Towards Interpretable Cryo-EM: Disentangling Latent Spaces of Molecular Conformations.

Molecules are essential building blocks of life and their different conformations (i.e., shapes) crucially determine the functional role that they play in living organisms. Cryogenic Electron Microscopy (cryo-EM) allows for acquisition of large image datasets of individual molecules. Recent advances in computational cryo-EM have made it possible to learn latent variable models of conformation landscapes. However, interpreting these latent spaces remains a challenge as their individual dimensions are often arbitrary. The key message of our work is that this interpretation challenge can be viewed as an Independent Component Analysis (ICA) problem where we seek models that have the property of identifiability. That means, they have an essentially unique solution, representing a conformational latent space that separates the different degrees of freedom a molecule is equipped with in nature. Thus, we aim to advance the computational field of cryo-EM beyond visualizations as we connect it with the theoretical framework of (nonlinear) ICA and discuss the need for identifiable models, improved metrics, and benchmarks. Moving forward, we propose future directions for enhancing the disentanglement of latent spaces in cryo-EM, refining evaluation metrics and exploring techniques that leverage physics-based decoders of biomolecular systems. Moreover, we discuss how future technological developments in time-resolved single particle imaging may enable the application of nonlinear ICA models that can discover the true conformation changes of molecules in nature. The pursuit of interpretable conformational latent spaces will empower researchers to unravel complex biological processes and facilitate targeted interventions. This has significant implications for drug discovery and structural biology more broadly. More generally, latent variable models are deployed widely across many scientific disciplines. Thus, the argument we present in this work has much broader applications in AI for science if we want to move from impressive nonlinear neural network models to mathematically grounded methods that can help us learn something new about nature.

Orthogonal outlier detection and dimension estimation for improved MDS embedding of biological datasets.

Conventional dimensionality reduction methods like Multidimensional Scaling (MDS) are sensitive to the presence of orthogonal outliers, leading to significant defects in the embedding. We introduce a robust MDS method, called DeCOr-MDS (Detection and Correction of Orthogonal outliers using MDS), based on the geometry and statistics of simplices formed by data points, that allows to detect orthogonal outliers and subsequently reduce dimensionality. We validate our methods using synthetic datasets, and further show how it can be applied to a variety of large real biological datasets, including cancer image cell data, human microbiome project data and single cell RNA sequencing data, to address the task of data cleaning and visualization.

Septins regulate border cell surface geometry, shape, and motility downstream of Rho in Drosophila.

Septins self-assemble into polymers that bind and deform membranes in vitro and regulate diverse cell behaviors in vivo. How their in vitro properties relate to their in vivo functions is under active investigation. Here, we uncover requirements for septins in detachment and motility of border cell clusters in the Drosophila ovary. Septins and myosin colocalize dynamically at the cluster periphery and share phenotypes but, surprisingly, do not impact each other. Instead, Rho independently regulates myosin activity and septin localization. Active Rho recruits septins to membranes, whereas inactive Rho sequesters septins in the cytoplasm. Mathematical analyses identify how manipulating septin expression levels alters cluster surface texture and shape. This study shows that the level of septin expression differentially regulates surface properties at different scales. This work suggests that downstream of Rho, septins tune surface deformability while myosin controls contractility, the combination of which governs cluster shape and movement.

Deep generative modeling for volume reconstruction in cryo-electron microscopy.

Advances in cryo-electron microscopy (cryo-EM) for high-resolution imaging of biomolecules in solution have provided new challenges and opportunities for algorithm development for 3D reconstruction. Next-generation volume reconstruction algorithms that combine generative modelling with end-to-end unsupervised deep learning techniques have shown promise, but many technical and theoretical hurdles remain, especially when applied to experimental cryo-EM images. In light of the proliferation of such methods, we propose here a critical review of recent advances in the field of deep generative modelling for cryo-EM reconstruction. The present review aims to (i) provide a unified statistical framework using terminology familiar to machine learning researchers with no specific background in cryo-EM, (ii) review the current methods in this framework, and (iii) outline outstanding bottlenecks and avenues for improvements in the field.

Defining an action of SO(d)-rotations on images generated by projections of d-dimensional objects: Applications to pose inference with Geometric VAEs.

Recent advances in variational autoencoders (VAEs) have enabled learning latent manifolds as compact Lie groups, such as SO(d). Since this approach assumes that data lies on a subspace that is homeomorphic to the Lie group itself, we here investigate how this assumption holds in the context of images that are generated by projecting a d-dimensional volume with unknown pose in SO(d). Upon examining different theoretical candidates for the group and image space, we show that the attempt to define a group action on the data space generally fails, as it requires more specific geometric constraints on the volume. Using geometric VAEs, our experiments confirm that this constraint is key to proper pose inference, and we discuss the potential of these results for applications and future work.

Les récents progrès dans le domaine des autoencodeurs variationnels (VAEs) ont permis l'apprentissage de variétés latentes sur des groupes de Lie compacts, tels que SO(d). Une telle approche supposant l'espace des données homéomorphe au groupe de Lie, nous étudions ici la validité de cette hypothèse dans le contexte d'images générées par projection d'un volume de dimension d, dont la pose dans SO(d) est inconnue. Après examen de différents candidats définissant l'espace des images et groupe, on montre que l'on ne peut de manière générale obtenir une action de groupe, sans une contrainte supplémentaire sur le volume. En appliquant des VAEs géométriques, nos expériences confirment que ces contraintes géométriques sont essentielles pour l'inférence de la pose associée au volume projeté, et nous discutons pour conclure des applications potentielles de ces résultats.

CryoAI: Amortized Inference of Poses for Ab Initio Reconstruction of 3D Molecular Volumes from Real Cryo-EM Images.

Cryo-electron microscopy (cryo-EM) has become a tool of fundamental importance in structural biology, helping us understand the basic building blocks of life. The algorithmic challenge of cryo-EM is to jointly estimate the unknown 3D poses and the 3D electron scattering potential of a biomolecule from millions of extremely noisy 2D images. Existing reconstruction algorithms, however, cannot easily keep pace with the rapidly growing size of cryo-EM datasets due to their high computational and memory cost. We introduce cryoAI, an ab initio reconstruction algorithm for homogeneous conformations that uses direct gradient-based optimization of particle poses and the electron scattering potential from single-particle cryo-EM data. CryoAI combines a learned encoder that predicts the poses of each particle image with a physics-based decoder to aggregate each particle image into an implicit representation of the scattering potential volume. This volume is stored in the Fourier domain for computational efficiency and leverages a modern coordinate network architecture for memory efficiency. Combined with a symmetrized loss function, this framework achieves results of a quality on par with state-of-the-art cryo-EM solvers for both simulated and experimental data, one order of magnitude faster for large datasets and with significantly lower memory requirements than existing methods.