Mathematical methods for 3D electron microscopy

This is an interdisciplinary project involving research in applied mathematics, statistical learning, and structural biology. It aims to develop mathematical theory and algorithms for 3D structure recovery in cryo-EM single-particle analysis.

It is based on using physics-informed deep learning, which has provided state-of-the-art result in many inverse problems, including some from medical imaging. A specific difficulty here is that the 3D structure recovery involves a large number of nuisance parameters. Data is also very noisy and the 3D molecular structure can be flexible.

Hence, using the physics-informed deep learning methods in this setting raises both theoretical and algorithmic challenges.

One challenge is to define the appropriate statistical learning problem to train the deep neural networks while marginalising over the nuisance parameters.

Further theoretical and algorithmic challenges are added when the molecule is flexible since the structure recovery also includes recovering the dynamics.The project seeks to address these theoretical and algorithic challenges for deep learning based 3D structure recovery in cryo-EM single-particle analysis.

Algorithms will be implemented directly as part of RELION, which is an established software framework for cryo-EM single-particle analysis. This ensures methods can be tested against experimental data. It also ensures a rapid dissemination where new algorithms are made available to end-users in the cryo-EM community.