The problem of finding the configuration of points given partial information on pairwise inter-point distances, the Euclidean distance geometry problem, appears in multiple applications. In this paper, we propose an approach that integrates structural similarity and a nonconvex distance geometry algorithm for the protein structure determination problem. When initialized with a homologous structure, reconstruction of ubiquitin structure with our non convex algorithm resulted in an RMSE of less than 2 Å with ~1.5% available inter proton distance and up to 20% relative error in the input distances. To test the robustness of this algorithm with regard to initialization, we also initialized with a nonhomologous structure on a larger protein with pdb coordinate 1W2E. Even though the initialization structure 1JYB is far different from 1W2E with an RMSE of 25 Å, reconstruction generated structures with RMSE of close to 2 Å, using ~1.7% available proton distances and up to 10% relative error in input distances. These results suggest EDG-based approach may be applied to fast NMR structure determination in the future.

中文翻译：

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通过距离几何基于结构相似性的初始化确定蛋白质结构

在成对的点间距离上获得部分信息的情况下，找到点的配置问题（欧几里德距离几何问题）出现在多种应用中。在本文中，我们提出了一种将结构相似性和非凸距离几何算法相结合的方法来解决蛋白质结构确定问题。当用同源结构初始化时，用我们的非凸算法重建泛素结构导致RMSE小于2Å，质子间距离约为1.5％，输入距离的相对误差高达20％。为了测试该算法在初始化方面的鲁棒性，我们还在pdb坐标为1W2E的较大蛋白质上使用非同源结构进行了初始化。即使初始化结构1JYB与RMSE为25Å的1W2E截然不同，重构仍会使用2％的可用质子距离和高达10％的输入距离相对误差，生成RMSE接近2Å的结构。这些结果表明，基于EDG的方法将来可能会应用于快速NMR结构测定。