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.

本研究基于DNA寡聚核苷酸链（DNA oligos）超过0.9微秒的全原子分子动力学（all-atom molecular dynamics）模拟结果，识别出DNA弯曲的局部主轴，以此探究DNA的弹性特性。所计算得到的序参数将DNA的运动行为描述为弹性杆模型。在10种可能的二核苷酸步骤（dinucleotide steps）中，绕两条主轴的弯曲呈现各向异性，但仍符合线弹性特性。绕质心轴的扭转运动与弯曲行为在很大程度上解耦，但当DNA的伸直变形超出典型热运动范围时，其倾向于发生过度扭转，这与实验观测到的扭转-拉伸耦合（twist–stretch coupling）现象一致。通过二核苷酸步骤的弹性刚度（elastic stiffness）计算得到的序列依赖型持久长度（persistence lengths），与此前单分子实验（single-molecule experiments）结果相符，本研究进一步通过DNA粗粒度（coarse-grained）模拟对该结果展开验证分析。基于模拟构建的寡聚核苷酸链柔性图谱，也与通过二核苷酸步骤预计算刚度得到的柔性图谱一致。上述结果佐证了这一前提：二核苷酸层面的碱基配对相互作用，是决定DNA弹性特性的主要因素。此外，本研究还分析了1381个蛋白质-DNA复合物（protein–DNA complexes）的晶体结构。在绝大多数结构中，DNA仅发生轻微变形，扭转运动占据总弹性能量的最高比例。与之相对，当每个二核苷酸步骤的弹性能量超过约4.16 kBT（热能量，thermal energy）时，主导性的弯曲变形成为主要的能量贡献形式。除了包含高度变形DNA、线弹性失效的结构之外，二核苷酸步骤的拉伸能量最多仅占总弹性能量的35%。不同变形模式间的这种能量分配特征，为DNA的构象动力学特性，以及其与其他分子、表面的相互作用机制提供了定量的认知视角。