them cannot be markoffian. This indicates the importance of multi-parameter observation of dynamic process of folding. Characteristic features of the method of trapping disulfide intermediates are discussed.

The theoretical model of proteins on the two-dimensional square lattice, introduced previously, is extended to include the hydrophobic interactions. Two proteins, whose native conformations have different folded patterns, are studied. Units in the protein chains are classified into polar units and nonpolar units. If there is a vacant lattice point next to a nonpolar unit, it is interpreted as being occupied by solvent water and the entropy of the system is assumed to decrease by a certain amount. Besides these hydrophobic free energies, the specific long-range interactions studied in previous papers are assumed to be operative in a protein chain. Equilibrium properties of the folding and unfolding transitions of the two proteins are found to be similar, even though one of them was predicted, based on the one globule model of the transitions, to unfold through a significant intermediate state (or at least to show a tendency toward such a behavior), when the hydrophobic interactions are strongly weighted. The failure of this prediction led to the development of a more refined model of transitions; a non-interacting local structure model. The hydrophobic interactions assumed here have a character of non-specific long-range interactions. Because of this character the hydrophobic interactions have the effect of decelerating the folding kinetics. The deceleration effect is less pronounced in one of the two proteins, whose native conformation is stabilized by many pairs of medium-range interactions. It is therefore inferred that the medium-range interactions have the power to cope with the decelerating effect of the non-specific hydrophobic interactions.

A theoretical method is developed by which the character of the process of protein denaturation (e.g., whether or not it is of the all-or-none type) can be discussed in terms of conformation of native proteins and the forces stabilizing it. An important role is played by a quantity S(H): entropy of a protein molecule in solution in the conformational states with a given value of enthalpy H. It is demonstrated that the all-or-none type denaturation of proteins is a rather direct consequence of the globularity and specificity of the native conformations. Denaturations with significant intermediate states are discussed. Denaturations induced by added denaturants are also discussed.