A polynucleotide CD probe: interactions with oligomers of a polycationic amine that exhibit positive extrinsic bands at greater than 300 nm

A set of large positive extrinsic CD bands ([θ]₃₃₃ = 2.6 X 10⁴ deg-cm²/decimole phosphate) in the > 300 nm region as well as diminution of the intrinsic signals (θ₂₇₅) have been observed in the CD spectra of various nucleic acids complexed with the achiral compound, N-poly{α-[N-(4-pyridylethylene-4-pyridyl-N′-)α′-p-xylyl]dibromide}-4-pyridylethylene-4-pyridinium bromide, (polymer X).^1,2,5 The signal changes are attributed to the binding of polymer X chromophores isogeometrically to the DNA helix in an ordered chiral arrangement. Fractionation of polymer X gives 10 well-separated oligomers. The oligomers were characterized by nmr. Their interactions with DNA have been investigated with respect to r(r = ratio of equivalents of polymer X charge/g-atoms DNA phosphorus) and n (oligomer chain length). In all cases where n ≥ 1, [θ]₃₃₃ increases linearly with increasing r between 0 and 0.32, and is accompanied by a corresponding decrease in [θ]₂₇₅, which becomes negative as r approaches .32. Extrinsic band intensities reveal a dependence on n up to n = 5, above which increases in nonspecific binding result in a reduction in normalized band intensities. Polymer X shows a strong preference for B-form nucleic acids and induces maximum extrinsic CD signal intensities with A-T homopolymers. Alterations in helix hydration are believed to accompany complex formation. Inversions in [θ]₂₇₅ of the octamer X-poly(dA-dT) complex have been attributed to the “alternating B” conformation of poly(dA-dT).³ Similar inversions are not observed in other nucleic acid-octamer X complexes. Visible and CD spectrometry data from competition studies in the presence of the antibiotics actinomycin D (AMD), daunomycin (DM), and distamycin A (DST) are consistent with “nonclassical” intercalation as the mode of binding, and these data place the potential binding site in or near the hydrophobic region of the minor groove. Reductions in [θ]₃₃₃ with increasing urea further implicate the involvement of hydrophobic interactions in the formation of an asymmetric complex. Stabilization of the helix results in all cases as evidenced by alterations in T_m; corresponding changes, however, in cooperativity are not clearly discernable. Viscosity and light-scattering data indicate no changes in molecular weight due to aggregation, and as such are not consistent with a transition to the ψ-DNA upon complex formation.     

Temperature dependence of CD spectra of DNA from various sources

The CD spectra of DNA from various sources (T2; T4; C_d; Escherichia coli; calf thymus; Streptomyces chrysomalis) were investigated. A new band Δ_ε210 in the CD spectra of glucosylated DNA of the T even phages was found. The temperature dependence of the CD spectra of DNA was obtained over a wide range of temperatures, including those of the helix–coil transition. The band Δ_ε275 for all DNAs does not appreciably change in the range of the helix–coil transition. The monotonic increase of this band before melting, and its decrease after melting is observed with an increase in temperature. The amplitude of the CD band Δ_ε245 for all the DNAs studied and Δ_ε210 (glucosylated DNA) parallels the change of E₂₆₀ absorbance.     

Interaction Mode between Inclusion Complex of Vitamin K3 with γ- Cyclodextrin and Herring-Sperm DNA

Methods including spectroscopy, electronic chemistry and thermodynamics were used to study the inclusion effect between γ-cyclodextrin (CD) and vitamin K₃(K₃), as well as the interaction mode between herring-sperm DNA (hsDNA) and γ-CD-K₃ inclusion complex. The results from ultraviolet spectroscopic method indicated that VK₃ and γ-CD formed 1:1 inclusion complex, with the inclusion constant K_f = 1.02 × 10⁴ L/mol, which is based on Benesi–Hildebrand's viewpoint. The outcomes from the probe method and Scatchard methods suggested that the interaction mode between γ-CD-K₃ and DNA was a mixture mode, which included intercalation and electrostatic binding effects. The binding constants were K ^θ_25°C = 2.16 × 10⁴ L/mol, and K^θ_37°C = 1.06 × 10⁴ L/mol. The thermodynamic functions of the interaction between γ-CD-K₃ and DNA were Δ_rH_m^θ = ?2.74 × 10⁴ J/mol, Δ_rS_m^θ = 174.74 J·mol^?1K^?1, therefore, both Δ_rH_m^θ (enthalpy) and Δ_rS_m^θ (entropy) worked as driven forces in this action.     

Tyrosine optical activity as a probe of the conformation and interactions of fibronectin

A very intense negative band is observed at ～ 183 nm in the CD spectrum of fibronectin from bovine plasma. This transition has not previously been reported, probably because it occurs in a spectral region that has not been readily accessible in earlier studies. At longer wavelength, the observed CD is very similar to spectra reported for human and chick material, having positive bands at ～230 and ～200 nm, and a negative band at ～215nm. The low molar ellipticity of the negative band ([θ] ≈ ?2.5 × 10³ deg cm² dmol^?1) suggests little α-helix or β-sheet structure. The new transition, and the two positive bands at higher wavelength, do not correspond to known transitions of the peptide backbone, but all three are present in the CD of N-acetyltyrosineamide. It is therefore suggested that the observed CD behavior of fibronectin arises predominantly from the optical activity of tyrosine side chains. The contribution of this side-chain optical activity to the CD of other proteins is discussed. On raising pH to ionize tyrosine residues, the positive CD band at ～230 nm is lost in both N-acetyltyrosineamide and in fibronectin. The spectral change is fully reversible in the model compound, but only partially reversible in fibronectin. From this evidence, and the magnitude of the 183-nm band, it is suggested that some or all of the tyrosine residues in fibronectin may be present within ordered domains. The possible role of S? S bonds in maintaining tertiary structure is discussed. The interaction of fibronectin with heparin is accompanied by a large increase in the 183-nm band and by slight enhancement of the negative band at 215 nm, consistent with some limited formation of β-sheet. Present results indicate that CD may be of considerable value in characterization of the molecular organization and biologically relevant interactions of fibronectins and of related glycoproteins of the extracellular matrix.     

Characterization of the binding of neomycin/paromomycin sulfate with DNA using acridine orange as fluorescence probe and molecular docking technique

The binding of neomycin sulfate (NS)/paromomycin sulfate (PS) with DNA was investigated by fluorescence quenching using acridine orange (AO) as a fluorescence probe. Fluorescence lifetime, FT-IR, circular dichroism (CD), relative viscosity, ionic strength, DNA melting temperature, and molecular docking were performed to explore the binding mechanism. The binding constant of NS/PS and DNA was 6.70 × 10³/1.44 × 10³ L mol^?1 at 291 K. The values of ΔH^θ, ΔS^θ, and ΔG^θ suggested that van der Waals force or hydrogen bond might be the main binding force between NS/PS and DNA. The results of Stern–Volmer plots and fluorescence lifetime measurements all revealed that NS/PS quenching the fluorescence of DNA–AO was static in nature. FT-IR indicated that the interaction between DNA and NS/PS did occur. The relative viscosity and melting temperature of DNA were almost unchanged when NS/PS was introduced to the solution. The fluorescence intensity of NS/PS–DNA–AO was decreased with the increase in the ionic strength. For CD spectra of DNA, the intensity of positive band at nearly 275 nm was decreased and that of negative band at nearly 245 nm was increased with the increase in the concentration of NS/PS. The binding constant of NS/PS with double-stranded DNA (dsDNA) was larger than that of NS/PS with single-stranded DNA (ssDNA). From these studies, the binding mode of NS/PS with DNA was evaluated to be groove binding. The results of molecular docking further indicated that NS/PS could enter into the minor groove in the A–T rich region of DNA.     

Stabilization of DNA-polycation complex by lithium perchlorate

The polycation forms a complex with DNA. The complex was stabilized to thermal denaturation by millimolar concentrations of LiClO4, in the range of 0.1-0.10 M LiClO4. No hyperchromicity was observed in the thermal profiles, and instead, hyperchromicity was observed. The complex showed no significant extrinsic CD band, but showed LiClO4-dependent alterations in the DNA intrinsic bands. It was found that Li+ was primarily responsible for the stabilization of the complex. It is proposed that Li+ stabilization arises through ternary complex formation and that the chaotropic ClO4- catalyzes conversion of less stable DNA-polycation complex into a more stable form.     

Structural polymorphism of liquid-crystalline dispersions of double-stranded DNA complexed with synthetic polycations

Linear double-stranded DNA molecules interact with positively charged polyconidine molecules in aqueous salt solutions to yield liquid-crystalline dispersions (LCDs) with a mean particle diameter of ～6000 Å. The packing density of (DNA-polycation) complexes differs among LCD particles formed at different ionic strengths. X-ray data on the liquid-crystalline phases of (DNA-polyconidine) complexes formed under different conditions were compared with a phase diagram, reflecting polymorphism of liquid crystals of linear double-stranded DNA. It was shown that LCD was hexagonal at 0.15 M ≤ C _NaCl < 0.4 M and cholesteric at 0.4 M ≤ C _NaCl < 0.55 M. Cholesteric LCD displayed abnormal optical activity in the circular dichroism spectrum. A similar situation was observed with poly(2,5-ionene), another polycation differing in chemical structure from polyconidine. The results demonstrated structural polymorphism of (DNA-polycation) LCDs. It was assumed that the packing mode of (DNA-polycation) complexes in LCD particles can be regulated by changing NaCl concentration. The mechanism generating the cholesteric liquid-crystalline state of DNA in a narrow range of NaCl concentrations is discussed.     

Synthesis and conformational study of poly(0,0′-dicarbobenzoxy-L-β-3,4-dihydroxyphenyl-α-alanine)

High-molecular-weight poly(0,0′-dicarbobenzoxy-L -β-3,4-dihydroxyphenyl-α-alanine) was prepared by the N-carboxyanhydride method. From the results obtained by a study of the optical rotation, nuclear magnetic resonance, and solution infrared absorption, the conformation of poly(0,0′-dicarbobenzoxy-L -β-3,4-dihydroxyphenyl-α-alanine) depended greatly on the solvent taking a right-handed helix with [θ]₂₂₅ = ?13,600 ～ ?18,900 in alkyl halides, a left-handed helix with [θ]₂₂₈ = 22,100 ～ 24,800 in cyclic ethers or trimethylphosphate, and a random coil structure in dichloroacetic acid, trifluoroacetic acid, or hexafluoroacetone sesquihydrate. The polypeptide underwent a right-handed helix-coil transition in chloroform/dichloroacetic acid (or trifluoroacetic acid) mixed solvents and a left-handed helix-coil transition in dioxane/dichloroacetic acid (or trifluoroacetic acid) mixed solvents. The results were compared with those of poly(0-carbobenzoxy-L -tyrosine).     

Circular dichrotic probes for aspects of chromatin structure: aromatic polycationic ionen probes

Two ionens (II and X) formed complexes with DNA and chromatin with extrinsic CD bands and reduced intrinsic bands. The salt and urea sensitive, AT-specific probe (II) gave Δε > 100 L-(residue II)^?1-cm^?1 with DNA and Δε=0–14 with chromatin; II reduced the intrinsic bands from Δε≈0.7 to Δε≈0.5. Ionen X gave Δε₃₄₅=30 with DNA, and Δε₃₄₅=15–20 with chromatin. X reduced the intrinsic band to ?1.6. X show less base specificity. Extrinsic Δε_λ of X increased linearly to r (residue/phosphate) = 0.5 for DNA and only 0.3 in chromatin. DNA in chromatin may have ～10% of the II and 50–60% of the X binding sites and those in an altered conformation.     

Circular dichroism of histone-bound regions in chromatin.

Native, NaCl-treated, trypsin-treated, and polylysine-bound nucleohistones were studied in 2.5 × 10^?4 M EDTA, pH 8.0, using circular dichroism (CD) and thermal denaturation. Removal of histone I by 0.6 M NaCl has a much smaller effect on both Δε₂₂₀ and Δε₂₇₈ than the removal of other histones. This indicates that histone I has less helical content and less conformational effect on the DNA in nucleohistone. By extrapolating to 100% binding by histones other than I, the positive CD band near 275 nm is close to zero. Comparison is also made between the effects of binding by the more basic and the less basic halves of histones by trypsin-digestion and polylysine-binding experiments. Trypsin digestion of nucleohistone reduces melting band IV at 82°C much more than melting band III at 72°C. However, the CD changes of Δε₂₇₈ and Δε₂₂₀ induced by trypsin digestion are small, unless melting band III is also reduced by the use of a higher trypsin level. This implies that the less basic halves of histones, which stabilize DNA to 72°C (melting band III), have more helical structure and are more responsible for conformational change in DNA than are the more basic halves, which stabilize DNA to 82°C (melting band IV). Polylysine binding to nucleohistone diminishes melting band III but has no effect on melting band IV. This binding affects only slightly the Δε₂₂₀ of nucleohistone, indicating that polylysine interferes very little with the structure of the less basic halves of bound histones. The implications of these studies with respect to chromatin structure are discussed.     

Crystallographic characterization of the α,γ C12 helix in hybrid peptide sequences

The solid‐state conformations of two αγ hybrid peptides Boc‐[Aib‐γ⁴(R)Ile]₄‐OMe 1 and Boc‐[Aib‐γ⁴(R)Ile]₅‐OMe 2 are described. Peptides 1 and 2 adopt C₁₂‐helical conformations in crystals. The structure of octapeptide 1 is stabilized by six intramolecular 4 → 1 hydrogen bonds, forming 12 atom C₁₂ motifs. The structure of peptide 2 reveals the formation of eight successive C₁₂ hydrogen‐bonded turns. Average backbone dihedral angles for αγ C₁₂ helices are peptide 1 , Aib; φ (°) = ?57.2 ± 0.8, ψ (°) = ?44.5 ± 4.7; γ⁴(R)Ile; φ (°) = ?127.3 ± 7.3, θ₁ (°) = 58.5 ± 12.1, θ₂ (°) = 67.6 ± 10.1, ψ (°) = ?126.2 ± 16.1; peptide 2 , Aib; φ (°) = ?58.8 ± 5.1, ψ (°) = ?40.3 ± 5.5; ψ⁴(R)Ile; φ (°) = ?123.9 ± 2.7, θ₁ (°) = 53.3 θ 4.9, θ ₂ (°) = 61.2 ± 1.6, ψ (°) = ?121.8 ± 5.1. The tendency of γ⁴‐substituted residues to adopt gauche–gauche conformations about the C^α–C^β and C^β–C^γ bonds facilitates helical folding. The αγ C₁₂ helix is a backbone expanded analog of α peptide 3₁₀ helix. The hydrogen bond parameters for α peptide 3₁₀ and α‐helices are compared with those for αγ hybrid C₁₂ helix. Copyright © 2016 European Peptide Society and John Wiley & Sons.     

Conformational studies on copolymers of L-lysine and L-leucine: circular dichroism and potentiometric titration studies

Conformational aspects of a series of copolymers of L -Leucine and L -leucine [poly-(Lys^xLeu^y)] containing 0 to 0.41 mole fraction L -leucine have been studied by circular dichroism (CD) and potentiometric titration in 0.05M KF solution. CD studies on the α-helical conformation showed a dependence of the magnitude of the CD ellipticity band at 222 nm on copolymer composition; the [θ]₂₂₂ decreasing with higher leucine contents. This was interpreted as the result of an increase of the hydrophobicity of the environment of the amide group due to the presence of the leucyl residues. Values of the Zimm-Rice parameter, σ, for the copolymers were obtained from the potentiometric titrations and used to fit theoretical curves to the experimental data. Using the variation of σ with polymer composition, a value of σ for the leucyl residue was estimated to be 6.3 × 10^?2, assuming independence of σ on the amino acid sequence in the copolymer. The free energy change for the conversion of one mole residue from uncharged helix to uncharged coil, ΔG_hc°, was also obtained from the titration data for each copolymer up to a leucine mole fraction of 0.16; a value of 385 cal mole^?1 was estimated for ΔG_hc° for a leucyl residue. These values for σ and ΔG_hc° are compared with other values in the literature for various amino acid residues obtained from titration and melting curve data.     

Intrinsic Birefringence of Multiple-Coiled DNA, Theory and Applications

The intrinsic birefringence of multiple-coiled DNA is computed in terms of an equally dense array of parallel DNA molecules. The birefringence for n times-coiled DNA molecules is given by [Formula: see text] where β_o = 0, β_i = tan^-1 (p_i/2πr_i), p_i = period of the i^th helix coil and r_i = radius of i^th helix coil. The formula is applied to two cases of helically coiled DNA in biological material and found to agree quantitatively with experimental results.     

Quasielastic light scattering by biopolymers. IV. Tertiary collapse of calf thymus DNA in 5.5M LiCl

Circular dichroism has been commonly employed to infer the conformation of DNA in solution. The basis of the conformational assignments is the work of Tunis-Schneider and Maestre, wherein CD spectra of DNA were obtained under conditions comparable to those employed in the x-ray diffraction studies of A-, B-, and C-DNA. It has recently been suggested that the CD spectrum of DNA in chromatin, which is similar to the CD spectrum of the C-form DNA, is a superposition of the normal B-DNA spectrum and a single negative band, centered at 275 nm. This negative band is qualitatively identical to the spectrum for condensed Ψ-form DNA. We have employed the hydrodynamic methods of quasielastic light scattering and sedimentation velocity to determine the extent of DNA tertiary structural alteration in 5.5M LiCl as a possible explanation of the C-form CD spectrum. These studies suggest an eightfold contraction of the Stokes hydrodynamic volume for calf thymus DNA in going from 0.4M NH₄Ac to 5.5M LiCl, with no change in molecular weight. The estimated maximum presistence length of DNA in 5.5M LiCl is estimated to be 20.0 nm compared to the “minimum” value of 44.7 nm in NaCl solutions. The value 20.0 nm corresponds to a maximum radius of 16.7 nm for a “continuously coiled” cylinder of DNA, which compares with the value 5.0 nm of DNA in the nucleosome unit of chromatin.     

Changes in the circular dichroic spectrum of calf thymus solubilized chromatin caused by ultraviolet irradiation

Summary UV irradiation of the chromatin caused an increase of the positive circular dichroic band in the vicinity of 275 nm (corresponding to DNA) and a deepening of the negative band of proteins at about 225 nm. These changes in the circular dichroic spectrum are monotonous in the range of doses studied (< 6 × 10⁴ J.m^–2). The increase of the positive circular dichroic band probably reflects the occurrence of local conformational changes in DNA, which include changes in base position (tilting, distance from helix axis) in the close neighbourhood of photoproducts. The presence of photoproducts in chromatin reduces changes in its circular dichroic spectra with temperature.     

Evaluation of the effect of Tb(IV)-NR complex on herring sperm DNA genetic information by mean of spectroscopic

Abstract

The interaction between Tb(IV)-NR complex and herring sperm DNA in buffer solution of Tris-HCl was investigated with the use of acridine orange(AO) as a spectral probe. The binding modes and other information were provided by the UV–spectrophotometry and fluorescence spectroscopy. The thermodynamic functions expressed that the binding constants of Tb(IV)-NR complex with DNA was K^θ_298.15K = 4.03?×?10⁵?L·mol^?1, K^θ_310.15K =1.30?×?10⁷?L·mol^?1, and the Δ_rGθ m _298.15?K＝?3.20?×?10⁴ J·mol^?1. The scatchard equation suggested that the interaction mode between Tb(IV)-NR complex and herring sperm DNA is electrostatic and weak intercalation bindings. FTIR spectroscopy results also indicate that there is a specific interaction between the Tb(IV)-NR complex and the A and G bases of DNA.     

Li+ counterion self-diffusion in ordered DNA

The anisotropic self-diffusion coefficient of ⁷Li⁺ (I = 3/2) counterions has been studied in hydrated, macroscopically oriented Li-(B)DNA fibers at relatively high water contents, corresponding to approximate DNA-DNA helix axis distances of 22–35 Å, using the pulsed field gradient hmr spin-echo method. Self-diffusion coefficients parallel (D_∥) and perpendicular (D_?) to the DNA helix axis increase with increasing salt content and with increasing DNA-DNA helix axis distance. The observed anisotropy D_∥/D_? decreases from 1.6 to 1.2 with the DNA-DNA separation increasing from 22 to 35 Å in the salt-free sample. This result can be understood by the obstruction effect caused by the DNA molecules themselves. The values of the Li⁺ self-diffusion coefficients in the most water-rich system with no added salt (corresponding to an approximate distance of 35 Å between the DNA helix axes) were D_∥ ～ 1.15 × 10^?10 m² s^?1 and D_? ～ 0.98 × 10^?10 m² s^?1, compared to 9.14 × 10^?10 m² s^?1 for the diffusion of Li⁺ in an aqueous solution of LiCl (～ 2.1M). The possible occurrence of restriction effects in the DNA fibers have also been studied by determining the self-diffusion coefficient at different effective diffusion times. The self-diffusion coefficient of Li⁺ in the sample with the largest DNA-DNA helix axis distance seems to be independent of the effective diffusion time, which indicates that the lithium ions are not trapped within impermeable barriers. The possibility of diffusion through permeable barriers has also been investigated, and is discussed. © 1994 John Wiley & Sons, Inc.     

Effect of conformation and configuration of arabinose residues on the circular dichroism of C-glycosylflavones

Examination of a variety of arabinose containing C-glycosylflavones has shown that the sign and intensity of the CD band at 250–275 nm (charge-transfer band) reflect not only the point of attachment of the sugar to the flavone but also depend upon the absolute and anomeric configuration, ring-size and ring-conformation in addition to the preferred rotameric conformation of the sugar about the C-aryl, C-l″ bond. A change in stereochemistry of arabinose from the α to β anomer resulted in sign inversion of the 250–275 nm CD band for 6-C-l-arabinosylflavones. Furthermore, a 6-C-arabinosylflavone containing α-l-arabinose exhibited an oppositely signed charge-transfer CD band in comparison to one which contained α-d-arabinose. 6,8-Di-C-glycosylflavones containing arabinose and glucose exhibited CD bands resulting from contributions due to both sugars, if the arabinose was not present as the β-pyranose form (¹C₄, conformation).     

Circular dichroism studies of α-aminoisobutyric acid-containing peptides: Chain length and solvent effects in alternating Aib-L-Ala and Aib-L-Val sequences

The CD spectra of the peptides Boc-X-(Aib-X)_n-OMe (n = 1, 2, 3) and Boc-(Aib-X)₅-OMe, where X = L -Ala or L -Val have been examined in several solvents. The X = Ala and Val peptides behave similarly in all solvents, suggesting that the Aib residues dominate the folding preferences of these peptides. The decapeptides adopt helical conformations in methanol and trifluoroethanol, with characteristic negative CD bands at 222 and 205 nm. In the heptapeptides, similar spectra with reduced intensities are observed. Comparison with nmr studies suggest that estimates of helical content in oligopeptides by CD methods may lead to erroneous conclusions. The pentapeptides yield solvent-dependent spectra indicative of conformational perturbations. Peptide association in dioxane results in an unusual spectrum with a single negative band at 210 nm for the decapeptides. Disaggregation is induced by the addition of methanol or water to dioxane solutions. Aggregation of the heptapeptides is less pronounced in dioxane, suggesting that a critical helix length may be necessary to promote association stabilized by helix dipole–dipole interactions.     

A critical evaluation of models for complex molecular dynamics: application of NMR studies of double- and single-stranded DNA

The nature of internal and overall motions in native (double-stranded) and denatured (single-stranded) DNA fragments 120–160 base pairs (bp) long is examined by molecular-dynamics modeling using ¹³C-nmr spin-relaxation data obtained over the frequency range of 37–125 MHz. The broad range of ¹³C frequencies is required to differentiate among various models. Relatively narrow linewidths, large nuclear Overhauser enhancements (NOEs), and short T₁ values all vary significantly with frequency and indicate the presence of rapid, restricted internal motions on the nanosecond time scale. For double-stranded DNA monomer fragments (147 bp, 24 Å diam at 32°C), the overall motion is that of an axially symmetric cylinder (τ_x = ～10^?6 s;τ_Z = ～1.8 × 10^?8s), which is in good agreement with values calculated from hydrodynamic theory (τ_x = ～1.8 × 10^?6 s; τ_Z = ～2.7 × 10^?8 s). The DNA internal motion can be modeled as restricted amplitude internal diffusion of individual C? H vectors of deoxyribose methine carbons C1′, C3′, and C4′, either with conic boundary conditions (τ_w = ～4 × 10^?9 s, θ_cone = ～21°) or as a bistable jump (τ_A = τ_B = ～2 × 10^?9 s, θ = ～15°). We discuss the critical role in molecular-dynamics modeling played by the angle (β) that individual C? H vectors make with the long axis of the DNA helix. Heat denaturation brings about increases in both the rate and amplitude of the internal motion (described by the wobble model with τ_W = ～0.2 × 10^?9 s, θ_cone = ～50°), and overall motion is affected by becoming essentially isotropic (τ_x = τ_Z = ～5 × 10^?8 s) for the single-stranded molecules. Since ¹³C-nmr data obtained at various DNA concentrations for C2′ of the deoxyribose ring is not described well by the above models, a new model incorporating an additional internal motion is proposed to take into account the rapid, extensive, and weakly coupled motion of C2′.