Common lines modeling for reference free Ab-initio reconstruction in cryo-EM

Investigating the Balance between Structural Conservation and Functional Flexibility in Photosystem I

Photosynthesis, as the primary source of energy for all life forms, plays a crucial role in maintaining the global balance of energy, entropy, and enthalpy in living organisms. Among its various building blocks, photosystem I (PSI) is responsible for light-driven electron transfer, crucial for generating cellular reducing power. PSI acts as a light-driven plastocyanin-ferredoxin oxidoreductase and is situated in the thylakoid membranes of cyanobacteria and the chloroplasts of eukaryotic photosynthetic organisms. Comprehending the structure and function of the photosynthetic machinery is essential for understanding its mode of action. New insights are offered into the structure and function of PSI and its associated light-harvesting proteins, with a specific focus on the remarkable structural conservation of the core complex and high plasticity of the peripheral light-harvesting complexes.

Novel Artificial Intelligence-Based Approaches for Ab Initio Structure Determination and Atomic Model Building for Cryo-Electron Microscopy

Single particle cryo-electron microscopy (cryo-EM) has emerged as the prevailing method for near-atomic structure determination, shedding light on the important molecular mechanisms of biological macromolecules. However, the inherent dynamics and structural variability of biological complexes coupled with the large number of experimental images generated by a cryo-EM experiment make data processing nontrivial. In particular, ab initio reconstruction and atomic model building remain major bottlenecks that demand substantial computational resources and manual intervention. Approaches utilizing recent innovations in artificial intelligence (AI) technology, particularly deep learning, have the potential to overcome the limitations that cannot be adequately addressed by traditional image processing approaches. Here, we review newly proposed AI-based methods for ab initio volume generation, heterogeneous 3D reconstruction, and atomic model building. We highlight the advancements made by the implementation of AI methods, as well as discuss remaining limitations and areas for future development.

CryoEM PSII structure reveals adaptation mechanisms to environmental stress in Chlorella ohadii

Performing photosynthesis in the desert is a challenging task since it requires a fast adaptation to extreme illumination and temperature changes. To understand adaptive mechanisms, we purified Photosystem II (PSII) from Chlorella ohadii , a green alga from the desert soil surface, and identified structural elements that might enable the photosystem functioning under harsh conditions. The 2.72 Å cryogenic electron-microscopy (cryoEM) structure of PSII exhibited 64 subunits, encompassing 386 chlorophylls, 86 carotenoids, four plastoquinones, and several structural lipids. At the luminal side of PSII, the oxygen evolving complex was protected by a unique subunit arrangement - PsbO (OEE1), PsbP (OEE2), CP47, and PsbU (plant OEE3 homolog). PsbU interacted with PsbO, CP43, and PsbP, thus stabilising the oxygen evolving shield. Substantial changes were observed on the stromal electron acceptor side - PsbY was identified as a transmembrane helix situated alongside PsbF and PsbE enclosing cytochrome b559, supported by the adjacent C-terminal helix of Psb10. These four transmembrane helices bundled jointly, shielding cytochrome b559 from the solvent. The bulk of Psb10 formed a cap protecting the quinone site and probably contributed to the PSII stacking. So far, the C. ohadii PSII structure is the most complete description of the complex, suggesting numerous future experiments. A protective mechanism that prevented Q B from rendering itself fully reduced is proposed.

Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms

The number of noisy images required for molecular reconstruction in single-particle cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed, randomly oriented, noisy projection images. In this work, we consider the effect of imposing sparsity priors on the molecule. We use techniques from signal processing, optimization, and applied algebraic geometry to obtain theoretical and computational contributions for this challenging nonlinear inverse problem with sparsity constraints. We prove that molecular structures modeled as sums of Gaussians are uniquely determined by the second-order autocorrelation of their projection images, implying that the sample complexity is proportional to the square of the variance of the noise. This theory improves upon the nonsparse case, where the third-order autocorrelation is required for uniformly oriented particle images and the sample complexity scales with the cube of the noise variance. Furthermore, we build a computational framework to reconstruct molecular structures which are sparse in the wavelet basis. This method combines the sparse representation for the molecule with projection-based techniques used for phase retrieval in X-ray crystallography.

Signal enhancement for two-dimensional cryo-EM data processing

Different tasks in the computational pipeline of single-particle cryo-electron microscopy (cryo-EM) require enhancing the quality of the highly noisy raw images. To this end, we develop an efficient algorithm for signal enhancement of cryo-EM images. The enhanced images can be used for a variety of downstream tasks, such as two-dimensional classification, removing uninformative images, constructing ab initio models, generating templates for particle picking, providing a quick assessment of the data set, dimensionality reduction, and symmetry detection. The algorithm includes built-in quality measures to assess its performance and alleviate the risk of model bias. We demonstrate the effectiveness of the proposed algorithm on several experimental data sets. In particular, we show that the quality of the resulting images is high enough to produce ab initio models of Å resolution. The algorithm is accompanied by a publicly available, documented, and easy-to-use code.

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.

3D reconstruction from cryo-EM projection images using two spherical embeddings

Single-particle analysis (SPA) in cryo-electron microscopy has become a powerful tool for determining and studying the macromolecular structure at an atomic level. However, since the SPA problem is a non-convex optimization problem with enormous search space and there is high level of noise in the input images, the existing methods may produce biased or even wrong final models. In this work, to deal with the problem, consistent constraints from the input data are explored in an embedding space, a 3D spherical surface. More specifically, the orientation of a projection image is represented by two intersection points of the normal vector and the local X-axis vector of the projection image on the unit spherical surface. To determine the orientations of the projection images, the global consistency constraints of the relative orientations of all the projection images are satisfied by two spherical embeddings which estimate the normal vectors and the local X-axis vectors of the projection images respectively. Compared to the traditional methods, the proposed method is shown to be able to rectify the initial computation errors and produce a more accurate estimation of the projection angles, which results in a better final model reconstruction from the noisy image data.

A 3D reconstruction method using two spherical embeddings to resolve projection angles of the cryo-EM images is shown to improve the initial model reconstruction for single-particle analysis.

End-to-end orientation estimation from 2D cryo-EM images

Cryo-electron microscopy (cryo-EM) is a Nobel Prize-winning technique for determining high-resolution 3D structures of biological macromolecules. A 3D structure is reconstructed from hundreds of thousands of noisy 2D projection images. However, existing 3D reconstruction methods are still time-consuming, and one of the major computational bottlenecks is recovering the unknown orientation of the particle in each 2D image. The dominant methods typically exploit an expensive global search on each image to estimate the missing orientations. Here, a novel end-to-end supervised learning method is introduced to directly recover the missing orientations from 2D cryo-EM images. A neural network is used to approximate the mapping from images to orientations. A robust loss function is proposed for optimizing the parameters of the network, which can handle both asymmetric and symmetric 3D structures. Experiments on synthetic data sets with various symmetry types confirm that the neural network is capable of recovering orientations from 2D cryo-EM images, and the results on a real cryo-EM data set further demonstrate its potential under more challenging imaging conditions.

Cryo-EM photosystem I structure reveals adaptation mechanisms to extreme high light in Chlorella ohadii

Photosynthesis in deserts is challenging since it requires fast adaptation to rapid night-to-day changes, that is, from dawn's low light (LL) to extreme high light (HL) intensities during the daytime. To understand these adaptation mechanisms, we purified photosystem I (PSI) from Chlorella ohadii, a green alga that was isolated from a desert soil crust, and identified the essential functional and structural changes that enable the photosystem to perform photosynthesis under extreme high light conditions. The cryo-electron microscopy structures of PSI from cells grown under low light (PSI_LL) and high light (PSI_HL), obtained at 2.70 and 2.71 Å, respectively, show that part of light-harvesting antenna complex I (LHCI) and the core complex subunit (PsaO) are eliminated from PSI_HL to minimize the photodamage. An additional change is in the pigment composition and their number in LHCI_HL; about 50% of chlorophyll b is replaced by chlorophyll a. This leads to higher electron transfer rates in PSI_HL and might enable C. ohadii PSI to act as a natural photosynthesiser in photobiocatalytic systems. PSI_HL or PSI_LL were attached to an electrode and their induced photocurrent was determined. To obtain photocurrents comparable with PSI_HL, 25 times the amount of PSI_LL was required, demonstrating the high efficiency of PSI_HL. Hence, we suggest that C. ohadii PSI_HL is an ideal candidate for the design of desert artificial photobiocatalytic systems.

Plankton reconstruction through robust statistical optical tomography

Plankton interact with the environment according to their size and three-dimensional (3D) structure. To study them outdoors, these translucent specimens are imaged in situ. Light projects through a specimen in each image. The specimen has a random scale, drawn from the population's size distribution and random unknown pose. The specimen appears only once before drifting away. We achieve 3D tomography using such a random ensemble to statistically estimate an average volumetric distribution of the plankton type and specimen size. To counter errors due to non-rigid deformations, we weight the data, drawing from advanced models developed for cryo-electron microscopy. The weights convey the confidence in the quality of each datum. This confidence relies on a statistical error model. We demonstrate the approach on live plankton using an underwater field microscope.

Structure and energy transfer pathways of the Dunaliella Salina photosystem I supercomplex

Oxygenic photosynthesis evolved more than 3 billion years ago in cyanobacteria. The increased complexity of photosystem I (PSI) became apparent from the high-resolution structures that were obtained for the complexes that were isolated from various organisms, ranging from cyanobacteria to plants. These complexes are all evolutionarily linked. In this paper, the researchers have uncovered the increased complexity of PSI in a single organism demonstrated by the coexistance of two distinct PSI compositions. The Large Dunaliella PSI contains eight additional subunits, six in PSI core and two light harvesting complexes. Two additional chlorophyll a molecules pertinent for efficient excitation energy transfer in state II transition were identified in PsaL and PsaO. Short distances between these newly identified chlorophylls correspond with fast excitation transfer rates previously reported during state II transition. The apparent PSI conformations could be a coping mechanism for the high salinity.

Single-particle cryo-electron microscopy: Mathematical theory, computational challenges, and opportunities

In recent years, an abundance of new molecular structures have been elucidated using cryo-electron microscopy (cryo-EM), largely due to advances in hardware technology and data processing techniques. Owing to these new exciting developments, cryo-EM was selected by Nature Methods as Method of the Year 2015, and the Nobel Prize in Chemistry 2017 was awarded to three pioneers in the field. The main goal of this article is to introduce the challenging and exciting computational tasks involved in reconstructing 3-D molecular structures by cryo-EM. Determining molecular structures requires a wide range of computational tools in a variety of fields, including signal processing, estimation and detection theory, high-dimensional statistics, convex and non-convex optimization, spectral algorithms, dimensionality reduction, and machine learning. The tools from these fields must be adapted to work under exceptionally challenging conditions, including extreme noise levels, the presence of missing data, and massively large datasets as large as several Terabytes. In addition, we present two statistical models: multi-reference alignment and multi-target detection, that abstract away much of the intricacies of cryo-EM, while retaining some of its essential features. Based on these abstractions, we discuss some recent intriguing results in the mathematical theory of cryo-EM, and delineate relations with group theory, invariant theory, and information theory.

Advances in image processing for single-particle analysis by electron cryomicroscopy and challenges ahead

Electron cryomicroscopy (cryoEM) is essential for the study and functional understanding of non-crystalline macromolecules such as proteins. These molecules cannot be imaged using X-ray crystallography or other popular methods. CryoEM has been successfully used to visualize macromolecular complexes such as ribosomes, viruses, and ion channels. Determination of structural models of these at various conformational states leads to insight on how these molecules function. Recent advances in imaging technology have given cryoEM a scientific rebirth. As a result of these technological advances image processing and analysis have yielded molecular structures at atomic resolution. Nevertheless there continue to be challenges in image processing, and in this article we will touch on the most essential in order to derive an accurate three-dimensional model from noisy projection images. Traditional approaches, such as k-means clustering for class averaging, will be provided as background. We will then highlight new approaches for each image processing subproblem, including a 3D reconstruction method for asymmetric molecules using just two projection images and deep learning algorithms for automated particle picking.