Integrating Molecular Models Into CryoEM Heterogeneity Analysis Using Scalable High-resolution Deep Gaussian Mixture Models

DynaMight: estimating molecular motions with improved reconstruction from cryo-EM images

How to deal with continuously flexing molecules is one of the biggest outstanding challenges in single-particle analysis of proteins from cryogenic-electron microscopy (cryo-EM) images. Here, we present DynaMight, a software tool that estimates a continuous space of conformations in a cryo-EM dataset by learning three-dimensional deformations of a Gaussian pseudo-atomic model of a consensus structure for every particle image. Inversion of the learned deformations is then used to obtain an improved reconstruction of the consensus structure. We illustrate the performance of DynaMight for several experimental cryo-EM datasets. We also show how error estimates on the deformations may be obtained by independently training two variational autoencoders on half sets of the cryo-EM data, and how regularization of the three-dimensional deformations through the use of atomic models may lead to important artifacts due to model bias. DynaMight is distributed as free, open-source software, as part of RELION-5.

Deep generative priors for biomolecular 3D heterogeneous reconstruction from cryo-EM projections

Cryo-electron microscopy has become a powerful tool to determine three-dimensional (3D) structures of rigid biological macromolecules from noisy micrographs with single-particle reconstruction. Recently, deep neural networks, e.g., CryoDRGN, have demonstrated conformational and compositional heterogeneity of complexes. However, the lack of ground-truth conformations poses a challenge to assess the performance of heterogeneity analysis methods. In this work, variational autoencoders (VAE) with three types of deep generative priors were learned for latent variable inference and heterogeneous 3D reconstruction via Bayesian inference. More specifically, VAEs with "Variational Mixture of Posteriors" priors (VampPrior-SPR), non-parametric exemplar-based priors (ExemplarPrior-SPR) and priors from latent score-based generative models (LSGM-SPR) were quantitatively compared with CryoDRGN. We built four simulated datasets composed of hypothetical continuous conformation or discrete states of the hERG K + channel. Empirical and quantitative comparisons of inferred latent representations were performed with affine-transformation-based metrics. These models with more informative priors gave better regularized, interpretable factorized latent representations with better conserved pairwise distances, less deformed latent distributions and lower within-cluster variances. They were also tested on experimental datasets to resolve compositional and conformational heterogeneity (50S ribosome assembly, cowpea chlorotic mottle virus, and pre-catalytic spliceosome) with comparable high resolution. Codes and data are available: https://github.com/benjamin3344/DGP-SPR.

Confronting heterogeneity in cryogenic electron microscopy data: Innovative strategies and future perspectives with data-driven methods

The surge in the influx of data from cryogenic electron microscopy (cryo-EM) experiments has intensified the demand for robust algorithms capable of autonomously managing structurally heterogeneous datasets. This presents a wealth of exciting opportunities from a data science viewpoint, inspiring the development of numerous innovative, application-specific methods, many of which leverage contemporary data-driven techniques. However, addressing the challenges posed by heterogeneous datasets remains a paramount yet unresolved issue in the field. Here, we explore the subtleties of this challenge and the array of strategies devised to confront it. We pinpoint the shortcomings of existing methodologies and deliberate on prospective avenues for improvement. Specifically, our discussion focuses on strategies to mitigate model overfitting and manage data noise, as well as the effects of constraints, priors, and invariances on the optimization process.

Identifying protein conformational states in the Protein Data Bank: Toward unlocking the potential of integrative dynamics studies

Studying protein dynamics and conformational heterogeneity is crucial for understanding biomolecular systems and treating disease. Despite the deposition of over 215 000 macromolecular structures in the Protein Data Bank and the advent of AI-based structure prediction tools such as AlphaFold2, RoseTTAFold, and ESMFold, static representations are typically produced, which fail to fully capture macromolecular motion. Here, we discuss the importance of integrating experimental structures with computational clustering to explore the conformational landscapes that manifest protein function. We describe the method developed by the Protein Data Bank in Europe - Knowledge Base to identify distinct conformational states, demonstrate the resource's primary use cases, through examples, and discuss the need for further efforts to annotate protein conformations with functional information. Such initiatives will be crucial in unlocking the potential of protein dynamics data, expediting drug discovery research, and deepening our understanding of macromolecular mechanisms.

Improving resolution and resolvability of single-particle cryoEM structures using Gaussian mixture models

Cryogenic electron microscopy is widely used in structural biology, but its resolution is often limited by the dynamics of the macromolecule. Here we developed a refinement protocol based on Gaussian mixture models that integrates particle orientation and conformation estimation and improves the alignment for flexible domains of protein structures. We demonstrated this protocol on multiple datasets, resulting in improved resolution and resolvability, locally and globally, by visual and quantitative measures.

Efficient high-resolution refinement in cryo-EM with stochastic gradient descent

Electron cryomicroscopy (cryo-EM) is an imaging technique widely used in structural biology to determine the three-dimensional structure of biological molecules from noisy two-dimensional projections with unknown orientations. As the typical pipeline involves processing large amounts of data, efficient algorithms are crucial for fast and reliable results. The stochastic gradient descent (SGD) algorithm has been used to improve the speed of ab initio reconstruction, which results in a first, low-resolution estimation of the volume representing the molecule of interest, but has yet to be applied successfully in the high-resolution regime, where expectation-maximization algorithms achieve state-of-the-art results, at a high computational cost. In this article, we investigate the conditioning of the optimization problem and show that the large condition number prevents the successful application of gradient descent-based methods at high resolution. Our results include a theoretical analysis of the condition number of the optimization problem in a simplified setting where the individual projection directions are known, an algorithm based on computing a diagonal preconditioner using Hutchinson's diagonal estimator, and numerical experiments showing the improvement in the convergence speed when using the estimated preconditioner with SGD. The preconditioned SGD approach can potentially enable a simple and unified approach to ab initio reconstruction and high-resolution refinement with faster convergence speed and higher flexibility, and our results are a promising step in this direction.

Methods for Cryo-EM Single Particle Reconstruction of Macromolecules Having Continuous Heterogeneity

Macromolecules change their shape (conformation) in the process of carrying out their functions. The imaging by cryo-electron microscopy of rapidly-frozen, individual copies of macromolecules (single particles) is a powerful and general approach to understanding the motions and energy landscapes of macromolecules. Widely-used computational methods already allow the recovery of a few distinct conformations from heterogeneous single-particle samples, but the treatment of complex forms of heterogeneity such as the continuum of possible transitory states and flexible regions remains largely an open problem. In recent years there has been a surge of new approaches for treating the more general problem of continuous heterogeneity. This paper surveys the current state of the art in this area.