Efficient conformational sampling of multiconformational cyclic molecules: application to 1,4,7,10,13-Pentaoxacyclopentadecane

The result of an exhaustive search of low-energy conformers of 1,4,7,10,13-Pentaoxacyclopentadecane is presented. The search method combines the generation of large number of trial conformers using local nonstochastic deformations known as the Conflex method, which is coupled to AMBER force field as the minimizer. The extent of the conformational space sampled was evaluated from the view point of the number of duplicates of each conformer, generation of inclusion type structures without considering the substrate and the spread of the allowed torsion angles visited during the search. It is shown that the conformational search is exhaustive and efficient as conformers, which the metal coordinated crown ether complexes adopt, were generated. Free energies using the AMBER structures were calculated using the model of Cramer and Truhlar. The study suggests that 1,4,7,10,13-Pentaoxacyclopentadecane exists as a mixture of conformers in solution. The results show the efficiency of the method and could be the method of choice in the design of synthetic macrocyclic receptors.     

Statistical analysis of RNA backbone

Local conformation is an important determinant of RNA catalysis and binding. The analysis of RNA conformation is particularly difficult due to the large number of degrees of freedom (torsion angles) per residue. Proteins, by comparison, have many fewer degrees of freedom per residue. In this work, we use and extend classical tools from statistics and signal processing to search for clusters in RNA conformational space. Results are reported both for scalar analysis, where each torsion angle is separately studied, and for vectorial analysis, where several angles are simultaneously clustered. Adapting techniques from vector quantization and clustering to the RNA structure, we find torsion angle clusters and RNA conformational motifs. We validate the technique using well-known conformational motifs, showing that the simultaneous study of the total torsion angle space leads to results consistent with known motifs reported in the literature and also to the finding of new ones.     

Simultaneous single-structure and bundle representation of protein NMR structures in torsion angle space

A method is introduced to represent an ensemble of conformers of a protein by a single structure in torsion angle space that lies closest to the averaged Cartesian coordinates while maintaining perfect covalent geometry and on average equal steric quality and an equally good fit to the experimental (e.g. NMR) data as the individual conformers of the ensemble. The single representative ‘regmean structure’ is obtained by simulated annealing in torsion angle space with the program CYANA using as input data the experimental restraints, restraints for the atom positions relative to the average Cartesian coordinates, and restraints for the torsion angles relative to the corresponding principal cluster average values of the ensemble. The method was applied to 11 proteins for which NMR structure ensembles are available, and compared to alternative, commonly used simple approaches for selecting a single representative structure, e.g. the structure from the ensemble that best fulfills the experimental and steric restraints, or the structure from the ensemble that has the lowest RMSD value to the average Cartesian coordinates. In all cases our method found a structure in torsion angle space that is significantly closer to the mean coordinates than the alternatives while maintaining the same quality as individual conformers. The method is thus suitable to generate representative single structure representations of protein structure ensembles in torsion angle space. Since in the case of NMR structure calculations with CYANA the single structure is calculated in the same way as the individual conformers except that weak positional and torsion angle restraints are added, we propose to represent new NMR structures by a ‘regmean bundle’ consisting of the single representative structure as the first conformer and all but one original individual conformers (the original conformer with the highest target function value is discarded in order to keep the number of conformers in the bundle constant). In this way, analyses that require a single structure can be carried out in the most meaningful way using the first model, while at the same time the additional information contained in the ensemble remains available.     

Conformational analysis of the 3'-5'-cyclic dinucleotide d less than pApA greater than by means of molecular mechanics

The conformational properties of the cyclic dinucleotide d less than pApA greater than were studied by means of molecular mechanics calculations in which a multiconformation analysis was combined with minimum energy calculations. In this approach models of possible conformers are built by varying the torsion angles of the molecule systematically. These models are then subjected to energy minimization; in the present investigation use was made of the AMBER Force field. It followed that the lowest energy conformer has a pseudo-two-fold axis of symmetry. In this conformer the deoxyribose sugars adopt a N-type conformation. The conformation of the sugar-phosphate backbone is determined by the following torsion angles: alpha +, beta t, gamma +, epsilon t and zeta +. The conformation of this ringsystem corresponds to the structure derived earlier by means of NMR spectroscopy and X-ray diffraction. The observation of a preference for N-type sugar conformations in this molecule can be explained by the steric hindrance induced between opposite H3' atoms when one sugar is switched from N- to S-type puckers. The sugars can in principle switch from N- to S-type conformations, but this requires at least the transition of gamma + to gamma -. In this process the molecule obtains an extended shape in which the bases switch from a pseudo-axial to a pseudo-equatorial position. The calculations demonstrate that, apart from the results obtained for the lowest energy conformation, the 180 degrees change in the propagation direction of the phosphate backbone can be achieved by several different combinations of the backbone torsion angles. It appeared that in the low energy conformers five higher order correlations are found. The combination of torsion angles which are involved in changes in the propagation direction of the sugar-phosphate backbone in DNA-hairpin loops and in tRNA, are found in the dataset obtained for cyclic d less than pApA greater than. It turns out, that in the available examples, 180 degrees changes in the backbone direction are localized between two adjacent nucleotides.     

Force field based conformational analysis of RNA structural motifs: GNRA tetraloops and their pyrimidine relatives

The protocol of conformational analysis applied here to ribonucleotide oligomers combines conformational search in the space of torsion angles and energy minimization using the AMBER4.1 force field with a continuum treatment of electrostatic solute-solvent interactions. RNA fragments with 5′-GGGCGNNAGCCU-3′ sequences commonly fold into hairpins with four-membered loops. The combinatorial search for acceptable conformations using the MC-SYM program was restricted to loop nucleotides and yielded roughly 1500 structures being compatible with a double-stranded stem. After energy minimization by the JUMNA program (without applying any experimental constraints), these structures converged into an ensemble of 74 different conformers including 26 structures which contained the sheared G-A base pair observed in experimental studies of GNRA tetraloops. Energetic analysis shows that inclusion of solvent electrostatic effects is critically important for the selection of conformers that agree with experimentally determined structures. The continuum model accounts for solvent polarization by means of the electrostatic reaction field. In the case of GNRA loop sequences, the contributions of the reaction field shift relative stabilities towards conformations showing most of the structural features derived from NMR studies. The agreement of computed conformations with the experimental structures of GAAA, GCAA, and GAGA tetraloops suggests that the continuum treatment of the solvent represents a definitive improvement over methods using simple damping models in electrostatic energy calculations. Application of the procedure described here to the evaluation of the relative stabilities of conformers resulting from searching the conformational space of RNA structural motifs provides some progress in (non-homology based) RNA 3D-structure prediction. Received: 20 January 1999 / Revised version: 4 June 1999 / Accepted: 10 June 1999     

An analysis of side-chain conformation in proteins.

The crystal structures of a number of globular proteins are currently available. An analysis of the distribution of side-chains among different allowed conformations in these proteins has been carried out. The observed conformations of individual residues are discussed on the basis of well-known stereochemical criteria. The population distribution of side-chains in different allowed regions in conformational space can be explained largely on the basis of simple steric considerations. In addition to examining the conformational behaviour of individual residues, some population distributions of conformational angles of general interest involving groups of residues have also been analyzed.     

Conformational comparison of mu-selective endomorphin-2 with its C-terminal free acid in DMSO solution, by 1H NMR spectroscopy and molecular modeling calculation.

In order to make clear the structural role of the C-terminal amide group of endomorphin-2 (EM2, H-Tyr-Pro-Phe-Phe-NH2), an endogenous mu-receptor ligand, in the biological function, the solution conformations of endomorphin-2 and its C-terminal free acid (EM2OH, H-Tyr-Pro-Phe-Phe-OH), studied using two-dimensional 1H NMR measurements and molecular modeling calculations, were compared. Both peptides were in equilibrium between the cis and trans isomers around the Tyr-Pro omega bond in a population ratio of approximately/= 1:2. The lack of significant temperature and concentration dependence of NH protons suggested that the NMR spectra reflected the conformational features of the respective molecules themselves. Fifty possible 3D structures for the each isomer were generated by the dynamical simulated annealing method under the proton-proton distance constraints derived from the ROE cross-peaks. These energy-minimized conformers, which were all in the phi torsion angles estimated from J(NHCalphaH) coupling constants within +/- 30 degrees, were then classified in groups one or two according to the folding backbone structures. All trans and cis EM2 conformers adopt an open conformation in which their extended backbone structures are twisted at the Pro2-Phe3 moiety. In contrast, the trans and cis conformers of EM2OH show conformational variation between the 'bow'-shaped extended and folded backbone structures, although the cis conformers of its zwitterionic form are refined into the folded structure of the close disposition of C- and N-terminal groups. These results indicate clearly that the substitution of carboxyl group for C-terminal amide group makes the peptide flexible. The conformational requirement for mu-receptor activation has been discussed based on the active form proposed for endomorphin-1 and by comparing conformational features of EM2 and EM2OH.     

Conformational analysis of protein and nucleic acid fragments with the new grid search algorithm FOUND

The new computer algorithm FOUND, which is implemented as an integrated module of the DYANA structure calculation program, is capable of performing systematic local conformation analyses by exhaustive grid searches for arbitrary contiguous fragments of proteins and nucleic acids. It uses torsion angles as the only degrees of freedom to identify all conformations that fulfill the steric and NMR-derived conformational restraints within a contiguous molecular fragment, as defined either by limits on the maximal restraint violations or by the fragment-based DYANA target function value. Sets of mutually dependent torsion angles, for example in ribose rings, are treated as a single degree of freedom. The results of the local conformation analysis include allowed torsion angle ranges and stereospecific assignments for diastereotopic substituents, which are then included in the input of a subsequent structure calculation. FOUND can be used for grid searches comprising up to 13 torsion angles, such as the backbone of a complete -helical turn or dinucleotide fragments in nucleic acids, and yields a significantly higher number of stereospecific assignments than the precursor grid search algorithm HABAS.     

Conformational Analysis of the 3′-5′-Cyclic Dinucleotide d<pApA> by Means of Molecular Mechanics

Abstract

The conformational properties of the cyclic dinucleotide d<(pApA)> were studied by means of molecular mechanics calculations in which a multiconformation analysis was combined with minimum energy calculations. In this approach models of possible conformers are built by varying the torsion angles of the molecule systematically. These models are then subjected to energy minimization; in the present investigation use was made of the AMBER Force field. It followed that the lowest energy conformer has a pseudo-two-fold axis of symmetry. In this conformer the deoxyribose sugars adopt a N-type conformation. The conformation of the sugar-phosphate backbone is determined by the following torsion angles: α⁺, β¹, γ⁺, ?¹ and ζ⁺. The conformation of this ringsystem corresponds to the structure derived earlier by means of NMR spectroscopy and X-ray diffraction. The observation of a preference for N-type sugar conformations in this molecule can be explained by the steric hindrance induced between opposite H3′ atoms when one sugar is switched from N- to S-type puckers. The sugars can in principle switch from N- to S-type conformations, but this requires at least the transition of γ⁺ to γ^?. In this process the molecule obtains an extended shape in which the bases switch from a pseudo-axial to a pseudo-equatorial position. The calculations demonstrate that, apart from the results obtained for the lowest energy conformation, the 180° change in the propagation direction of the phosphate backbone can be achieved by several different combinations of the backbone torsion angles. It appeared that in the low energy conformers five higher order correlations are found. The combination of torsion angles which are involved in changes in the propagation direction of the sugar-phosphate backbone in DNA-hairpin loops and in tRNA are found in the dataset obtained for cyclic d<(pApA)>. It turns out that in the available examples, 180° changes in the backbone direction are localized between two adjacent nucleotides.     

Predominant torsional forms adopted by dipeptide conformers in solution: parameters for molecular recognition.

The present paper describes the predominant conformational forms adopted by dipeptides in aqueous solution. More than 50 dipeptides were subjected to conformational analysis using SYBYL Random Search. The resultant collections of conformers for individual dipeptides, for small groups with related side chain residues and for large groups of about 50 dipeptides were visualized graphically and analysed using a novel three-dimensional pseudo-Ramachandran plot. The distribution of conformers, weighted according to the percentage of each in the total conformer pool, was found to be restricted to nine main combinations of backbone psi (psi) and phi (phi) torsion angles. The preferred psi values were in sectors A7 (+150 degrees to +/-180 degrees), A10 (+60 degrees to +90 degrees) and A4 (-60 degrees to -90 degrees), and these were combined with preferred phi values in sectors B12 (-150 degrees to +/-180 degrees), B9 (-60 degrees to -90 degrees) and B2 (+30 degrees to +60 degrees). These combinations of psi and phi values are distinct from those found in common secondary structures of proteins. These results show that although dipeptides can each adopt many conformations in solution, each possesses a profile of common conformers that is quantifiable. A similarly weighted distribution of dipeptide conformers according to distance between amino-terminal nitrogen and carboxyl-terminal carbon shows how the preferred combinations of backbone torsional angles result in particular N-C geometries for the conformers. This approach gives insight into the important conformational parameters of dipeptides that provide the basis for their molecular recognition as substrates by widely distributed peptide transporters. It offers a basis for the rational design of peptide-based bioactive compounds able to exploit these transporters for targeting and delivery.     

A Monte Carlo method for generating structures of short single-stranded DNA sequences

A Monte Carlo method has been developed for generating the conformations of short single-stranded DNAs from arbitrary starting states. The chain conformers are constructed from energetically favorable arrangements of the constituent mononucleotides. Minimum energy states of individual dinucleotide monophosphate molecules are identified using a torsion angle minimizer. The glycosyl and acyclic backbone torsions of the dimers are allowed to vary, while the sugar rings are held fixed in one of the two preferred puckered forms. A total of 108 conformationally distinct states per dimer are considered in this first stage of minimization. The torsion angles within 5 kcal/mole of the global minimum in the resulting optimized states are then allowed to vary by ±10° in an effort to estimate the breadth of the different local minima. The energies of a total of 2187 (3⁷) angle combinations are examined per local conformational minimum. Finally, the energies of all dinucleotide conformers are scaled so that the populations of differently puckered sugar rings in the theoretical sample match those found in nmr solution studies. This last step is necessitated by limitations in the theoretical methods to predict DNA sugar puckering accurately. The conformer populations of the individual acyclic torsion angles in the composite dimer ensembles are found to be in good agreement with the distributions of backbone conformations deduced from nmr coupling constants and the frequencies of glycosyl conformations in x-ray crystal structures, suggesting that the low energy states are reasonable. The low energy dimer forms (consisting of 150–325 conformational states per dimer step) are next used as variables in a Monte Carlo algorithm, which generates the conformations of single-stranded d(CX_nG) chains, where X = A, T and n = 3, 4, 5. The oligonucleotides are built sequentially from the 5′ end of the chain using random numbers to select the conformations of overlapping dimer units. The simulations are very fast, involving a total of 10⁶ conformations per chain sequence. The potential errors in the buildup procedure are minimized by taking advantage of known rotational interdependences in the sugar–phosphate backbone. The distributions of oligonucleotide conformations are examined in terms of the magnitudes, positions, and orientations of the end-to-end vectors of the chains. The differences in overall flexibility and extension of the oligomers are discussed in terms of the conformations of the constituent dinucleotide steps, while the general methodology is discussed and compared with other nucleic acid model building techniques. © 1993 John Wiley & Sons, Inc.     

Identification of dynamical hinge points of the L1 ligase molecular switch

The L1 ligase is an in vitro selected ribozyme that uses a noncanonically base-paired ligation site to catalyze regioselectively and regiospecifically the 5′ to 3′ phosphodiester bond ligation, a reaction relevant to origin of life hypotheses that invoke an RNA world scenario. The L1 ligase crystal structure revealed two different conformational states that were proposed to represent the active and inactive forms. It remains an open question as to what degree these two conformers persist as stable conformational intermediates in solution, and along what pathway are they able to interconvert. To explore these questions, we have performed a series of molecular dynamics simulations in explicit solvent of the inactive–active conformational switch in L1 ligase. Four simulations were performed departing from both conformers in both the reactant and product states, in addition to a simulation where local unfolding in the active state was induced. From these simulations, along with crystallographic data, a set of four virtual torsion angles that span two evolutionarily conserved and restricted regions were identified as dynamical hinge points in the conformational switch transition. The ligation site visits three distinct states characterized by hydrogen bond patterns that are correlated with the formation of specific contacts that may promote catalysis. The insights gained from these simulations contribute to a more detailed understanding of the coupled catalytic/conformational switch mechanism of L1 ligase that may facilitate the design and engineering of new catalytic riboswitches.     

Conformational and model-building studies of the hairpin form of the mismatched DNA octamer d(m5C-G-m5C-G-T-G-m5C-G)

The hairpin form of the mismatched octamer d(m5C-G-m5C-G-T-G-m5C-G) was studied by means of NMR spectroscopy. In a companion study it is shown that the hairpin form of this DNA fragment consists of a structure with a stem of three Watson-Crick-type base pairs and a loop consisting of only two nucleotides. The non-exchangeable proton resonances were assigned by means of two-dimensional correlation spectroscopy and two-dimensional nuclear Overhauser effect spectroscopy. Proton-proton coupling constants were used for the conformational analysis of the deoxyribose ring and for some of the backbone torsion angles. From the two-dimensional NMR spectra and the coupling-constant analysis it is concluded that: (i) the stem of the hairpin exhibits B-DNA characteristics; (ii) the sugar rings are not conformationally pure, but display a certain amount of conformational flexibility; (iii) the stacking interaction in the stem of the hairpin is elongated from the 3'-side in a more or less regular fashion with the two loop nucleotides; (iv) at the 5'-side of the stem a stacking discontinuity occurs between the stem and the loop; (v) at the 5'-side of the stem the loop is closed by means of a sharp backbone turn which involves unusual gamma' and beta+ torsion angles in residue dG(6). The NMR results led to the construction of a hairpin-loop model which was energy-minimized by means of a molecular-mechanics program. The results clearly show that a DNA hairpin-loop structure in which the loop consists of only two nucleotides bridging the minor groove in a straightforward fashion, (i) causes no undue steric strain, and (ii) involves well-known conformational principles throughout the course of the backbone. The hairpin form of the title compound is compared with the hairpin form of d(A-T-C-C-T-A-T4-T-A-G-G-A-T), in which the central -T4- part forms a loop of four nucleotides. Both models display similarities as far as stacking interactions are concerned.     

Efficient search on energy minima for structure prediction of nucleic acid motifs

Structure prediction of non-canonical motifs such as mismatches, extra unmatched nucleotides or internal and hairpin loop structures in nucleic acids is of great importance for understanding the function and design of nucleic acid structures. Systematic conformational analysis of such motifs typically involves the generation of many possible combinations of backbone dihedral torsion angles for a given motif and subsequent energy minimization (EM) and evaluation. Such approach is limited due to the number of dihedral angle combinations that grows very rapidly with the size of the motif. Two conformational search approaches have been developed that allow both an effective crossing of barriers during conformational searches and the computational demand grows much less with system size then search methods that explore all combinations of backbone dihedral torsion angles. In the first search protocol single torsion angles are flipped into favorable states using constraint EM and subsequent relaxation without constraints. The approach is repeated in an iterative manner along the backbone of the structural motif until no further energy improvement is obtained. In case of two test systems, a DNA-trinucleotide loop (sequence: GCA) and a RNA tetraloop (sequence: UUCG), the approach successfully identified low energy states close to experiment for two out of five start structures. In the second method randomly selected combinations of up to six backbone torsion angles are simultaneously flipped into preset ranges by a short constraint EM followed by unconstraint EM and acceptance according to a Metropolis acceptance criterion. This combined stochastic/EM search was even more effective than the single torsion flip approach and selected low energy states for the two test cases in between two and four cases out of five start structures.     

Determination and comparative analysis of the conformation of bovine pancreatic trypsin inhibitor and trypsin inhibitors E and K from the data of two-dimensional 1H-NMR spectroscopy

On the basis of joint consideration of distance dependences between amide proton NH and protons C alpha H, NH, C beta H of the preceding in amino acid sequence residue from the torsion angles phi psi, chi 1, the correlation diagram of these proton-proton distances with the regions of sterically allowed conformational space (phi, psi) is presented and the method for the determination of the L-amino acid residues backbone conformations is proposed. The diagram was used for the determination of backbone conformations of bovine pancreatic trypsin inhibitor and trypsin inhibitors E and K from Dendroaspis polylepis using the data from two-dimensional 1H-NMR spectroscopy. The analysis of backbone conformations was carried out. The individual elements of these protein molecules secondary structure were characterized and their high conformational homology was shown. The inference about qualitative coincidence of three protein molecules conformation in solution, preservation of secondary structure basic elements and their similarity with bovine pancreatic trypsin inhibitor crystalline structure was made.     

Conformational studies of nucleic acids: IV. The conformational energetics of oligonucleotides: d(ApApApA) and ApApApA

Utilizing a new method for modeling furanose pseudorotation (D. A. Pearlman and S.-H. Kim, J. Biomol. Struct. Dyn. 3, 85 (1985)) and the empirical multiple correlations between nucleic acid torsion angles we derived in the previous report (D. A. Pearlman and S.-H. Kim, previous paper in this issue), we have made an energetic examination of the entire conformational spaces available to two nucleic acid oligonucleotides: d(ApApApA) and ApApApA. The energies are calculated using a semi-empirical potential function. From the resulting body of data, energy contour map pairs (one for the DNA molecule, one for the RNA structure) have been created for each of the 21 possible torsion angle pairs in a nucleotide repeating unit. Of the 21 pairs, 15 have not been reported previously. The contour plots are different from those made earlier in that for each point in a particular angle-angle plot, the remaining five variable torsion angles are rotated to the values which give a minimum energy at this point. The contour maps are overall quite consistent with the experimental distribution of oligonucleotide data. A number of these maps are of particular interest: delta (C5'-C4'-C3'-O3')-chi (O4'-C1'-N9-C4), where the energetic basis for an approximately linear delta-chi correlation can be seen: zeta (C3'-O3'-P-O5')-delta, in which the experimentally observed linear correlation between zeta and delta in DNA(220 degrees less than zeta less than 280 degrees) is clearly predicted; zeta-epsilon (C4'-C3'-O3'-P), which shows that epsilon increases with decreasing zeta less than 260 degrees; alpha (O3'-P-O5'-C5')-gamma (O5'-C5'-C4'-C3') where a clear linear correlation between these angles is also apparent, consistent with experiment; and several others. For the DNA molecule studied here, the sugar torsion delta is predicted to be the most flexible, while for the RNA molecule, the greatest amount of flexibility is expected to reside in alpha and gamma. Both the DNA and RNA molecules are predicted to be highly polymorphic. Complete energy minimization has been performed on each of the minima found in the energy searches and the results further support this prediction. Possible pathways for B-form to A-form DNA interconversion suggested by the results of this study are discussed. The results of these calculations support use of the new sugar modeling technique and torsion angle correlations in future conformational studies of nucleic acids.     

Global mapping of nucleic acid conformational space: dinucleoside monophosphate conformations and transition pathways among conformational classes

A global conformational space of 6253 dinucleoside monophosphate (DMP) units consisting of RNA and DNA (free and protein/drug-bound) was 'mapped' using high resolution crystal structures cataloged in the Nucleic Acid Database (NDB). The torsion angles of each DMP were clustered in a reduced three-dimensional space using a classical multi-dimensional scaling method. The mapping of the conformational space reveals nine primary clusters which distinguish among the common A-, B- and Z-forms and their various substates, plus five secondary clusters for kinked or bent structures. Conformational relationships and possible transitional pathways among the substates are also examined using the conformational states of DNA and RNA bound with proteins or drugs as potential pathway intermediates.     

Correlation between 13Calpha chemical shifts and helix content of peptide ensembles

Replica exchange molecular dynamics simulations are used to generate three ensembles of an S-peptide analog (AETAAAKFLREHMDS). Percent helicity of the peptide ensembles calculated using STRIDE is compared to percent helicity calculated from (13)C(alpha) chemical shift deviations (CSD) from random coil in order to test the assumption that CSD can be correlated to percent helicity. The two estimates of helicity, one based on structure and the other on CSD, are in close to quantitative agreement, except at the edges of helical stretches where disagreements of as much as 50% can be found. These disagreements can occur by CSDs both as an under- and an overestimate of peptide helicity. We show that underestimation arises due to ensemble averaging of positive CSDs from conformers with torsion angles in the helical region of Ramachandran space with negative CSDs corresponding to conformers of the peptide in the extended region. In contrast, overestimation comes about due to the fact that a large number of conformations with torsion angles in the helical region are not counted as helical by STRIDE due to a lack of correlated helical torsion angles in neighboring residues.