Solving Inverse Problems in Protein Space Using Diffusion-Based Priors

The interaction of a protein with its environment can be understood and controlled via its 3D structure. Experimental methods for protein structure determination, such as X-ray crystallography or cryogenic electron microscopy, shed light on biological processes but introduce challenging inverse problems. Learning-based approaches have emerged as accurate and efficient methods to solve these inverse problems for 3D structure determination, but are specialized for a predefined type of measurement. Here, we introduce a versatile framework to turn raw biophysical measurements of varying types into 3D atomic models. Our method combines a physics-based forward model of the measurement process with a pretrained generative model providing a task-agnostic, data-driven prior. Our method outperforms posterior sampling baselines on both linear and non-linear inverse problems. In particular, it is the first diffusion-based method for refining atomic models from cryo-EM density maps.

Scalable 3D Reconstruction From Single Particle X-Ray Diffraction Images Based on Online Machine Learning

X-ray free-electron lasers (XFELs) offer unique capabilities for measuring the structure and dynamics of biomolecules, helping us understand the basic building blocks of life. Notably, high-repetition-rate XFELs enable single particle imaging (X-ray SPI) where individual, weakly scattering biomolecules are imaged under near-physiological conditions with the opportunity to access fleeting states that cannot be captured in cryogenic or crystallized conditions. Existing X-ray SPI reconstruction algorithms, which estimate the unknown orientation of a particle in each captured image as well as its shared 3D structure, are inadequate in handling the massive datasets generated by these emerging XFELs. Here, we introduce X-RAI, an online reconstruction framework that estimates the structure of a 3D macromolecule from large X-ray SPI datasets. X-RAI consists of a convolutional encoder, which amortizes pose estimation over large datasets, as well as a physics-based decoder, which employs an implicit neural representation to enable high-quality 3D reconstruction in an end-to-end, self-supervised manner. We demonstrate that X-RAI achieves state-of-the-art performance for small-scale datasets in simulation and challenging experimental settings and demonstrate its unprecedented ability to process large datasets containing millions of diffraction images in an online fashion. These abilities signify a paradigm shift in X-ray SPI towards real-time capture and reconstruction.

Identifying Interpretable Visual Features in Artificial and Biological Neural Systems

Single neurons in neural networks are often interpretable in that they represent individual, intuitively meaningful features. However, many neurons exhibit $\textit{mixed selectivity}$, i.e., they represent multiple unrelated features. A recent hypothesis proposes that features in deep networks may be represented in $\textit{superposition}$, i.e., on non-orthogonal axes by multiple neurons, since the number of possible interpretable features in natural data is generally larger than the number of neurons in a given network. Accordingly, we should be able to find meaningful directions in activation space that are not aligned with individual neurons. Here, we propose (1) an automated method for quantifying visual interpretability that is validated against a large database of human psychophysics judgments of neuron interpretability, and (2) an approach for finding meaningful directions in network activation space. We leverage these methods to discover directions in convolutional neural networks that are more intuitively meaningful than individual neurons, as we confirm and investigate in a series of analyses. Moreover, we apply the same method to three recent datasets of visual neural responses in the brain and find that our conclusions largely transfer to real neural data, suggesting that superposition might be deployed by the brain. This also provides a link with disentanglement and raises fundamental questions about robust, efficient and factorized representations in both artificial and biological neural systems.

Reconstructing Heterogeneous Cryo-EM Molecular Structures by Decomposing Them into Polymer Chains

Cryogenic electron microscopy (cryo-EM) has transformed structural biology by allowing to reconstruct 3D biomolecular structures up to near-atomic resolution. However, the 3D reconstruction process remains challenging, as the 3D structures may exhibit substantial shape variations, while the 2D image acquisition suffers from a low signal-to-noise ratio, requiring to acquire very large datasets that are time-consuming to process. Current reconstruction methods are precise but computationally expensive, or faster but lack a physically-plausible model of large molecular shape variations. To fill this gap, we propose CryoChains that encodes large deformations of biomolecules via rigid body transformation of their polymer instances (chains), while representing their finer shape variations with the normal mode analysis framework of biophysics. Our synthetic data experiments on the human $\text{GABA}_{\text{B}}$ and heat shock protein show that CryoChains gives a biophysically-grounded quantification of the heterogeneous conformations of biomolecules, while reconstructing their 3D molecular structures at an improved resolution compared to the current fastest, interpretable deep learning method.

Heterogeneous reconstruction of deformable atomic models in Cryo-EM

Cryogenic electron microscopy (cryo-EM) provides a unique opportunity to study the structural heterogeneity of biomolecules. Being able to explain this heterogeneity with atomic models would help our understanding of their functional mechanisms but the size and ruggedness of the structural space (the space of atomic 3D cartesian coordinates) presents an immense challenge. Here, we describe a heterogeneous reconstruction method based on an atomistic representation whose deformation is reduced to a handful of collective motions through normal mode analysis. Our implementation uses an autoencoder. The encoder jointly estimates the amplitude of motion along the normal modes and the 2D shift between the center of the image and the center of the molecule . The physics-based decoder aggregates a representation of the heterogeneity readily interpretable at the atomic level. We illustrate our method on 3 synthetic datasets corresponding to different distributions along a simulated trajectory of adenylate kinase transitioning from its open to its closed structures. We show for each distribution that our approach is able to recapitulate the intermediate atomic models with atomic-level accuracy.

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.

Estimation of Orientation and Camera Parameters from Cryo-Electron Microscopy Images with Variational Autoencoders and Generative Adversarial Networks

Cryo-electron microscopy (cryo-EM) is capable of producing reconstructed 3D images of biomolecules at near-atomic resolution. As such, it represents one of the most promising imaging techniques in structural biology. However, raw cryo-EM images are only highly corrupted - noisy and band-pass filtered - 2D projections of the target 3D biomolecules. Reconstructing the 3D molecular shape starts with the removal of image outliers, the estimation of the orientation of the biomolecule that has produced the given 2D image, and the estimation of camera parameters to correct for intensity defects. Current techniques performing these tasks are often computationally expensive, while the dataset sizes keep growing. There is a need for next-generation algorithms that preserve accuracy while improving speed and scalability. In this paper, we combine variational autoencoders (VAEs) and generative adversarial networks (GANs) to learn a low-dimensional latent representation of cryo-EM images. We perform an exploratory analysis of the obtained latent space, that is shown to have a structure of "orbits", in the sense of Lie group theory, consistent with the acquisition procedure of cryo-EM images. This analysis leads us to design an estimation method for orientation and camera parameters of single-particle cryo-EM images, together with an outliers detection procedure. As such, it opens the door to geometric approaches for unsupervised estimations of orientations and camera parameters, making possible fast cryo-EM biomolecule reconstruction.