Conformational analysis of single-base bulges in A-form DNA and RNA using a hierarchical approach and energetic evaluation with a continuum solvent model.

The analysis and prediction of non-canonical structural motifs in RNA is of great importance for an understanding of the function and design of RNA structures. A hierarchical method has been employed to generate a large variety of sterically possible conformations for a single-base adenine bulge structure in A -form DNA and RNA. A systematic conformational search was performed on the isolated bulge motif and neighboring nucleotides under the constraint to fit into a continuous helical structure. These substructures were recombined with double-stranded DNA or RNA. Energy minimization resulted in more than 300 distinct bulge conformations. Energetic evaluation using a solvation model based on the finite-difference Poisson-Boltzmann method identified three basic classes of low-energy structures. The three classes correspond to conformations with the bulge base stacked between flanking nucleotides (I), location of the bulge base in the minor groove (II) and conformations with a continuous stacking of the flanking helices and a looped out bulge base (III). For the looped out class, two subtypes (IIIa and IIIb) with different backbone geometries at the bulge site could be distinguished. The conformation of lowest calculated energy was a class I structure with backbone torsion angles close to those in standard A -form RNA. Conformations very close to the extra-helical looped out bulge structure determined by X-ray crystallography were also among the low-energy structures. In addition, topologies observed in other experimentally determined bulge structures have been found among low-energy conformers. The implicit solvent model was further tested by comparing an uridine and adenine bulge flanked by guanine:cytosine base-pairs, respectively. In agreement with the experimental observation, a looped out form was found as the energetically most favorable form for the uridine bulge and a stacked conformation in case of the adenine bulge. The inclusion of solvation effects especially electrostatic reaction field contributions turned out to be critically important in order to select realistic low-energy bulge structures from a large number of sterically possible conformations. The results indicate that the approach might be useful to model the three-dimensional structure of non-canonical motifs embedded in double-stranded RNA, in particular, to restrict the number of possible conformations to a manageable number of conformers with energies below a certain threshold.     

Conformational energy calculations for dinucleotide molecules. A systematic study of dinucleotide conformation, with application to diadenosine pyrophosphate.

A systematic study of the conformational states of the dinucleotide diadenosine 5′,5′-pyrophosphate (AppA), an analog of the coenzyme NAD⁺, has been made using semi-empirical energy calculations. Taking low-energy mononucleotide structures as starting conformations, energy minimizations have been performed. The most stable structures exhibit stacking interactions between the adenine bases; there are many different stacked states of similar energy; their stability is derived from nonbonded interactions primarily between the bases but also from base–sugar interactions. The most common form of stacking in the most stable structures was found to be antiparallel A-A helix. These findings are consistent with the experimental data, which suggest that AppA adopts predominantly a stacked state in solution, and this state incorporates a variety of stacked conformations.     

The Study of Possible A and B Conformations of Alternating DNA Using a New Program for Conformational Analysis of Duplexes (CONAN)

Abstract

A new program, CONAN has been designed for CONformational ANalysis of oligonucleotide duplexes with natural and modified bases. It allows to model both regular DNA fragments with different types of symmetry and irregular ones including bends, junctions, mismatched pairs and base lesions. Computations and minimization of the energy are performed in a space of internal structural variables chosen to build start structure easier and conveniently analyze the results obtained. These internal structural variables determine mutual base-base and base-sugar arrangement and sugar puckering. The analytical closure procedure is applied both to sugar rings and to backbone fragments between adjacent sugars. For more effective energy minimization, analytical gradient is calculated. The CONAN was applied to the search for low-energy conformations of poly(dA-dT)·poly(dA-dT) and poly(dG-dC)·poly(dG-dC) duplexes. Extended regions of low-energy A and B conformations are revealed and characterized. These regions contain structures with different relative values of helical twist, τ, for pur-pyr and pyr-pur steps, namely, conformations with τ(pur-pyr)>τ(pyr-pur) and with τ(pur-pyr)<τ(pyr-pur). Two types of sugar puckering were found for B-form low-energy conformations, the first type with all C2′-endo sugar residues and the second one—;with C2′-endo purines and O1′-endo pyrimidines. The calculated conformations are compared with X-ray diffraction data for crystals and fibers and NMR data for solution.     

Conformational stability in dinucleoside phosphate crystals. Semiempirical potential energy calculations for uridylyl-3'-5'-adenosine monophosphate (UpA) and guanylyl-3',5'-cytidine monophosphate (GpC)

Classical potential energy calculations were performed for the dinucleoside phosphates UpA and GpC. Two widely accessible low-energy regions of conformation space were found for the ω′, ω pair. That of lowest energy contains conformations similar to helical RNA, with ω′ and ω in the vicinity of 300° and 280°, respectively. All five experimental observations of crystalline GpC, two of ApU, and the helical fragment of ApApA fall in this range. The second lowest region has ω′ and ω at about 20° and 80°, respectively, which is in the general region of one experimentally observed crystalline conformer of UpA, and the nonhelical region of ApApA. It is concluded that GpC and ApU, which were crystallized as either sodium or calcium salts, are shielded from each other in the crystal by the water of hydration and are therefore free to adopt their predicted in vacuo minimum energy helical conformations. By contrast, crystalline UpA had only 1/2 water per molecule, and was forced into higher energy conformations in order to maximize intermolecular hydrogen bonding.     

Conformational studies of (2''-5'') polynucleotides: theoretical computations of energy, base morphology, helical structure, and duplex formation.

A detailed theoretical analysis has been carried out to probe the conformational characteristics of (2'-5') polynucleotide chains. Semi-empirical energy calculations are used to estimate the preferred torsional combinations of the monomeric repeating unit. The resulting morphology of adjacent bases and the tendency to form regular single-stranded structures are determined by standard computational procedures. The torsional preferences are in agreement with available nmr measurements on model compounds. The tendencies to adopt base stacked and intercalative geometries are markedly depressed compared to those in (3'-5') chains. Very limited families of regular monomerically repeating single-stranded (2'-5') helices are found. Base stacking, however, can be enhanced (but helix formation is at the same time depressed) in mixed puckered chains. Constrained (2'-5') duplex structures have been constructed from a search of all intervening glycosyl and sugar conformations that form geometrically feasible phosphodiester linkages. Both A- and B-type base stacking are found to generate non-standard backbone torsions and mixed glycosyl/sugar combinations. The 2'- and 5'-residues are locked in totally different arrangements and are thereby prevented from generating long helical structures.     

Conformational characteristics of dApdA,dApdT, dTpdA,and dTpdT from energy minimization studies

The conformational characteristics of the deoxydinucleoside monophosphates with adenine and thymine bases in all possible sequences, namely, dApdA, dApdT, dTpdA, and dTpdT have been studied using an improved set of energy parameters to calculate the total potential energy and an improved set of energy parameters to calculate the total potential energy and an improved version of the minimization technique to minimize the total energy by allowing all seven dihedral angles of the molecular fragment to vary simultaneously. The results reveal that the most preferred conformation in all these units usually corresponds to one of the four helical conformations, namely, the A-DNA, B-DNA, C-DNA, and Watson-Crick DNA models. These helical conformations differ in energies by about 3 kcal/mol with respect to one another. The conformations which could promote a loop or bend in the backbone are, in general, less stable by about 3.5 kcal/mol with respect to the respective lowest-energy helical conformation. The results indicate that there is a definite influence of bases and their actual sequences on the preferred conformations of the deoxydinucleoside monophosphates. The lowest-energy structure, although corresponding to one of the four helical conformations, differ with the type of the deoxydinucleoside monophosphate. Good or reasonable base stacking is noted in dApdA and dTpdA with both C(3′)-endo and C(2′)-endo sugars and in dApdT and dTpdT with only C(3′)-endo sugar. The inversion of the base sequence in deoxydinucleoside monophosphates alters the order of preference of low-energy conformations as well as the base-stacking property of the unit. The paths linking the starting and final states in the (ω′, ω) plane show interesting features with regard to the energy spread, thus providing insight into the path of conformational movement ofthe molecule under slight perturbation. The stabilities of the A and B forms, including the internal energies of the C(3′)-endo ans C(2′)-endo sugar systems, indicate that for dTpdT the B → A transition is less probable. For dApdA, dApdT, and dTpdA this transition is probable in the same order of preference. We propose that the T-A sequence in the polynucleotide chain might serve as the site accessible for B ? A transitions. The theoretical predictions are in good agreement with the experimental observations.     

Conformational characteristics of mixed sugar puckered deoxytetranucleoside triphosphate d-GpCpGpC from energy minimization studies

As a continuation of our theoretical studies on nucleic acid subunit systems, in this article we consider the case of the tetranucleoside d-GpCpGpC, the minimally ideal representative unit for analyzing the relative stabilities of different forms of homo- and mixed helical conformation of polynucleotides. The four sugar rings are kept so as to generate B-genus, B+A genus and Z-genus conformations. Twenty five helical conformational states which resulted from judicious mixing of A-, B-, C-, W-, and Z-, states locally are subjected to energy minimization permitting the 19 dihedral angles to vary simultaneously. Conformational states corresponding to regular helical forms and mixed helical forms, when analyzed provide valuable information as to the local conformational flexibility and transitions available to polynucleotides.     

Conformation and Configuration at the Central Amine Nitrogen of a Nucleotide Adduct of the Carcinogen 2-(Acetylamino)flourene as Studied by 13C and 15N NMR Spectroscopy

Abstract

The conformation and configuration at the central nitrogen of the adduct 8-(N-fluoren-2-ylamino)-2′-deoxyguanosine 5′-monophosphate has been investigated by high-field ¹³C and ¹⁵N NMR spectroscopy. One-bond nitrogen-hydrogen coupling constants and ¹³C chemical shifts for the adduct as well as for the model compounds diphenylamine, 4-nitrodiphenylamine and 2-aminofluorene have been measured in nonaqueous solutions. The data indicate a near planar configuration at the amine nitrogen that links the guanine and fluorene rings of the adduct. The orientations about the guanyl-nitrogen and fluorenyl-nitrogen bonds place the two ring systems in either perpendicular (Type A) or helical (Type B) conformations. It is suggested, based on structural similarities to diarylamines, that the C-N-C bond angle of the adduct is greater than 120° in order to reduce unfavorable steric interactions between the two ring systems. Space-filling molecular models of the adduct in duplex DNA show that the aminofluorene moiety can be oriented into both Type A and Type B conformations within the major groove. The configuration at nitrogen of diphenylamine, 4-nitrodiphenylamine and 2-aminofluorene has also been examined.     

Low temperature solution structures and base pair stacking of double helical d(CGTACG)(2)

Solution structures and base pair stacking of a self- complementary DNA hexamer d(CGTACG)(2) have been studied at 5, 10 and 15 degrees C, respectively. The stacking interactions among the center base pair steps of the DNA duplex are found to improve when the terminal base pairs became less stable due to end fraying. A new structural quantity, the stacking sum (Sigma(s)), is introduced to indicate small changes in the stacking overlaps between base pairs. The improvements in the stacking overlaps to maintain the double helical conformation are probably the cause for the observed temperature dependent structural changes in double helical DNA molecule. A detailed analysis of the helical parameters, backbone torsion angles, base orientations and sugar conformations of these structures has been performed.     

Refinement of the thrombin-bound structure of a hirudin peptide by a restrained electrostatically driven Monte Carlo method.

Energy refinement of the structure of a linear peptide, hirudin56-65, bound to thrombin was carried out using a conformational search method in combination with restrained minimization. Five conformations originated from nmr data and distance geometry calculations having a similar global folding pattern but quite different backbone conformations were used as the starting structures. As a result of this approach, a series of low-energy conformations compatible with a set of upper and lower bounds of interproton distances determined from transferred nuclear Overhauser effects were found. A comparison among the lowest energy conformations of each run showed that the combination of energy refinement plus distance constraints led to a very well-defined structure for both the backbone and the side chains of the last 7 residues of the polypeptide. Furthermore, the low-energy conformations generated with this technique contain a segment of 3(10)-helix involving the last 5 residues at the COOH terminal end.     

Conformational behavior of α,α-dialkylated peptides

The preferred conformations of N-acetyl-N′-methyl amides of some dialkylglycines have been determined by empirical conformational-energy calculations; minimum-energy conformations were located by minimizing the energy with respect to all the dihedral angles of the molecules. The conformational space of these compounds is sterically restricted, and low-energy conformations are found only in the regions of fully extended and helical structures. Increasing the bulkiness of the substituents on the C^α, the fully extended conformation becomes gradually more stable than the helical structure preferred in the cases of dimethylglycine. This trend is, however, strongly dependent on the bond angles between the substituents on the C^α atom: In particular, helical structures are favored by standard values (111°) of the N-C^α-C′ angle, while fully extended conformations are favored by smaller values of the same angle, as experimentally observed, for instance, in the case of α,α-di-n-propylglycine.     

Conformational behavior of hyaluronan in relation to its physical properties as probed by molecular modeling

Hyaluronan (HA) is a linear charged polysaccharide whose structure is made up of repeating disaccharide units. Apparently conflicting reports have been published about the nature of the helical structure of HA in the solid state. Recent developments in the field of molecular modeling of polysaccharides offer new opportunities to reexamine the structural basis underlying the formation and stabilization of ordered structures and their interactions with counterions. The conformational spaces available and the low energy conformations for the disaccharide, trisaccharide, and tetrasaccharide segments of HA were investigated via molecular mechanics calculations using the MM3 force field. First, the results were used to access the configurational statistics of the corresponding polysaccharide. A disordered chain having a persistence length of 75 A at 25 degrees C is predicted. Then, the exploration of the stable ordered forms of HA led to numerous helical conformations, both left- and right-handed, having comparable energies. Several of these conformations correspond to the experimentally observed ones and illustrate the versatility of the polysaccharide. The double stranded helical forms have also been explored and theoretical structures have been compared to experimentally derived ones.     

Conformational energy calculations for dinucleotide molecules: a study of the nucleotide coenzyme nicotinamide adenine dinucleotide (NAD+).

A study of the conformational states of the dinucleotide coenzyme NAD⁺ has been made using semiempirical energy calculations. Taking low-energy mononucleotide structures as starting conformations, energy minimizations have been performed. The lowest energy states are stacked structures, with interactions between the adenine and nicotinamide rings. Some structures show stabilization gained from electrostatic attractions between the positively charged nicotinamide and negatively charged phosphate oxygens. These predictions correlate well with the available experimental data.     

Exploring the free energy landscape of a model β‐hairpin peptide and its isoform

Secondary structural transitions from α‐helix to β‐sheet conformations are observed in several misfolding diseases including Alzheimer's and Parkinson's. Determining factors contributing favorably to the formation of each of these secondary structures is therefore essential to better understand these disease states. β‐hairpin peptides form basic components of anti‐parallel β‐sheets and are suitable model systems for characterizing the fundamental forces stabilizing β‐sheets in fibrillar structures. In this study, we explore the free energy landscape of the model β‐hairpin peptide GB1 and its E2 isoform that preferentially adopts α‐helical conformations at ambient conditions. Umbrella sampling simulations using all‐atom models and explicit solvent are performed over a large range of end‐to‐end distances. Our results show the strong preference of GB1 and the E2 isoform for β‐hairpin and α‐helical conformations, respectively, consistent with previous studies. We show that the unfolded states of GB1 are largely populated by misfolded β‐hairpin structures which differ from each other in the position of the β‐turn. We discuss the energetic factors contributing favorably to the formation of α‐helix and β‐hairpin conformations in these peptides and highlight the energetic role of hydrogen bonds and non‐bonded interactions. Proteins 2014; 82:2394–2402. © 2014 Wiley Periodicals, Inc.     

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.     

Influence of ribose 2′-O-methylation on GpC conformation by classical potential energy calculations

Potential energy calculations were employed to examine the effect of ribose 2′-O-methylation on the conformation of GpC. Minimum energy conformations and allowed conformational regions were calculated for 2′MeGpC and Gp2′MeC. The two lowest energy conformations of 2′MeGpC and Gp2′MeC are similar to those of GpC itself. The helical RNA conformation (sugar pucker-C(3′)-endo, ω′ and ω,g^?g^?, bases-anti) is the global minimum, and a helix-reversing conformation with ω′, ω in the vicinity of 20°, 80° is next in energy. However, subtle differences between the three molecules are noted. When the substitution is on the 5′ ribose (Gp2′MeC), the energy of the helical conformation is less than that of GpC, due to favorable interactions of the added methyl group. When the substitution is at the 3′ ribose (2′MeGpC) these stabilizing interactions are outweighed by steric restrictions, and the helical conformation is of higher energy than for GpC. Furthermore, the statistical weight of the 2′MeGpC g^? g^? helical region is substantially less than the corresponding weight for Gp2′MeC. In addition, 2′MeGpC′s methoxy group is conformationally restricted to a narrow range centered at 76°. This group has a broadly allowed region between 50 and 175° in Gp2′MeC. These differences occur because the appended methyl group in 2′MeGpC is located in the interior of the helix cylinder, as it would be in polynucleotide, while it hangs unimpeded in Gp2′MeC. These findings suggest that 2′-O-methylation has both stabilizing and destabilizing influences on the helical conformation of RNA. For 2′MeGpC the destabilizing steric hindrance imposed by the nature of the guanine base dominates.     

Discrimination Between A-type and B-type Conformations of Double Helical Nucleic Acid Fragments in Solution by Means of Two-dimensional Nuclear Overhauser Experiments

Abstract

The solution structure of two double helical nucleic acid fragments, viz. r(CGCGCG) and d(CGCGCG), was probed by means of two-dimensional nuclear Overhauser effect spectroscopy. The two compounds were selected as models for the A-type and B-type double helical conformations, respectively, and it is shown that for each of the two model compounds the intensities of the NOE cross peaks between base- and H2′ (deoxy)ribose proteins are qualitatively in correspondence with the relative NOE intensities expected on basis of the supposed duplex conformations. Thus our results indicate that NOE-data can be used to differentiate between A- and B-type double helical conformations in solution.

Coupling constant data show that, except for G(6), all ribose rings in r(CGCGCG) adopt pure N (C3′-endo) conformations thereby manifesting that this molecule takes up a regular A-type double helical conformation in solution. In contrast, the deoxyribose rings in d(CGCGCG) retain conformational freedom in the duplex state, albeit that the N/S- equilibrium is biased towards the S (C2′-endo) sugar conformation. This finding indicates that in solution the B-DNA backbone is highly dynamic.     

Solution structure of [d(ATGAGCGAATA)]2. Adjacent G:A mismatches stabilized by cross-strand base-stacking and BII phosphate groups.

The solution structure of a rather unusual B-form duplex [d(ATGAGCGAATA)]2 has been determined using two-dimensional nuclear magnetic resonance (2D-NMR) and distance geometry methods. This sequence forms a stable ten base-pair B-form duplex with 3' overhangs and two pairs of adjacent G:A mismatches paired via a sheared hydrogen-bonding scheme. All non-exchangeable protons, including the stereo-specific H-5'S/H-5'R of the 3G and 7G residues, were assigned by 2D-NMR. The phosphorus spectrum was assigned using heteronuclear correlation with H-3' and H-4' reasonances. The complete assignments reveal several unusual nuclear Overhauser enhancements (NOEs) and unusual chemical shifts for the neighboring G:A mismatch pairs and their adjacent nucleotides. Inter-proton distances were derived from time-dependent NOEs and used to generate initial structures, which were further refined by iterative back-calculation of the two-dimensional nuclear Overhauser enhancement spectra; 22 final structures were calculated from the refined distance bounds. All these final structures exhibit fully wound helical structures with small penalty values against the refined distance bounds and small pair-wise root-mean-square deviation values (typically 0.5 A to 0.9 A). The two helical strands exchange base stacking at both of the two G:A mismatch sites, resulting in base stacking down each side rather than down each strand of the twisted duplex. Very large twist angles (77 degrees) were found at the G:A mismatch steps. All the final structures were found to have BII phosphate conformations at the adjacent G:A mismatch sites, consistent with observed downfield 31P chemical shifts and Monte-Carlo conformational search results. Our results support the hypothesis that 31P chemical shifts are related to backbone torsion angles. These BII phosphate conformations in the adjacent G:A mismatch step suggest that hydrogen bonding of the G:A pair G-NH2 to a nearby phosphate oxygen atom is unlikely. The unusual structure of the duplex may be stabilized by strong interstrand base stacking as well as intrastrand stacking, as indicated by excellent base overlap within the mismatch stacks.     

The energy of formation of internal loops in triple-helical collagen polypeptides

The sequence-dependent local destabilization in the interior of the collagen triple helix has been evaluated by means of conformational energy computations. Using a model poly(Gly-Pro-Pro) triple helix as the reference state, a method was developed for generating local loops, i.e., internal deformations, and analyzing their conformations. A seven-residue Gly-Pro-Pro-Gly-Pro-Pro-Gly fragment was replaced by the Gly-Pro-Ala-Gly-Ala-Ala-Gly sequence in one, two, or all three of the strands of the loop region. A set of loop conformations was generated in which the ends of the loop were initially fixed in the triple-helical structure. The potential energy of the entire deformed triple helix was then minimized, resulting in a variety of structures that contained deformed loops. The conformations of the triple helices at the two ends of the loops remained essentially unchanged in many of the low-energy conformations. In numerous high-energy conformations, however, the triple-helical segments were also partially or totally disrupted. The minimum-energy conformations of the whole structures were compared in terms of rms deviations of atomic coordinates with respect to the original triple helix, and of the shapes of the loops (using a distance function derived from differential geometry). Three new geometrical parameters—stretch S, kink K, and unwinding U—were defined to describe the changes in the overall orientation of the triple helices at the two ends of the loop. It is shown that, when the number of Pro residues in a short fragment is reduced, the triple helical structure can accomodate internal loops (i.e., distortions) within a 5 kcal/mol cutoff from the essentially unperturbed triple helical structure. For structures with a Gly-Pro-Ala-Gly-Ala-Ala-Gly sequence in all three strands, the probability of finding conformations with internal loops is small, i.e., 0.06. Internal loops affect the overall orientation of these structures, as measured by the helix-distortion parameters S, K, and U. © 1995 John Wiley & Sons, Inc.     

Conformational Characteristics of Mixed Sugar Puckered Deoxytetranucleoside Triphosphate d-GpCpGpC from Energy Minimization Studies

Abstract

As a continuation of our theoretical studies on nucleic acid subunit systems, in this article we consider the case of the tetranucleoside d-GpCpGpC, the minimally ideal representative unit for analyzing the relative stabilities of different forms of homo- and mixed helical conformation of polynucleotides. The four sugar rings are kept so as to generate B-genus, B+A genus and Z-genus conformations. Twenty five helical conformational states which resulted from judicious mixing of A-, B-, C-, W-, and Z-, states locally are subjected to energy minimization permitting the 19 dihedral angles to vary simultaneously. Conformational states corresponding to regular helical forms and mixed helical forms, when analyzed provide valuable information as to the local conformational flexibility and transitions available to polynucleotides.