基于高斯曲率的蛋白质嵌入到对称低温电镜密度图的方法
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摘要
为了解决低温电镜三维重构得到的对称生物大分子三维结构分辨率低的问题,提出一种新的基于高斯曲率计算的自动化的方法.通过计算生物分子表面的高斯曲率和优化模型等数学方法把单个蛋白质或其他亚基嵌入到对称的低温电镜密度图中,通过计算蛋白质和对称低温电镜密度图的离散高斯曲率来定义特征点,对低温电镜密度图,利用K-means分类来定义相应的特征点.用均方根偏差值、曲率的交叉关联系数和优化模型来匹配对应的特征点,用最小二乘法计算旋转矩阵和平移向量.最后,用同样的方法把其他部分也嵌入到对称的生物大分子中.给出了椭球体x~2+y~2/2+z~2/3=1的解析高斯曲率和数值计算的高斯曲率的比较、蛋白质1DOR的高斯曲率计算和特征点的计算结果、蛋白质1DOR和2REC的分子装配结果可视化.数值实验结果表明所提出来的一系列的方法是准确和有效的.
To solve the problem of low resolution of three-dimensional symmetric biomacromolecule structure obtained by cryo-electron microscopy(cryo-EM) density maps, a new method based on Gaussian curvature calculation was proposed. The new feature points were defined by calculating the discrete Gaussian curvature of the protein and the symmetrical cryo-EM density maps. For the symmetrical cryo-EM density maps,the K-means method was used to define the corresponding feature points. The corresponding feature points were matched by the cross correlation score of root mean square deviation(RMSD) values and Gaussian curvature and the optimization model. The rotation matrix and the translation vector were then calculated using the least squares method. Finally,the other parts werefitted into the symmetrical cryo-EM density map in the same way. The Gaussian curvature of ellipsoid was calculated,x~2+y~2/2+z~2/3= 1,and the analyzed Gaussian curvature was compared with the numerical Gaussian curvature. The Gaussian curvature of the protein 1DOR was calculated and the feature point was also calculated. The fitting results of the macromolecules assembly of protein 1DOR and 2REC were visualized. The numerical experiments show that this method is accurate and effective.
To solve the problem of low resolution of three-dimensional symmetric biomacromolecule structure obtained by cryo-electron microscopy(cryo-EM) density maps, a new method based on Gaussian curvature calculation was proposed. The new feature points were defined by calculating the discrete Gaussian curvature of the protein and the symmetrical cryo-EM density maps. For the symmetrical cryo-EM density maps,the K-means method was used to define the corresponding feature points. The corresponding feature points were matched by the cross correlation score of root mean square deviation(RMSD) values and Gaussian curvature and the optimization model. The rotation matrix and the translation vector were then calculated using the least squares method. Finally,the other parts werefitted into the symmetrical cryo-EM density map in the same way. The Gaussian curvature of ellipsoid was calculated,x~2+y~2/2+z~2/3= 1,and the analyzed Gaussian curvature was compared with the numerical Gaussian curvature. The Gaussian curvature of the protein 1DOR was calculated and the feature point was also calculated. The fitting results of the macromolecules assembly of protein 1DOR and 2REC were visualized. The numerical experiments show that this method is accurate and effective.
引文
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[3]ESWAR N,WEBB B,MARTI-RENOM M A,et al.Comparative protein structure modeling using MODELLER[J].Curr Protoc Protein Sci,2007,50(2),912-931.
[4]ZHANG K,ZHANG Y,HU Z J,et al.Development and frontier of electron microscopy 3d reconstruction[J].Acta Biophysica Sinica,2010,26(7):533-559.
[5]GABASHVILI I S,AGRAWAL R K,SPAHN C M,et al.Solution structure of the e.coli 70 s ribosome at 11.5resolution[J].Cell,2000,100(5):537-549.
[6]FABIAN K,MAREIKE K,MARKUS G G,et al.Projection structure of the secondary citrate/sodium symporter Cit S at 6resolution by electron crystallography[J].Journal of Molecular Biology,2012,418:117-126.
[7]HENDERSONR.The potential and limitations of neutrons,electrons and x-rays for atomic resolution micro scopy of unstained biological molecules[J].Q Rev Biophys,1995,28(2):171-193.
[8]WANG D N,WERNER K.High-resolution electron crystallography of light-harvesting chlorophyll a/b-protein complex in three different media[J].Journal of Molecular Biology,1991,217(4):691-699.
[9]STEFAN B,WILLY W.Multi-resolution anchor-point registration of biomolecular assemblies and their components[J].Journal of Structural Biology,2007,157:271-280.
[10]ROSSMANN M G,MORAIS M C,LEIMAN P G,et al.Combining X-ray crystallography and electron microscopy[J].Structure,2005,13:355-362.
[11]FABIOLA F,CHAPMAN M S.Fitting of high-resolution structures into electron microscopy reconstruction images[J].Structure,2005,13:389-400.
[12]SALI A,GLAESER R,EARNEST T,et al.From words to literature in structural proteomics[J].Nature,2003,422(6928):216-225.
[13]FRANK J.Single-particle imaging of macromolecules by cryo-electron microscopy[J].Annu Rev Biophys Biomol Struct,2002,31:303-319.
[14]WRIGGERS W,BIRMANNS S.Using situs for flexible and rigid-body fitting of multiresolution singlemoleculedata[J].J Struct Biol,2001,133(2):193-202.
[15]TOPF M,SALI A.Combining electron microscopy and comparative protein structure modeling[J].Curr Opin Struct Biol,2005,15:578-585.
[16]ALBER F,DOKUDOVSKAYA S,VEENHOFF L M,et al.Determining the architectures of macromole cular assemblies[J].Nature,2007,450(7170):683-694.
[17]ROBERT M G,KENNETH H D.High-resolution electron crystallography of protein molecules[J].Ultramicroscopy,1993,52:478-486.
[18]DEMPSTER A P,LAIRD NM,RUBIN D B.Sur la division des corps materiels en parties[J].Bull Acad Polon Sci,1957,4(12):801-804.
[19]MACKAY D J C.Information theory,inference and learning algorithms[M].Cambridge:Cambridge University Press,2003:284-292.
[20]WRIGGERS W,MILLIGAN R A,MCCAMMON J A.Situs:a package for docking crystal structures intolowresolution maps from electron microscopy[J].J Struct Biol,1999,125(2):185-195.
[21]HUGO C,ROBERT B R.Fast fitting of atomic structures to low-resolution electron density maps by surface overlap maximization[J].J Mol Biol,2004,338:783-793.
[22]PINTILIE G D,ZHANG J,GODDARD T D,et al.Quantitative analysis of cryo-em density map segmentation by watershed and scale-space filtering,and fitting of structures by alignment to regions[J].Journal of Structural Biology,2010,170:427-438.
[23]KAWABATA T.Multiple subunit fitting into a lowresolution density map of a macromolecular complex using a gaussian mixture model[J].Biophysical Journal,2008,95:4643-4658.
[24]TOPF M,LASKER K,WEBB B,et al.Protein structure fitting and refinement guidedby cryo-EM density[J].Structure,2008,16:295-307.
[25]ZHANG S H,DAVEB V,MIN X,et al.A fast mathematical programming programming procedure for simultaneous fitting of assembly components into cryoem density maps[J].Bioinformatics,2010,26:261-268.
[26]JI Z,SHI J.A robust algorithm for feature point matching[J],Computers and Graphics,2002,26,429-436.
[27]LOWE D G.Distinctive image features from scaleinvariant key points[J],International Journal of Computer Vision,2004,60(2):91-110.
[28]GODDARD T D,HUANG C C,FERRIN T E.Visualizing density maps with UCSF chimera[J].J Struct Biol,2007,157:281-287.
[29]ZHANG W,KAUFMANN B,CHIPMAN P R,et al.Membrane curvature in flaviviruses[J].Journal of Structural Biology,2013,183:86-94.
[30]ZHANG W,BARBEL K,PAUL R C,et al.Membrane curvature if flaviviruses[J],Journal of Structural Biology,2013,183:86-94.
[31]LU J,XU G,ZHANG S,et al.An effective sequencealignment-free superpositioning of pairwise or multiple structures with missing data[J].Algorithms Mol Biol,2016,11(18):1-10.
[32]DOUGLAS L T,PHILLIP A S.Optimal simultaneous superpositioning of multiple structures with missing data[J].Bioinformatics,2012,28:1972-1979.
[33]EVANS D J.On the representation of orientation space[J].Mol Phys,1977,34(2):317-325.