1Geometric Processing ofReconstructed 3D Maps of MolecularComplexesChandrajit BajajThe University of Texas at AustinZeyun YuThe University of Texas at Austin1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11.2 Map Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2Contrast Enhancement•Noise Reduction•GradientVector Diffusion1.3 Structural Feature Identification . . . . . . . . . . . . . . . . . . . . 1-7Symmetry Detection•Boundary Segmentation•Secondary Structure Identification1.4 Structure Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-131.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-151.1 IntroductionToday, hybrid experimental approaches for capturing molecular structures (henceforth, com-plexes), utilizing cryo-electron microscopy (cryo-EM), electron tomography (ET), X-raycrystallography (X-ray) or nuclear magnetic resonance spectroscopy (NMR), need to beably complemented with faster and more accurate computational and geometric processingfor ultrastructure elucidation at the best level of resolution that is possible [Fra96].Electron Microscopy (EM) and in particular single particle reconstruction using cryo-EM, has rapidly advanced over recent years, such that several complexes can be resolvedroutinely at low resolution (10-20˚A) and in some cases at sub-nanometer (intermediate)resolution (7-10˚A) [BOF99]. These complexes provide not only insights into protein andnucleic acid folds, but perhaps even more importantly provide information about how thevarious structural components interact. There are increasing numbers of molecules wherethe tertiary or secondary structure of a complex can be fully determined using EM [ZBJ+01].Often the crystal structures of individual domains or components of these complexes arealso known. An emerging trend in these fields is to fit the atomic resolution X-ray crystalstructures into the cryo-EM map, to provide a quasi-atomic resolution model of the overallcomplex, possibly revealing details about molecular interactions within the assembly. Inaddition, with the increasing capability of determining multiple functional conformers of acomplex, there is the promise of studying the dynamics of such interacting systems. Thelarge physical size and complexity of such complexes combined with intermediate to lowresolution models, presents challenges for structure to biological function determination.0-8493-8597-0/01/$0.00+$1.50c° 2001 by CRC Press, LLC 1-11-2This chapter reviews some of the crucial three dimensional geometric post-processing oncea volumetric cryo-EM map (henceforth a 3D map) has been reconstructed, as essential stepstowards an enhanced and automated computational ultrastructure determination pipeline.In particular the paper addresses 3D Map contrast enhancement, filtering, automated struc-tural feature and subunit identification, and segmentation, as well as the development ofquasi-atomic models from the reconstructed 3D Map via structure fitting.1.2 Map Preprocessing1.2.1 Contrast EnhancementMany reconstructed 3D Maps, as well as captured 2D EM images, possess low contrast,or narrow intensity ranges i.e small differences between structural features and backgrounddensities, thereby making structure elucidation all the more difficult. Image contrast en-hancement is a process used to ”stretch” the intensity ranges, thereby improving the 2Dimage or 3D Map quality for better geometric postprocessing such as feature recognition,boundary segmentation, and visualization. The most commonly used methods in the pastutilized global contrast manipulation based on histogram equalization [GW92, Pra91]. Itis however well recognized today that using primarily global information is insufficient forproper contrast enhancement, as it often causes intensity saturation. Solutions to thisproblem include localized (or adaptive) histogram equalization [CLMS98, Sta00], whichconsiders a local window for each individual image pixel and computes the new intensityvalue based on the local histogram defined within the local window. A more recently devel-oped technique called the retinex model [JRW97b], in which the contribution of each pixelwithin its local window is weighted by computing the local average based on a Gaussianfunction. A later version, called the multiscale retinex model [JRW97a], gives better re-sults but is computationally more intensive. Another technique for contrast enhancement isbased on wavelet decomposition and reconstruction and has been largely used for medicalimage enhancement especially digital mammograms [LHW94, LSFH94].A fast and local method for 2D image or 3D Map contrast enhancement that we haveobtained very good success with, is presented in [YB04a]. This is a localized version ofclassical contrast manipulations [GW92, Pra91]. The basic idea of this localized methodis to design an adaptive one dimensional transfer function (mapping intensity ranges tointensity ranges) for each individual pixel (2D) or voxel (3D), based on the intensities ina suitable local neighborhood. There are three major steps, which we briefly describe for2D images as its generalization to 3D Maps is straightforward. First, one computes localstatistics (local average, minimum, and maximum) for each pixel using a fast propagationscheme [Der90, YV95]. The propagation rule from a pixel, say, (m − 1, n) to a neighboringpixel (m, n) is defined as follows (similar propagation rules exist for other neighbors):lavgm,n= (1 − C) × lavgm,n+ C × lavgm−1,n(1.1)where C is called the conductivity factor, ranging from 0 to 1. The matrix lavg stands for thelocal average map, initialized with the input image’s intensity values. The above propaga-tion rule is sequentially applied in row & column order [Der90, YV95]. In order to computelocal min/max maps, some modifications are required for the above propagation scheme. Tothis end, a conditional propagation scheme is introduced in [YB04a]. Assume that lmin andlmax stand for the local min/max maps, respectively. The conditional propagation schemefrom (m − 1, n) to (m, n) is defined as follows:Geometric Processing of Reconstructed 3D Maps of Molecular Complexes 1-3if(lminm−1,n< lminm,n)lminm,n= (1 − C) × lminm,n+ C × lminm−1,nif(lmaxm−1,n> lmaxm,n)lmaxm,n= (1 − C) ×
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