Helicon: Helical parameter determination and 3D reconstruction from one image.

Helical symmetry is a common structural feature of many biological macromolecules. However, determination of the helical parameters and de novo 3D reconstruction remain challenging. We have developed a computational method, Helicon, which poses helical reconstruction as a linear regression problem with the projection matrix parameterized by the helical twist, rise, and axial symmetry. A sparse search of the twist and rise parameters would allow determination of helical parameters and 3D reconstruction directly from one 2D class average or a raw cryo-EM image. The Helicon method has been validated with simulation tests and experimental cryo-EM images of helical tubes, non-amyloid filaments, and amyloid fibrils. Imaging stitching and L1 regularization of linear regression were shown to improve the robustness for low-twist amyloids and noisy raw cryo-EM images. Using Helicon, we could successfully determine the helical parameters and perform de novo reconstruction of a previously unreported, low-abundance tau amyloid structure from a publicly available dataset.