Orientation Determination For Cryo-EM Data:An Improved Bayesian Algorithm Utilizing Angular Correlation

The cryo-electron microscopy(cryo-EM)has become popular and cutting-edge tech-nology in structure biology.Here,we review the development of single particle analysis(SPA)in cryo-EM technology for past decades and the major workflow of data analysis in single particle problem.And we discuss recent researches of Bayesian approaches in cryo-EM reconstruc-tion.A powerful and flexible Expectation-Maximization Maximum-Likelihood(EM-ML)framework works well at different stages of cryo-EM data analysis.Several popular meth-ods in machine leanring have been introduced into cryo-EM density estimation by for-mulating the problem as a stochastic optimization.Stochastic average gradient decent and importance sampling techniques allow random initializations and reduce the cost of computing.Single particle reconstruction problem is always challenging.Three-dimensional structure determination by analysis of cryo-EM images requires many parameters to be determined from extremely noisy data.The goal is to reconstruct the 3D structure of a molecule from a large number of orientation-unknown 2D projections.Our researches yield new solution into orientation problem of single particle analysis.Angular auto-correlation function(ACF)of each projection is utilized to formulate the determination of three Euler angles to stepwise determination of first two Euler angles and the subsequent third an-gle,the in-plane rotation.This approach reduces computational cofplexity from O(n3)to O(n2).Implementation of initial research show its good peformance in reducing the computational cost.X-ray free electron laser(XFEL)is showing its potential applications in structure biology.A few researches have applied expectation maximization method in XFEL.Here,a framework based stochastic optimization and importance sampling is introduced to reconstruct density map of XFEL data.Initial implementation of algorithm is able to refine 3D density.Besides,we discuss advantages for applying angular correlation function to XFEL single particle analysis.