How does averaging affect protein structure comparison on the ensemble level?
How does averaging affect protein structure comparison on the ensemble level?
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DOI：
10.1529/biophysj.104.042184
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发表时间：
2004-10-01
影响因子：
3.4
通讯作者：
Pande, VS
中科院分区：
文献类型：
--
作者：
Zagrovic, B;Pande, VS
最近的算法进步和计算能力的不断增加使在系综水平上模拟蛋白质折叠和动力学成为可能。此外，通过使用系综表示来分析蛋白质结构是某些实验技术所固有的，例如核磁共振。这就产生了一个问题，即如何将一组分子与给定的参考结构进行比较。最近，我们使用基于距离的均方根偏差(DRMS)来比较蛋白质的天然结构及其未折叠状态的集合。我们发现，对于小的，主要是α-螺旋蛋白质，平均未折叠状态的Calpha-Calpha距离矩阵比对应于未折叠整体的单个成员的Calpha-Calpha距离矩阵更接近本地。这里，我们给出了一个数学推导，它表明，对于任何结构集合，集合平均距离矩阵与任何给定参考距离矩阵之间的DRMS偏差总是小于或等于该集合的单个成员相对于相同参考矩阵的平均DRMS偏差。无论参考结构或结构集合的性质如何，这一点都是成立的。换言之，距离矩阵的平均只会增加它们相对于组成集合的各个矩阵与给定参考矩阵的相似度。此外，我们还证明了在基于笛卡尔坐标的均方根偏差的情况下，上述不等式也是成立的。我们在我们的建议的背景下讨论了这一点，即小螺旋蛋白的展开系综的平均结构接近于天然结构，并证明了这一发现超出了上述数学事实。
Recent algorithmic advances and continual increase in computational power have made it possible to simulate protein folding and dynamics on the level of ensembles. Furthermore, analyzing protein structure by using ensemble representation is intrinsic to certain experimental techniques, such as nuclear magnetic resonance. This creates a problem of how to compare an ensemble of molecules with a given reference structure. Recently, we used distance-based root-mean-square deviation (dRMS) to compare the native structure of a protein with its unfolded-state ensemble. We showed that for small, mostly alpha-helical proteins, the mean unfolded-state Calpha-Calpha distance matrix is significantly more nativelike than the Calpha-Calpha matrices corresponding to the individual members of the unfolded ensemble. Here, we give a mathematical derivation that shows that, for any ensemble of structures, the dRMS deviation between the ensemble-averaged distance matrix and any given reference distance matrix is always less than or equal to the average dRMS deviation of the individual members of the ensemble from the same reference matrix. This holds regardless of the nature of the reference structure or the structural ensemble in question. In other words, averaging of distance matrices can only increase their level of similarity to a given reference matrix, relative to the individual matrices comprising the ensemble. Furthermore, we show that the above inequality holds in the case of Cartesian coordinate-based root-mean-square deviation as well. We discuss this in the context of our proposal that the average structure of the unfolded ensemble of small helical proteins is close to the native structure, and demonstrate that this finding goes beyond the above mathematical fact.