Lesk A M
Department of Haematology, University of Cambridge Clinical School, MRC Centre, UK.
Fold Des. 1997;2(3):S12-4. doi: 10.1016/s1359-0278(97)00057-6.
The extraction of well-fitting substructures of two or more sets of proteins has applications to analysis of mechanisms of conformational change in proteins, including pathways of evolution, to classification of protein folding patterns, and to evaluation of protein structure predictions. Many methods are known for extracting some substantial common substructure with low root-mean-square deviation (r.m.s.d.). A harder problem is addressed here: finding all common substructures with r.m.s.d. less than a prespecified threshold. Our approach is to consider the minimum value of the maximum distance between corresponding points, corresponding to superposition in the Chebyshev norm. Using the properties of Chebyshev superposition, we derive relationships between the r.m.s.d. and the maximum element of the difference matrix, two common measures of structural similarity. The results provide a basis for developing algorithms and software to identify all well-fitting subsets.
提取两组或多组蛋白质的拟合良好的子结构，可应用于分析蛋白质构象变化的机制，包括进化途径、蛋白质折叠模式的分类以及蛋白质结构预测的评估。已知有许多方法可用于提取具有低均方根偏差（r.m.s.d.）的一些实质性共同子结构。本文解决了一个更具挑战性的问题：找到所有均方根偏差小于预先指定阈值的共同子结构。我们的方法是考虑对应点之间最大距离的最小值，这对应于切比雪夫范数中的叠加。利用切比雪夫叠加的性质，我们推导出均方根偏差与差异矩阵的最大元素之间的关系，这是两种常见的结构相似性度量。这些结果为开发识别所有拟合良好子集的算法和软件提供了基础。
