3D Rotation Invariant Features for the Characterization of Molecular Density Maps

Cryo electron microscopy produces 3D density maps of large macromolecular structures. An important task lies in the efficient identification of structural similarities between different molecular density maps. Here we construct and test three different types of 3D rotation invariant features for template free similarity detection in molecular density maps. The density map comparison is based on feature vectors that describe the surrounding density distribution for a given map position. We propose Fast Fourier Transform based methods to speed up the computation of feature vectors. Previously, little is known about the discriminative power of rotation invariant features for noisy maps. Here, we test the three feature types with density maps at different noise levels. We assess the performance of our feature vectors by a classification experiment of protein density maps. Our results show that at low noise levels the three types of features perform equally well. However, at high noise levels the features that are constructed by a spherical harmonics decomposition of the density neighborhood is significantly more reliable and outperform the other two feature types, which are based on the moments and intensity histograms of the density distribution.