Author: Tianyi Wang

Tools for heterogeneity in cryo-EM: manifold learning, disentanglement and optimal transport

Despite much recent progress, the reconstruction and analysis of macromolecules with continuous conformational heterogeneity remains a key challenge.  In this talk we present two promising tools that can aid in various stages of the reconstruction and analysis pipelines.

In the first part of the talk, the notion of manifold factorization and disentanglement is presented.  This is an approach to dimensionality reduction where different aspects of the data are assigned separate coordinates.  It has potential applications both for the reconstruction of single-particle cryo-EM samples with continuous heterogeneity and for the analysis of the reconstructed volumetric datasets.

In the second part of the talk, we will discuss the potential applications of optimal transport for cryo-EM, in particular for the analysis of heterogeneous samples, as well as for class-averaging and particle picking.  Optimal transport metrics are closely related to physical motion, making them a natural choice for many of the core problems in cryo-EM.  Historically, computational bottlenecks have limited the applicability of optimal transport.  However, recent advances in computational optimal transport have yielded fast approximation schemes that can be readily used for the analysis of high-resolution images and volumetric arrays.

Bias, variance and map validation in Single Particle Analysis by CryoEM

Single Particle Analysis by CryoEM has established as a mature technique to elucidate the three-dimensional structure of biological macromolecules. Once the experimental data is acquired, reconstructing the macromolecule’s map involves the estimation of millions of parameters. Due to the low Signal-to-Noise Ratio, this estimation is prone to mistakes. Depending on the error size, these mistakes may result into small perturbations in the reconstructed map (variance) or large artifacts (bias). In this talk we will discuss different kinds of mistakes that can be committed and how to identify and tackle them.

Laser phase-contrast Cryo-EM and associated computational opportunities

A phase plate can provide optimum image contrast for weak-phase objects in transmission  electron microscopy, but approaches toward realizing a phase plate have suffered from  instabilities. We have developed a phase plate that is based on coherently phase-shifting the  electron wave function by a laser beam, which is built up to a record-high intensity of ~400  GW/cm^2 by resonance in a Fabry-Perot cavity. We have demonstrated contrast enhancement  with the laser phase plate (LPP) and shown the long-term stability of the device, as well as  generated a high-resolution map of 20S proteasome particles using a standard single-particle  cryo-electron microscopy (Cryo-EM) workflow. 

This talk will focus on our recent work to move beyond proof-of-concept, as well as the  computational opportunities that lie ahead. To demonstrate the benefits of the LPP to Cryo-EM  as well as cryo-electron tomography, we will soon begin working with a state-of-the-art  microscope equipped with a spherical aberration corrector, gun monochromator, and post column energy filter. We will explore improvements to the phase plate design and pursue new  strategies for image acquisition and processing, such as high-resolution two-dimensional  template matching.

Recovering small molecular structures using Cryo-EM

Any current Cryo-EM algorithmic pipeline entails recovering the 3-D structure after particle picking. However, the signal-to-noise ratio of the data, and thus the reliability of particle picking, drops with the molecular mass of the specimens. Accordingly, it is commonly believed that Cryo-EM cannot be used to map molecules with a molecular mass below a certain threshold. Challenging this misconception, I will argue that finding the particle picking is not a prerequisite for structure determination and thus small molecules are, at least in principle, within reach of Cryo-EM. Then, I will introduce two computational frameworks to bypass particle picking and show numerical results.

Revisiting Orientation Estimation in Cryo-EM Volume Refinement

In Cryo-EM 3D map refinement, popular software packages jointly reconstruct the 3D map while estimating orientations. The orientation estimation can roughly be categorised in two type of approaches: marginalisation and optimisation. While the former tends to be more robust to noise, the latter has better consistency with respect to the data. So far it appears difficult to obtain both data-consistency and noise-robustness in a single method.

In this talk we will revisit the orientation estimation process. In particular, we develop an alternative that can be interpreted as being “in between marginalisation and optimisation” and argue that this new method is both robust to noise and data-consistent. Additionally, the framework of lifting-based global optimisation on manifolds allows analysis of the proposed methods that lead to several practical theoretical guarantees. Both theoretical results and performance on simulated data will be tested in numerical experiments.