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.

Changes in an enzyme ensemble during catalysis observed by high-resolution XFEL crystallography.

Enzymes populate ensembles of structures necessary for catalysis that are difficult to experimentally characterize. We use time-resolved mix-and-inject serial crystallography at an x-ray free electron laser to observe catalysis in a designed mutant isocyanide hydratase (ICH) enzyme that enhances sampling of important minor conformations. The active site exists in a mixture of conformations, and formation of the thioimidate intermediate selects for catalytically competent substates. The influence of cysteine ionization on the ICH ensemble is validated by determining structures of the enzyme at multiple pH values. Large molecular dynamics simulations in crystallo and time-resolved electron density maps show that Asp17 ionizes during catalysis and causes conformational changes that propagate across the dimer, permitting water to enter the active site for intermediate hydrolysis. ICH exhibits a tight coupling between ionization of active site residues and catalysis-activated protein motions, exemplifying a mechanism of electrostatic control of enzyme dynamics.

Structural biology in the age of X-ray free-electron lasers and exascale computing.

Serial femtosecond X-ray crystallography has emerged as a powerful method for investigating biomolecular structure and dynamics. With the new generation of X-ray free-electron lasers, which generate ultrabright X-ray pulses at megahertz repetition rates, we can now rapidly probe ultrafast conformational changes and charge movement in biomolecules. Over the last year, another innovation has been the deployment of Frontier, the world's first exascale supercomputer. Synergizing extremely high repetition rate X-ray light sources and exascale computing has the potential to accelerate discovery in biomolecular sciences. Here we outline our perspective on each of these remarkable innovations individually, and the opportunities and challenges in yoking them within an integrated research infrastructure.

AlignOT: An Optimal Transport Based Algorithm for Fast 3D Alignment With Applications to Cryogenic Electron Microscopy Density Maps.

Aligning electron density maps from Cryogenic electron microscopy (cryo-EM) is a first key step for studying multiple conformations of a biomolecule. As this step remains costly and challenging, with standard alignment tools being potentially stuck in local minima, we propose here a new procedure, called AlignOT, which relies on the use of computational optimal transport (OT) to align EM maps in 3D space. By embedding a fast estimation of OT maps within a stochastic gradient descent algorithm, our method searches for a rotation that minimizes the Wasserstein distance between two maps, represented as point clouds. We quantify the impact of various parameters on the precision and accuracy of the alignment, and show that AlignOT can outperform the standard local alignment methods, with an increased range of rotation angles leading to proper alignment. We further benchmark AlignOT on various pairs of experimental maps, which account for different types of conformational heterogeneities and geometric properties. As our experiments show good performance, we anticipate that our method can be broadly applied to align 3D EM maps.

RNA structures and dynamics with Å resolution revealed by x-ray free-electron lasers.

RNA macromolecules, like proteins, fold to assume shapes that are intimately connected to their broadly recognized biological functions; however, because of their high charge and dynamic nature, RNA structures are far more challenging to determine. We introduce an approach that exploits the high brilliance of x-ray free-electron laser sources to reveal the formation and ready identification of angstrom-scale features in structured and unstructured RNAs. Previously unrecognized structural signatures of RNA secondary and tertiary structures are identified through wide-angle solution scattering experiments. With millisecond time resolution, we observe an RNA fold from a dynamically varying single strand through a base-paired intermediate to assume a triple-helix conformation. While the backbone orchestrates the folding, the final structure is locked in by base stacking. This method may help to rapidly characterize and identify structural elements in nucleic acids in both equilibrium and time-resolved experiments.

Modeling diffuse scattering with simple, physically interpretable models.

Diffuse scattering has long been proposed to probe protein dynamics relevant for biological function, and more recently, as a tool to aid structure determination. Despite recent advances in measuring and modeling this signal, the field has not been able to routinely use experimental diffuse scattering for either application. A persistent challenge has been to devise models that are sophisticated enough to robustly reproduce experimental diffuse features but remain readily interpretable from the standpoint of structural biology. This chapter presents eryx, a suite of computational tools to evaluate the primary models of disorder that have been used to analyze protein diffuse scattering. By facilitating comparative modeling, eryx aims to provide insights into the physical origins of this signal and help identify the sources of disorder that are critical for reproducing experimental features. This framework also lays the groundwork for the development of more advanced models that integrate different types of disorder without loss of interpretability.

Structural insights into functional properties of the oxidized form of cytochrome c oxidase.

Cytochrome c oxidase (CcO) is an essential enzyme in mitochondrial and bacterial respiration. It catalyzes the four-electron reduction of molecular oxygen to water and harnesses the chemical energy to translocate four protons across biological membranes. The turnover of the CcO reaction involves an oxidative phase, in which the reduced enzyme (R) is oxidized to the metastable OH state, and a reductive phase, in which OH is reduced back to the R state. During each phase, two protons are translocated across the membrane. However, if OH is allowed to relax to the resting oxidized state (O), a redox equivalent to OH, its subsequent reduction to R is incapable of driving proton translocation. Here, with resonance Raman spectroscopy and serial femtosecond X-ray crystallography (SFX), we show that the heme a3 iron and CuB in the active site of the O state, like those in the OH state, are coordinated by a hydroxide ion and a water molecule, respectively. However, Y244, critical for the oxygen reduction chemistry, is in the neutral protonated form, which distinguishes O from OH, where Y244 is in the deprotonated tyrosinate form. These structural characteristics of O provide insights into the proton translocation mechanism of CcO.

Changes in an Enzyme Ensemble During Catalysis Observed by High Resolution XFEL Crystallography.

Enzymes populate ensembles of structures with intrinsically different catalytic proficiencies that are difficult to experimentally characterize. We use time-resolved mix-and-inject serial crystallography (MISC) at an X-ray free electron laser (XFEL) to observe catalysis in a designed mutant (G150T) isocyanide hydratase (ICH) enzyme that enhances sampling of important minor conformations. The active site exists in a mixture of conformations and formation of the thioimidate catalytic intermediate selects for catalytically competent substates. A prior proposal for active site cysteine charge-coupled conformational changes in ICH is validated by determining structures of the enzyme over a range of pH values. A combination of large molecular dynamics simulations of the enzyme in crystallo and time-resolved electron density maps shows that ionization of the general acid Asp17 during catalysis causes additional conformational changes that propagate across the dimer interface, connecting the two active sites. These ionization-linked changes in the ICH conformational ensemble permit water to enter the active site in a location that is poised for intermediate hydrolysis. ICH exhibits a tight coupling between ionization of active site residues and catalysis-activated protein motions, exemplifying a mechanism of electrostatic control of enzyme dynamics.

XFEL Microcrystallography of Self-Assembling Silver n-Alkanethiolates.

New synthetic hybrid materials and their increasing complexity have placed growing demands on crystal growth for single-crystal X-ray diffraction analysis. Unfortunately, not all chemical systems are conducive to the isolation of single crystals for traditional characterization. Here, small-molecule serial femtosecond crystallography (smSFX) at atomic resolution (0.833 Å) is employed to characterize microcrystalline silver n-alkanethiolates with various alkyl chain lengths at X-ray free electron laser facilities, resolving long-standing controversies regarding the atomic connectivity and odd-even effects of layer stacking. smSFX provides high-quality crystal structures directly from the powder of the true unknowns, a capability that is particularly useful for systems having notoriously small or defective crystals. We present crystal structures of silver n-butanethiolate (C4), silver n-hexanethiolate (C6), and silver n-nonanethiolate (C9). We show that an odd-even effect originates from the orientation of the terminal methyl group and its role in packing efficiency. We also propose a secondary odd-even effect involving multiple mosaic blocks in the crystals containing even-numbered chains, identified by selected-area electron diffraction measurements. We conclude with a discussion of the merits of the synthetic preparation for the preparation of microdiffraction specimens and compare the long-range order in these crystals to that of self-assembled monolayers.

RNA structures and dynamics with Å resolution revealed by x-ray free electron lasers.

RNA macromolecules, like proteins, fold to assume shapes that are intimately connected to their broadly recognized biological functions; however, because of their high charge and dynamic nature, RNA structures are far more challenging to determine. We introduce an approach that exploits the high brilliance of x-ray free electron laser sources to reveal the formation and ready identification of Å scale features in structured and unstructured RNAs. New structural signatures of RNA secondary and tertiary structures are identified through wide angle solution scattering experiments. With millisecond time resolution, we observe an RNA fold from a dynamically varying single strand through a base paired intermediate to assume a triple helix conformation. While the backbone orchestrates the folding, the final structure is locked in by base stacking. In addition to understanding how RNA triplexes form and thereby function as dynamic signaling elements, this new method can vastly increase the rate of structure determination for these biologically essential, but mostly uncharacterized macromolecules.

Structural basis for functional properties of cytochrome c oxidase.

Cytochrome c oxidase (CcO) is an essential enzyme in mitochondrial and bacterial respiration. It catalyzes the four-electron reduction of molecular oxygen to water and harnesses the chemical energy to translocate four protons across biological membranes, thereby establishing the proton gradient required for ATP synthesis1. The full turnover of the CcO reaction involves an oxidative phase, in which the reduced enzyme (R) is oxidized by molecular oxygen to the metastable oxidized OH state, and a reductive phase, in which OH is reduced back to the R state. During each of the two phases, two protons are translocated across the membranes2. However, if OH is allowed to relax to the resting oxidized state (O), a redox equivalent to OH, its subsequent reduction to R is incapable of driving proton translocation2,3. How the O state structurally differs from OH remains an enigma in modern bioenergetics. Here, with resonance Raman spectroscopy and serial femtosecond X-ray crystallography (SFX)4, we show that the heme a3 iron and CuB in the active site of the O state, like those in the OH state5,6, are coordinated by a hydroxide ion and a water molecule, respectively. However, Y244, a residue covalently linked to one of the three CuB ligands and critical for the oxygen reduction chemistry, is in the neutral protonated form, which distinguishes O from OH, where Y244 is in the deprotonated tyrosinate form. These structural characteristics of O provide new insights into the proton translocation mechanism of CcO.

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.

Electrically stimulated droplet injector for reduced sample consumption in serial crystallography.

With advances in X-ray free-electron lasers (XFELs), serial femtosecond crystallography (SFX) has enabled the static and dynamic structure determination for challenging proteins such as membrane protein complexes. In SFX with XFELs, the crystals are typically destroyed after interacting with a single XFEL pulse. Therefore, thousands of new crystals must be sequentially introduced into the X-ray beam to collect full data sets. Because of the serial nature of any SFX experiment, up to 99% of the sample delivered to the X-ray beam during its "off-time" between X-ray pulses is wasted due to the intrinsic pulsed nature of all current XFELs. To solve this major problem of large and often limiting sample consumption, we report on improvements of a revolutionary sample-saving method that is compatible with all current XFELs. We previously reported 3D-printed injection devices coupled with gas dynamic virtual nozzles (GDVNs) capable of generating samples containing droplets segmented by an immiscible oil phase for jetting crystal-laden droplets into the path of an XFEL. Here, we have further improved the device design by including metal electrodes inducing electrowetting effects for improved control over droplet generation frequency to stimulate the droplet release to matching the XFEL repetition rate by employing an electrical feedback mechanism. We report the improvements in this electrically triggered segmented flow approach for sample conservation in comparison with a continuous GDVN injection using the microcrystals of lysozyme and 3-deoxy-D-manno-octulosonate 8-phosphate synthase and report the segmented flow approach for sample injection applied at the Macromolecular Femtosecond Crystallography instrument at the Linear Coherent Light Source for the first time.

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.

Skopi: a simulation package for diffractive imaging of noncrystalline biomolecules.

X-ray free-electron lasers (XFELs) have the ability to produce ultra-bright femtosecond X-ray pulses for coherent diffraction imaging of biomolecules. While the development of methods and algorithms for macromolecular crystallography is now mature, XFEL experiments involving aerosolized or solvated biomolecular samples offer new challenges in terms of both experimental design and data processing. Skopi is a simulation package that can generate single-hit diffraction images for reconstruction algorithms, multi-hit diffraction images of aggregated particles for training machine learning classifiers using labeled data, diffraction images of randomly distributed particles for fluctuation X-ray scattering algorithms, and diffraction images of reference and target particles for holographic reconstruction algorithms. Skopi is a resource to aid feasibility studies and advance the development of algorithms for noncrystalline experiments at XFEL facilities.

Application of transport-based metric for continuous interpolation between cryo-EM density maps.

Cryogenic electron microscopy (cryo-EM) has become widely used for the past few years in structural biology, to collect single images of macromolecules "frozen in time". As this technique facilitates the identification of multiple conformational states adopted by the same molecule, a direct product of it is a set of 3D volumes, also called EM maps. To gain more insights on the possible mechanisms that govern transitions between different states, and hence the mode of action of a molecule, we recently introduced a bioinformatic tool that interpolates and generates morphing trajectories joining two given EM maps. This tool is based on recent advances made in optimal transport, that allow efficient evaluation of Wasserstein barycenters of 3D shapes. As the overall performance of the method depends on various key parameters, including the sensitivity of the regularization parameter, we performed various numerical experiments to demonstrate how MorphOT can be applied in different contexts and settings. Finally, we discuss current limitations and further potential connections between other optimal transport theories and the conformational heterogeneity problem inherent with cryo-EM data.

Protocol for structure determination of SARS-CoV-2 main protease at near-physiological-temperature by serial femtosecond crystallography.

The SARS-CoV-2 main protease of (Mpro) is an important target for SARS-CoV-2 related drug repurposing and development studies. Here, we describe the steps for structural characterization of SARS-CoV-2 Mpro, starting from plasmid preparation and protein purification. We detail the steps for crystallization using the sitting drop, microbatch (under oil) approach. Finally, we cover data collection and structure determination using serial femtosecond crystallography. For complete details on the use and execution of this protocol, please refer to Durdagi et al. (2021).

Cooperative allostery and structural dynamics of streptavidin at cryogenic- and ambient-temperature.

Multimeric protein assemblies are abundant in nature. Streptavidin is an attractive protein that provides a paradigm system to investigate the intra- and intermolecular interactions of multimeric protein complexes. Also, it offers a versatile tool for biotechnological applications. Here, we present two apo-streptavidin structures, the first one is an ambient temperature Serial Femtosecond X-ray crystal (Apo-SFX) structure at 1.7 Å resolution and the second one is a cryogenic crystal structure (Apo-Cryo) at 1.1 Å resolution. These structures are mostly in agreement with previous structural data. Combined with computational analysis, these structures provide invaluable information about structural dynamics of apo streptavidin. Collectively, these data further reveal a novel cooperative allostery of streptavidin which binds to substrate via water molecules that provide a polar interaction network and mimics the substrate biotin which displays one of the strongest affinities found in nature.

Chemical crystallography by serial femtosecond X-ray diffraction.

Inorganic-organic hybrid materials represent a large share of newly reported structures, owing to their simple synthetic routes and customizable properties1. This proliferation has led to a characterization bottleneck: many hybrid materials are obligate microcrystals with low symmetry and severe radiation sensitivity, interfering with the standard techniques of single-crystal X-ray diffraction2,3 and electron microdiffraction4-11. Here we demonstrate small-molecule serial femtosecond X-ray crystallography (smSFX) for the determination of material crystal structures from microcrystals. We subjected microcrystalline suspensions to X-ray free-electron laser radiation12,13 and obtained thousands of randomly oriented diffraction patterns. We determined unit cells by aggregating spot-finding results into high-resolution powder diffractograms. After indexing the sparse serial patterns by a graph theory approach14, the resulting datasets can be solved and refined using standard tools for single-crystal diffraction data15-17. We describe the ab initio structure solutions of mithrene (AgSePh)18-20, thiorene (AgSPh) and tethrene (AgTePh), of which the latter two were previously unknown structures. In thiorene, we identify a geometric change in the silver-silver bonding network that is linked to its divergent optoelectronic properties20. We demonstrate that smSFX can be applied as a general technique for structure determination of beam-sensitive microcrystalline materials at near-ambient temperature and pressure.

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.