METHODS AND SYSTEMS FOR RECONSTRUCTION OF THREE-DIMENSIONAL STRUCTURE AND THREE-DIMENSIONAL MOTION OF A PROTEIN MOLECULE

Provided are systems and methods for determining 3D structure and 3D motion of a protein molecule from 2D or 3D particle observation images. The method including: initializing pose parameters and unknown model parameters; the parameters of the one or more flow generators; image formation including: generating one or more 3D deformation fields by inputting the latent coordinate vector into the one or more flow generators; performing a convection and projection operation; and performing CTF corruption; fitting the unknown model parameters to the experimental images by gradient-based optimization of an objective function; latent variable search for a given experimental image including: performing the image formation one or more times to generate simulated images; selecting one or more latent coordinate vectors based on similarity; updating the at least one of the unknown model parameters including: generating simulated images; evaluating the objective function; computing the gradient of the objective function.