Residual Conformational Entropies on the Sugar–Phosphate Backbone of Nucleic Acids: An Analysis of the Nucleosome Core DNA and the Ribosome

A nucleic acid folds according to its free energy, but persistent residual conformational fluctuations remain along its sugar-phosphate backbone even after secondary and tertiary structures have been assembled, and these residual conformational entropies provide a rigorous lower bound for the folding free energy. We extend a recently reported algorithm to calculate the residual backbone entropy along a RNA or DNA given configuration of its bases and apply it to the crystallographic structures of the 23S ribosomal subunit and DNAs in the nucleosome core particle. In the 23S rRNAs, higher entropic strains are concentrated in helices and certain tertiary interaction platforms while residues with high surface accessibility and those not involved in base pairing generally have lower strains. Upon folding, residual backbone entropy in the 23S subunit accounts for an average free energy penalty of +0.47 (kcal/mol)/nt (nt = nucleotide) at 310 K. In nucleosomal DNAs, backbone entropies show periodic oscillations with sequence position correlating with the superhelical twist and shifts in the base-pair-step geometries, and nucleosome positioning on the bound DNA exerts strong influence over where entropic strains are located. In contrast to rRNAs, residual backbone entropies account for a free energy penalty of only +0.09 (kcal/mol)/nt in duplex relative to single-stranded DNAs.