Modeling Protein Structure Features from Three Dimensional Cryo-EM Images

Secondary structure of protein, such as α-helix and βsheet, is the general three-dimensional (3D) form of local segments. It can be identified from the 3D electron cryomicroscopy (cryo-EM) density images at medium resolutions (~5-10Å). A detected β-sheet can be represented by either the voxels of β-sheet density or by many piecewise polygons to compose a rough surface. However, none of these is effective in capturing the global surface feature of the β-sheet. In addition to the single layer sheet, β-barrel as a particular sheet structural feature is formed by multiple βstrands in a barrel shape. We present a novel mathematical model to represent the single layer β-sheet density, and also an optimized model to represent the β-barrel density. These surface models can be potentially used for further detection of β-strands when the resolution is not high enough to resolve the molecular details, it is critical for the de-novo backbone structure derivation in cryo-EM density images at the medium resolutions.