Spatial configuration of single‐stranded polynucleotides. Calculations of average dimensions and nmr coupling constants

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Abstract
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.