DNA tri- and tetra-loops and RNA tetra-loops hairpins fold as elastic biopolymer chains in agreement with PDB coordinates

The biopolymer chain elasticity (BCE) approach and the new molecular modelling methodology presented previously are used to predict the tri- dimensional backbones of DNA and RNA hairpin loops. The structures of eight remarkably stable DNA or RNA hairpin molecules closed by a mispair, recently determined in solution by NMR and deposited in the PDB, are shown to verify the predicted trajectories by an analysis automated for large numbers of PDB conformations. They encompass: one DNA tetraloop, -GTTA-; three DNA triloops, -AAA- or -GCA-; and four RNA tetraloops, -UUCG-. Folding generates no distortions and bond lengths and bond angles of main atoms of the sugar-phosphate backbone are well restored upon energy refinement. Three different methods (superpositions, distance of main chain atoms to the elastic line and RMSd) are used to show a very good agreement between the trajectories of sugar-phosphate backbones and between entire molecules of theoretical models and of PDB conformations. The geometry of end conditions imposed by the stem is sufficient to dictate the different characteristic DNA or RNA folding shapes. The reduced angular space, consisting of the new parameter, angle Omega, together with the chi angle offers a simple, coherent and quantitative description of hairpin loops.