A kinetic model for solving a combination optimization problem in ab-initio Cryo-EM 3D reconstruction

Cryo-Electron Microscopy (cryo-EM) is a widely used and effective method for determining the three-dimensional (3D) structure of biological molecules. For ab-initio Cryo-EM 3D reconstruction using single particle analysis (SPA), estimating the projection direction of the projection image is a crucial step. However, the existing SPA methods based on common lines are sensitive to noise. The error in common line detection will lead to a poor estimation of the projection directions and thus may greatly affect the final reconstruction results. To improve the reconstruction results, multiple candidate common lines are estimated for each pair of projection images. The key problem then becomes a combination optimization problem of selecting consistent common lines from multiple candidates. To solve the problem efficiently, a physics-inspired method based on a kinetic model is proposed in this work. More specifically, hypothetical attractive forces between each pair of candidate common lines are used to calculate a hypothetical torque exerted on each projection image in the 3D reconstruction space, and the rotation under the hypothetical torque is used to optimize the projection direction estimation of the projection image. This way, the consistent common lines along with the projection directions can be found directly without enumeration of all the combinations of the multiple candidate common lines. Compared with the traditional methods, the proposed method is shown to be able to produce more accurate 3D reconstruction results from high noise projection images. Besides the practical value, the proposed method also serves as a good reference for solving similar combinatorial optimization problems.