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.     

The application of polyelectrolyte limiting laws to the helix–coil transition of DNA. VI. The numerical value of the axial phosphate spacing for the coil form

It is concluded on the basis of comparison of polyelectrolyte theory with published data that the mean phosphate spacing b along the contour axis of an unfolded polynucleotide single strand is in the range 3–4 Å (polyelectrolyte parameter ξ ≈ 2), regardless of temperature, base composition, or extent of stacking. This result is consistent with the low-angle X-ray scattering measurements of Gulik, Inoue, and Luzzati on poly(C). No conclusion may be drawn from this value of b concerning the structure of the chain skeleton or the spatial arrangement of the bases other than that the chain is far from an all-trans local conformation (for which b would be about 6–7 Å, the length of a nucleotide unit). The structural implications, or lack thereof, are discussed in detail in the following paper.     

Configuration-dependent properties of randomly coiling polynucleotide chains. I. A comparison of theoretical energy estimates

Various theoretical estimates of the conformational energy associated with polynucleotides in solution have been compared with each other and also with the experimentally observed conformations found in X-ray crystallographic investigations of low-molecular-weight nucleic acid analogs. In view of the disparities between these data, certain configuration-dependent properties (i.e., the mean-square unperturbed end-to-end distance 〈r²〉₀ and the average vicinal nmr coupling constant 〈J〉) appropriate to randomly coiling polynucleotides described by either the energy estimates or by the crystallographically preferred conformations have also been calculated and compared with the known solution behavior of polynucleotide chains. Both the theoretical energy surfaces and the X-ray data show good agreement with the nmr coupling constant indications of the preferred rotations about the O-C and C-C bonds of the chain backbone. The principal discrepancies between the theoretical methods and X-ray data arise in their ability to predict successfully the preferred rotations about the two phosphodiester bonds of the chain backbone and the unperturbed dimensions of randomly coiling polynucleotide chains.     

Geometry of experimentally observed RNA residues in tRNA and dinucleoside monophosphates: the effect of small variations in the backbone angles.

The polymerization of various experimentally observed conformers of RNA from tRNA and some dinucleoside monophosphates have been examined with a program that computes the basic helix parameters directly from the six backbone torsion angles ω′, ?′, ψ′, ψ, ?, ω to give n (= 360/θ), the number of residues per turn; h, the rise per residue; and r, the radius of the phosphate atoms from the helix axis. The single-stranded regions of tRNA that have A-form residues have a notably lower value of n than the double-stranded regions. The G-U “wobble” base pair is shown to be an energetically strained left-handed form. The A-form dinucleoside monophosphates also have a low value of n. A model of UpAl polymerized as a fourfold left-handed helix with the bases on the outside and phosphates on the inside is investigated for its sharp 90° turn angle characteristics. UpA2 cannot be polymerized due to a low values of h (1.31 Å) and r (2.72 Å), which cause steric hindering. An eightfold model of poly(rA) is discussed as are the nonhelical residues of tRNA. Finally, the effects of small changes in dihedral angles and bond lengths and angles on the helical parameters are investigated and discussed by way of explaining this behavior.     

Theory of the influence of oligonucleotide chain conformation on double helix stability

We consider theoretical aspects of reactions that form base pairs in a double helix. The equilibrium constant for such reactions depends on the probability of finding the two bases in the correct orientation for pairing. This probability can be expressed in terms of the spatial and angular distribution of one micleotide around the other. In this paper we use Monte-Carlo techniques to calculate the distribution of distances between chosen phosphates in nonhclical oligonucleotide backbones, using crystallographic data for bond lengths and angles, and a screened Coulomb potential for phosphate–phosphate interactions. The model chosen is one that predicts correctly the observed dimensions of an unperturbed polynucleotide chain. Knowledge of distance distribution functions permits calculation of the dependence on loop size of the probability of closing a single backbone strand into a hairpin helix. Our results agree roughly, although not exactly, with the semiempirical ring-weighting functions determined by Schefller. Elson, and Baldwin. Further results are a comparison of intramolecular and bimolecular helix nucleation equilibrium constants and a calculation of the stacking free energy in a double helix.     

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.     

Na+ effects on transition of DNA and polynucleotides of variable linear charge density.

A range of linear charge densities of the ordered and disordered forms of DNA or polynucleotides can be obtained experimentally by acid or alkaline titration, or by the investigation of unusual complexes involving protonated bases or three-stranded helices. The variation of melting temperatures with Na⁺ concentration for various of these systems is known and in some cases is complemented by structural and thermodynamic information. We have extended the condensation–screening theory of Manning [Biopolymers, 11 , 937–955 (1972)] to these systems. The stabilizing and destabilizing effects of Na⁺ (condensation and screening, respectively) and be independently varied, and the theory is successful in predicting the qualitative (in some cases, quanittative) behaviour that is observed. Comparison of theory and experiment indicates that the axial phosphate distance b for single-stranded polynucleotides increases with increasing pH. Values of the critical parameter ξ are obtained for the various polynucleotide structures. These values are essential for an understanding of ionic effects on charged ligand–polynucleotide interactions.     

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.     

Polynucleotide folding in yeast tRNAPhe: elucidation of short-, medium-, and long-range interactions of sugar-phosphate-sugar backbone and base using a "blocked" nucleotide probe

It has recently been proposed that the repeating backbone nucleotide may be regarded as consisting of two blocks of equal magnitude representable by two virtual bonds. Implicit consideration of the nucleotide (ψ,ψ) and internucleotide (ω′,ω) geometry that generate variety in polynucleotide conformations, and of the constancy of the repeating structural moieties (P-C4′ and C4′-P) independent of the above rotations, has enabled us to utilize this scheme in the study of ordered structures such as di-, oligonucleotides and, most significantly, tRNA. The polynucleotide folding dictated by short-, intermediate-, and long-range interactions in the monoclinic and orthorhombic forms is described and compared through circular plots depicting the virtual bond torsions and distance plots constructed independently for backbone as well as bases. The torsions and the bond angles associated with the virtual bonds afford a clear distinction between ordered helical segments from loops and bends of tRNA. Lower virtual bond torsions (?60° to 60°) concomitant with higher values of virtual bond angles characterize various bend regions, while torsions around 160°–210° typify ordered helical strands. The distance plot elucidates the type of interaction associated with various sub-structures (helix–helix, helix–loop, and loop–loop) that form the constituents of different structural domains. Several other features such as the manifestation of the P₁₀ loop and the approximate twofold symmetry in the tRNA molecule are conspicuous on the distance plot.     

A spectrophotometric study of the secondary structure of ribonucleic acid based on a method for diminishing single-stranded base-`stacking'' without affecting multihelical structures

1. On the basis of studies with model compounds it was concluded that in 8m-urea-m-potassium chloride (or 4m-guanidinium chloride) in 0.01m-potassium phosphate buffer, pH7.0, multi-helical structures have about the same stability as in 0.1m-potassium phosphate buffer, pH7.0, whereas the tendency of base residues to ;stack' along a single polynucleotide chain is much decreased. 2. Base-pairing was eliminated whereas base-;stacking' persisted after RNA in 1% formaldehyde-0.1m-potassium phosphate buffer, pH7.0, was heated to 95 degrees . 3. From a study of the thermal denaturation of unfractionated transfer RNA from Escherichia coli and of RNA from the fractionated sub-units of rabbit reticulocyte ribosomes in 8m-urea-m-potassium chloride (or 4m-guanidinium chloride) in 0.01m-potassium phosphate buffer, pH7.0, it was inferred that ;stacked' residues may account for up to 25% of the increase in E(260) found on heating RNA in solvents such as 0.1m-potassium phosphate buffer, pH7.0. 4. Changes in the spectrum with temperature were analysed on the basis of the assumptions that (a) the polynucleotide chain is amorphous on denaturation (which is probable in 8m-urea-m-potassium chloride-0.01m-potassium phosphate buffer, pH7.0) and that (b) the polynucleotide chain adopts a single-stranded ;stacked' conformation on denaturation (which is probable when ordinary solvents such as 0.1m-potassium phosphate buffer, pH7.0, are used).     

Effect of side-chain hydrophobic bonding on the stability of homopolyamino acid alpha-helices: conformational studies of poly-l-leucine in water

The conformational properties of block copolymers of poly-L -leucine in water have been examined. The degree of polymerization of the poly-L -leucine block was 11 and 21, respectively, for samples prepared by the Merrifield procedure, and 56 for a sample prepared by the polymerization of leucine N-carboxyanhydride. The optical rotatory dispersion parameter b₀ was used to obtain the helix content θ_h at various temperatures. Application of the Lifson-Roig theory gave the following parameters for the transition of a residue from a coil to a helical state: v = 0.05–0.011, ΔH = +100 cal/mole, ΔS = +0.70–1.00 e. u. These parameters, as well as those for other polyamino acids, are accounted for by hydrophobic bonds involving the nonpolar side chains in the helical and randomly coiled forms. From the data for poly-L -alanine and theoretical values of the thermodynamic parameters for hydrophobic bond formation, the parameters for formation of a polyglycine helix are computed. By separating the contributions of the backbone, it is possible to obtain a set of thermodynamic parameters for the side-chain contributions of a number of polyamino acids. Increased size of the nonpolar side chain (with a larger contribution from hydrophobic bonding) makes a larger contribution to the stability of the α-helix which is reflected, among other ways, in a higher helix content at given temperature.     

Configurational statistics of the DNA duplex: Extended generator matrices to treat the rotations and translations of adjacent residues

The base-to-base virtual bond treatment of nucleic acids used in statistical mechanical calculations of polynucleotide chain properties has been refined by incorporating the six parameters that relate the positions and orientations of sequential rigid bodies. The scheme allows for the sequence-dependent bending, twisting, and displacement of base pairs as well as for asymmetry in the angular and translational fluctuations of individual residues. Expressions are developed for the generator matrices required for the computation, as a function of chain length, of various parameters measuring the overall mean extension and shape of the DNA. Quantities of interest include the end-to-end vector r , the square of the end-to-end distance r², the square radius of gyration s², the center-of-gravity vector g , the second moments of inertia S ^×2, and the higher moments of r and g . The matrix expressions introduced in the 1960s by Flory and co-workers for the determination of configuration-dependent polymer chain averages are decomposed into their translational and orientational contributions so that the methods can be extended to the rigid body analysis of chemical moieties. The new expressions permit, for the first time, examination of the effects of sequence-dependent translations, such as the lateral sliding of residues in A- and B-helices and the vertical opening of base pairs in drug–DNA complexes, on the average extension and shape of the long flexible double helix. The approach is illustrated in the following paper using conformational energy estimates of the base sequence-dependent flexibility of successive B-DNA base pairs. © 1994 John Wiley & Sons, Inc.     

General method for calculating helical parameters of polymer chains from bond lengths,bond angles,and internal-rotation angles

Helical conformations of infinite polymer chains may be described by the helical parameters, d and θ (the translation along the helix axis and the angle of rotation about the axis per repeat unit), _pi (the distance of the ith atom from the axis), d_ij, and d_ij (the translation along the axis and the angle of rotation, respectively, on passing from the ith atom to the jth). A general method has been worked out for calculating all those helical parameters from the bond lengths, bond angles, and internal-rotation angles. The positions of the main chain and side chain atoms with respect to the axis may also be calculated. All the equations are applicable to any helical polymer chain and are readily programmed for electronic computers. A method is also presented for calculating the partial derivatives of helical parameters with respect to molecular parameters.     

Structure prediction for the di-heme cytochrome b561 protein family

Summary.  Atomic models possessing the common structural features identified for the cytochrome b ₅₆₁ (cyt b ₅₆₁) protein family are presented. A detailed and extensive sequence analysis was performed in order to identify and characterize protein sequences in this family of transmembrane electron transport proteins. According to transmembrane helix predictions, all sequences contain 6 transmembrane helices of which 2–6 are located closely in the same regions of the 26 sequences in the alignment. A mammalian (Homo sapiens) and a plant (Arabidopsis thaliana) sequence were selected to build 3-dimensional structures at atomic detail using molecular modeling tools. The main structural constraints included the 2 pairs of heme-ligating His residues that are fully conserved in the family and the lipid-facing sides of the helices, which were also very well conserved. The current paper proposes 3-dimensional structures which to our knowledge are the first ones for any protein in the cyt b ₅₆₁ family. The highly conserved His residues anchoring the two hemes on the cytoplasmic side and noncytoplasmic side of the membrane are in all proteins located in the transmembrane helices 2, 4 and 3, 5, respectively. Several highly conserved amino acids with aromatic side chain are identified between the two heme ligation sites. These residues may constitute a putative transmembrane electron transport pathway. The present study demonstrates that the structural features in the cyt b ₅₆₁ family are well conserved at both the sequence and the protein level. The central 4-helix core represents a transmembrane electron transfer architecture that is highly conserved in eukaryotic species. Received May 12, 2002; accepted September 20, 2002; published online May 21, 2003 RID="*" ID="*" Correspondence and reprints: Institute of Biophysics, Biological Research Centre, P.O. Box 521, 6701 Szeged, Hungary. E-mail: tpali@nucleus.szbk.u-szeged.hu     

On the application of polyelectrolyte limiting laws to the helix-coil transition of DNA. III. TDependence of helix stability on excess univalent salt and on polynucleotide phosphate concentration for variable equivalent ratios of divalent metal ion to phosphate.

Using the free energy difference between double-helix and random-coil forms of DNA as a measure of the stability of the double helix, we calculate the dependence of the stability on excess univalent cation concentration and on polynucleotide phosphate concentration, both as functions of the equivalent ratio r of divalent cation-to-phosphate concentrations. The theoretical tool is merely to compare the free energy of one polyelectrolyte solution, characterized by the polyelectrolyte linear charge density, with the free energy of another, characterized by a different value of the charge density. It is assumed only that the charge density of the double helix is greater than that of the coil form. The calculation represents the only molecular theory given to date (for r ≠ O) for these aspects of helix stability. We find that, as excess univalent cation concentration increases, the helix stability increases if r is small but decreases if r is large (i.e., of the order of unity). Moreover, as the concentration of nucleotide phosphate increases, the helix stability does not change for small values of r but increases for large values. For both effects, a continuous transition as a function of r bridges the low-r and high-r behaviour.     

UDP-glucose dehydrogenase: substrate binding stoichiometry and affinity

Precise structural parameters of polyribonucleotides single stranded helices are determined as well as those of double stranded helices of poly 2′-O-methyl A and of poly A at neutral and acid pH. Infrared linear dichroism investigations indicate the similarity of the conformation of the sugar-phosphate backbone of these single and double stranded helices. The angles of the phosphate group for single stranded helix at neutral pH is found to be oriented at 48° for the 02P02 bisector and at about 65° for the 02–03 line to the helix axis. Similar values were found for double stranded poly A helix at acid pH. These structural parameters obtained for the first time on single stranded polynucleotide helices are proposed to be valid for other similar helical chains such as poly A segments of nuclear or messenger RNA and single stranded CCA acceptor end of transfer RNA.     

Packing analysis of carbohydrates and polysaccharides. V. Crystal structures of two polymorphs of pachyman triacetate

The crystal structures of two polymorphic forms of pachyman triacetate, the fully acetylated derivative of a naturally occuring β-(1 → 3)-D -glucan, were determined by a combination of stereochemical and x-ray diffraction analysis. The two polymorphs could be obtained depending on the temperature and the degree of stretching of film specimens of the substance: polymorph I resulted from stretching 25–50% at 125°C and polymorph II resulted from further stretching to 300% at 215°C. Both polymorphs had previously been shown to have sixfold helical chain conformations, but of unequal pitch. Subsequent detailed structure refinement performed with bond lengths, bond angles, conformational angles, and helix-packing parameters as refinement variables, and the simultaneous minimization of packing and conformational energy and the crystallographic R-factor as refinement criteria, resulted in a complete determination of the two crystal structures. Pachyman triacetate I was found to be a right-handed helix packing with antiparallel polarity and space group P2₁2₁2₁ symmetry (unit-cell parameters a = 11.0, b = 19.0, c (fiber repeat) = 22.38 Å). The acetate groups were nearly planar and the O(2) and O(4) acetates were oriented in such a fashion that the carbonyl double-bond nearly eclipsed the corresponding C—H bond of the ring. The O(6) was in the tg position and its acetate was oriented in such a fashion that the bond sequence C(6)—O(6)—C(6C)—C(6M) was nearly trans-planar, with the carbonyl double-bond bisecting the tetrahedral angle formed by C(6) and its two hydrogens. The final R = 0.221. Pachyman triacetate II was similarly found to be a right-handed helix, but packing as a 50:50 mixture of parallel and antiparallel polarities (unit-cell parameters a = 11.49, b = 20.13, c (fiber repeat) = 18.6 Å). The acetate positions in pachyman triacetate II were substantially the same as in pachyman triacetate I. The final R for the 50:50 mixture was 0.234. Probable reasons for the change in packing polarities are discussed, as are the difficulties encountered in the structure refinement of acetate derivatives.     

A revisit to the three-dimensional structure of B-type starch

A new three-dimensional structure of B-starch is proposed in which the unit cell contains 12 glucose residues located in two left-handed, parallel-stranded double helices packed in a parallel register; 36 water molecules are located between these helices. Chains are crystallized in the hexagonal space group P6₁, with lattice parameters a = b = 1.85 nm, c = 1.04 nm. The space group symmetry was derived from an exhaustive analysis of the large body of structural studies published so far. Diffraction data used in this work were taken from the previously reported x-ray fiber diffractogram [H.C. Wu and A. Sarko (1978), Carbohydrate Research, 61 , 7–25] after adequate reindexing. The final R factor is 0.145 for the three-dimensional data. The repeating unit consists of a maltose molecule where the glucose residues have the ⁴C₁ pyranose conformation and are α(1 → 4) linked. The conformation of the glycosidic linkage is characterized by torsion angles (Φ, Ψ) that take the values (83.8°, ?144.6°) and (84.3°, ?144.1°), whereas the valence angles at the glycosidic bridge have a magnitude of 115.8° and 116.5°, respectively. The primary hydroxyl groups exist in a gauche–gauche conformation. There is no intramolecular hydrogen bond. Within the double helix, interstrand stabilization is achieved without any steric conflict and through the occurrence of O(2)…O(6) type of hydrogen bonds. The model presented here, with an hydration around 27% w/w, corresponds to a well-ordered crystalline sample, since all the water molecules could be located with no apparent sign of a disorder. Half of the water molecules are tightly bound to the double helices; the remainder forms a complex network centered around the sixfold screw axis of the unit cell. The consistency of the present structural model, with both physicochemical and biochemical aspects of the crystalline component of tuber starch granules, is analyzed.