We present a variational approach to smooth molecular (proteins, nucleic acids) surface constructions, starting from atomic coordinates, as available from the protein and nucleic-acid data banks. Molecular dynamics (MD) simulations traditionally used in understanding protein and nucleic-acid folding processes, are based on molecular force fields, and require smooth models of these molecular surfaces. To accelerate MD simulations, a popular methodology is to employ coarse grained molecular models, which represent clusters of atoms with similar physical properties by psuedo- atoms, resulting in coarser resolution molecular surfaces. We consider generation of these mixed-resolution or adaptive molecular surfaces. Our approach starts from deriving a general form second order geometric partial differential equation in the level-set formulation, by minimizing a first order energy functional which additionally includes a regularization term to minimize the occurrence of chemically infeasible molecular surface pockets or tunnel-like artifacts. To achieve even higher computational efficiency, a fast cubic B-spline C(2) interpolation algorithm is also utilized. A narrow band, tri-cubic B-spline level-set method is then used to provide C(2) smooth and resolution adaptive molecular surfaces.

中文翻译：

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构建分辨率自适应光滑分子表面的快速变分法


我们提出了一种平滑分子（蛋白质、核酸）表面结构的变分方法，从原子坐标开始，可从蛋白质和核酸数据库中获得。分子动力学（MD）模拟传统上用于理解蛋白质和核酸折叠过程，基于分子力场，并且需要这些分子表面的平滑模型。为了加速 MD 模拟，一种流行的方法是采用粗粒度分子模型，该模型用伪原子表示具有相似物理性质的原子簇，从而产生分辨率较粗的分子表面。我们考虑生成这些混合分辨率或自适应分子表面。我们的方法从在水平集公式中推导一般形式的二阶几何偏微分方程开始，通过最小化一阶能量泛函，该能量泛函还包括正则化项，以最小化化学上不可行的分子表面袋或隧道状伪影的出现。为了实现更高的计算效率，还利用了快速三次B样条C(2)插值算法。然后使用窄带三三次 B 样条水平集方法来提供 C(2) 平滑且分辨率自适应的分子表面。