Calculation of protein conformations by proton-proton distance constraints. A new efficient algorithm

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: the use of variable target functions; and 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.     

1H-NMR studies on nucleotide binding to the sarcoplasmic reticulum Ca2+ ATPase. Determination of the conformations of bound nucleotides by the measurement of proton-proton transferred nuclear Overhauser enhancements

The glycosidic bond torsion angles and the conformations of the ribose of Mg2+ATP, Mg2+ADP and Mg2+AdoPP[NH]P (magnesium adenosine 5'-[beta, gamma-imido]triphosphate) bound to Ca2+ATPase, both native and modified with fluorescein isothiocyanate (FITC), in intact sarcoplasmic reticulum have been determined by the measurement of proton-proton transferred nuclear Overhauser enhancements by 1H-NMR spectroscopy. This method shows clearly the existence of a low-affinity ATP binding site after modification of the high-affinity site with FITC. For all three nucleotides bound to both the high-affinity (catalytic) site and the low-affinity site, we find that the conformation about the glycosidic bond is anti, the conformation of the ribose 3'-endo of the N type and the conformation about the ribose C4'-C5' bond either gauche-trans or trans-gauche. The values for the glycosidic bond torsion angles chi (O4'-C1'-N9-C4) for Mg2+ATP, Mg2+ADP and Mg2+AdoPP[NH]P bound to the low-affinity site of FITC-modified Ca2+ATPase are approximately equal to 270 degrees, approximately equal to 260 degrees and approximately equal to 240 degrees respectively. In the case of the nucleotides bound to the high-affinity (catalytic) site of native Ca2+ATPase, chi lies in the range 240-280 degrees.     

An evaluation of the combined use of nuclear magnetic resonance and distance geometry for the determination of protein conformations in solution

An evaluation of the potential of nuclear magnetic resonance (n.m.r.) as a means of determining polypeptide conformation in solution is performed with the aid of a new distance geometry program which is capable of computing complete spatial structures for small proteins from n.m.r. data. Ten sets of geometric constraints which simulate the results available from n.m.r. experiments of varying precision and completeness were extracted from the crystal structure of the basic pancreatic trypsin inhibitor, and conformers consistent with these constraints were computed. Comparison of these computed structures with each other and with the original crystal structure shows that it is possible to determine the global conformation of a polypeptide chain from the distance constraints which are available from n.m.r. experiments. The results obtained with the different data sets also provide a standard by which the quality of protein structures computed from n.m.r. data can be evaluated when no crystal structure is available, and indicate directions in which n.m.r. experiments for protein structure determination could be further improved.     

The sampling properties of some distance geometry algorithms applied to unconstrained polypeptide chains: a study of 1830 independently computed conformations

In this paper we study the statistical geometry of ensembles of poly (L-alanine) conformations computed by several different distance geometry algorithms. Since basic theory only permits us to predict the statistical properties of such ensembles a priori when the distance constraints have a very simple form, the only constraints used for these calculations are those necessary to obtain reasonable bond lengths and angles, together with a lack of short- and long-range atomic overlaps. The geometric properties studied include the squared end-to-end distance and radius of gyration of the computed conformations, in addition to the usual rms coordinate and phi/psi angle deviations among these conformations. The distance geometry algorithms evaluated include several variations of the well-known embed algorithm, together with optimizations of the torsion angles using the ellipsoid and variable target function algorithms. The conclusions may be summarized as follows: First, the distribution with which the trial distances are chosen in most implementations of the embed algorithm is not appropriate when no long-range upper bounds on the distances are present, because it leads to unjustifiably expanded conformations. Second, chosing the trial distances independently of one another leads to a lack of variation in the degree of expansion, which in turn produces a relatively low rms square coordinate difference among the members of the ensemble. Third, when short-range steric constraints are present, torsion angle optimizations that start from conformations obtained by choosing their phi/psi angles randomly with a uniform distribution between -180 degrees and +180 degrees do not converge to conformations whose angles are uniformly distributed over the sterically allowed regions of the phi/psi plane. Finally, in an appendix we show how the sampling obtained with the embed algorithm can be substantially improved upon by the proper application of existing methodology.     

Pseudo-structures for the 20 common amino acids for use in studies of protein conformations by measurements of intramolecular proton-proton distance constraints with nuclear magnetic resonance

"Pseudo-structures" of the 20 common amino acid residues are introduced for use in protein spatial structure determinations, which rely on the use of intramolecular proton-proton distance constraints determined by nuclear Overhauser effects as input for distance geometry calculations. The proposed structures satisfy requirements for the initial structural interpretation of the nuclear magnetic resonance data that arise from the absence of stereospecific assignments and/or limited spectral resolution for certain resonance lines. The pseudo-atoms used as reference points for the experimental distance constraints can be used in conjunction with the real amino acid structures representing the van der Waals' constraints on the spatial molecular structure, or with simplified models in order to reduce the computing time for the distance geometry calculations.     

Conformation of NAD+ bound to yeast and horse liver alcohol dehydrogenase in solution. The use of the proton-proton transferred nuclear Overhauser enhancement

Changes in reduced viscosity of nuclear lysates from rat liver cells have been studied, in conditions of very low shear stress by the use of an oscillating viscometer, as a function of incubation time in alkaline (pH 12.5) and neutral (pH 8.0) solutions. In non-denaturing conditions, nuclear DNA showed a stepwise, time-dependent increase of reduced viscosity, which suggests that it behaves as a single hydrodynamic unit that progressively changes its radius and viscoelastic properties because of a very slow unfolding, through discrete successive transitions, from a highly superpacked structure toward a linear relaxed B-form fiber. Experimental conditions shown to reduce chromatin-DNA superpacking without changing DNA length (e.g. G₁ cycling versus G₀ non-cycling liver cells, or young versus old rat liver cells) dramatically increased the initial value of reduced viscosity and its time-dependent increment. Conversely, in denaturing conditions, reduced viscosity increased in the initial phase (probably because DNA unfolding prevails on DNA unwinding), then exhibited a plateau level (when unfolding balances unwinding), and subsequently decreased progressively to the value of sheared DNA (when unwinding becomes more rapid due to the progressive breakage of phosphodiester bridges in alkali). Experimental conditions known to induce DNA single- or double-strand breaks (i.e. the use of liver cells from rats treated with dimethylnitrosamine or 2-acetylaminofluorene, or of liver cells exposed to X-rays) caused in both neutral and alkaline solution an increment in the initial reduced viscosity and in the slope of its time-dependent increase, which may be related to a reduction of chromatin-DNA superpacking. Moreover, it became evident in denaturing conditions that a decrease of the maximum viscosity and of the time taken to reach it both related to a reduced DNA length. These viscoelastic properties are constantly correlated with independent DNA structural measurements on the same nuclear lysates, to discriminate the effect due to mere aggregation and disaggregation.     

Solution conformations of human growth hormone releasing factor: comparison of the restrained molecular dynamics and distance geometry methods for a system without long-range distance data

A series of three-dimensional structures of the 1-29 fragment of human growth hormone releasing factor in trifluoroethanol have been determined by molecular dynamics and distance geometry methods. The resulting structures satisfy information from nuclear Overhauser effect (NOE) distance data and an empirical potential energy function. Although the polypeptide was found to have an ordered structure in all simulations, the NOE data were not sufficient for global convergence to a unique three-dimensional geometry. Several satisfactory structures have been determined, all of which are extended conformations consisting of a short beta-strand and two alpha-helices (residues 6-13 and residues 16-29) connected by short segments of less well defined secondary structure. Because of the lack of NOE data connecting the helix segments, their relative orientation is not uniquely determined.     

Variable ranges of interactions in polypeptide conformations with a method to complement molecular modeling.

Formulations of conformational weights for helix-coil transitions can be extended to substantially more complex situations than are usually pursued. General rules for matrix multiplication that depend parametrically on the interaction ranges and numbers of rotamers of residues are presented. The orders of the matrices of statistical weights can be increased with chain length, so that an individual matrix element can represent any specified single conformation, as needed. By the appropriate choice of interaction ranges and numbers of available conformers, approximations can be introduced in which: (1) an average of the conformations of any chain segment is obtained, (2) specific residue-residue interactions are excluded, or (3) the conformation of a part of the chain is restricted or fixed. The method is appropriate for treating specific interactions in peptides and could be used together with available experimental information to develop models of conformational transitions. As such, the methods represent a class of calculations aimed at more rigorous calculations built around known features of a molecule. The aim is to facilitate calculations that bridge the gap between nonquantitative molecular model building and more rigorous but less directed molecular mechanics calculations. The method can directly include any desired longer range of interactions, if the interaction range is not too long to make impossible the manipulation of the requisite matrices. An outline is presented of an application to treat salt bridges in the C peptide of ribonuclease A.     

The conformations of hirudin in solution: a study using nuclear magnetic resonance, distance geometry and restrained molecular dynamics

The solution conformations of the protein hirudin have been investigated by the combined use of distance geometry and restained molecular dynamics calculations. The basis for the structure determination comprised 359 approximate inter-proton distance restrains and 10 phi backbone torsion angle restrains derived from n.m.r. measurements. It is shown that hirudin is composed of three domains: a central core made up of residues 3-30, 37-46 and 56-57; a protruding 'finger' (residues 31-36) consisting of the tip of an antiparallel beta sheet, and an exposed loop (residues 47-55). The structure of each individual domain is relatively well defined with average backbone atomic r.m.s. differences of <2 A between the final seven converged restrained dynamic structures and the mean structure obtained by averaging their coordinates. The orientation of the two minor domains relative to the central core, however, could not be determined as no long-range (i-h >5) interdomain proton-proton contacts could be observed in the two-dimensional nuclear Overhauser enhancement spectra. From the restrained molecular dynamics calculations it appears that the two minor domains exhibit large rigid-body motions relative to the central core.     

Systematic application of two-dimensional 1H nuclear-magnetic-resonance techniques for studies of proteins. 2. Combined use of correlated spectroscopy and nuclear Overhauser spectroscopy for sequential assignments of backbone resonances and elucidation of polypeptide secondary structures

This paper describes a new nuclear magnetic resonance approach for the determination of secondary structure in globular proteins. To illustrate the practical application of the new procedure, two-dimensional correlated spectroscopy and two-dimensional nuclear Overhauser enhancement spectroscopy were used to obtain individual assignments for all the backbone protons of the beta-sheet secondary structures in the basic pancreatic trypsin inhibitor. First, combined connectivity diagrams of these two methods recorded in both 2H2O solution and H2O solution of the inhibitor were employed to obtain sequential, individual resonance assignments for the separate strands in the beta sheet. Second, a 2D nuclear Overhauser enhancement spectrum recorded with a long mixing time was used to determine how the separate, extended polypeptide strands are linked by hydrogen bonds in the sheet structures. By combination of these results with the identifications of the amino acid side-chain resonances described in the preceding paper, the beta-sheet structures can, without reference to data on the spatial structure obtained with other techniques, be localized in the amino acid sequence. This investigation confirms results on limited regions of the beta sheet in the inhibitor obtained previously with one-dimensional nuclear magnetic resonance experiments and demonstrates that the entire beta-sheet structure seen in single crystals of the inhibitor is preserved in aqueous solution.     

Application of a genetic algorithm in the conformational analysis of methylene-acetal-linked thymine dimers in DNA: Comparison with distance geometry calculations

The three-dimensional spatial structure of a methylene-acetal-linked thymine dimer presentin a 10 base-pair (bp) sense–antisense DNA duplex was studied with a geneticalgorithm designed to interpret NOE distance restraints. Trial solutions were represented bytorsion angles. This means that bond angles for the dimer trial structures are kept fixed duringthe genetic algorithm optimization. Bond angle values were extracted from a 10 bpsense–antisense duplex model that was subjected to energy minimization by means ofa modified AMBER force field. A set of 63 proton–proton distance restraints definingthe methylene-acetal-linked thymine dimer was available. The genetic algorithm minimizesthe difference between distances in the trial structures and distance restraints. A largeconformational search space could be covered in the genetic algorithm optimization byallowing a wide range of torsion angles. The genetic algorithm optimization in all cases ledto one family of structures. This family of the methylene-acetal-linked thymine dimer in theduplex differs from the family that was suggested from distance geometry calculations. It isdemonstrated that the bond angle geometry around the methylene-acetal linkage plays animportant role in the optimization.     

Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. III. Probable and average conformations of enkephalin

The program SMAPPS (Statistical-Mechanical Algorithm for Predicting Protein Structure) was originally designed to determine the probable and average backbone (?, ψ) conformations of a polypeptide by the application of equilibrium statistical mechanics in conjunction with an adaptive importance sampling Monte Carlo procedure. In the present paper, the algorithm has been extended to include the variation of all side-chain (χ) and peptide-bond (ω) dihedral angles of a polypeptide during the Monte Carlo search of the conformational space. To test the effectiveness of the generalized algorithm, SMAPPS was used to calculate the probable and average conformations of Met-enkephalin for which all dihedral angles of the pentapeptide were allowed to vary. The total conformational energy for each randomly generated structure of Met-enkephalin was obtained by summing over the interaction energies of all pairs of nonbonded atoms of the whole molecule. The interaction energies were computed by the program ECEPP /2 (Empirical Conformational Energy Program for Peptides). Solvent effects were not included in the computation. The results of the Monte Carlo calculation of the structure of Met-enkephalin indicate that the thermodynamically preferred conformation of the pentapeptide contains a γ-turn involving the three residues Gly²-Gly³-Phe⁴. The γ-turn conformation, however, does not correspond to the structure of lowest conformational energy. Rather, the global minimum-energy conformation, recently determined by a new optimization technique developed in this laboratory, contains a type II′ β-bend that is formed by the interaction of the four residues Gly²-Gly³-Phe⁴-Met⁵. A similar minimum-energy conformation is found by the SMAPPS procedure. The thermodynamically preferred γ-turn structure has a conformational energy of 4.93 kcal/mole higher than the β-bend structure of lowest energy but, because of the inclusion of entropy in the SMAPPS procedure, it is estimated to be ～ 9 kcal/mole lower in free energy. The calculation of the average conformation of Met-enkephalin was repeated until a total of ten independent average conformations were established. As far as the phenylalanine residue of the pentapeptide is concerned, the results of the ten independent average conformations were all found to lie in the region of conformational space corresponding to the γ-turn. These results further support the conclusion that the γturn conformation is thermodynamically favored.     

Characterization and genetic control of the immune response to synthetic polypeptide antigens of defined geometry.

Both humoral and cell-mediated immune responses to the synthetic helical hapten-carrier conjugate poly-Glu-Tyr-Lys(TNP)-(Glu-Tyr-Ala)5 were found to be linked to the major histocompatibility locus in mice and guinea pigs. The responder mouse strains (H-2d haplotype) showed a primary IgM response with an IgG component appearing after the secondary immunization. The antibody response was accompanied by a positive DTH reaction in responder strains. Nonresponder mice (H-2b or H-2k haplotypes) showed neither IgM nor IgG antibodies and the DTH reaction was negative. Administration of the antigen as a complex with an immunogenic carrier was not effective in inducing a response in nonresponder mice. In guinea pig studies, it was found that strain 2 animals were able to mount an antibody response against the TNP-hapten and a DTH response against the polypeptide backbone. Strain 13 animals gave no anti-TNP antibodies at the lower dose levels and DTH activity was entirely negative for all doses of immunizing antigen. Replacement of the TNP hapten by the arsanilazo dipeptide derivative, BOC-gly-ARA-tyrosine, converted the nonresponder strain 13 guinea pigs into complete responders showing antibody and DTH reactions to both the hapten and the polypeptide backbone.     

The combined use of NMR, distance geometry, and restrained molecular dynamics for the conformational study of a cyclic somatostatin analogue

A cyclic peptide analogue of somatostatin, including the o-aminomethylphenylacetic acid spacer, was studied by the combined use of two-dimensional nmr spectroscopy, distance geometry, and restrained molecular dynamics. Analysis of distances determined from nuclear Overhauser effect (NOE) buildup rates revealed that these were inconsistent with a unique backbone conformation near the spacer. Assuming that the conformational heterogeneity is localized to the spacer, the NOE distances measured for the remaining part of the molecule were used to generate a large number of structures with the distance geometry algorithm, which were then refined by restrained energy minimization. Four classes of structures emerged, which together account for all observed NOEs. A representative structure of each class was further refined with the restrained molecular dynamics technique, and shown to be stable on a 20-ps time scale. The flexibility of the spacer was examined by simulating interconversions induced by an appropriate restraining potential. As a result, the explanation for the lack of somatostatin activity of the analogue studied was reconsidered.     

Determining local conformational variations in DNA. Nuclear magnetic resonance structures of the DNA duplexes d(CGCCTAATCG) and d(CGTCACGCGC) generated using back-calculation of the nuclear Overhauser effect spectra, a distance geometry algorithm and constrained molecular dynamics

Two-dimensional nuclear magnetic resonance (n.m.r.) spectroscopy and a variety of computational techniques have been used to generate three-dimensional structures of the two DNA duplexes d(CGCCTAATCG) and d(CGTCACGCGC). The central six base-pairs in these two decamers contain all ten dinucleotide pairs in DNA and thus, represent a model system for investigating how the local structure of DNA varies with base sequence. Resonance assignments were made for the non-exchangeable base protons and most of the C-1'-C-4' sugar protons in both decamers. Three-dimensional structures were generated using a distance geometry algorithm and these initial structures were refined by optimizing the fit of back-calculated spectra against the experimental two-dimensional nuclear Overhauser effect (NOE) spectra. This back-calculation procedure consists of calculating NOE cross relaxation rates for a given structure by solution of the Bloch equations, and directly accounts for spin diffusion effects. Use of this refinement procedure eliminates some assumptions that have been invoked when generating structures of DNA oligomers from n.m.r. data. Constrained energy minimization and constrained quenched molecular dynamics calculation were also performed on both decamers to help generate energetically favorable structures consistent with the experimental data. Analysis of the local conformational parameters of helical twist, helical rise, propeller twist, displacement and the alpha, beta, gamma, epison and zeta backbone torsion angles in these structures shows that these parameters span a large range of values relative to the X-ray data of nucleic acids. However, the glycosidic and pseudorotation angles are quite well defined in these structures. The implications that these results have for determination of local structural variations of DNA in solution, such as those predicted by Callidine's rules, are discussed. Our results differ significantly from some previous studies on determining local conformations of nucleic acids and comparisons with these studies are made.     

Combined procedure of distance geometry and restrained molecular dynamics techniques for protein structure determination from nuclear magnetic resonance data: application to the DNA binding domain of lac repressor from Escherichia coli

The technique of two-dimensional nuclear magnetic resonance (2D-NMR) has recently assumed an active role in obtaining information on structures of polypeptides, small proteins, sugars, and DNA fragments in solution. In order to generate spatial structures from the atom-atom distance information obtained by the NMR method, different procedures have been developed. Here we introduce a combined procedure of distance geometry (DG) and molecular dynamics (MD) calculations for generating 3D structures that are consistent with the NMR data set and have reasonable internal energies. We report the application of the combined procedure on the lac repressor DNA binding domain (headpiece) using a set of 169 NOE and 17 "hydrogen bond" distance constraints. Eight of ten structures generated by the distance geometry algorithm were refined within 10 ps MD simulation time to structures with low internal energies that satisfied the distance constraints. Although the combination of DG and MD was designed to combine the good sampling properties of the DG algorithm with an efficient method of lowering the internal energy of the molecule, we found that the MD algorithm contributes significantly to the sampling as well.     

Solution conformation of endothelin, a potent vaso-constricting bicyclic peptide. A combined use of 1H NMR spectroscopy and distance geometry calculations

The solution structure of endothelin-1, a newly discovered potent bicyclic peptide vaso-constrictor agent, has been investigated using 1H NMR conformational constraints and distance geometry calculations. The conformation is constrained by two disulphide bridges between Cys1-Cys15 and Cys3-Cys11 but the NMR data and computed conformers show additional helical structure between residues Leu6 and Cys11. Our results are compared with previous conflicting reports on the solution conformation of this peptide.