Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing polarizable force fields for handling more complicated biomolecular processes. Here, we focus on a recently proposed polarizable Gaussian Multipole (pGM) model for biomolecular simulations. A key benefit of pGM is its screening of all short-range electrostatic interactions in a physically consistent manner, which is critical for stable charge-fitting and is needed to reproduce molecular anisotropy. Another advantage of pGM is that each atom’s multipoles are represented by a single Gaussian function or its derivatives, allowing for more efficient electrostatics than other Gaussian-based models. In this study, we present an efficient formulation for the pGM model defined with respect to a local frame formed with a set of covalent basis vectors. The covalent basis vectors are chosen to be along each atom’s covalent bonding directions. The new local frame can better accommodate the fact that permanent dipoles are primarily aligned along covalent bonds due to the differences in electronegativity of bonded atoms. It also allows molecular flexibility during molecular simulations and facilitates an efficient formulation of analytical electrostatic forces without explicit torque computation. Subsequent numerical tests show that analytical atomic forces agree excellently with numerical finite-difference forces for the tested system. Finally, the new pGM electrostatics algorithm is interfaced with the particle mesh Ewald (PME) implementation in Amber for molecular simulations under the periodic boundary conditions. To validate the overall pGM/PME electrostatics, we conducted an NVE simulation for a small water box of 512 water molecules. Our results show that to achieve energy conservation in the polarizable model, it is important to ensure enough accuracy on both PME and induction iteration. It is hoped that the reformulated pGM model will facilitate the development of future force fields based on the pGM electrostatics for applications in biomolecular systems and processes where polarization plays crucial roles.

中文翻译：

---

用于生物分子模拟的可极化高斯多极静电的有效公式。

生物分子的分子动力学模拟已被广泛应用于生物医学研究。随着经典点电荷模型继续用于常规生物分子应用，对开发可极化力场以处理更复杂的生物分子过程的需求不断增长。在这里，我们专注于最近提出的用于生物分子模拟的极化高斯多极 (pGM) 模型。pGM 的一个主要优点是以物理一致的方式筛选所有短程静电相互作用，这对于稳定电荷拟合至关重要，并且是重现分子各向异性所必需的。pGM 的另一个优点是每个原子的多极点由单个高斯函数或其导数表示，与其他基于高斯的模型相比，允许更有效的静电学。在这项研究中，我们为 pGM 模型提出了一个有效的公式，该模型是针对由一组共价基向量形成的局部框架定义的。共价基向量被选择为沿着每个原子的共价键合方向。由于键合原子的电负性不同，新的局部框架可以更好地适应永久偶极子主要沿共价键排列的事实。它还允许分子模拟过程中的分子灵活性，并有助于在没有明确扭矩计算的情况下有效地制定分析静电力。随后的数值测试表明，分析原子力与测试系统的数值有限差分力非常吻合。最后，新的 pGM 静电算法与 Amber 中的粒子网格 Ewald (PME) 实现接口，用于在周期性边界条件下进行分子模拟。为了验证整体 pGM/PME 静电，我们对一个包含 512 个水分子的小水箱进行了 NVE 模拟。我们的结果表明，为了在可极化模型中实现能量守恒，确保 PME 和感应迭代具有足够的精度非常重要。希望重新制定的 pGM 模型将促进基于 pGM 静电的未来力场的发展，用于在极化起着至关重要作用的生物分子系统和过程中的应用。我们对一个包含 512 个水分子的小水箱进行了 NVE 模拟。我们的结果表明，为了在可极化模型中实现能量守恒，确保 PME 和感应迭代具有足够的精度非常重要。希望重新制定的 pGM 模型将促进基于 pGM 静电的未来力场的发展，用于在极化起着至关重要作用的生物分子系统和过程中的应用。我们对一个包含 512 个水分子的小水箱进行了 NVE 模拟。我们的结果表明，为了在可极化模型中实现能量守恒，确保 PME 和感应迭代具有足够的精度非常重要。希望重新制定的 pGM 模型将促进基于 pGM 静电的未来力场的发展，用于在极化起着至关重要作用的生物分子系统和过程中的应用。