Implicit solvent models, such as Poisson–Boltzmann models, play important roles in computational studies of biomolecules. A vital step in almost all implicit solvent models is to determine the solvent–solute interface, and the solvent excluded surface (SES) is the most widely used interface definition in these models. However, classical algorithms used for computing SES are geometry-based, so that they are neither suitable for parallel implementations nor convenient for obtaining surface derivatives. To address the limitations, we explored a machine learning strategy to obtain a level set formulation for the SES. The training process was conducted in three steps, eventually leading to a model with over 95% agreement with the classical SES. Visualization of tested molecular surfaces shows that the machine-learned SES overlaps with the classical SES in almost all situations. Further analyses show that the machine-learned SES is incredibly stable in terms of rotational variation of tested molecules. Our timing analysis shows that the machine-learned SES is roughly 2.5 times as efficient as the classical SES routine implemented in Amber/PBSA on a tested central processing unit (CPU) platform. We expect further performance gain on massively parallel platforms such as graphics processing units (GPUs) given the ease in converting the machine-learned SES to a parallel procedure. We also implemented the machine-learned SES into the Amber/PBSA program to study its performance on reaction field energy calculation. The analysis shows that the two sets of reaction field energies are highly consistent with a 1% deviation on average. Given its level set formulation, we expect the machine-learned SES to be applied in molecular simulations that require either surface derivatives or high efficiency on parallel computing platforms.

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机器学习分子表面及其在隐式溶剂模拟中的应用

隐式溶剂模型，例如 Poisson-Boltzmann 模型，在生物分子的计算研究中发挥着重要作用。几乎所有隐式溶剂模型中的一个重要步骤是确定溶剂-溶质界面，而溶剂排除表面 (SES) 是这些模型中使用最广泛的界面定义。然而，用于计算 SES 的经典算法是基于几何的，因此它们既不适合并行实现，也不便于获得表面导数。为了解决这些限制，我们探索了一种机器学习策略来获得 SES 的水平集公式。训练过程分三个步骤进行，最终导致模型与经典 SES 的一致性超过 95%。测试分子表面的可视化表明，机器学习的 SES 在几乎所有情况下都与经典 SES 重叠。进一步的分析表明，机器学习的 SES 在测试分子的旋转变化方面非常稳定。我们的时序分析表明，在经过测试的中央处理器 (CPU) 平台上，机器学习 SES 的效率大约是在 Amber/PBSA 中实现的经典 SES 例程的 2.5 倍。鉴于将机器学习的 SES 转换为并行程序很容易，我们预计在诸如图形处理单元 (GPU) 等大规模并行平台上会进一步提高性能。我们还在 Amber/PBSA 程序中实施了机器学习的 SES，以研究其在反应场能量计算方面的性能。分析表明，两组反应场能高度一致，平均有1%的偏差。鉴于其水平集公式，我们预计机器学习的 SES 将应用于需要表面导数或并行计算平台上的高效率的分子模拟。