The reconstruction of side-chain conformations from protein Cα coordinates

A model of nine proteins including side-chain atoms have been built from the known C^α coordinates and amino acid sequences using a Monte Carlo Protein Building Annealing method. The Cartesian coordinates for the side-chain atoms were established with bond lengths and angles selected randomly from within previously determined ranges. A simulated annealing technique is used to generate some 300 structures with differing side-chain conformations. The atomic coordinates of the backbone atoms are fixed during the simulated annealing process. The coordinates of the side-chain atoms of 300 low energy conformations are averaged to obtain a mean structure that is minimized with the C^α atoms constrained to their position in the x-ray structure using the OPLS/AMBER force field with the GB/SA water model. The rms deviation of the main-chain atoms (without C^β) compared with the corresponding crystal structures is in the range 0.20–0.64 Å. The rms deviation of the side-chain atoms is between 1.72 and 2.71 Å and for all atoms is between 1.19 and 1.99 Å. The method is insensitive to random errors in the C^α positions and the computational requirement is modest. © 1997 John Wiley & Sons, Inc.     

Directional structural features of globular proteins

We describe a novel presentation of the conformation of the backbone atoms for proteins of known structure. Given the C^α atom cartesian co-ordinates from X-ray crystallography, a matrix is calculated, where the ijth element of the matrix is the cosine of the angle between the direction of the chain at residue i and the direction of the chain at residue j. These “direction matrices” have distinctive patterns which correspond to α-helix, extended structure, straight or bent segments, “superhelix”, and many other important structural features. We discuss the direction matrices for a number of proteins, and make some generalizations on the basic principles of protein folding.     

Characterization of multiple bends in proteins

The concept of bends or chain reversals [nonhelical dipeptide sequences in which the distance R₃ (i,i+3) between the C^α atoms of residues i and i+3 is ≦ 7.0 Å] has been extended to define double bends as tripeptide sequences, not in an α-helix, in which two successive distances R₃(i,i+3) and R₃ (i+1, i+4) are both ≦7.0 Å, with analogous definitions for higher-order multiple bends. A sample of 23 proteins, consisting of 4050 residues, contains 235 single, 58 double, and 11 higher-order multiple bends. Multiple bends may occur as combinations of the “standard” type I, II, and III chain reversals (as well as their mirror images), but usually they require distortions from these well-defined conformations. The frequency of occurrence of amino acids often differs significantly between single and multiple bends. The probability distribution of R₃ distances does not differ in single and multiple bends. However, R₄ (the distance between the C^α atoms of residues i and i+4) in multiple bends is generally shorter than in tripeptide sequences containing single bends. The value of R₄ in many multiple bends is near those for α-helices. In some other multiple bends, R₄ is even shorter, indicating that these structures are very compact. The signs of the dihedral angles about the virtual bonds connecting C^α atoms and the values of curvature and torsion, as defined by means of differential geometry, indicate that there is a preference for single and multiple bends to be right-handed (like an α-helical sequence, for example) and that there is a strong tendency to conserve the handedness in both single-bend components of many multiple bends. These often have a strong resemblance to distorted single turns of an α-helix and do not constitute chain reversals. Double bends, in which the signs of two successive virtual-bond dihedral angles differ, have conformations that are very different from an α-helix. They act as chain reversals occuring over three residues. These chain reversals have not been described previously. Multiple bends may play an important role in protein folding because they occur fairly frequently in proteins and cause major changes in the direction of the polypeptide chain.     

Accurate geometries for “Mountain pass” regions of the Ramachandran plot using quantum chemical calculations

Unusual local arrangements of protein in Ramachandran space are not well represented by standard geometry tools used in either protein structure refinement using simple harmonic geometry restraints or in protein simulations using molecular mechanics force fields. In contrast, quantum chemical computations using small poly‐peptide molecular models can predict accurate geometries for any well‐defined backbone Ramachandran orientation. For conformations along transition regions—ϕ from −60 to 60°—a very good agreement with representative high‐resolution experimental X‐ray (≤1.5 Å) protein structures is obtained for both backbone C⁻¹‐N‐C_α angle and the nonbonded O⁻¹…C distance, while “standard geometry” leads to the “clashing” of O…C atoms and Amber FF99SB predicts distances too large by about 0.15 Å. These results confirm that quantum chemistry computations add valuable support for detailed analysis of local structural arrangements in proteins, providing improved or missing data for less understood high‐energy or unusual regions.     

Conformational energy calculations with averaged potential functions: Application to the repeat peptides of elastin

We present a method that can reduce conformational energy calculations for an arbitrary peptide consisting of n residues (n-peptide) to the complexity of a computation for (Gly)_n. This reduction, and the concomitant savings in computer time, is accomplished by replacing all side chains, as well as the backbone C^αH^α and C^αH₂^α groups, by “interaction centers.” The backbone CONH group is left intact in order to preserve its directional character. The interaction centers “see” each other, and the atoms of the CONH group via Boltzmann and space-averaged effective center-center and center-atom potentials, respectively. This averaged-interaction method is tested on the repeat tetra-, penta-, and hexapeptides of elastin, Val-Pro-Gly-Gly (VPGG), Val-Pro-Gly-Val-Gly (VPGVP), and Ala-Pro-Gly-Val-Gly-Val (APGVGV), using the stereoalphabet strategy for the energy calculations. The excellent qualitative and quantitative agreement we obtain with both full atom-atom calculations and extensive nmr data, coupled with the order-of-magnitude reduction in computer time, augurs well for the potential usefulness of the method.     

Improving the physical realism and structural accuracy of protein models by a two-step atomic-level energy minimization

Most protein structural prediction algorithms assemble structures as reduced models that represent amino acids by a reduced number of atoms to speed up the conformational search. Building accurate full-atom models from these reduced models is a necessary step toward a detailed function analysis. However, it is difficult to ensure that the atomic models retain the desired global topology while maintaining a sound local atomic geometry because the reduced models often have unphysical local distortions. To address this issue, we developed a new program, called ModRefiner, to construct and refine protein structures from Cα traces based on a two-step, atomic-level energy minimization. The main-chain structures are first constructed from initial Cα traces and the side-chain rotamers are then refined together with the backbone atoms with the use of a composite physics- and knowledge-based force field. We tested the method by performing an atomic structure refinement of 261 proteins with the initial models constructed from both ab initio and template-based structure assemblies. Compared with other state-of-art programs, ModRefiner shows improvements in both global and local structures, which have more accurate side-chain positions, better hydrogen-bonding networks, and fewer atomic overlaps. ModRefiner is freely available at http://zhanglab.ccmb.med.umich.edu/ModRefiner.     

The isochore patterns of mammalian genomes and their phylogenetic implications

The compositional distributions of high molecular weight DNA fragments from 20 species belonging to 9 out of the 17 eutherian orders were investigated by analytical CsCl density gradient centrifugation and by preparative fractionation in Cs₂SO₄/BAMD density gradients followed by analysis of the fractions in CsCl. These compositional distributions reflect those of the isochores making up the corresponding genomes. A “general distribution” was found in species belonging to eight mammalian orders. A “myomorph distribution” was found in Myomorpha, but not in the other rodent infraorders Sciuromorpha and Histricomorpha, which share the general distribution. Two other distributions were found in a megachiropteran (but not in microchiropteran, which, again, shares the general distribution) and in pangolin (a species from the only genus of the order Pholidota), respectively. The main difference between the general distribution and all other distributions is that the former contains sizable amounts (6–10%) of GC-rich isochores (detected as DNA fragments equal to, or higher than, 1.710 g/cm³ in modal buoyant density), which are scarce, or absent, in the other distributions. This difference is remarkable because gene concentrations in mammalian genomes are paralleled by GC levels, the highest gene concentrations being present in the GC-richest isochores. The compositional distributions of mammalian genomes reported here shed light on mammalian phylogeny. Indeed, all orders investigated, with the exception of Pholidota, seem to share a common ancestor. The compositional patterns of the megachiropteran and of Myomorpha may be derived from the general pattern or have independent origins.     

Structural versatility of peptides from Cα,α-dialkylated glycines. I. A conformational energy computation and x-ray diffraction study of homo-peptides from Cα,α-diethylglycine

Conformational energy computations on a derivative and a homo-dipeptide of C^α,α-diethylglycine were performed. In both cases the N- and C-terminal groups are blocked as acetamido and methylamido moieties, respectively. It was found that the C^α,α-diethylglycine residues are conformationally restricted and that the minimum energy conformation corresponds to the fully extended C₅ structure when the N? C^α? C′ bond angle is smaller than 108° (as experimentally observed). The results of the theoretical analysis are in agreement with the crystal-state structural propensity of the complete series of N-trifluoroacetylated homo-peptides of this C^α,α-dialkylated residue from monomer to pentamer, determined by x-ray diffraction and also described in this work. Interestingly, for the first time, a crystallographically planar peptide backbone was observed (in the protected tripeptide). A comparison with peptides of C^α,α-dimethylglycine, C^α-methyl, C^α-ethylglycine, and C^α,α-di-n-propylglycine indicates that the fully extended conformation becomes more stable than the helical structures when both amino acid side-chain C^β atoms are substituted.     

Hash: a program to accurately predict protein Hα shifts from neighboring backbone shifts

Chemical shifts provide not only peak identities for analyzing nuclear magnetic resonance (NMR) data, but also an important source of conformational information for studying protein structures. Current structural studies requiring H^α chemical shifts suffer from the following limitations. (1) For large proteins, the H^α chemical shifts can be difficult to assign using conventional NMR triple-resonance experiments, mainly due to the fast transverse relaxation rate of C^α that restricts the signal sensitivity. (2) Previous chemical shift prediction approaches either require homologous models with high sequence similarity or rely heavily on accurate backbone and side-chain structural coordinates. When neither sequence homologues nor structural coordinates are available, we must resort to other information to predict H^α chemical shifts. Predicting accurate H^α chemical shifts using other obtainable information, such as the chemical shifts of nearby backbone atoms (i.e., adjacent atoms in the sequence), can remedy the above dilemmas, and hence advance NMR-based structural studies of proteins. By specifically exploiting the dependencies on chemical shifts of nearby backbone atoms, we propose a novel machine learning algorithm, called Hash, to predict H^α chemical shifts. Hash combines a new fragment-based chemical shift search approach with a non-parametric regression model, called the generalized additive model, to effectively solve the prediction problem. We demonstrate that the chemical shifts of nearby backbone atoms provide a reliable source of information for predicting accurate H^α chemical shifts. Our testing results on different possible combinations of input data indicate that Hash has a wide rage of potential NMR applications in structural and biological studies of proteins.     

Hemoglobin switching in sheep: commitment of erythroid stem cells to expression of the betaC-globin gene and accumulation of betaC-globin mRNA

The switch from HbA (α₂β₂^A) to HbC (α₂β₂^C) synthesis was induced by injection of erythropoietin into a lamb homozygous for HbA. Serial samples of bone marrow were analyzed to detect the initial commitment of erythroid stem cells (CFU-E) to form colonies which made HbC in vitro, and to detect the initial accumulation of β^C-globin mRNA and the onset of HbC synthesis in erythroblasts in vivo. CFU-E-derived erythroid colonies were formed in plasma clot culture at a low erythropoietin concentration, and the relative amounts of β^A- and β^C-globin synthesized were determined after a 24 hr pulse of ³H-leucine, added after 84 hr in culture. RNA was extracted from nuclei and cytoplasm of “early” and “late” populations of bone marrow erythroblasts which had been fractionated by Ficoll-Hypaque density centrifugation. The concentration of β^A- and β^C-globin mRNA was determined by annealing to purified synthetic DNAs (cDNAs) complementary to β^A and β^C mRNA. No β^C-globin was synthesized in erythroblasts or in CFU-E-derived erythroid colonies prior to the injection of erythropoietin. An increase in the concentration of CFU-E in the bone marrow and the appearance of β^C-globin synthesis in CFU-E-derived colonies were detected 12 hr after the erythropoietin injection. In contrast, β^C mRNA was not detected in either “early” or “late” erythroid cells until 36 hr later. The first measurable β^C-globin mRNA was accompanied by the appearance of β^C-globin synthesis in bone marrow erythroblasts. Our results suggest that the accumulation of β^C-globin mRNA is a relatively late event following induction of HbA to HbC switching by erythropoietin. The expansion of the compartment of erythroid stem cells and the commitment of CFU-E to β^C-globin synthesis appear to precede the detectable accumulation of β^C mRNA by 24–36 hr.     

A simple two-dimensional representation for the common secondary structural elements of polypeptides and proteins

A simple method is presented for projecting the conformation of extended secondary structure elements of peptides and proteins that extend over four C^αatoms onto a simple two-dimensional surface. A new set of two degrees of freedom is defined, a pseudo-dihedral involving four sequential C^αatoms, as well as the triple scalar product for the vectors describing the orientation of the three intervening peptide groups. The method provides a reduction in dimensionality, from the usual combination of multiple ϕ,ψ pairs to a single pair, yielding valuable information concerning the structure and dynamics of these important elements. The new two-dimensional surface is explored by reference to 63 selected protein crystal structures together with a comparison of model built peptides representing the common secondary structural elements. Dynamical aspects on this new surface are examined using a molecular dynamics trajectory of Basic Pancreatic Trypsin Inhibitor. © 1997 Wiley-Liss, Inc.     

Conformational Preferences of Modified Nucleoside N(4)-Acetylcytidine, ac4C Occur at “Wobble” 34th Position in the Anticodon Loop of tRNA

Conformational preferences of modified nucleoside, N(4)-acetylcytidine, ac⁴C have been investigated using quantum chemical semi-empirical RM1 method. Automated geometry optimization using PM3 method along with ab initio methods HF SCF (6-31G**), and density functional theory (DFT; B3LYP/6-31G**) have also been made to compare the salient features. The most stable conformation of N(4)-acetyl group of ac⁴C prefers “proximal” orientation. This conformation is stabilized by intramolecular hydrogen bonding between O(7)···HC(5), O(2)···HC2′, and O4′···HC(6). The “proximal” conformation of N(4)-acetyl group has also been observed in another conformational study of anticodon loop of E. coli elongator tRNA^Met. The solvent accessible surface area (SASA) calculations revealed the role of ac⁴C in anticodon loop. The explicit molecular dynamics simulation study also shows the “proximal” orientation of N(4)-acetyl group. The predicted “proximal” conformation would allow ac⁴C to interact with third base of codon AUG/AUA whereas the ‘distal’ orientation of N(4)-acetyl cytidine side-chain prevents such interactions. Single point energy calculation studies of various models of anticodon–codon bases revealed that the models ac⁴C₍₃₄₎(Proximal):G₃, and ac⁴C₍₃₄₎(Proximal):A₃ are energetically more stable as compared to models ac⁴C₍₃₄₎(Distal):G₃, and ac⁴C₍₃₄₎(Distal):A₃, respectively. MEPs calculations showed the unique potential tunnels between the hydrogen bond donor–acceptor atoms of ac⁴C₍₃₄₎(Proximal):G₃/A₃ base pairs suggesting role of ac⁴C in recognition of third letter of codons AUG/AUA. The “distal” conformation of ac⁴C might prevent misreading of AUA codon. Hence, this study could be useful to understand the role of ac⁴C in the tertiary structure folding of tRNA as well as in the proper recognition of codons during protein biosynthesis process.     

Influence of methanol on the rotational diffusion of poly(L-lysine) in the helix–coil transition

¹³C spin-lattice relaxation times of poly(L -lysine) have been obtained at 67.9 MHz in aqueous solution and in a mixed solvent (40% methanol/60% water). A concomitant determination of the conformation by CD permits the correlation of conformation and rotational diffusion of the polymer. The dependence on pH of the spin-lattice relaxation times of the ¹³C^α and the side-chain carbon resonances reflects the diffusional motion in the random-coil conformation, in the helix–coil transition, and in the conformation of the α-helix. In the mixed solvent the reorientational correlation time of the C^α-H^α vector increases from τ = 0.37 nsec (random coil) to τ = 12.0 nsec (α-helix). In aqueous solution the correlation time of this vector increases from τ = 0.33 nsec (random coil) to τ ? 11 nsec. The reorientation rates of the side-chain methylene groups in the two solvents are markedly different. The reorientation of all methylene groups is reduced in the mixed solvent.     

Measurement of non-randomness in spatial distributions

The measurement of departure from randomness in spatial distributions has widespread application in ecological work. Several “indices of non-randomness” are compared with regard to their dependence on sample number, sample size and density. Criteria for the best choice of index for specific situations are discussed. A new coefficient C_x is proposed for use with positively contagious distributions and tests of significance are given. When C_x and another index (S²/m−1) are used for positive and negative contagion respectively, values ranging from −1 through 0 (random) to +1 are obtained, regardless of sample number, sample size or density.     

Anisotropic rotational motions of poly(L-glutamic acid) in the alpha-helix conformation

The anisotropic rotational motion of the backbone and the side chains of poly(L -glutamic acid) in the α-helical structure was investigated using the ¹³C-T₁ and T₂ relaxation times of all carbon atoms with directly attached protons, obtained at a ¹³C-Larmor frequency of 67.89 MHz. The evaluation of the nmr data was carried out according to the previously derived anisotropic diffusion model, in which the macromolecule is considered a rigid rod. The rotation of the backbone is characterized by two diffusion constants, D₁ and D₃, describing the rotation perpendicular to and around the symmetry axis. The additional internal motion of the C^β-methylene group is described as a jump process with a jump rate, k₁, between two allowed rotametric states. Steric considerations indicate that the occupation of the third rotameric position is forbidden. The rotation of the C^γ-methylene group is decribed as a one-dimensional diffusion process around the C^β–C^γ bond. Investigation of the temperature dependence of the relaxation parameters led to the temperature dependence of the dynamic parameters. Activation energies were determined from these data. The dynamic parameters obtained for poly(L -glutamic acid) at 291 K are compared with the corresponding results of a previous study of poly(L -lysine). The development of an anisotropic diffusion model for the motions of the rod-shaped poly(L -lysine) α-helix and its application to the interpretation of the ¹³C-relaxation data of this molecule have already been published previously. In this model, both the overall molecular tumbling and the various internal motions have been characterized by diffusion constants or jump rates typical for each process. These dynamic parameters can be calculated from the spin–lattice relaxation times, the spin–spin relaxation times and the NOE factors of the C^α, C^β, and C^γ nuclei of the polypetide. In the present paper, we describe the application of the above-mentioned dynamic model to the interpretation of ¹³C-relaxation studies of a further homopolypeptide, poly(L -glutamic acid), in the α-helical structure. Furthermore, we studied the temperature dependence of the relaxation times of this polymer and determined the anisotropic diffusion parameters at each temperature. From their temperature dependence and from comparison of our present results with the data of our previous study of poly(L -lysine), we were able to derive new insights into the intramolecular diffusion processes and the excitation of various motions.     

Anharmonic Normal Mode Analysis of Elastic Network Model Improves the Modeling of Atomic Fluctuations in Protein Crystal Structures

Protein conformational dynamics, despite its significant anharmonicity, has been widely explored by normal mode analysis (NMA) based on atomic or coarse-grained potential functions. To account for the anharmonic aspects of protein dynamics, this study proposes, and has performed, an anharmonic NMA (ANMA) based on the C_α-only elastic network models, which assume elastic interactions between pairs of residues whose C_α atoms or heavy atoms are within a cutoff distance. The key step of ANMA is to sample an anharmonic potential function along the directions of eigenvectors of the lowest normal modes to determine the mean-squared fluctuations along these directions. ANMA was evaluated based on the modeling of anisotropic displacement parameters (ADPs) from a list of 83 high-resolution protein crystal structures. Significant improvement was found in the modeling of ADPs by ANMA compared with standard NMA. Further improvement in the modeling of ADPs is attained if the interactions between a protein and its crystalline environment are taken into account. In addition, this study has determined the optimal cutoff distances for ADP modeling based on elastic network models, and these agree well with the peaks of the statistical distributions of distances between C_α atoms or heavy atoms derived from a large set of protein crystal structures.     

Conformational constraints of amino acid side chains in alpha-helices

The conformational freedom of amino acid side chains is strongly reduced when the side chains occur on an α-helix. A quantitative evaluation of this freedom has been carried out by means of conformational energy computations for all naturally occurring amino acids and for α-aminobutyric acid when they are placed in the middle of a right-handed poly(L-alanine) α-helix. One of the three possible rotameric states for rotation around the C^α ? C^β bond (viz. g⁺) is excluded completely on the helix because of steric hindrance, and the relative populations of the other two rotamers (t and g^?) are altered because of steric interactions and the reduction of hydrogen-bonding possibilities. The computed tendencies of the changes in distributions of rotamers, on going from an ensemble of all backbone conformations to the α-helix, agree with the observed tendencies in proteins. Minimum-energy side-chain conformations in an α-helix have been tabulated for use in conformational energy computations on polypeptides.     

Influence du groupe trichloroacéthyle sur les déplacements chimiques des signaux des atomes de carbone du 1,2,3,4,6-penta-O-acéthyl-β-d-glucopyranose et du β-gentiobiose octaacétate en R.M.N.-13C

The influence of the trichloroacetyl group on the ¹³C chemical shift of the substituted and vicinal carbon atoms allows the unambiguous assignment of the signals of the carbon atoms. For derivatives of 1,2,3,4,6-penta-O-acetyl-β-d-glucopyranose and β-gentiobiose octaacetate, the “α-effect” is +4 to +5 p.p.m. (deshielding), whereas the “β-effect” has smaller and always negative values.     

Relationship between conformation and geometry as evidenced by molecular dynamics simulation of Cα,α-dialkylated glycines

The relationship between the local backbone conformation and bond angles at C^α of symmetrically substituted C^α,α-dialkylated glycines (C^α,α-dimethylglycine or α-aminoisobutyric acid, Aib; C^α,α-diethylglycine, Deg; C^α,α-di-n-propylglycine, Dpg) has been investigated by molecular dynamics (MD) simulation adopting flat bottom harmonic potentials, instead of the usual harmonic restraints, for the C^α bond angles. The MD simulations show that the C^α bond angles are related to the local backbone conformation, irrespectively of the side-chain length of Aib, Deg, and Dpg residues. Moreover, the N-C^α-C′ (τ) angle is the most sensitive conformational parameter and, in the folded form, is always larger and more flexible than in the extended one. © 1998 John Wiley & Sons, Inc. Biopoly 46: 239–244, 1998