structures for: Towards biochemically relevant QM computations on nucleic acids. Controlled electronic structure geometry optimizations of nucleic acids structural motifs using penalty restraint functions.

Recent developments of dispersion-corrected density functional theory methods allow for the first time to describe large fragments of nucleic acids (hundreds of atoms) with an accuracy clearly surpassing the accuracy of common biomolecular force fields. Such calculations can significantly improve the description of the potential energy surface of nucleic acids molecules, which may be useful for studies of molecular interactions and conformational preferences of nucleic acids, as well as verification and parameterization of other methods. The first of such studies, however, demonstrated that successful applications of accurate QM calculations to larger nucleic acids building blocks are hampered by difficulties to obtain geometries that are biochemically relevant and are not biased by non-native structural features. We present an approach that can greatly facilitate large-scale QM studies on nucleic acids, namely, electronic structure geometry optimizations of nucleic acid fragments utilizing a penalty function to restrain key internal coordinates with a specific focus on the torsional backbone angles. The work explores the viability of these restraint optimizations for DFT-D3, PM6-D3H and HF-3c optimizations on a set of examples (an UpA dinucleotide, a DNA G-quadruplex and a B-DNA fragment). Evaluation of different penalty function strengths reveals only a minor system-dependency and reasonable restraint values range from 0.01 to 0.05 Eh/rad2 for the backbone torsions. Restraints are crucial to perform the QM calculations on biochemically relevant conformations in implicit solvation and gas phase geometry optimizations. The reasons why to use restrained instead of constrained or unconstrained optimizations are explained and an open-source external optimizer is provided.

色散校正密度泛函理论（dispersion-corrected density functional theory）方法的最新进展，首次实现了对含数百个原子的大型核酸（nucleic acids）片段的精准描述，其精度显著优于常用生物分子力场（biomolecular force fields）。此类计算可大幅优化核酸分子势能面（potential energy surface）的描述精度，有望在核酸分子相互作用、构象偏好研究，以及其他方法的验证与参数化工作中发挥重要价值。然而，首批此类研究表明，将高精度量子力学（QM）计算应用于更大尺寸的核酸结构单元时，其应用受到阻碍——难以获得兼具生物化学相关性且未受非天然结构特征干扰的几何构型。本文提出一种可极大简化核酸大规模量子力学研究的方案：利用罚函数（penalty function）约束关键内坐标（internal coordinates），重点针对主链扭转角（torsional backbone angles）开展核酸片段的电子结构几何优化（electronic structure geometry optimizations）。本工作以若干示例体系（UpA二核苷酸（dinucleotide）、DNA G-四链体（G-quadruplex）以及B型DNA（B-DNA）片段）为研究对象，探究了该约束优化方法在DFT-D3、PM6-D3H与HF-3c几何优化中的可行性。对不同罚函数强度的评估结果显示，该方法仅存在微弱的体系依赖性，主链扭转角的合理约束参数取值范围为0.01至0.05 Eh/rad²。在隐式溶剂化（implicit solvation）与气相（gas phase）几何优化中，约束操作对获取具有生物化学相关性的构象并开展量子力学计算至关重要。本文阐释了相较于约束优化或无约束优化，采用罚函数约束优化的优势，并提供了一款开源外部优化器（open-source external optimizer）。