Water-mediated proton transfer reactions are central for catalytic processes in a wide range of biochemical systems, ranging from biological energy conversion to chemical transformations in the metabolism. Yet, the accurate computational treatment of such complex biochemical reactions is highly challenging and requires the application of multiscale methods, in particular hybrid quantum/classical (QM/MM) approaches combined with free energy simulations. Here, we combine the unique exploration power of new advanced sampling methods with density functional theory (DFT)-based QM/MM free energy methods for multiscale simulations of long-range protonation dynamics in biological systems. In this regard, we show that combining multiple walkers/well-tempered metadynamics with an extended system adaptive biasing force method (MWE) provides a powerful approach for exploration of water-mediated proton transfer reactions in complex biochemical systems. We compare and combine the MWE method also with QM/MM umbrella sampling and explore the sampling of the free energy landscape with both geometric (linear combination of proton transfer distances) and physical (center of excess charge) reaction coordinates and show how these affect the convergence of the potential of mean force (PMF) and the activation free energy. We find that the QM/MM-MWE method can efficiently explore both direct and water-mediated proton transfer pathways together with forward and reverse hole transfer mechanisms in the highly complex proton channel of respiratory Complex I, while the QM/MM-US approach shows a systematic convergence of selected long-range proton transfer pathways. In this regard, we show that the PMF along multiple proton transfer pathways is recovered by combining the strengths of both approaches in a QM/MM-MWE/focused US (FUS) scheme and reveals new mechanistic insight into the proton transfer principles of Complex I. Our findings provide a promising basis for the quantitative multiscale simulations of long-range proton transfer reactions in biological systems.

中文翻译：

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通过自适应和聚焦采样进行远程生物质子化动力学的 QM/MM 自由能计算

水介导的质子转移反应是各种生化系统中催化过程的核心，从生物能量转换到代谢中的化学转化。然而，对此类复杂生化反应的精确计算处理极具挑战性，需要应用多尺度方法，特别是与自由能模拟相结合的混合量子/经典（QM/MM）方法。在这里，我们将新型先进采样方法的独特探索能力与基于密度泛函理论 (DFT) 的 QM/MM 自由能方法相结合，用于生物系统中远程质子化动力学的多尺度模拟。在这方面，我们表明，将多个步行者/调和的元动力学与扩展系统自适应偏置力方法（MWE）相结合，为探索复杂生化系统中水介导的质子转移反应提供了一种强大的方法。我们将 MWE 方法与 QM/MM 伞式采样进行比较和结合，探索具有几何（质子转移距离的线性组合）和物理（过剩电荷中心）反应坐标的自由能景观采样，并展示它们如何影响平均力势 (PMF) 和活化自由能的收敛。我们发现 QM/MM-MWE 方法可以有效地探索直接和水介导的质子转移途径以及呼吸复合物 I 高度复杂的质子通道中的正向和反向空穴转移机制，而 QM/MM-US 方法显示选定的远程质子转移路径的系统收敛。在这方面，我们表明，通过在 QM/MM-MWE/聚焦 US (FUS) 方案中结合两种方法的优点，可以恢复沿着多个质子转移路径的 PMF，并揭示了对复合物 I 的质子转移原理的新机制见解我们的研究结果为生物系统中长程质子转移反应的定量多尺度模拟提供了有希望的基础。