Search

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.

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.

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 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.

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 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.

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

Atoms in proteins, viewed as interlinked hubs, communicate with each other in complying with governed physical forces. The deviations of their positions from the mean, known as fluctuations, are essential in mediating functionally relevant biological processes maintaining one's daily life. The coupled fluctuations between pairs of atoms, the fluctuation covariance, can be determined analytically by Normal Mode Analysis, or numerically by MD simulations. Our study considers how this network of atoms reacts in response to external perturbations. Effects of such perturbations are exemplified by ligand- or (another) protein-induced conformational changes as well as the appreciated structural distortion of crystalline structures from its solution conformers. We assume the response of the system has linear departure from the mean under small perturbations on the Hamiltonian at equilibrium state. The formulated linear response theories, either time-dependent or -independent [1], says that the positional change of a given atom i is the accumulative sum of fluctuation covariance ij, at unperturbed state, multiplied by the force exerted on atom j. The time-dependent response function determined from MD simulation of carbonmonoxy myoglobin is used to track time-dependent conformational changes upon photo-dissociation of CO. The consequently obtained understanding of perturbation propagation is compared with experimental results. Also, the structural distortion of X-ray-characterized ubiquitin from its solution conformer can be well explained by the induce-fit theory, in a wider sense, while population-shift does not account for such a deviation.[1] Ikeguchi M, Ueno J, Sato M, and Kidera A. (2005) Phys Rev Lett, 94, 078102.

Despite sharing many common features, adenine-binding and guanine-binding sites in proteins often show a clear preference for the cognate over the non-cognate ligand. We have analyzed electrostatic potential (ESP) patterns at adenine and guanine-binding sites of a large number of non-redundant proteins where each binding site was first annotated as adenine/guanine-specific or non-specific from a survey of primary literature. We show that more than 90% of ESP variance at the binding sites is accounted for by only two principal component ESP vectors, each aligned to molecular dipoles of adenine and guanine. Projected on these principal component vectors, the adenine/guanine-specific and non-specific binding sites, including adenine-containing dinucleotides, show non-overlapping distributions. Adenine or guanine specificities of the binding sites also show high correlation with the corresponding electrostatic replacement (cognate by non-cognate ligand) energies. High correlation coefficients (0.94 for 35 adenine-binding sites and 1.0 for 20 guanine-binding sites) were obtained when adenine/guanine specificities were predicted using the replacement energies. Our results demonstrate that ligand-free protein ESP is an excellent indicator for discrimination between adenine and guanine-specific binding sites and that ESP of ligand-free protein can be used as a tool to annotate known and putative purine-binding sites in proteins as adenine or guanine-specific.

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.

We have developed a method to determine the three-dimensional structure of a protein molecule from such a set of distance constraints as can be determined by nuclear magnetic resonance studies. The currently popular methods for distance geometry based on the use of the metric matrix are applicable only to small systems. The method developed here is applicable to large molecules, such as proteins, with all atoms treated explicitly. This method works in the space of variable dihedral angles and determines a three-dimensional structure by minimization of a target function. We avoid difficulties hitherto inherent in this type of approach by two new devices: (1) the use of variable target functions; and (2) a method of rapid calculation of the gradient of the target functions. The method is applied to the determination of the structures of a small globular protein, bovine pancreatic trypsin inhibitor, from several artificial sets of distance constraints extracted from the X-ray crystal structure of this molecule. When a good set of constraints was available for both short- and long-range distances, the crystal structure was regenerated nearly exactly. When some ambiguities, such as those expected in experimental information, are allowed, the protein conformation can be determined up to a few local deformations. These ambiguities are mainly associated with the low resolving power of the short-range information.

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.

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.

Normal modes of low-frequency vibrations are calculated for a small globular protein, bovine pancreatic trypsin inhibitor. In modes with frequencies below 120 cm-1 the protein molecule behaves like a continuous elastic body. Most modes with frequencies above 50 cm-1 are shown to behave harmonically within the range of thermal fluctuations at room temperature. Those with frequencies below 50 cm-1 show some anharmonicity. Magnitudes of displacements of atoms are mainly determined by the modes with frequencies below 30 cm-1. These very-low-frequency modes contribute significantly to the entropy of the system. The dynamic structure of the globular protein is described as a superposition of harmonic high-frequency motions and coupled anharmonic low-frequency motions of collective variables corresponding to the normal modes of vibration.

A powerful method of conformational energy minimization which uses both first and second derivatives of the energy function is applied both to a small globular protein, bovine pancreatic trypsin inhibitor (BPTI), consisting of 58 amino acid residues and to its chemical derivative obtained by carboxamidomethylation of cysteinyl residues of the 14–38 disulphide bond. Conformational fluctuations are also calculated from the second derivative matrix obtained at the respective minimum energy conformations. Appreciable conformational changes upon chemical modification are observed only in the vicinity of the site of the modification. The nuclear magnetic resonance data on both BPTI and the modified BPTI are analyzed to compare with the calculated conformational changes upon chemical modification. Good correlations are found between the theoretically predicted and experimentally deduced conformational changes. The theoretical method employed here has a general application for the calculation of small conformational changes of globular proteins upon their chemical modification or an amino acid substitution.

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.

Optical activity in anisotropic solutions of helical polymers in which the orientational distribution of the polymers is given arbitrarily is studied theoretically. The Moffitt-Yang plot for the optical rotatory dispersion (ORD) in anisotropic solutions and the corresponding one for the circular dichroism (CD) in anisotropic solutions are discussed. The electronic states of helical polymers are assumed to be described in terms of the degenerate coupled oscillator theory of Moffitt, Fitts and Kirkwood. For fibrous helical polymers it is shown that information about the directions of induced dipole moment vectors relative to the helical axis can be obtained from the measurements of ORD or CD in anisotropic solutions. It is also shown that for globular polymers containing helical parts in them informations about the directional distribution of the helical parts can be obtained.

Optical activities of macromolecules, characteristic lengths of which are larger than or comparable to the wavelength of the incident light, are discussed. Long helical polymers are treated in detail. No special length dependent phenomena are found to be expected. The effectiveness of the small (compared with the wavelength) molecule treatment of long helical polymers is thus assured.

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 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.

The computational algorithm that works in the coordinate space of dihedral angles (i.e., bond lengths and bond angles are kept fixed and only rotatable dihedral angles are treated as independent variables) is extended to deal with the pseudorotational motion of furanose rings by introducing a variable of pseudorotation. Then, this algorithm is applied to a distance geometry calculation that generates three-dimensional (3D) structures that are consistent with given constraints of interatomic distances. This method efficiently generates 3D structures of an RNA hairpin loop which satisfy a set of experimental NMR data. 0 1996 by John Wiley & Sons, Inc. Introduction C omputational chemistry has made various contributions to conformational analyses of macromolecules. Many computer programs have been developed to analyze their static and/or dy- namic conformations at the atomic level. They can be classified into two types from the viewpoint of independent variables used to describe conforma- tions of macromolecules: one in which Cartesian *Author to whom