Lipid conformation in crystalline bilayers and in crystals of transmembrane proteins

Dihedral torsion angles evaluated for the phospholipid molecules resolved in the X-ray structures of transmembrane proteins in crystals are compared with those of phospholipids in bilayer crystals, and with the phospholipid conformations in fluid membranes. Conformations of the lipid glycerol backbone in protein crystals are not restricted to the gauche C1-C2 rotamers found invariably in phospholipid bilayer crystals. Lipid headgroup conformations in protein crystals also do not conform solely to the bent-down conformation, with gauche-gauche configuration of the phospho-diester, that is characteristic of phospholipid bilayer membranes. This suggests that the lipids that are resolved in crystals of membrane proteins are not representative of the entire lipid-protein interface. Much of the chain configurational disorder of the membrane-bound lipids in crystals arises from energetically disallowed skew conformations. This indicates a configurational heterogeneity in the lipids at a single binding site: eclipsed conformations occur also in some glycerol backbone torsion angles and C-C torsion angles in the lipid headgroups. Stereochemical violations in the protein-bound lipids are evidenced by one-third of the ester carboxyl groups in non-planar configurations, and certain of the carboxyls in the cis configuration. Some of the lipid structures in protein crystals have the incorrect enantiomeric configuration of the glycerol backbone, and many of the branched methyl groups in structures of the phytanyl chains associated with bacteriorhodopsin crystals are in the incorrect S-configuration.     

Using quantum mechanics to improve estimates of amino acid side chain rotamer energies

Amino acid side chains adopt a discrete set of favorable conformations typically referred to as rotamers. The relative energies of rotamers partially determine which side chain conformations are more often observed in protein structures and accurate estimates of these energies are important for predicting protein structure and designing new proteins. Protein modelers typically calculate side chain rotamer energies by using molecular mechanics (MM) potentials or by converting rotamer probabilities from the protein database (PDB) into relative free energies. One limitation of the knowledge‐based energies is that rotamer preferences observed in the PDB can reflect internal side chain energies as well as longer‐range interactions with the rest of the protein. Here, we test an alternative approach for calculating rotamer energies. We use three different quantum mechanics (QM) methods (second order Møller‐Plesset (MP2), density functional theory (DFT) energy calculation using the B3LYP functional, and Hartree‐Fock) to calculate the energy of amino acid rotamers in a dipeptide model system, and then use these pre‐calculated values in side chain placement simulations. Energies were calculated for over 36,000 different conformations of leucine, isoleucine, and valine dipeptides with backbone torsion angles from the helical and strand regions of the Ramachandran plot. In a subset of cases these energies differ significantly from those calculated with standard molecular mechanics potentials or those derived from PDB statistics. We find that in these cases the energies from the QM methods result in more accurate placement of amino acid side chains in structure prediction tests. Proteins 2008. © 2007 Wiley‐Liss, Inc.     

Orientation and conformation of lipids in crystals of transmembrane proteins

Orientational order parameters and individual dihedral torsion angles are evaluated for phospholipid and glycolipid molecules that are resolved in X-ray structures of integral transmembrane proteins in crystals. The order parameters of the lipid chains and glycerol backbones in protein crystals are characterised by a much wider distribution of orientational order than is found in fluid lipid bilayers and reconstituted lipid–protein membranes. This indicates that the lipids that are resolved in crystals of membrane proteins are mostly not representative of the entire lipid–protein interface. Much of the chain configurational disorder of the membrane-bound lipids in crystals arises from C–C bonds in energetically disallowed skew conformations. This suggests configurational heterogeneity of the lipids at a single binding site: eclipsed conformations occur also in the glycerol backbone torsion angles and the C–C torsion angles of the lipid head groups. Conformations of the lipid glycerol backbone in protein crystals are not restricted to the gauche C1–C2 rotamers found invariably in phospholipid bilayer crystals. Lipid head-group conformations in the protein crystals also do not conform solely to the bent-down conformation, with gauche–gauche configuration of the phosphodiester, that is characteristic of phospholipid bilayer membranes. Stereochemical violations in the protein-bound lipids are evidenced by ester carboxyl groups in non-planar configurations, and even in the cis configuration. Some lipids have the incorrect enantiomeric configuration of the glycerol backbone, and many of the branched methyl groups in the phytanyl chains associated with bacteriorhodopsin have the incorrect S configuration.     

Statistical and energetic analysis of side-chain conformations in oligopeptides

The distributions of side-chain conformations in 258 crystal structures of oligopeptides have been analyzed. The sample contains 321 residues having side chains that extend beyond the C beta atom. Statistically observed preferences of side-chain dihedral angles are summarized and correlated with stereochemical and energetic constraints. The distributions are compared with observed distributions in proteins of known X-ray structures and with computed minimum-energy conformations of amino acid derivatives. The distributions are similar in all three sets of data, and they appear to be governed primarily by intraresidue interactions. In side chains with no beta-branching, the most important interactions that determine chi 1 are those between the C gamma H2 group and atoms of the neighboring peptide groups. As a result, the g- conformation (chi 1 congruent to -60 degrees) occurs most frequently for rotation around the C alpha-C beta bond in oligopeptides, followed by the t conformation (chi 1 congruent to 180 degrees), while the g+ conformation (chi 1 congruent to 60 degrees) is least favored. In residues with beta-branching, steric repulsions between the C gamma H2 or C gamma H3 groups and backbone atoms govern the distribution of chi 1. The extended (t) conformation is highly favored for rotation around the C beta-C gamma and C gamma-C delta bonds in unbranched side chains, because the t conformer has a lower energy than the g+ and g- conformers in hydrocarbon chains. This study of the observed side-chain conformations has led to a refinement of one of the energy parameters used in empirical conformational energy computations.     

Determination of the local structure of the protein insectotoxin I5A from the scorpion Buthus eupeus from 1H-NMR spectroscopy data

The local structure (torsion angles phi, psi and chi 1 of amino acid residues) of insectotoxin I5A (35 residues) of scorpion Buthus eupeus has been determined from cross-peak integral intensities in two-dimensional nuclear Overhauser enhancement (NOESY) spectra and spin coupling constants of vicinal H--NC alpha--H and H--C alpha C beta--H protons. The local structure determination was carried out by fitting complete relaxation matrix of peptide unit protons (protons of a given residue and NH proton of the next residue in the amino acid sequence) with experimental NOESY cross-peak intensities. The obtained intervals of backbone torsional angles phi and psi consistent with NMR data were determined for all but Gly residues. The predominant C alpha--C beta rotamer of the side chain has been unambiguously determined for 42% of the insectotoxin amino acid residues whereas for another 46% residues experimental data are fitted equally well with two rotamers. Stereospecific assignments were obtained for 38% of beta-methylene groups. The determined torsional angles phi, psi and chi 1 correspond to the sterically allowed conformations of the amino acid residues and agree with the insectotoxin secondary structure established earlier by 1H NMR spectroscopy.     

Lipid-binding proteins: structure of the phospholipid ligands

Dihedral angles are evaluated for the phospholipid ligands of the lipid-binding proteins found in the Protein Data Base (PDB). Phospholipid structures occur with a trans C1-C2 configuration of the glycerol backbone and oppositely extended chains, in addition to the gauche C1-C2 rotamers found in membranes. Headgroup conformations are not restricted to the single bent-down configuration and gauche-gauche configuration of the phosphodiester that is found in phospholipid crystals. Additionally, fully extended headgroups and orientations directed away from the lipid chains are found for phospholipids in the protein binding pockets. On average, the hydrocarbon chains of the protein-bound lipids are conformationally more disordered than in fluid bilayer membranes. However, much of this configurational disorder arises from energetically disallowed skew conformations. This suggests a configurational heterogeneity in the lipids at a single binding site: Eclipsed conformations occur also in some lipid headgroups and glycerol backbones. Stereochemical violations appear for some of the ester carboxyl groups of the protein-bound phospholipids in the PDB, and two glycerol backbones have the incorrect enantiomeric configuration.     

Excluded volume in protein side-chain packing

The excluded volume occupied by protein side-chains and the requirement of high packing density in the protein interior should severely limit the number of side-chain conformations compatible with a given native backbone. To examine the relationship between side-chain geometry and side-chain packing, we use an all-atom Monte Carlo simulation to sample the large space of side-chain conformations. We study three models of excluded volume and use umbrella sampling to effectively explore the entire space. We find that while excluded volume constraints reduce the size of conformational space by many orders of magnitude, the number of allowed conformations is still large. An average repacked conformation has 20 % of its chi angles in a non-native state, a marked reduction from the expected 67 % in the absence of excluded volume. Interestingly, well-packed conformations with up to 50 % non-native chi angles exist. The repacked conformations have native packing density as measured by a standard Voronoi procedure. Entropy is distributed non-uniformly over positions, and we partially explain the observed distribution using rotamer probabilities derived from the Protein Data Bank database. In several cases, native rotamers that occur infrequently in the database are seen with high probability in our simulation, indicating that sequence-specific excluded volume interactions can stabilize rotamers that are rare for a given backbone. In spite of our finding that 65 % of the native rotamers and 85 % of chi(1) angles can be predicted correctly on the basis of excluded volume only, 95 % of positions can accommodate more than one rotamer in simulation. We estimate that, in order to quench the side-chain entropy observed in the presence of excluded volume interactions, other interactions (hydrophobic, polar, electrostatic) must provide an additional stabilization of at least 0.6 kT per residue in order to single out the native state.     

NMR solution structure and conformational analysis of the calcium release agent cyclic adenosine 5'-diphosphate ribose (cADPR)

A high-resolution NMR study of the solution structure of the calcium release agent cADPR has been performed. Pseudorotationals analysis reveals that in solution both sugar rings in cADPR adopt predominantly (approximately 75%) South conformations, with the A and N rings adopting approximately 2T3 (C2'-endo(major)-C3'-exo(minor) and 4(3)T (C3'-exo-C4'-endo) conformations, respectively. The backbone torsion angles beta and gamma have also been determined. While the minor North conformers were not observed in the crystal structure of cADPR, the solution values of the major South conformers compare well to those found in crystal structure.     

Conformational spaces of Cinchona alkaloids

A systematic and comprehensive study of the conformational spaces of the Cinchona alkaloids quinine, quinidine, cinchonine, cinchonidine, epiquinine, epiquinidine, epicinchonine, and epicinchonidine using the semiempirical PM3 method is described. The results were analyzed in terms of syn/anti and open/closed/hindered and alpha/beta/gamma conformations. Special emphasis was given to the torsion angles T(1) (C(4a')-C(4')-C(9)-C(8)), T(2) (C(4')-C(9)-C(8)-N(1)) and T(3) (H-O(9)-C(9)-C(8)) that define the backbone and the hydroxy conformation, respectively. The results reveal the quasi-enantiomeric relationships between quinine and quinidine and between epiquinine and epiquinidine, and the main structural differences that exist between the therapeutically active Cinchona alkaloids, quinine and quinidine, and their inactive epimers, epiquinine and epiquinidine. The lowest energy conformation of quinine and quinidine is anti-closed-alpha. The lowest energy conformations of epiquinine and epiquinidine are anti-open-beta and anti-open-alpha, respectively. Low energy conformations with an intramolecular hydrogen bond (N(1.)H(.)O(9)) were found in epiquinine (the global minimum) and epiquinidine, but not in quinine and quinidine.     

Molecular conformation prostaglandin A1 monoclinic crystalline polymorph.

The molecular conformation of the monoclinic crystalline polymorph of prostaglandin A1 has been determined by X-ray diffraction techniques. The space group is P21 with a = 13.637(2), b = 7.567(1), c = 10.576(2) A, beta = 107.37(3) degrees; Dc = 1.073 g.cm-3 for Z = 2. The molecular conformation is characterized by the nearly parallel arrangement of the C1-C7 and C13-C20 side chains, with a general flattening of the overall structure when compared with the orthorhombic polymorph. The cyclopentenone moiety assumes a C8 envelope conformation with C8 and O9 displaced +0.29 A and -0.18 A from the C9-C10=C11-C12 plane respectively. Concerted, small varations of the torsion angles, primarily about the C8-C12, C14-C15 and C16-C17 bonds, bring the monoclinic and orthorhombic conformations into coincidence.     

Side-chain rotamers in protein α-α hairpins and a mechanism of their selection

Several regularities were observed for the distribution of side-chain rotamers in α-α hairpins of globular proteins. In left-turned α-α hairpins, most side chains adopt t rotamers in d-positions and g^? rotamers in g-positions. In right-turned α-α hairpins, most side-chains adopt g^? rotamers in a-positions and t rotamers in e-positions. Analysis of these regularities suggested that selection of the side-chain conformation in α-α hairpins depends on two main factors, the mode of α-helix packing and the positions of side chains in α-helices. The regularities were explained by the squeezing mechanism: interhelical interactions bring the α-helices close together so that the side chains are squeezed out of the helix-helix interface and adopt unique conformations.     

Secondary structures without backbone: an analysis of backbone mimicry by polar side chains in protein structures.

Backbone mimicry by the formation of closed-loop C7, C10 and C13 (mimics of gamma-, beta- and alpha-turns) conformations through side chain-main chain hydrogen bonds by polar groups is a frequent observation in protein structures. A data set of 250 non-homologous and high-resolution protein crystal structures was used to analyze these conformations for their characteristic features. Seven out of the nine polar residues (Ser, Thr, Asn, Asp, Gln, Glu and His) have hydrogen bonding groups in their side chains which can participate in such mimicry and as many as 15% of all these polar residues engage in such conformations. The distributions of dihedral angles of these mimics indicate that only certain combinations of the dihedral angles involved aid the formation of these mimics. The observed examples were categorized into various classes based on these combinations, resulting in well defined motifs. Asn and Asp residues show a very high capability to perform such backbone secondary structural mimicry. The most highly mimicked backbone structure is of the C10 conformation by the Asx residues. The mimics formed by His, Ser, Thr and Glx residues are also discussed. The role of such conformations in initiating the formation of regular secondary structures during the course of protein folding seems significant.     

Criteria that discriminate between native proteins and incorrectly folded models

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.     

Packing and recognition of protein structural elements: A new approach applied to the 4-helix bundle of myohemerythrin

We present a novel search strategy for determining the optimal packing of protein secondary structure elements. The approach is based on conformational energy optimization using a predetermined set of side chain rotamers and appropriate methods for sampling the conformational space of peptide fragments having fixed backbone geometries. An application to the 4-helix bundle of myohemerythrin is presented. It is shown that the conformations of the amino acid side chains are largely determined at the level of helix pairs and that superposition of these results can be used to construct the full bundle. The final solution obtained, taking into account restrictions due to the lateral amphiphilicity of the helices, differs from the native structure by only a 20° rotation of a single helix. © 1993 Wiley-Liss, Inc.     

DNA sequence modulates the conformation of the food mutagen 2-amino-3-methylimidazo[4,5-f]quinoline in the recognition sequence of the NarI restriction enzyme

The conformations of C8-dG adducts of 2-amino-3-methylimidazo[4,5-f]quinoline (IQ) positioned in the C-X1-G, G-X2-C, and C-X3-C contexts in the C-G1-G2-C-G3-C-C recognition sequence of the NarI restriction enzyme were compared, using the oligodeoxynucleotides 5'-d(CTCXGCGCCATC)-3'.5'-d(GATGGCGCCGAG)-3', 5'-d(CTCGXCGCCATC)-3'.5'-d(GATGGCGCCGAG)-3', and 5'-d(CTCGGCXCCATC)-3'.5'-d(GATGGCGCCGAG)-3' (X is the C8-dG adduct of IQ). These were the NarIIQ1, NarIIQ2, and NarIIQ3 duplexes, respectively. In each instance, the glycosyl torsion angle chi for the IQ-modified dG was in the syn conformation. The orientations of the IQ moieties were dependent upon the conformations of torsion angles alpha' [N9-C8-N(IQ)-C2(IQ)] and beta' [C8-N(IQ)-C2(IQ)-N3(IQ)], which were monitored by the patterns of 1H NOEs between the IQ moieties and the DNA in the three sequence contexts. The conformational states of IQ torsion angles alpha' and beta' were predicted from the refined structures of the three adducts obtained from restrained molecular dynamics calculations, utilizing simulated annealing protocols. For the NarIIQ1 and NarIIQ2 duplexes, the alpha' torsion angles were predicted to be -176 +/- 8 degrees and -160 +/- 8 degrees , respectively, whereas for the NarIIQ3 duplex, torsion angle alpha' was predicted to be 159 +/- 7 degrees . Likewise, for the NarIIQ1 and NarIIQ2 duplexes, the beta' torsion angles were predicted to be -152 +/- 8 degrees and -164 +/- 7 degrees , respectively, whereas for the NarIIQ3 duplex, torsion angle beta' was predicted to be -23 +/- 8 degrees . Consequently, the conformations of the IQ adduct in the NarIIQ1 and NarIIQ2 duplexes were similar, with the IQ methyl protons and IQ H4 and H5 protons facing outward in the minor groove, whereas in the NarIIQ3 duplex, the IQ methyl protons and the IQ H4 and H5 protons faced into the DNA duplex, facilitating the base-displaced intercalated orientation of the IQ moiety [Wang, F., Elmquist, C. E., Stover, J. S., Rizzo, C. J., and Stone, M. P. (2006) J. Am. Chem. Soc. 128, 10085-10095]. In contrast, for the NarIIQ1 and NarIIQ2 duplexes, the IQ moiety remained in the minor groove. These sequence-dependent differences suggest that base-displaced intercalation of the IQ adduct is favored when both the 5'- and 3'-flanking nucleotides in the complementary strand are guanines. These conformational differences may correlate with sequence-dependent differences in translesion replication.     

Side-chain modeling with an optimized scoring function

Modeling side-chain conformations on a fixed protein backbone has a wide application in structure prediction and molecular design. Each effort in this field requires decisions about a rotamer set, scoring function, and search strategy. We have developed a new and simple scoring function, which operates on side-chain rotamers and consists of the following energy terms: contact surface, volume overlap, backbone dependency, electrostatic interactions, and desolvation energy. The weights of these energy terms were optimized to achieve the minimal average root mean square (rms) deviation between the lowest energy rotamer and real side-chain conformation on a training set of high-resolution protein structures. In the course of optimization, for every residue, its side chain was replaced by varying rotamers, whereas conformations for all other residues were kept as they appeared in the crystal structure. We obtained prediction accuracy of 90.4% for chi(1), 78.3% for chi(1 + 2), and 1.18 A overall rms deviation. Furthermore, the derived scoring function combined with a Monte Carlo search algorithm was used to place all side chains onto a protein backbone simultaneously. The average prediction accuracy was 87.9% for chi(1), 73.2% for chi(1 + 2), and 1.34 A rms deviation for 30 protein structures. Our approach was compared with available side-chain construction methods and showed improvement over the best among them: 4.4% for chi(1), 4.7% for chi(1 + 2), and 0.21 A for rms deviation. We hypothesize that the scoring function instead of the search strategy is the main obstacle in side-chain modeling. Additionally, we show that a more detailed rotamer library is expected to increase chi(1 + 2) prediction accuracy but may have little effect on chi(1) prediction accuracy.     

Determination of nucleic acid backbone conformation by 1H NMR.

In DNA or RNA duplexes, the six-bond C3'-O3'-P-O5'-C5'-C4'-C3' backbone linkage connecting adjacent residues contains six torsion angles (epsilon, zeta, alpha, beta, gamma, delta) but only four protons. This seriously limits the ability to define the backbone conformation by NMR using purely 1H-1H distance geometry (DG) methods. The problem is further compounded by the inability to assign two of the four backbone protons, namely the poorly resolved H5' and H5' protons, and invariably leads to DG structures with poorly defined backbone conformations. We have developed and tested a reliable method to constrain the beta, gamma, and epsilon (and indirectly alpha and zeta) backbone torsion angles by lower-bound NOE distances to unassigned H5'/H5' resonances combined with either 1H line widths or the conservative use of sigma J measurements; the method relies only on 1H 2-D NMR data, does not involve any structural assumptions, and leads to much improved backbone convergence among DG structures. The C4'-C5' torsion angle gamma is constrained by lower-bound NOE distances from H2' and from H6/H8 to any H5'/H5', as well as by sigma JH4, coupling measurements in the 3.9-4.4 ppm region; delta is constrained by H1'-H4' NOE distances and by H3'-H4' and H3'-H2' J couplings in COSY data; epsilon is partially constrained by H3' line width and/or further constrained by subtracting the minimum possible sigma JH3'-H from the observed sigma JH3' (COSY) to arrive at the maximum possible JH3'-P, which is then converted to H3'-P distance bounds. The angle beta is partially constrained via H5'-P and H5'-P distance bounds consistent with the maximum H5'-P and H5'-P J couplings derived from the observed H5' and H5' line widths, while alpha and zeta are indirectly constrained by lower distance bounds on the observed (n)H1' to (n + 1)H5'/H5' NOEs combined with the prior partial constraints on beta, gamma, delta, and epsilon. The combined effects of these additional constraints in determining distance geometry structures have been demonstrated using a 12-base duplex, [d(GCCGTTAACGGC)]2. Coordinate RMSDs per atom between structures refined with these constraints from random-embedded DG structures, from ideal A-DNA, and from B-DNA starting structures were less than 0.4 A for the central 8 base pairs indicating good convergence. All backbone angles for the central 8 base pairs are very well constrained with less than 10 degrees variation in any of the 48 torsion angles.     

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 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.