Deep Generative Modeling for Volume Reconstruction in Cryo-Electron Microscopy

Abstract

Recent breakthroughs in high resolution imaging of biomolecules in solution with cryo-electron microscopy (cryo-EM) have unlocked new doors for the reconstruction of molecular volumes, thereby promising further advances in biology, chemistry, and pharmacological research amongst others. Despite significant headway, the immense challenges in cryo-EM data analysis remain legion and intricately inter-disciplinary in nature, requiring insights from physicists, structural biologists, computer scientists, statisticians, and applied mathematicians. Meanwhile, recent next-generation volume reconstruction algorithms that combine generative modeling with end-to-end unsupervised deep learning techniques have shown promising results on simulated data, but still face considerable hurdles when applied to experimental cryo-EM images. In light of the proliferation of such methods and given the interdisciplinary nature of the task, we propose here a critical review of recent advances in the field of deep generative modeling for high resolution cryo-EM volume reconstruction. The present review aims to (i) compare and contrast these new methods, while (ii) presenting them from a perspective and using terminology familiar to scientists in each of the five aforementioned fields with no specific background in cryo-EM. The review begins with an introduction to the mathematical and computational challenges of deep generative models for cryo-EM volume reconstruction, along with an overview of the baseline methodology shared across this class of algorithms. Having established the common thread weaving through these different models, we then dive into the specifics and provide a practical comparison of these state-of-the-art algorithms, highlighting their relative strengths and weaknesses, along with the assumptions that they rely on. This allows us to identify bottlenecks in current methods and avenues for future research. This review might also raise the interest of computer vision practitioners, as it highlights current limits of deep generative models in a very challenging imaging regime where, for example, the signal-to-noise ratio is considerably lower than that found in traditional images.

Stability and Inference of the Euler Characteristic Transform

“…If l > j, let m = min(x l , ε − x j ). Equation (12) shows that if we replace x j with x j + m and replace x l with x l − m, the value of i f (x i ) does not decrease. Therefore, by applying this replacement procedure several times, we can always find a maximiser of i f (x i ) on S(L) with j ≥ l. This condition forces the value of i f (x i ) to be…”

“…Classifying shapes is a ubiquitous task in data science and machine learning. A wealth of theory has been developed to distinguish different shapes and a large array of applications of these methods in the natural sciences exist [3,12,15,30]. In particular the Euler characteristic transform (ECT) [27], arising from topological data analysis (TDA), provides a sufficient statistic for a large class of shapes [10,16] (e.g., compact semi-algebraic sets) embedded in Euclidean space by considering intersections of a shape with half-spaces.…”