The discovery of the three-dimensional shape of protein molecules using interatomic distance information from nuclear magnetic resonance (NMR) can be modeled as a discretizable molecular distance geometry problem (DMDGP). Due to its combinatorial characteristics, the problem is conventionally solved in the literature as a depth-first search in a binary tree. In this work, we introduce a new search strategy, which we call frequency-based search (FBS), that for the first time utilizes geometric information contained in the protein data bank (PDB). We encode the geometric configurations of 14,382 molecules derived from NMR experiments present in the PDB into binary strings. The obtained results show that the sample space of the binary strings extracted from the PDB does not follow a uniform distribution. Furthermore, we compare the runtime of the symmetry-based build-Up (SBBU) algorithm (the most efficient method in the literature to solve the DMDGP) combined with FBS and the depth-first search (DFS) in finding a solution, ascertaining that FBS performs better in about 70% of the cases.

中文翻译：

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分子距离几何问题搜索空间中的概率方法。


利用核磁共振 （NMR） 的原子间距离信息发现蛋白质分子的三维形状，可以建模为可离散分子距离几何问题 （DMDGP）。由于其组合特性，该问题在文献中通常作为二叉树中的深度优先搜索来解决。在这项工作中，我们引入了一种新的搜索策略，我们称之为基于频率的搜索 （FBS），它首次利用了蛋白质数据库 （PDB） 中包含的几何信息。我们将 PDB 中存在的 14,382 个分子的几何构型编码为二进制字符串。所得结果表明，从 PDB 中提取的二进制字符串的样本空间不遵循均匀分布。此外，我们将基于对称性的构建 （SBBU） 算法（文献中解决 DMDGP 的最有效方法）与 FBS 和深度优先搜索 （DFS） 相结合来寻找解决方案的运行时间进行了比较，确定 FBS 在大约 70% 的情况下表现更好。