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.

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.

Generative Novel View Synthesis with 3D-Aware Diffusion Models

We present a diffusion-based model for 3D-aware generative novel view synthesis from as few as a single input image. Our model samples from the distribution of possible renderings consistent with the input and, even in the presence of ambiguity, is capable of rendering diverse and plausible novel views. To achieve this, our method makes use of existing 2D diffusion backbones but, crucially, incorporates geometry priors in the form of a 3D feature volume. This latent feature field captures the distribution over possible scene representations and improves our method's ability to generate view-consistent novel renderings. In addition to generating novel views, our method has the ability to autoregressively synthesize 3D-consistent sequences. We demonstrate state-of-the-art results on synthetic renderings and room-scale scenes; we also show compelling results for challenging, real-world objects.

MELON: NeRF with Unposed Images Using Equivalence Class Estimation

Neural radiance fields enable novel-view synthesis and scene reconstruction with photorealistic quality from a few images, but require known and accurate camera poses. Conventional pose estimation algorithms fail on smooth or self-similar scenes, while methods performing inverse rendering from unposed views require a rough initialization of the camera orientations. The main difficulty of pose estimation lies in real-life objects being almost invariant under certain transformations, making the photometric distance between rendered views non-convex with respect to the camera parameters. Using an equivalence relation that matches the distribution of local minima in camera space, we reduce this space to its quotient set, in which pose estimation becomes a more convex problem. Using a neural-network to regularize pose estimation, we demonstrate that our method - MELON - can reconstruct a neural radiance field from unposed images with state-of-the-art accuracy while requiring ten times fewer views than adversarial approaches.

Amortized Inference for Heterogeneous Reconstruction in Cryo-EM

Cryo-electron microscopy (cryo-EM) is an imaging modality that provides unique insights into the dynamics of proteins and other building blocks of life. The algorithmic challenge of jointly estimating the poses, 3D structure, and conformational heterogeneity of a biomolecule from millions of noisy and randomly oriented 2D projections in a computationally efficient manner, however, remains unsolved. Our method, cryoFIRE, performs ab initio heterogeneous reconstruction with unknown poses in an amortized framework, thereby avoiding the computationally expensive step of pose search while enabling the analysis of conformational heterogeneity. Poses and conformation are jointly estimated by an encoder while a physics-based decoder aggregates the images into an implicit neural representation of the conformational space. We show that our method can provide one order of magnitude speedup on datasets containing millions of images without any loss of accuracy. We validate that the joint estimation of poses and conformations can be amortized over the size of the dataset. For the first time, we prove that an amortized method can extract interpretable dynamic information from experimental datasets.

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.

Deep Generative Modeling for Volume Reconstruction in Cryo-Electron Microscopy

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 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.