Helical Three Dimensional Reconstruction Using Bayesian Optimization for Cryogenic Electron Microscopy

Three-dimensional (3D) reconstruction for cryogenic electron microscopy (cryo-EM) often falls into an ill-posed problem owing to several uncertainties in observations, including noise. To reduce excessive degree of freedom and avoid overfitting, the structural symmetry is often used as a powerful constraint. In the case of the helix, the entire 3D structure is determined by the subunit 3D structure and two helical parameters. There is no analytical method to simultaneously obtain both of the subunit structure and helical parameters. A common approach is to employ an iterative reconstruction in which the two optimizations are performed alternately. However, iterative reconstruction does not necessarily converge when a heuristic objective function is used for each optimization step. Also, the obtained 3D reconstruction highly depends on the initial guess of the 3D structure and the helical parameters. Herein, we propose a method for estimating the 3D structure and helical parameters that also performs an iterative optimization; however, the objective function for each step is derived from a single objective function to make the algorithm convergent and less sensitive to the initial guess. Finally, we evaluated the effectiveness of the proposed method by testing it on cryo-EM images, which were challenging to reconstruct using conventional methods.