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.     

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. 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.     

Loop formation in polynucleotide chains. II. Flexibility of the anticodon loop of tRNAPhe

The flexibility of hairpin loops containing n bases (residues) has been examined using a theoretical model [N. L. Marky and W. K. Olson (1982), Biopolymers, 21 , 2329–2344] of oligonucleotide loop closure. The study is based on correlated probabilities of chain separation and terminal residue orientation as outlined previously. The probabilities are calculated using standard statistical mechanical methods as functions of local conformational changes of the chain backbone. Our results for an RNA chain of 9 residues suggest that the anticodon loop is a dynamic structure capable of assuming a variety of different spatial conformations. Free energy values related to the various conformations span a narrow range of values (2–4 kcal/mole) and compare well with experimental observations in aqueous solution. Conformational transitions between the loop conformations are within less than 0.5 kcal/mole in free energy. The different spatial loop conformations and the likely pathways between them may have potential relevance to the molecular translation of the genetic code.     

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.     

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.     

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.     

Conformational studies on polynucleotide chains. IV. Backbone structure of ribonucleic acids.

In preceding papers the energies associated with the internal rotations in the sugar–phosphate–sugar complex were described with an analytical potential consisting of a Lennard-Jones 6–12 term and an intrinsic torsional term and representing the best fit to a large number of energies computed with a quantum mechanical ab initio technique. The complex considered there (of 37 atoms and with the chemical formula C₁₀H₁₈O₈P) is repesentative of deoxyribonucleic acids. In this paper we apply our potential to evaluating the intramolecular energies of the 39-atom complex C₁₀H₁₈O₁₀P, representative of the ribonucleic acids. The potential energies for the internal rotations (considered independent from one another) and the energy maps for rotations about consecutive bonds of the backbone chain are critically compared, both with those obtained for the deoxy system and with those obtained from different theoretical approaches as available from literature. It is shown that, at least for certain combinations of the internal rotation angles, the choice of the starting geometry for the sugarphosphate–sugar molecule (bond lengths and valence angles) strongly affects the value of the computed energy. If a proper geometry is used, very low energies are predicted by our potential in correspondence of the sets of torsional angles found in various RNAs by x-ray crystallography.     

Computer simulation of hydrodynamic properties of semiflexible macromolecules: randomly broken chains, wormlike chains, and analysis of properties of DNA

The translational and rotational diffusion coefficients and the intrinsic viscosity of semiflexible, randomly broken, and wormlike chains have been obtained by Monte Carlo simulation in the context of the rigid-body treatment. Both approximate and rigorous rigid-body hydrodynamics are used, so that the error introduced by the approximate methods can be evaluated. A randomly broken chain and a wormlike chain having the same contour length and persistence length have the same radius of gyration but different values for any of the hydrodynamic properties. The two types of chains are compared in this regard. Considering that the cross section of the chain is represented by a cylinder better than by a string of spheres, we devise a cylindrical correction to be applied to the results simulated for chains of beads. Application is made to the analysis of experimental data for the translational and rotational coefficients of DNA fragments with up to 10(3) base pairs, obtaining the persistence length for each model. The values for the wormlike chain agree well with model-independent values obtained from radii of gyration and with other literature data at varying ionic strength. The randomly broken chain is equally able to reproduce the experimental length dependence of the properties, but the resulting persistence length may be too high.     

Physicochemical properties of T4 polynucleotide kinase.

Some physicochemical properties of T4 polynucleotide kinase (EC2.7.1.78) have been studied. The enzyme is an oligomer of one polypeptide chain. The molecular weight of the monomer is 33000, as determined from the amino acid analysis. Phenylalanine is the N-terminal amino acid. Each monomer contains two --SH groups, one exposed and one more buried. Circular dichroic spectra suggest a high content of alpha-helical structure, 45--55%. Excitation at 280 nm gave a strong emission fluorescence spectrum with a maximum centering at 340 nm. Sedimentation studies suggested the enzymically active form to be a tetramer. High ionic strength (0.1 M KC1), spermine, and the substrates ATP and thymidine 3'-monophosphate were found to be essential factors in order to stabilize the protein in an oligomeric structure. The association constants for ATP, thymidine 3'-monphosphate, and P1 were determined fluorimetrically to be 7.9 x 105, 4.8 x 105, and 7.2 x 10(2) M-1 respectively.     

Enzymatic analysis of oligonucleotides containing cyclobutane pyrimidine photodimers with a cleaved intradimer phosphodiester linkage.

Our recent studies indicate that enzymatic hydrolysis of the intradimer phosphodiester linkage constitutes an early reaction in processing UV light-induced cis-syn-cyclobutane pyrimidine dimers in cultured human fibroblasts. Before characterizing the resultant modified dimer sites in cellular DNA, it is necessary to establish experimental conditions that can distinguish backbone-nicked from intact dimers. We thus constructed a model substrate, i.e. p(dT) 10 <> p(dT)10 containing a dimer with a ruptured sugar-phosphate bond, and determined the products of its reaction with snake venom phosphodiesterase and alkaline phosphatase, an enzymatic digestion mixture known to release dimers from UV-treated poly(dA).poly(dT) within trinucleotides with the photoproduct intact at the 3'-end (d-TpTT). The model substrate was prepared by (i) end labeling p(dT)9 using terminal deoxynucleotidyltransferase and [3H]thymine-labeled TTP; and (ii) annealing the chromatographically purified p(dT)10 oligomers to poly(dA) followed by UV (290 nm)-induced ligation. Photoligated 20-mers with one radioactive and modified internal dimer were isolated and enzymatically digested. High performance liquid chromatographic analysis of the reaction products revealed a novel trithymidylate with its backbone severed at the 3'-terminus (d-TpT<>dT), demonstrating that this procedure could discriminate between intact and modified dimers. The procedure was then exploited to show that (i) Escherichia coli DNA photolyase can monomerize, albeit inefficiently, backbone-ruptured dimers; and (ii) phage T4 polynucleotide kinase can catalyze the phosphorylation of d-TpT<>dT, thus facilitating the development of a sensitive postlabeling assay suitable for modified dimer detection under biologically relevant conditions.