We present a fast, accurate, and robust approach for determination of free energy profiles and kinetic isotope effects for RNA 2′-O-transphosphorylation reactions with inclusion of nuclear quantum effects. We apply a deep potential range correction (DPRc) for combined quantum mechanical/molecular mechanical (QM/MM) simulations of reactions in the condensed phase. The method uses the second-order density-functional tight-binding method (DFTB2) as a fast, approximate base QM model. The DPRc model modifies the DFTB2 QM interactions and applies short-range corrections to the QM/MM interactions to reproduce ab initio DFT (PBE0/6-31G*) QM/MM energies and forces. The DPRc thus enables both QM and QM/MM interactions to be tuned to high accuracy, and the QM/MM corrections are designed to smoothly vanish at a specified cutoff boundary (6 Å in the present work). The computational speed-up afforded by the QM/MM+DPRc model enables free energy profiles to be calculated that include rigorous long-range QM/MM interactions under periodic boundary conditions and nuclear quantum effects through a path integral approach using a new interface between the AMBER and i-PI software. The approach is demonstrated through the calculation of free energy profiles of a native RNA cleavage model reaction and reactions involving thio-substitutions, which are important experimental probes of the mechanism. The DFTB2+DPRc QM/MM free energy surfaces agree very closely with the PBE0/6-31G* QM/MM results, and it is vastly superior to the DFTB2 QM/MM surfaces with and without weighted thermodynamic perturbation corrections. ¹⁸O and ³⁴S primary kinetic isotope effects are compared, and the influence of nuclear quantum effects on the free energy profiles is examined.

中文翻译：

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结合 QM/MM、机器学习路径积分方法来计算 RNA 裂解反应中的自由能分布和动力学同位素效应

我们提出了一种快速、准确且稳健的方法，用于确定包含核量子效应的 RNA 2'-O-转磷酸化反应的自由能谱和动力学同位素效应。我们应用深电位范围校正（DPRc）来对凝聚相反应进行量子力学/分子力学（QM/MM）组合模拟。该方法使用二阶密度泛函紧束缚方法 (DFTB2) 作为快速、近似的基础 QM 模型。DPRc 模型修改了 DFTB2 QM 相互作用，并对 QM/MM 相互作用应用短程校正，以从头开始重现DFT (PBE0/6-31G*) QM/MM 能量和力。因此，DPRc 能够将 QM 和 QM/MM 相互作用调整到高精度，并且 QM/MM 校正被设计为在指定的截止边界（当前工作中为 6 Å）处平滑消失。QM/MM+DPRc 模型提供的计算加速能够计算自由能分布，其中包括周期性边界条件下严格的长程 QM/MM 相互作用和核量子效应，通过路径积分方法使用AMBER 和 i-PI 软件。该方法通过计算天然 RNA 裂解模型反应和涉及硫代取代的反应的自由能曲线来证明，这是该机制的重要实验探针。比较¹⁸ O 和^{34 S 初级动力学同位素效应，并检查核量子效应对自由能分布的影响。}