Tatsuo Ooi

Tertiary Structure of Proteins. I. Representation and Computation of the Conformations

A protein conformation can be computed by connecting peptide units of usual trans-planar structure successively with a given set of dihedral angles ϕ and ψ. It is, however, not easy to generate the native conformations such as myoglobin and lysozyme by the computation. In order to show the discrepancy between the native conformation and the computed one, we have introduced a map, where the mutual distance between C α -atoms of i -th and j -th residue , r i j , is listed against the residue number, in row and column. This map represents a tertiary structure of the protein (e. g. α-helix, β-structure) as the characteristic patterns. It becomes possible to estimate the difference of the computed conformation from the native one numerically by comparing the corresponding maps. The improvement of the dihedral angles, ϕ and ψ, as made by minimizing the deviation of the computed map from the native one on both myoglobin and lysozyme.

Comparison of homologous tertiary structures of proteins.

Homology in sequences of proteins which have the same or similar function has been studied as a problem of comparative biochemistry and molecular evolution. It is therefore of interest to examine homology in three-dimensional structures, e.g. whether folding of polypeptides having common residues gives rise to the same tertiary structure or not. Two methods, a difference map and a superposition technique, were used to evaluate the similarity in tertiary structures of proteins; hemoglobin α -chain, β -chain, and myoglobin: α -chymotrypsin and elastase. The results show that homologous folding of homologous chains is found for sequences of internal residues, while discrepancies occur mostly at surface regions, and some portions having common residues do not have the same structure. Another spatial homology was found in two halves of chymotrypsin separated about the middle of the chain, one folded from the N-terminus toward the C-terminus and the other from the C-terminus toward the N-terminus, forming a symmetrical pattern in the distance map. The results of superposition show that 80% of the internal residues correspond in space. Those results suggest the importance of internal residues for the tertiary structure of a protein.

Homology in protein sequences expressed by correlation coefficients

Abstract Internal homologies in an amino acid sequence of a protein and in amino acid sequences of two different proteins are examined, using correlation coefficients calculated from the sequences when residues are replaced by various quantitative properties of the amino acids such as hydrophobicity. To improve the signal-noise ratio the average correlation coefficient is used to detect homology because the correlation depends on the property considered. In this way, any sequence repetition in a protein and the extent of the similarity and difference among proteins can be estimated quantitatively. The procedure was applied first to the sequences of proteins which have been assumed on other grounds to contain some internal sequence repetitions, α-tropomyosin from rabbit skeletal muscle, calmodulin from bovine brain, troponin C from skeletal and cardiac muscle, and then to the sequences of calcium binding proteins, calmodulin, troponin C, and L2 light chain of myosin. The results show that α-tropomyosin has a markedly periodic sequence at intervals of multiples of seven residues throughout the whole sequence, and calmodulin and skeletal troponin C contain two homologous sequences, the homology of troponin C being weaker than that of calmodulin. Candidates for the calcium binding regions of both troponin C, calmodulin, and L2 light chain are the homologous parts having a high average correlation coefficient (about 0·5) with respect to the sequences of the CD and EF hand regions of carp parvalbumin. The procedure may be a useful method for searching for homologous segments in amino acid sequences.

Relation between sequence similarity and structural similarity in proteins. Role of important properties of amino acids

In a previous paper we obtained ten (orthogonal) factors, linear combinations of which can express the properties of the 20 naturally occurring amino acids. In this paper, we assume that the most important properties (linear combinations of these ten factors) that determine the three-dimensional structure of a protein are conserved properties, i.e., are those that have been conserved during evolution. Two definitions of a conserved property are presented: (1) a conserved property for an average protein is defined as that linear combination of the ten factors that optimally expresses the similarity of one amino acid to another (hence, little change during evolution), as given by the relatedness odds matrix of Dayhoff et al.; (2) a conserved property for each position in the amino acid sequence (locus) of a specific family of homologous proteins (the cytochromec family or the globin family) is defined as that linear combination of the ten factors that is common among a set of amino acids at a given locus when the sequences are properly aligned. When the specificity at each locus is averaged over all loci, the same features are observed for three expressions of these two definitions, namely the conserved property for an average protein, the average conserved property for the cytochromec family, and the average conserved property for the globin family; we find that bulk and hydrophobicity (information about packing and long-range interactions) are more important than other properties, such as the preference for adopting a specific backbone structure (information about short-range interactions). We also demonstrate that the sequence profile of a conserved property, defined for each locus of a protein family (definition 2), corresponds uniquely to the three-dimensional structure, while the conserved property for an average protein (definition 1) is not useful for the prediction of protein structure. The amino acid sequences of numerous proteins are searched to find those that are similar, in terms of the conserved properties (definition 2), to sequences of the same size from one of the homologous families (cytochromec and globin, respectively) for whose loci the conserved properties were defined. Many similar sequences are found, the number of similarities decreasing with increasing size of the segment. However, the segments must be rather long (≥15 residues) before the comparisons become meaningful. As an example, one sufficiently large sequence (20 residues) from a protein of known structure (apo-liver alcohol dehydrogenase that is not a member of either family) is found to be similar in the conserved properties to a particular sequence of a member of the family of human hemoglobin α chains, and the two sequences have similar structures. This means that, since conserved properties are expected to be structure determinants, we can use the conserved properties to predict an initial protein structure for subsequent energy minimization for a protein for which the conserved properties are similar to those of a family of proteins with a sufficiently large number of homologous amino acid sequences; such a large number of homologous sequences is required to define a conserved property for each locus of the homologous protein family.

An analysis of non-bonded energy of proteins

Abstract Non-bonded energy of 16 proteins was calculated using the atomic co-ordinates obtained by X-ray crystallography. The curve of total energy against the number of atoms in proteins is approximately linear with a slight concaved shape. According to a linear equation to fit the curve, the extrapolated length of a polypeptide chain of a globular shape is expected to be 18 residues, which corresponds conceivably to an approximate size of nucleus for a folding of the polypeptide chain. Contributions from short-range and medium-range energies are always much greater than those from long-range energy for all the proteins and there seems to exist a change of each contribution in a range from 1200 to 1700 atoms. The energies with a lag less than four residues are a major part of the total energy and the contribution of energy from main-chain atoms is considerably higher than that from side-chain atoms. Side-chain atoms of a residue have a tendency to interact more strongly with main-chain atoms of N-terminal, than with those of C-terminal side of the residue, indicating asymmetry of the interaction in a protein. Amino acid residues in proteins may be divided into three groups by the order of strength of average energy. The first group exhibiting strong interaction consists mainly of hydrophobic amino acids and the third group consists of hydrophilic ones corresponding to the location in a protein molecule. Cys, val, leu and met are important for medium-range and long-range energies; gly and ala for medium-range energy; ile, trp, phe, tyr and arg for long-range energy. One simple application of the average energy of amino acid residues is illustrated to estimate local energy of a segment of nine residues given by a protein sequence. There is a good correlation between the curve computed by the average energy and the experimental curve for myoglobin.

Multiple pathways for regenerating ribonuclease A

This paper is concerned with the pathways for the regeneration of RNase A from the reduced protein by a mixture of GSSG and GSH. Experimental work on the regeneration has led to the identification of several different pathways, depending on the concentrations of GSH and GSSG, and an energetic analysis has provided information about the stabilities of the various intermediates. The equilibrium and kinetic data for the regeneration process have led to two models of protein-folding pathways. The intermediates in the regeneration process were trapped without chemical modification, and were fractionated on a carboxymethyl-cellulose column. The regeneration pathway(s) could be represented in terms of two simple reactions (Eqs. (1) and (2)). The system rapidly reaches a pre-equilibrium among the intermediates prior to the rate-limiting steps, and the concentrations of the intermediates (and hence the equilibrium constants among them) were determined. The regeneration process was also re-started from several of the isolated intermediates, and led to the predicted distribution of intermediates in the pre-equilibrium. Kinetic data, obtained by following the time dependence of the regain of enzymatic activity, together with the distributions of the intermediates at pre-equilibrium, led to the identification of the rate limiting steps, which differed according to the concentrations of GSH and GSSG. The relative apparent standard state conformational chemical potentials of the intermediates were estimated by using data for the apparent equilibrium constants (among the species in pre-equilibrium) and for the redox potentials of cysteine/cystine and GSH/GSSG. The two models deduced from the equilibrium and kinetic data are designated as growth-type and rearrangement-type models. In the growth-type model, nucleation of the native-like structure occurs in the folding process, in the rate-limiting step(s), and subsequent folding around the nucleation sites proceeds smoothly to form the native disulfide bonds and conformation. In the rearrangement-type model, proper nucleation does not occur in the folding process; instead, non-native interactions play a significant role in the folding pathways and lead to metastable intermediate species. Such non-native interactions must be disrupted or rearranged to nucleate the native interactions (in the rate limiting step(s)) for the protein to fold. Other protein foldings, reported in the literature, can be shown to conform to this model.

Correspondence of homologies in amino acid sequence and tertiary structure of protein molecules

According to the method developed previously (Kubota, Y., Takahashi, S., Nishikawa, K. and Ooi, T. (1981) J. Theor, Biol. 91, 347-361), homology among proteins may be estimated quantitatively. We extended the method to investigate the relationship of an amino acid sequence to its teritary structure and identify homologous segments which have homologous native conformations in proteins. First, we selected proper indices for the computation of correlation coefficients from 32 properties inherent to amino acids, such as hydrophobicity. The arithmetic average of correlation coefficients using six indices gave rise to a good correlation for the CD- and EF-hand regions (Ca2+ binding sites) in carp parvalbumin, but poor ones for other segments. We then applied the method to homologous proteins, the three-dimensional structures of which are known: horse hemoglobin alpha-chain and beta-chain; cytochrome c and c2; serine proteases, chymotrypsinogen and elastase; alpha-lytic protease and protease A from prokaryotic organisms. The results show that the sequence homology estimated by the present method has a good correspondence to the homology in three-dimensional structures and therefore the method is promising for the identification of important sites in sequences which have similar native conformations. For an example of the application of the method, two sequences of human interferon, one from fibroblast and the other from leukocyte, are compared, suggesting functional sites in the molecule.

Actin: Volume Change on Transformation of G-Form to F-Form

The volume change occurring on polymerizing actin was measured by dilatometry. A large positive value of + 391 ml/mole was obtained for the volume change during the transformation of G- to F-actin. This large increase in volume could be interpreted as arising from the local change in the ordered water structure on the proteins surface at polymerizing sites.

Comparison of amino acid sequences between phosphoenolpyruvate carboxylases from Escherichiacoli (allosteric) and anacystisnidulans (non-allosteric): Identification of conserved and variable regions

Amino acid sequences of phosphoenolpyruvate carboxylases of Escherichia coli (allosteric) and a cyanobacterium Anacystis nidulans (non-allosteric) were aligned. The pattern of homology suggests that the enzyme molecule is comprised of two distinct regions, namely, a conserved region (C-terminal half) and a variable region (N-terminal half). Among the amino acid residues which have previously been presumed essential for the catalytic activity, three histidine residues were found to be conserved, but cysteine residues were not. Furthermore, the conserved sequence unique to the enzyme was identified by comparison of the enzyme sequence with amino acid sequences in our data bank.

Flexibility of bovine pancreatic trypsin inhibitor.

The native conformation of a protein may be expressed in terms of the dihedral angles, phis and psis for the backbone, and kappas for the side chains, for a given geometry (bond lengths and bond angles). We have developed a method to obtain the dihedral angles for a low-energy structure of a protein, starting with the X-ray structure; it is applied here to examine the degree of flexibility of bovine pancreatic trypsin inhibitor. Minimization of the total energy of the inhibitor (including nonbonded, electrostatic, torsional, hydrogen bonding, and disulfide loop energies) yields a conformation having a total energy of -221 kcal/mol and a root mean square deviation between all atoms of the computed and experimental structures of 0.63 A. The optimal conformation is not unique, however, there being at least two other conformations of low-energy (-222 and -220 kcal/mol), which resemble the experimental one (root mean square deviations of 0.66 and 0.64 A, respectively). These three conformations are located in different positions in phi, psi space, i.e., with a total deviation of 81 degrees, 100 degrees and 55 degrees from each other (with a root mean square deviation of several degrees per dihedral angle from each other). The nonbonded energies of the backbones, calculated along lines in phi, psi space connecting these three conformations, are all negative, without any intervening energy barriers (on an energy contour map in the phi, psi plane). Side chains were attached at several representative positions in this plane, and the total energy was minimized by varying the kappas. The energies were of approximately the same magnitude as the previous ones, indicating that the conformation of low energy is flexible to some extent in a restricted region of phi, psi space. Interestingly, the difference delta phi i+1 in phi i+1 for the (i + 1)th residue from one conformation to another is approximately the same as -delta psi i for the ith residue; i.e., the plane of the peptide group between the ith and (i + 1)th residues re-orient without significant changes in the positions of the other atoms. The flexibility of the orientations of the planes of the peptide groups is probably coupled in a cooperative manner to the flexibility of the positions of the backbone and side-chain atoms.