Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis
Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis
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DOI：
10.1063/1.4882258
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发表时间：
2014-06-21
影响因子：
4.4
通讯作者：
Wei, Guo-Wei
中科院分区：
文献类型：
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作者：
Opron, Kristopher;Xia, Kelin;Wei, Guo-Wei
蛋白质结构波动，通常通过Debye-Waller因子或B因子测量，是蛋白质柔性的表现，其与蛋白质功能密切相关。柔度-刚度指数（FRI）是一种新提出的构造原子刚度函数的方法，它是描述超大型生物分子系统的一种新的多尺度形式。FRI方法分析蛋白质的刚性和柔性，并且能够预测蛋白质B因子，而无需求助于矩阵对角化。FRI中使用的一个基本假设是，蛋白质结构由各种内部和外部相互作用唯一决定，而蛋白质功能，如稳定性和灵活性，仅由结构决定。因此，人们可以预测蛋白质的灵活性，而不诉诸蛋白质相互作用的哈密顿量。因此，绕过矩阵对角化，原始FRI具有O（N-2）的计算复杂度。介绍了一种用于大分子柔性分析的快速FRI算法。所提出的fFRI进一步将计算复杂度降低到O（N）。此外，我们提出了各向异性FRI（aFRI）算法的蛋白质集体动力学分析。aFRI算法允许自适应Hessian矩阵，从完全全局的3NX3N矩阵到完全局部的3X3矩阵。这些3x3矩阵尽管是局部计算的，但也包含非局部相关信息。从所提出的aFRI算法获得的特征向量能够证明集体运动。此外，我们研究的性能FRI采用四个家庭的径向基相关函数。参数优化和无参数FRI方法进行了探索。此外，我们比较的准确性和效率的FRI与一些既定的方法，即正常模式分析和高斯网络模型（GNM）的灵活性分析。使用四组蛋白质，三组相对较小，中等和较大尺寸的结构和一组扩展的365种蛋白质来测试FRI方法的准确性。第五组蛋白质用于比较FRI、fFRI、aFRI和GNM方法的效率。密集的验证和比较表明，FRI，特别是fFRI，比该领域最流行的一些方法效率高出几个数量级，总体准确度高出约10%。建议的fFRI是能够预测B因子的a-碳的HIV病毒衣壳（313 - 236个残基）在不到30秒的时间内，在一个处理器上，仅使用一个核心。最后，我们展示了FRI和aFRI蛋白质结构域分析的应用。(C)2014 AIP Publishing LLC.
Protein structural fluctuation, typically measured by Debye-Waller factors, or B-factors, is a manifestation of protein flexibility, which strongly correlates to protein function. The flexibility-rigidity index (FRI) is a newly proposed method for the construction of atomic rigidity functions required in the theory of continuum elasticity with atomic rigidity, which is a new multiscale formalism for describing excessively large biomolecular systems. The FRI method analyzes protein rigidity and flexibility and is capable of predicting protein B-factors without resorting to matrix diagonalization. A fundamental assumption used in the FRI is that protein structures are uniquely determined by various internal and external interactions, while the protein functions, such as stability and flexibility, are solely determined by the structure. As such, one can predict protein flexibility without resorting to the protein interaction Hamiltonian. Consequently, bypassing the matrix diagonalization, the original FRI has a computational complexity of O(N-2). This work introduces a fast FRI (fFRI) algorithm for the flexibility analysis of large macromolecules. The proposed fFRI further reduces the computational complexity to O(N). Additionally, we propose anisotropic FRI (aFRI) algorithms for the analysis of protein collective dynamics. The aFRI algorithms permit adaptive Hessian matrices, from a completely global 3N x 3N matrix to completely local 3 x 3 matrices. These 3 x 3 matrices, despite being calculated locally, also contain non-local correlation information. Eigenvectors obtained from the proposed aFRI algorithms are able to demonstrate collective motions. Moreover, we investigate the performance of FRI by employing four families of radial basis correlation functions. Both parameter optimized and parameter-free FRI methods are explored. Furthermore, we compare the accuracy and efficiency of FRI with some established approaches to flexibility analysis, namely, normal mode analysis and Gaussian network model (GNM). The accuracy of the FRI method is tested using four sets of proteins, three sets of relatively small-, medium-, and large-sized structures and an extended set of 365 proteins. A fifth set of proteins is used to compare the efficiency of the FRI, fFRI, aFRI, and GNM methods. Intensive validation and comparison indicate that the FRI, particularly the fFRI, is orders of magnitude more efficient and about 10% more accurate overall than some of the most popular methods in the field. The proposed fFRI is able to predict B-factors for a-carbons of the HIV virus capsid (313 236 residues) in less than 30 seconds on a single processor using only one core. Finally, we demonstrate the application of FRI and aFRI to protein domain analysis. (C) 2014 AIP Publishing LLC.