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

Abstract We have developed a computer program, named PDBETA, that performs normal mode analysis (NMA) based on an elastic network model that uses dihedral angles as independent variables. Taking advantage of the relatively small number of degrees of freedom required to describe a molecular structure in dihedral angle space and a simple potential-energy function independent of atom types, we aimed to develop a program applicable to a full-atom system of any molecule in the Protein Data Bank (PDB). The algorithm for NMA used in PDBETA is the same as the computer program FEDER/2, developed previously. Therefore, the main challenge in developing PDBETA was to find a method that can automatically convert PDB data into molecular structure information in dihedral angle space. Here, we illustrate the performance of PDBETA with a protein-DNA complex, a protein-tRNA complex, and some non-protein small molecules, and show that the atomic fluctuations calculated by PDBETA reproduce the temperature factor data of these molecules in the PDB. A comparison was also made with elastic-network-model based NMA in a Cartesian-coordinate system. © 2013 Elsevier Ltd. All rights reserved.

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

The database ProMode-Oligomer (http://promode.socs.waseda.ac.jp/promode_oligomer) was constructed by collecting normal-mode-analysis (NMA) results for oligomeric proteins including protein-protein complexes. As in the ProMode database developed earlier for monomers and individual subunits of oligomers (Bioinformatics vol. 20, pp. 2035-2043, 2004), NMA was performed for a full-atom system using dihedral angles as independent variables, and we released the results (fluctuations of atoms, fluctuations of dihedral angles, correlations between atomic fluctuations, etc.). The vibrating oligomer is visualized by animation in an interactive molecular viewer for each of the 20 lowest-frequency normal modes. In addition, displacement vectors of constituent atoms for each normal mode were decomposed into two characteristic motions in individual subunits, i.e., internal and external (deformation and rigid-body movements of the individual subunits, respectively), and then the mutual movements of the subunits and the movement of atoms around the interface regions were investigated. These results released in ProMode-Oligomer are useful for characterizing oligomeric proteins from a dynamic point of view. The analyses are illustrated with immunoglobulin light- and heavy-chain variable domains bound to lysozyme and to a 12-residue peptide. © Wako and Endo.

The conformational change of a protein upon ligand binding was examined by normal mode analysis (NMA) based on an elastic-network model (ENM) for a full-atom system using dihedral angles as independent variables. Specifically, we investigated the extent to which conformational change vectors of atoms from an apo form to a holo form of a protein can be represented by a linear combination of the displacement vectors of atoms in the apo form calculated for the lowest-frequency m normal modes (m = 1, 2, ..., 20). In this analysis, the latter vectors were best fitted to the former ones by the least-squares method. Twenty-two paired proteins in the holo and apo forms, including three dimer pairs, were examined. The results showed that, in most cases, the conformational change vectors were reproduced well by a linear combination of the displacement vectors of a small number of low-frequency normal modes. The conformational change around an active site was reproduced as well as the entire conformational change, except for some proteins that only undergo significant conformational changes around active sites. The weighting factors for 20 normal modes optimized by the least-squares fitting characterize the conformational changes upon ligand binding for these proteins. The conformational changes sampled around the apo form of a protein by the linear combination of the displacement vectors obtained by ENM-based NMA may help solve the flexible-docking problem of a protein with another molecule because the results presented herein suggest that they have a relatively high probability of being involved in an actual conformational change. (C) 2011 Elsevier B.V. All rights reserved.

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

The folding/unfolding kinetics of a three-dimensional lattice protein was studied using a simple statistical mechanical model for protein folding that we developed earlier. We calculated a characteristic relaxation rate for the free energy profile starting from a completely unfolded structure (or native structure) that is assumed to be associated with a folding rate (or an unfolding rate). The chevron plot of these rates as a function of the inverse temperature was obtained for four lattice proteins, namely, proteins a1, a2, b1, and b2, in order to investigate the dependency of the folding and unfolding rates on their native structures and amino acid sequences. Proteins a1 and a2 fold to the same native conformation, but their amino acid sequences differ. The same is the case for proteins b1 and b2, but their native conformation is different from that of proteins a1 and a2. However, the chevron plots of proteins a1 and a2 are very similar to each other, and those of proteins b1 and b2 differ considerably. Since the contact orders of proteins b1 and b2 are identical, the differences in their kinetics should be attributed to the amino acid sequences and consequently to the interactions between the amino acid residues. A detailed analysis revealed that long-range interactions play an important role in causing the difference in the folding rates. The chevron plots for the four proteins exhibit a chevron rollover under both strongly folding and strongly unfolding conditions. The slower relaxation time on the broad and flat free energy surfaces of the unfolding conformations is considered to be the main origin of the chevron rollover, although the free energy surfaces have features that are rather complicated to be described in detail here. Finally, in order to concretely examine the relationship between changes in the free energy profiles and the chevron plots, we illustrate some examples of single amino acid substitutions that increase the folding rate. (C) 2009 Elsevier B.V. All rights reserved.

The folding of lattice proteins with single amino acid substitutions was studied using a statistical mechanical model for protein folding. All possible single amino acid substitutions were analyzed for two different native conformations, and two amino acid sequences foldable to the given native conformation were considered for each native conformation. First, the transition temperature change Delta T-m(xi(i)) with the conformational energy change Delta E(xi(i)) caused by the substitution of the amino acid residue type xi(i) at the i-th residue was examined. Although both Delta E(xi(i)) and Delta Tm(xi(i)) strongly depend on the amino acid sequence (as a result, these two changes for the two proteins with different amino acid sequences foldable to the same native conformation differ considerably from each other), it is indicated that the correlations between Delta E(xi(i)) and Delta T-m(xi(i)) for the given residue i of the two proteins are mainly determined by their native conformations and are less dependent on their amino acid sequences. We classified the residues into three groups according to the coefficient of regression chi(i) of Delta T-m(xi(i)) on Delta E(xi(i)), i.e., the susceptibility of the conformational stability to the amino acid substitutions. Some of the residues in two of the three groups, which have clear correlations between Delta E(xi(i)) and Delta T-m(xi(i)) but have different chi(i)'s, are clustered to form domains in the native conformations. The residues in the third group, in which Delta T-m(xi(i)) is independent of Delta E(xi(i)), are located in the loop and terminal regions. Secondly, phi(eta, xi(i)), which is defined by referring to the Phi value that characterizes the transition state, but into which the progress variable of protein folding eta is introduced in this study, was examined for the mutants described above. It is shown that phi(eta, xi(i)) can reveal the states of individual amino acid residues and characterize their cooperative behaviors not only in the transition state but also at various stages of the folding process.

The statistical mechanical theory of the structural transitions of proteins is developed in accordance with the island model by considering the hydrophobic interactions and the entropy factors while connecting the two hydrophobic residues. The proteins treated here are apo-alpha-lactalbumin (IB9O), lysozyme (1LZ1), ferrocytochrome c (1CYC), cytochrome c (isozyme 1) (1YCC), chymotrypsin inhibitor 2 (202), and ubiquitin (1UBQ). Among them, according to the experiments, 202 and 1UBQ do not exhibit intermediate structures (two-state model), but others do exhibit intermediate structures that are sometimes termed molten globules (three-state model). The theory related to these facts is given in terms of the island model, specifically IB9O and 1LZ1. The stability or instability of the intermediate structures is explained by the effects of entropy during folding and the amino acid sequence. The intermediate structure is composed of several stable islands, which become unstable during unfolding.

Folding and unfolding simulations of three-dimensional lattice proteins were analyzed using a simplified statistical mechanical model in which their amino acid sequences and native conformations were incorporated explicitly. Using this statistical mechanical model, under the assumption that only interactions between amino acid residues within a local structure in a native state are considered, the partition function of the system can be calculated for a given native conformation without any adjustable parameter. The simulations were carried out for two different native conformations, for each of which two foldable amino acid sequences were considered. The native and non-native contacts between amino acid residues occurring in the simulations were examined in detail and compared with the results derived from the theoretical model. The equilibrium thermodynamic quantities (free energy, enthalpy, entropy, and the probability of each amino acid residue being in the native state) at various temperatures obtained from the simulations and the theoretical model were also examined in order to characterize the folding processes that depend on the native conformations and the amino acid sequences. Finally, the free energy landscapes were discussed based on these analyses. (c) 2006 American Institute of Physics.

Folding and unfolding simulations of three-dimensional lattice proteins were analyzed using a simplified statistical mechanical model in which their amino acid sequences and native conformations were incorporated explicitly. Using this statistical mechanical model, under the assumption that only interactions between amino acid residues within a local structure in a native state are considered, the partition function of the system can be calculated for a given native conformation without any adjustable parameter. The simulations were carried out for two different native conformations, for each of which two foldable amino acid sequences were considered. The native and non-native contacts between amino acid residues occurring in the simulations were examined in detail and compared with the results derived from the theoretical model. The equilibrium thermodynamic quantities (free energy, enthalpy, entropy, and the probability of each amino acid residue being in the native state) at various temperatures obtained from the simulations and the theoretical model were also examined in order to characterize the folding processes that depend on the native conformations and the amino acid sequences. Finally, the free energy landscapes were discussed based on these analyses. © 2006 The American Physical Society.

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

A statistical mechanical model for protein folding is applied to the three-dimensional lattice protein using a foldable amino acid sequence. The key to the model lies in the concept of its local structure, defined as a continuous region which takes the same local conformation as in the native conformation, and in the assumption of the absence of interactions between local structures. The partition function is precisely calculated for a given native conformation without any adjustable parameters. The model can well reproduce the equilibrium thermodynamic quantities obtained from the simulation.

By using the method to define a local structural motif of proteins by the Delaunay tessellation proposed by Wako and Yamato (Protein Eng. 11, 981-990 (1998)), we analyzed environment-dependent and position-specific frequencies of amino-acid occurrences in α-helices. In that method the three-dimensional structure of a protein molecule is uniquely divided into non-overlapping Delaunay tetrahedrons, each vertex of which is occupied by one of the comprising residues. A code is then assigned to each tetrahedron so as to characterize the local structure containing it. The tetrahedrons located in the interior of the α-helices are assigned 36 kinds of codes. The differences in the codes reflect the existence and absence of four residues surrounding the relevant region of the α-helix. In other words, the environment of the α-helix can be differentiated by these codes. Accordingly, we analyzed the frequencies of amino acid occurrences on each vertex of the tetrahedrons for each of these codes. Such data provide information about possible amino acid substitutions specific to a vertex position (i.e., a position in the α-helix) for a given code (i.e., environment around the α-helix). Furthermore, the principal component analysis was carried out to reveal general features of the amino acid occurrences in the α-helices. In relation to these results, such frequencies at the N- and C-terminals of the α-helix are also discussed.

An amino acid sequence pattern conserved among a family of proteins is called motif. It is usually related to the specific function of the family. On the other hand, functions of proteins are realized through their 3D structures. Specific local structures, called structural motifs, are considered as related to their functions. However, searching for common structural motifs in different proteins is much more difficult than for common sequence motifs. We are attempting in this study to convert the information about the structural motifs into a set of one-dimensional digital strings, i.e., a set of codes, to compare them more easily by computer and to investigate their relationship to functions more quantitatively. By applying the Delaunay tessellation to a 3D structure of a protein, we can assign each local structure to a unique code that is defined so as to reflect its structural feature. Since a structural motif is defined as a set of the local structures in this paper, the structural motif is represented by a set of the codes. In order to examine the ability of the set of the codes to distinguish differences among the sets of local structures with a given PROSITE pattern that contain both true and false positives, we clustered them by introducing a similarity measure among the set of the codes. The obtained clustering shows a good agreement with other results by direct structural comparison methods such as a superposition method. The structural motifs in homologous proteins are also properly clustered according to their sources. These results suggest that the structural motifs can be well characterized by these sets of the codes, and that the method can be utilized in comparing structural motifs and relating them with function.

Molecular dynamics (MD) and Monte Carlo (MC) method were compared in terms of the sampling efficiency in protein simulations. In the comparison, both methods use torsion angles as the degrees of freedom and the same force field, ECEPP/2. The MC method used here is the force-bias scaled-collective-variable Monte Carlo (SCV MC) [A. Kidera, Int. J. Quant. Chem. 75 (1999) 207], which corresponds to a finite step size extension to Brownian dynamics. It is shown that MD has about 1.5 times larger sampling efficiency. This difference is attributed to the inertia force term in MD, which does not exist in MC. (C) 2001 Elsevier Science B.V. All rights reserved.

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

In order to detect a motif of local structures in different protein conformations, the Delaunay tessellation is applied to protein structures represented by C-alpha atoms only. By the Delaunay tessellation the interior space of the protein is uniquely divided up into Delaunay tetrahedra whose vertices are the C-alpha atom positions. Some edges of the tetrahedra are virtual bonds connecting adjacent residues' C-alpha atoms along the polypeptide chain and others indicate interactions between residues nearest neighbouring in space. The rules are proposed to assign a code, i.e., a string of digits, to each tetrahedron to characterize the local structure constructed by the vertex residues of one relevant tetrahedron and four surrounding it. Many sets comprised of the local structures with the same code are obtained from 293 proteins, each of which has relatively low sequence similarity with the others, The local structures in each set are similar enough to each other to represent a motif, Some of them are parts of secondary or supersecondary structures, and others are irregular, but definite structures. The method proposed here can find motifs of local structures in the Protein Data Bank much more easily and rapidly than other conventional methods, because they are represented by codes. The motifs detected in this method can provide more detailed information about specific interactions between residues in the local structures, because the edges of the Delaunay tetrahedra are regarded to express interactions between residues nearest neighbouring in space.

Two DNA binding proteins, Cro and the amino-terminal domain of the repressor of bacteriophage 434 (434 Cro and 434 repressor) that regulate gene expression and contain a helix-turn-helix (HTH) motif responsible for their site-specific DNA recognition adopt very similar three-dimensional structures when compared to each other. To reveal structural differences between these two similar proteins, their dynamic structures, as examined by normal mode analysis, are compared in this paper. Two kinds of structural data, one for the monomer and the other for a complex with DNA, for each protein, are used in the analyses. From a comparison between the monomers it is found that the interactions of Ala-24 in 434 Cro or VaI-24 in 434 repressor, both located in the HTH motif, with residues 44, 47, 48, and 51 located in the domain facing the motif, and the interactions between residues 17, 18, 28, and 32, located in the PITH motif, cause significant differences in the correlative motions of these residues. From the comparison between the monomer and the complex with DNA for each protein, it was found that the first helix in the HTH motif is distorted in the complex form. While the residues in the HTH motif in 434 Cro have relatively larger positive correlation coefficients of motions with other residues within the HTH motif, such correlations are not large in the HTH motif of 434 repressor. It is suggestive to their specificity because the 434 repressor is less specific than 434 Cro, Although a structural comparison of proteins has been performed mainly from a static or geometrical point of view, this study demonstrates that the comparison from a dynamic point of view, using the normal mode analysis, is useful and convenient to explore a difference that is difficult to find only from a geometrical point of view, especially for proteins very similar in structure. (C) 1996 Wiley-Liss, Inc.

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. (C) 1996 by John Wiley & Sons, Inc.

The extended simulated annealing process (ESAP) is a useful method for modeling the partial structure of proteins [J. Higo et al., Biopolymers, 32, 33 (1992)]. In ESAP, a protein molecule is divided into two parts: small, flexible fragments constituting the concerned partial structure, and the remaining part, for which the structure is kept rigid during the simulation. We have improved the program of ESAP so that it can be adapted to general macromolecules. Any sidechain on the rigid part can be set to rotate. Soft repulsion between van der Waals spheres is introduced to avoid conformational trapping into local minima. This improved program was tested for modeling structural changes caused by eight kinds of amino acid mutation at the 86th residue in T4 lysozyme. For each mutant we obtained a model structure that was close to the X-ray structure. The root mean square (rms) deviations from the X-ray structure were 0.3 to 0.8 Angstrom for all heavy atoms and about 0.2 Angstrom for the main-chain atoms. We also modeled the structure of an Ile mutant, for which the X-ray structure has not yet been reported. ESAP can be used to model structural changes due to a single residue mutation in proteins. (C) 1996 by John Wiley & Sons, Inc.

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

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

The explosion of DNA sequence data from genome projects presents many challenges. For instance, we must extend our current knowledge of protein structure and function so that it can be applied to these new sequences. The derivation of rules for the relationships between sequence and structure allow us to recognize a common fold by the use of tertiary templates. New techniques enable us to begin to meet the challenge of rule-based modelling of distantly related proteins. This paper describes an integrated and knowledge-based approach to the prediction of protein structure and function which can maximize the value of sequence information.

An analysis of higher-order structures of globular proteins by means of a distance-constraint approach is presented. Conformations are generated for each of 21 test proteins of small and medium sizes by optimizing an objective function f = SIGMA-SIGMA-w(ij)(d(ij) - &lt;d(ij)&gt;)2, where d(ij) is a distance between residues i and j in a calculated conformation, &lt;d(ij)&gt; is an assigned distance to the (ij) pair of residues which is determined based on the statistics of known three-dimensional structures of 14 proteins in the earlier study, and w(ij) is a weighting factor. &lt;d(ij)&gt; involves information about hydrophobicity and hydrophilicity of each amino acid residue and about connectivity of a polypeptide chain. In these calculations, only the amino acid sequence is used as input data specific to a calculated protein. With respect to higher-order structures regenerated in the optimized conformations, the following properties are analyzed: (a) N14 of a residue, defined as the number of residues surrounding the residue located within a sphere of radius of 14 angstrom; (b) root-mean-square differences of the global and localconformations from the corresponding X-ray conformations; (c) distance profiles in the short and medium ranges; and (d) distance maps. The effects of supplementary information about locations of secondary structures and disulfide bonds are also examined to discuss the potential ability of this methodology to predict the three-dimensional structures of globular proteins.