Computational approaches for automatic structural analysis of large biomolecular complexes.

We present computational solutions to two problems of macromolecular structure interpretation from reconstructed three-dimensional electron microscopy (3D-EM) maps of large bio-molecular complexes at intermediate resolution (5A-15 A). The two problems addressed are: 1) 3D structural alignment (matching) between identified and segmented 3D maps of structure units (e.g. trimeric configuration of proteins), and 2) the secondary structure identification of a segmented protein 3D map (i.e.locations of alpha-helices, beta-sheets). For problem 1, we present an efficient algorithm to correlate spatially (and structurally) two 3D maps of structure units. Besides providing a similarity score between structure units, the algorithm yields an effective technique for resolution refinement of repeated structure units, by 3D alignment and averaging. For problem 2, we present an efficient algorithm to compute eigenvalues and link eigenvectors of a Gaussian convoluted structure tensor derived from the protein 3D Map, thereby identifying and locating secondary structural motifs of proteins. The efficiency and performance of our approach is demonstrated on several experimentally reconstructed 3D maps of virus capsid shells from single-particle cryo-electron microscopy (cryo-EM), as well as computationally simulated protein structure density 3D maps generated from protein model entries in the Protein Data Bank.