Elastic Energy Partitioning in DNA Deformation and Binding to Proteins

We study the elasticity of DNA based on local principal axes of bending identified from over 0.9-μs all-atom molecular dynamics simulations of DNA oligos. The calculated order parameters describe motion of DNA as an elastic rod. In 10 possible dinucleotide steps, bending about the two principal axes is anisotropic yet linearly elastic. Twist about the centroid axis is largely decoupled from bending, but DNA tends to overtwist for unbending beyond the typical range of thermal motion, which is consistent with experimentally observed twist-stretch coupling. The calculated elastic stiffness of dinucleotide steps yield sequence-dependent persistence lengths consistent with previous single-molecule experiments, which is further analyzed by performing coarse-grained simulations of DNA. Flexibility maps of oligos constructed from simulation also match with those from the precalculated stiffness of dinucleotide steps. These support the premise that base pair interaction at the dinucleotide-level is mainly responsible for the elasticity of DNA. Furthermore, we analyze 1381 crystal structures of protein-DNA complexes. In most structures, DNAs are mildly deformed and twist takes the highest portion of the total elastic energy. By contrast, in structures with the elastic energy per dinucleotide step greater than about 4.16 kBT (kBT: thermal energy), the major bending becomes dominant. The extensional energy of dinucleotide steps takes at most 35% of the total elastic energy except for structures containing highly deformed DNAs where linear elasticity breaks down. Such partitioning between different deformational modes provides quantitative insights into the conformational dynamics of DNA as well as its interaction with other molecules and surfaces.