An Auto-Encoder to Reconstruct Structure with Cryo-EM Images via Theoretically Guaranteed Isometric Latent Space, and Its Application for Automatically Computing the Conformational Pathway

Structural analysis by cryo-electron microscopy (Cryo-EM) has become well-established in the field of structural biology. Recently, cutting-edge methods have been proposed for the purpose of reconstructing either a small set of structures or a conformational pathway (continuous structural change), where a 3D density map represents the structure. However, we usually perform heavy manual labor to define the plausible pathway related to biological significance. In this study, for automatizing such manual labor, we propose a deep Auto-Encoder (AE) with a trainable prior. The AE is trained using only a set of single particle Cryo-EM images. The trained AE reconstructs the corresponding structures for the latent variables of the Cryo-EM images. The latent distribution can not only be theoretically proportional to a distribution of the structure but also consistent with the trained prior. Taking advantage of this property, we can automatically compute the pathway by only accessing the latent space as follows: i) generating a ridgeline on the latent distribution and ii) defining the conformational pathway as a sequence of the reconstructed structures along the ridgeline using the trained decoder. In our numerical experiments, we evaluate the computed pathways by comparing them with existing ones that were manually determined by other researchers, and confirm that they are sufficiently consistent.