Spatial configuration of ordered polynucleotide chains. V. Conformational energy estimates of helical structure

Semiempirical potential energy functional used previously to account successfully for the mean-square unperturbed dimensions and nmr coupling constants of randomly coiling polynucleotides are used, after modifications, to account for base stacking and interstrand hydrogen bonding, and to evaluate the conformational energies of single- and double-stranded polynucleotide helices. Attention is focused upon the variety of A-genus helices with local backbone conformations resembling the known double-helical structures of RNA. Distinct structural differences between single- and double-stranded helices are predicted from the energy calculations. A second point of interest is the apparent failure of two conformationally identical left-handed polynucleotide chains to form a left-handed duplex. The third major observation of the study is the wide morphological variety of theoreticaly allowed right-handed polynucleotide duplexes. In addition to the familiar double helix stabilized by horizontal base stacking and hydrogen bonding, an unusual vertical double helix is predicted to form between complementary bases fixed in the unusual but not energetically forbidden high anti glycosyl conformation. Experimental results bearing upon the theoretical predictions are discussed.     

Configuration-dependent properties of randomly coiling polynucleotide chains. II. The role of the phosphodiester linkage

The dependence of the unperturbed dimensions of randomly coiling polynucleotides on the rotations about the phosphodiester linkages of the chain has been examined in order to understand the conformational discrepancies, set forth in paper I, regarding these angles (ω′ and ω). Large values of the characteristic ratio 〈r²〉₀/nl² , which agree with the experimental behavior of the chain, are obtained only if a sizeable proportion of the polymer residues have trans ω′ values. The asymmetric torsional potential that is believed to arise from gauche effects associated with the P-O bonds has been approximated using a hard core model. The calculated characteristic ratio exhibits a strong dependence upon the magnitude of this torsional barrier (separating trans and gauche conformations) and shows agreement with experimental values for polyribonucleotides only if this energy difference is 1 kcal/mol or less.     

Spatial configuration of single-stranded polynucleotides. Calculations of average dimensions and Nmr coupling constants

The probability distributions of the torsional angles (Φ′, ω′, ω, Φ, and ψ), which fix the structure of nucleotide backbone, have been calculated using the results of energy calculations based on extended Huckel theory (EHT), complete neglect of differential overlap (CNDO), perturbative configuration interaction using localized orbitals (PCILO), and classical potential functions (CPF) methods. Statistical average values of the vicinal ¹H? ¹H, ¹H? ³¹P, and ¹³C? ³¹P nmr coupling constants 〈J〉 have been calculated from the generalized Karplus relations using the probability distribution in the Φ′, Φ, and ψ space. Experimental 〈J〉 values for polyribouridylic acid (polyU) support the theoretical predictions for these torsional angles. Using Monte Carlo technique, random coils of single-stranded polynucleotides have been simulated and the mean-square end-to-end distance 〈r²〉 has been calculated. Molecular orbital methods (EHT, CNDO, and PCILO) suggest considerable flexibility around O? P bonds, leading to fairly small values for the characteristic ratio (C_∞ ～ 4). Observed values of the unperturbed characteristic ratio for polynucleotides are quite large (C_∞ ～ 18) suggesting a relatively rigid nucleotide backbone. The results based on molecular orbital calculations can be reconciled with the experimental values by introducing an additional stabilization of ～2 kcal mol^?1 for the predicted minimum energy ragion (Φ′ ～ 240°, ω′ ～ 290°, ω 290°, Φ 180°, and ψ 60°). Such a stabilization may arise from the association of water molecules and metal ions with the phosphate group and (or) Coulomb interaction between neighboring phosphate groups. The calculations provide a semiquantitative estimate of torsional rigidity in the nucleotide backbone.     

The spatial distributions of randomly coiling polynucleotides

Statistical mechanical averages of vectors and tensors characterizing the allowed configurations of randomly coiling polynucleotides have been calculated for chains of 2⁰–2¹⁰ repeating units. Specifically, the persistence vector p = 〈 r 〉 has been obtained as a function of chain length. Configurational averages of the Cartesian tensors formed from the displacement vector ρ = r – p have been computed up to and including the tensor of seventh rank. From these tensors the three-dimensional spatial distributions of end-to-end vectors have been constructed to provide comprehensive pictures of the directional tendencies of the randomly coiling polynucleotide. The elements of the third and fourth moment tensors, however, give sufficient information to represent accurately the qualitative features of the spatial distributions. For long chains, more than 2⁶ (64) repeating units, the spatial distributions assume spherically symmetric shapes that can be adequately characterized by one-dimensional radial distribution functions. These radial distribution functions agree well with the radial distributions calculated from Monte Carlo samples containing more than 5000 chains. The constraints of fixed bond lengths, fixed bond angles, and hindered internal rotations severely distort the spatial distributions of short polynucleotide chains to mushroom-shaped volumes. These skewed distributions provide information useful to the analysis of small, single-stranded loops, bulges, and circles. The formation of these structures requires the termini of the polynucleotides to lie within specifically delineated volumes with respect to coordinate systems affixed to the first bonds of the chains. The extent to which these loop closure volumes overlap the three-dimensional spatial distributions provides estimates of loop formation that are much more reliable than earlier studies based upon the radial distribution function.     

The spatial configuration of ordered polynucleotide chains. I. Helix formation and base stacking.

A single virtual bond scheme set forth previously for the treatment of average properties of randomly coiling polynucleotides is here applied to the calculation of helical parameters which characterize a regularly repeating polynucleotide molecule. Only a fraction of the enormous number of conformationally feasible helixes fulfill the geometric criteria of vertical base stacking usually associated with ordered polynucleotide chains. Detailed examination of the nature and mode of base stacking feasible in a single helical backbone structure indicates that the handedness of a base stacking arrangement does not correlate either quantitatively or qualitatively with the handedness of the polymer backbone. A number of polynucleotide chains which exhibit lefthanded base stacking patterns in nmr and CD studies may, in fact, be righthanded helixes.     

Stereochemistry of nucleic acids and polynucleotides. VI. Minimum energy conformations of dimethyl phosphate

As part of a study on the conformation of polynucleotides and nucleic acids the preferred conformations of the model conpound dimethyl phosphate are worked out using potential energy functions. In calculating the total potential energy associated with the conformation, nonbonded, torsional, and electrostatic terms have been considered. The variation of the total conformational energy is represented as a function of two torsion angles ? and ψ which are the rotations about the two phosphoester bonds. The most stable conformations are found to be the gauche–gauche conformations about these bonds. The conformations observed for phosphodiesters in the solid state and in the proposed structures of polynucleotides and nucleic acids cluster around the minimum. Also, regions of minimum energy correspond well with the typical allowed regions of a representative dinucleotide.     

Syn-anti effects on the spatial configuration of polynucleotide chains

Semiempirical energy calculations have beeb performed on model nucleic acid systems to assess the preferred conformation of the rotation χ about the glycosidic linkage and also the effect of this rotation on the spatial configuration of the sugar-phosphate chain backbone. The rotation angle ?? about bond C_5′–C_4′ in purine polyribonucleotides and 5′-monoribonucleotides is found to depend on whether the conformational range of χ is syn or anti. The preferred conformation of χ in these molecules is also found to depend upon the nature of the attached base. The orientation of χ in poly rA chains is predicted to be predominantly anti, whereas in poly rG the syn conformer is expected to occur in significant proportions. The syn conformer is preferred almost exclusively in certain unusual purine polynucleotides, such as poly 8Br-rA. It is noted that the preferred conformation of x in polynucleotides is not necessarily the same as that calculated for 5′-mononucleotides and nucleosides. On the basis of these calculations, the influence of the orientation and nature of a purine base on the spatial configuration of a polynucleotide chain as a whole has been examined. The random coil dimensions of a syn polynucleotide chain are found to be larger than those of an anti chain as a consequence of the effect of a syn base on the local conformation of the chain skeleton. Finally, it is found that the occurrence of a syn base in an ordered polynucleotide chain may prevent the formation of normal stacking with the preceding base.     

A configurational interpretation of the axial phosphate spacing in polynucleotide helices and random coils

The structural implications arising from the observation (set forth in the preceding paper) that the charge density of a single-stranded randomly coiling polynucleotide chain is approximately equal to that of one strand of the familiar double helix are here examined. A computational scheme is described to obtain (using bond lengths, valence bond angles, and internal rotation angles) the mean phosphate–phosphate spacing parameter b along the chain axes of any single-stranded polynucleotide molecule. Attention is then focused upon the computed interphosphate spacing associated with both the theoretical randomly coiling polynucleotide that reproduces the observed experimental unperturbed dimensions and the familiar single-stranded helix. The calculations clearly demonstrate that the parameter b only weakly reflects the spatial configuration of the chain. The approximate equivalence of the b values associated with the single-stranded helix and the unperturbed randomly coiling polynucleotide is not indicative of strong configurational similarities between the two forms. The familiar helix is composed of a sequence of identically conformed compact structural residues while the random coil is characterized by a variety of chain-repeating residues of which a large proportion are extended units.     

The spatial configuration of ordered polynucleotide chains. II. The poly(rA) helix.

Approximate details of the spatial configuration of the ordered single-stranded poly(rA) molecule in dilute solution have been obtained in a combined theoretical analysis of base stacking and chain flexibility. Only those regularly repeating structures which fulfill the criterion of conformational flexibility (based upon all available experimental and theoretical evidence of preferred bond rotations) and which also exhibit the right-handed base stacking pattern observed in nmr investigations of poly(rA) are deemed suitable single-stranded helices. In addition, the helical geometry of the stacked structures is required to be consistent with the experimentally observed dimensions of both completely ordered and partially ordered poly(rA) chains. Only a single category of poly(rA) helices (very similar in all conformational details to the individual chains of the poly(rA) double-stranded X-ray structure) is thus obtained. Other conformationally feasible polynucleotide helices characterized simply by a parallel and overlapping base stacking arrangement are also discussed.     

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.     

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.     

Spatial configurations of polynucleotide chains. 3. Polydeoxyribonucleotides

The virtual bond scheme set forth in preceding papers for treating the average properties of polyriboadenylic acid (poly rA) is here applied to the calculation of the unperturbed mean-square end-to-end distance of polydeoxyriboadenylic acid (poly dA). The modifications in structure and in charge distribution resulting from the replacement of the hydroxyl group at C_2′ in the ribose residue by hydrogen in deoxyribose produce only minor modifications in the conformational energies associated with the poly dA chain as compared to those found for poly rA. The main difference is manifested in the energy associated with rotations about the C_3′–O_3′ bond of the deoxyribose residue in the C_2′-endo conformation; accessible rotations are confined to the range between 0° and 30° relative to the trans conformation, whereas in the ribose unit the accessible regions comprise two ranges centered at approximately 35° and 85°. The characteristic ratio 〈r²〉0/nl² calculated on the basis of the conformational energy estimates is ≈9 for the poly dA chain with all deoxyribose residues in the C_3′-endo conformation and ≈21 with all residues in the C_2′-endo form. Satisfactory agreement is achieved between the theoretical values and experimental results on apurinic acid by treating the poly dA chain as a random copolymer of C_3′-endo and C_2′-endo conformational isomers present in a ratio of ～1 to 9.     

Correlation between the backbone and side chain conformations in 5′-nucleotides. The concept of a ‘rigid’ nucleotide conformation

Conformational energies of the 5′-adenosine monophosphate have been computed as a function of χ and ψ, of the torsion angles about the side-chain glycosyl C(1′)–N(9) and of the main-chain exocyclic C(4′)–C(5′) bonds by considering nonbonded, torsion, and electrostatic interactions. The two primary modes of sugar puckering, namely, C(2′)-endo and C(3′)-endo have been considered. The results indicate that there is a striking correlation between the conformations about the side-chain glyocsyl bond and the backbone C(4′)–C(5′) bond of the nucleotide unit. It is found that the anti and the Gauche–Gauche (gg), conformations about the glycosyl and the C(4′)–C(5′) bonds, respectively, are energetically the most favored conformations for 5′-adenine nucleotide irrespective of whether the puckering of the ribose is C(2′)-endo or C(3′)-endo. Calculations have also shown that the other common 5′-pyrimidine nucleotides will show similar preferences for the glycosyl and C(4′)–C(5′) bond conformations. These results are in remarkable agreement with the concept of the “rigid” nucleotide unit that has been developed from available data on mononucleotides and dinucleoside monophosphates. It is found that the conformational ‘rigidity’ in 5′-nucleotides compared with that of nucleosides is a consequence of, predominantly, the coulombic interactions between the negatively charged phosphate group and the base. The above result permits one to consider polynucleotide conformations in terms of a “rigid” C(2′)-endo or C(3′)-endo nucleotide unit with the major conformational changes being brought about by rotations about the P–O bonds linking the internucleotide phosphorus atom. IT is predicted that the anti and the gg conformations about the glycosyl and the C(4′)–C(5′) bonds would be strongly preferred in the mononucleotide components of different purine and pyrimidine coenzymes and also in the nucleotide phosphates like adenodine di- and triphosphates.     

A molecular dynamics simulation of the flavin mononucleotide–RNA aptamer complex

We report on an unrestrained molecular dynamics simulation of the flavin mononucleotide (FMN)–RNA aptamer. The simulated average structure maintains both cross‐strand and intermolecular FMN–RNA nuclear Overhauser effects from the nmr experiments and has all qualitative features of the nmr structure including the G10–U12–A25 base triple and the A13–G24, A8–G28, and G9–G27 mismatches. However, the relative orientation of the hairpin loop to the remaining part of the molecule differs from the nmr structure. The simulation predicts that the flexible phosphoglycerol part of FMN moves toward G27 and forms hydrogen bonds. There are structurally long‐lived water molecules in the FMN binding pocket forming hydrogen bonds within FMN and between FMN and RNA. In addition, long‐lived water is found bridging primarily RNA backbone atoms. A general feature of the environment of long‐lived “structural” water is at least two and in most cases three or four potential acceptor atoms. The 2′‐OH group of RNA usually acts as an acceptor in interactions with the solvent. There are almost no intrastrand O2′H(n)⋮O4′(n + 1) hydrogen bonds within the RNA backbone. In the standard case the preferred orientation of the 2′‐OH hydrogen atoms is approximately toward O3′ of the same nucleotide. However, a relatively large number of conformations with the backbone torsional angle γ in the trans orientation is found. A survey of all experimental RNA x‐ray structures shows that this backbone conformation occurs but is less frequent than found in the simulation. Experimental nmr RNA aptamer structures have a higher fraction of this conformation as compared to the x‐ray structures. The backbone conformation of nucleotide n + 1 with the torsional angle γ in the trans orientation leads to a relatively short distance between 2′‐OH(n) and O5′(n + 1), enabling hydrogen‐bond formation. In this case the preferred orientation of the 2′‐OH hydrogen atom is approximately toward O5′(n + 1). We find two relatively short and dynamically stable types of backbone–backbone next‐neighbor contacts, namely C2′(H)(n)⋮O4′(n + 1) and C5′(H)(n + 1)⋮O2′(n). These interactions may affect both backbone rigidity and thermodynamic stability of RNA helical structures. © 1999 John Wiley & Sons, Inc. Biopoly 50: 287–302, 1999     

Conformations of cyclic peptide/calcium complexes in solution

Synthetic cyclic octapeptides of general structure cyclo[Glu(γOBzl)-Sar-Gly-(N-R)Gly]₂ (R = n-hexyl and cyclohexyl) transport calcium ions selectively across organic phases and phospholipid membranes. We have now used proton nmr spectroscopy (360 MHz) to study the solution conformation(s) of their calcium complexes. When Ca(ClO₄)₂ was added to solutions of these peptides in CDCl₃, nmr spectra of the resulting calcium complexes were characteristic of a single C₂-symmetric conformer. From a Karplus-Bystrov analysis of vicinal coupling constants in both the peptide backbone and Glu side chain (treated as an ABCC′MX spin system), in conjuction with model-building studies, a structure was proposed in which the calcium ion is bound in an octahedral-type complex by the four (coplanar) carbonyl groups of the (all-trans) Glu-Sar and Gly-(N-R)Gly peptide bonds. Occurrence of preferred rotamers about Glu side chain C^α–C^β bonds indicated that restricted rotation in peptide side chains arises upon calcium binding.     

Spatial configurations of polynucleotide chains. I. Steric interactions in polyribonucleotides: a virtual bond model

A simplified scheme for treating the spatial configurations of polynucleotide chains is developed using the rotational isomeric state approximation and statistical methods applicable to linear systems of interacting subunits. As a consequence of geometric constraints imposed by the skeletal structure and of the severity of certain steric interactions, it is possible to represent the repeat unit comprising six skeletal bonds by two virtual bonds of fixed length. The configuration of the polynucleotide chain as a whole may be conveniently described by an alternating succession of these two virtual bonds. Moreover, analysis of steric interactions suggests that bond rotations governing the mutual orientation of a given pair of successive virtual bonds should be sensibly independent of the rotations affecting the mutual orientation of other pairs. The statistical mechanical treatment of configuration-dependent properties is much simplified in consequence of this mutual independence. Mean-square dimensions calculated by giving equal weights to all sterically allowed conformations are much smaller than values determined by Felsenfeld and co-workers. The calculated dimensions are markedly increased, however, by placing certain arbitrary restrictions on the rotations about selected pairs of skeletal bonds. It is thus demonstrated that steric interactions alone are insufficient to account for the spatial characteristics of polynucleotide chains. The dimensions are also found to be sensitive to the conformation of the ribose ring of each nucleotide unit, but, insofar as the influences of steric interactions are concerned, the dimensions do not depend on the heterocyclic base attached to the ribose ring.     

Conformational studies on pyrimidine 5'-monophosphates and 3',5'-diphosphates. Effect of the phosphate groups on the backbone conformation of polynucleotides

In continuation of our studies on the effect of the base and the phosphate groups on the glycosyl and the sugar-phosphate backbone conformation, we have carried out semi-empirical potential energy calculations on the common 5′- and 3′5′-ribopyrimidine mono- and diphosphates by considering simultaneous rotations about the glycosyl (χ) and the C(4′)–C(5′) (ψ) bonds. This calculation provides an assessment of the nature and orientation of the base on the sugar–phosphate backbone conformation of nucleotides and polynucleotides. It is found that the attractive inetractions between the 5′-phosphate group and the base mutually stabilize the antiand the gauche-gauche (gg) conformations about χ and ψ, respectively, in 5′-ribopyrimidine nucleotides. The introduction of the 3′-phosphate group as in 3′,5′-ribopyrimidine diphosphates, still leaves the anti-gg as the most favored conformation with the important difference that the probability of occurrence of the anti, gauche-trans (gt) is how substantially increased. This is dependent to a large extent on the sugar conformation and to a lesser extent on the base. Uracil and thymine show a greater probability for the anti-gt than cytosine. The syn conformation is considerably less likely and its occurrence is also dependent on the base type, cytosine showing a lesser tendency than uracil and thymine. For the syn base, the most favourec conformation for ψ is gt, since gg is sterically disallowed and tg is destabilized by electrostatic repulsive interactions between the 3′ and 5′-phosphate groups. Thus, there is a striking correlation between the glycoysl and the backbone C(4′)–C(5′) bond conformations. The rest of the bonds of the backbone are considerable less dependent on the glycosyl conformation. These studies reveal that in poly-ribopyrimidine nucletides the majority of the nucleotide residues are expected to occur in the anti-gg conformation.     

The poly(rU) coil: A minimum-energy model that matches experimental observations

A model of the randomly coiling form of poly(rU) based on minimum-energy conformers of UpU is described. The blend of conformers is chosen to fit the C? C rotational populations derived in nmr studies of UpU and poly(rU) and to match the experimental unperturbed dimensions of the poly(rU) chain. In addition, estimates of loop closure based on the model are comparable to the sizes of loops most frequently seen in model oligonucleotides. Approximately 60% of the conformers constituting the model are characterized by stacked, extended C2′-endo ω′ωψ = tg^?g⁺ rotations. The remainder of the chain is described by equal numbers of C3′-endo A (ω′ωψ = g^?g^?g⁺) and Watson-Crick (ω′ωψ = g^?tt) helical arrangements.     

Interpretation of energy-transfer experiments by theoretical studies of model compounds using semiempirical potential functions. I. Three-linked aromatic peptide units

It is shown that theoretical conformational analysis, based on the evaluation of semiempirical potential functions, can be used to compute the quantities relevant to the interpretation of energy-transfer experiments. The relevant properties are computed for a segment of a polypeptide chain with the sequence Tyr-Tyr. In particular, the average value of the orientation factor 〈κ²〉 and its distribution ?(κ²) are examined. It appears that the degrees of freedom for rotation of the side chains are not sufficient to randomize completely the orientation factor of the transition dipoles. Two additional degrees of freedom, namely the torsion angles around the valence bonds of the backbone, ψ₁ and ?₂, bring 〈κ²〉 close to the value that corresponds to randomly oriented transition dipoles.