Analyzing the normal mode dynamics of macromolecules by the component synthesis method: Residue clustering and multiple-component approach

A study of the component synthesis method (CSM) for analyzing the normal mode dynamics of macromolecules is reported. The procedure involves a reduction of the dimensions of the normal mode problems for large molecular systems and the accurate extraction of the low-frequency modes. A macromolecule is divided into small components based on a hierarchical clustering of the residues in the structure. Interactions between coupled components are treated by the method of static correlation. The normal modes of the components are obtained first, and a fraction of the low-frequency normal modes of the components under mutual correlations are then used as a reduced basis for solving for the normal modes of the whole molecule. Multiple components are introduced for large macromolecules so that the dimensions of the eigenvalue problems at the component level are small. The method is applied to the protein crambin. In test calculations in which the dimensions of the eigenvalue equations are reduced to 1/6 of their natural size, the errors in the normal mode frequencies calculated by the CSM procedure are only about 1–2% when compared with the exact values. The rms fluctuations of all atoms in crambin calculated by the CSM procedure are basically identical to the exact results. The CSM procedure is shown to be accurate for calculating the normal modes of large macromolecules with a significant reduction of the size of the problem. © 1994 John Wiley & Sons, Inc.     

Conformations of the central transforming region (Ile 55-Met 67) of the p21 protein and their relationship to activation of the protein

The GTP-binding p21 protein, encoded by the ras-oncogene, becomes transforming if amino acid substitutions are made at critical positions in the polypeptide chain, e.g., at Gly 12, Gly 13, Ala 59, Gln 61 and Glu 63. Most of these substitutions occur in two phosphate-binding loop regions, Tyr 4-Thr 20, herein designated as segment 1, and Ile 55-Met 67, herein designated, as segment 2. These two segments are homologous to two corresponding regions in the two purine nucleotide binding proteins, bacterial elongation factor (EF-tu) (Val 12-Thr 28 corresponds to segment 1; His 78-Ile 92 corresponds to segment 2) and adenylate kinase (ADK) (Lys 9-Cys 25 corresponds to segment 1 and Tyr 95-Arg 107 corresponds to segment 2). We find that the conformations of the segment 1 region in the p21 protein, EF-tu and ADK are similar to one another and that the conformation of the segment 2 region of EF-tu is superimposable on that of segment 2 of ADK. Furthermore, the relative position of the two segments in EF-tu is strikingly similar to that of the two segments in ADK. In the originally proposed X-ray structure for the p21 protein, the conformation of segment 2 in the p21 protein is not similar to that found for the other two proteins, and its disposition relative to segment 1 and the remainder of the protein is also different from that observed for the other two proteins.(ABSTRACT TRUNCATED AT 250 WORDS)     

Theoretical studies of protein conformation by means of energy computations

In this review we describe fundamental concepts and applications of conformational energy computations, with emphasis on some recent advances and problems being investigated. The formulation of potential energy functions is described, including the nature of the intramolecular force field, the representation of interactions with the solvent, and considerations of entropy contributions. Approaches to the search for the optimal potential energy are summarized. Examples cited among applications of conformational energy computations include refinement of X-ray crystallographic structures, the use of computations in conjunction with NMR data, prediction of the structures of proteins based on either homology or on other procedures that surmount the multiple-minima problem, the analysis of hierarchical levels of structure and assembly, and interactions in enzyme-substrate complexes.     

Prediction of the packing arrangement of strands in β-sheets of globular proteins

A method is proposed for predicting the adjacency order in which strands pack in a -sheet in a protein, on the basis of its amino acid sequence alone. The method is based on the construction of a predicted contact map for the protein, in which the probability that various residue pairs are close to each other is computed from statistically determined average distances of residue pairs in globular proteins of known structure. Compact regions, i.e., portions of the sequence with many interresidue contacts, are determined on the map by using an objective search procedure. The proximity of strands in a -sheet is predicted from the density of contacts in compact regions associated with each pair of strands. The most probable -sheet structures are those with the highest density of contacts. The method has been tested by computing the probable strand arrangements in a five-strand -sheet in five proteins or protein domains, containing 62–138 residues. Of the theoretically possible 60 strand arrangements, the method selects two to eight arrangements as most probable; i.e., it leads to a large reduction in the number of possibilities. The native strand arrangement is among those predicted for three of the five proteins. For the other two, it would be included in the prediction by a slight relaxation of the cutoff criteria used to analyze the density of contacts.     

Local interactions favor the native 8-residue disulfide loop in the oxidation of a fragment corresponding to the sequence Ser-50-Met-79 derived from bovine pancreatic ribonuclease A

A 30-residue peptide was obtained from ribonuclease A by chemical cleavage with cyanogen bromide, subsequent sulfitolysis with concomitant S-sulfonation, and finally enzymatic cleavage withStaphylococcus aureus protease. The peptide was converted to the free thiol form by reductive cleavage of the S-sulfo-protecting groups withd,l-dithiothreitol. This peptide consisted of residues 50–79 of the native sequence of ribonuclease A, with the exception that methionine-79 had been converted to homoserine. Included in this sequence are residues cysteine-65 and cysteine-72, which form a disulfide bond in the native enzyme, as well as cysteine-58. This molecule may form one of three possible intramolecular disulfide bonds upon thiol oxidation, viz. one loop of 15 and 2 of 8 residues each. These isomeric peptides were prepared by oxidation with cystamine, 2-aminoethanethiolation of residual thiols, and fractionation by reverse-phase high-performance liquid chromatography. Disulfide pairings were established by mapping the tryptic fragments and confirming their composition by amino acid analysis. After protracted incubation under oxidizing conditions at 25.0°C andp H 8.0, the 26-member ring incorporating the native disulfide bond between residues 65 and 72 is the dominant product. Assuming that equilibrium is established, we infer that local interactions in the sequence of ribonuclease A significantly stabilize the native 8-residue disulfide loop with respect to the non-native 8-residue loop (G°=–1.1±0.1 kcal mole^–1). The implications of this observation for the oxidative folding of the intact protein are discussed.     

Calculations on crystal packing of a flexible molecule, Leu-enkephalin

Crystal packing calculations have been carried out on a substantial number of conformations of Leu-enkephalin; namely, those obtained both from crystal structures and from energy minimizations on isolated molecules, and with and without waters of crystallization. The known crystal structures represent the most energetically stable packings found. The conformations of the enkephalin molecules in the crystal are not the most stable for an isolated molecule; i.e. intermolecular interactions force the isolated molecule to change conformation in order to achieve a small packing volume and an optimal packing energy in the crystal. It is found that the packing energy of an enkephalin molecule is a reasonably smooth function of its molecular volume in the unit cell, if structures with intermolecular hydrogen bonding are excluded, and is substantially independent of other details of the molecular conformation or of the crystal packing. Hydrogen bonding provides additional stabilization of the crystal structure, and would likely permit crystallization of the system if it is sufficiently dense. Solvent molecules further stabilize the structure when they can also provide intermolecular hydrogen bonds.     

Stability of polypeptide conformational states. II. Folding of a polypeptide chain by the scanning simulation method, and calculation of the free energy of the statistical coil

The scanning simulation method suggested by Meirovitch is extended to a study of the stability of decaglycine at 100 and 300 K. The model is based on the potential energy function ECEPP (Empirical Conformational Energy Program for Peptides) with rigid geometry and without solvent. The free energy of the statistical coil, which is defined over the whole phase space excluding the region of the right-handed α-helix, is calculated. At 100 K, the molecule is found to be unstable in the statistical coil region, and the method generates (i.e., “folds”) conformations that are left-handed or right-handed α-helices with very high preference. Their free energy is found to be comparable with that obtained by another method developed in our previous paper (paper I) [H. Meirovitch, M. Vásquez, and H. A. Scheraga, (1987) Biopolymers 26 , 651–671]. At 300 K the statistical coil becomes the most stable state; sample conformations of the coil are generated efficiently with the scanning method and the free energy is calculated. It appears that both the scanning method and the method of paper I can be used to carry out a complete analysis of the stability of a polypeptide based on free energy considerations.     

Preliminary crystallographic data for cross-linked (lysine7-lysine41)-ribonuclease A

A cross-linked derivative of ribonuclease A, N^ε,N^ε′-(2,4-dinitrophenylene-1,5)-(lysine⁷-lysine⁴¹)-RNase A, has been crystallized by dialysis against 30% ($\text{v}\text{v}$) ethanol/water mixtures buffered at high pH. Single crystals belong to the orthorhombic space group P2₁2₁2₁, $\text{a = 37.2}\text{A}\text{?}\text{, b = 41.2}\text{A}\text{?}\text{, b = 41.2}\text{A}\text{?}$, with one molecule in the Crystallographic asymmetric unit.