Multiple subunit fitting into a low-resolution density map of a macromolecular complex using a gaussian mixture model.
Multiple subunit fitting into a low-resolution density map of a macromolecular complex using a gaussian mixture model.
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DOI：
10.1529/biophysj.108.137125
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发表时间：
2008-11-15
影响因子：
3.4
通讯作者：
Kawabata T
中科院分区：
文献类型：
--
作者：
Kawabata T
最近，单颗粒的电子显微镜测量使我们能够重建大生物分子复合体的低分辨率3D密度图。如果复杂亚基的结构可以通过原子分辨率的x射线结晶学来解决，那么将这些模型拟合到3D密度图中就可以生成整个大型络合物的原子分辨率模型。然而，多个子单元的拟合通常需要很大的计算成本；因此，需要开发一种高效的算法。我们开发了一个快速拟合程序“gmfit”，它使用高斯混合模型(GMM)来表示3D密度图和原子模型的近似形状。GMM是由几个3D高斯密度函数相加而成的分布函数。由于我们的模型解析地提供了两个分布函数的乘积的积分，因此它使我们能够快速计算密度图和原子模型的适合度。利用该积分，引入了两种势能函数：三维密度图与每个子单元之间的吸引势能和子单元之间的排斥势能。对称性的约束能也被用来构建对称的原基络合物。为了找出子单元的最优构型，我们随机生成子单元模型的初始构型，并利用三个势能的力和力矩执行最陡下降法。原始密度图与其GMM图的比较表明，给定精度所需的高斯分布函数的数目取决于分辨率和分子大小。然后，我们使用不同的搜索参数，对同源二聚体、三聚体和六聚体原子模型的模拟低分辨率密度图进行了测试拟合计算。结果表明，如果对每个亚基采用足够数量(8个或更多)的高斯分布函数，并且对具有3个以上亚基的络合物赋予对称约束，即使对于30？分辨率的地图，我们的方法也能够重建一个络合物的原子模型。作为一项更现实的测试，我们试图通过将21个亚基原子模型拟合到使用C7对称约束的低温电子显微镜获得的3D密度图中，来建立GroEL/ES络合物的原子模型。得到了一个均方根偏差较小(14.7？)的模型作为最低能量模型，表明我们的拟合方法是相当准确的。纳入生物和生化实验的其他限制条件可以进一步提高准确性。
Recently, electron microscopy measurement of single particles has enabled us to reconstruct a low-resolution 3D density map of large biomolecular complexes. If structures of the complex subunits can be solved by x-ray crystallography at atomic resolution, fitting these models into the 3D density map can generate an atomic resolution model of the entire large complex. The fitting of multiple subunits, however, generally requires large computational costs; therefore, development of an efficient algorithm is required. We developed a fast fitting program, “gmfit”, which employs a Gaussian mixture model (GMM) to represent approximated shapes of the 3D density map and the atomic models. A GMM is a distribution function composed by adding together several 3D Gaussian density functions. Because our model analytically provides an integral of a product of two distribution functions, it enables us to quickly calculate the fitness of the density map and the atomic models. Using the integral, two types of potential energy function are introduced: the attraction potential energy between a 3D density map and each subunit, and the repulsion potential energy between subunits. The restraint energy for symmetry is also employed to build symmetrical origomeric complexes. To find the optimal configuration of subunits, we randomly generated initial configurations of subunit models, and performed a steepest-descent method using forces and torques of the three potential energies. Comparison between an original density map and its GMM showed that the required number of Gaussian distribution functions for a given accuracy depended on both resolution and molecular size. We then performed test fitting calculations for simulated low-resolution density maps of atomic models of homodimer, trimer, and hexamer, using different search parameters. The results indicated that our method was able to rebuild atomic models of a complex even for maps of 30 Å resolution if sufficient numbers (eight or more) of Gaussian distribution functions were employed for each subunit, and the symmetric restraints were assigned for complexes with more than three subunits. As a more realistic test, we tried to build an atomic model of the GroEL/ES complex by fitting 21-subunit atomic models into the 3D density map obtained by cryoelectron microscopy using the C7 symmetric restraints. A model with low root mean-square deviations (14.7 Å) was obtained as the lowest-energy model, showing that our fitting method was reasonably accurate. Inclusion of other restraints from biological and biochemical experiments could further enhance the accuracy.
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影响因子：
3
作者：
Henrick, K;Newman, R;Chagoyen, M
通讯作者：
Chagoyen, M
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