Data-guided Multi-Map variables for ensemble refinement of molecular movies

Adaptive Ensemble Refinement of Protein Structures in High Resolution Electron Microscopy Density Maps with Radical Augmented Molecular Dynamics Flexible Fitting

Recent advances in cryo-electron microscopy (cryo-EM) have enabled modeling macromolecular complexes that are essential components of the cellular machinery. The density maps derived from cryo-EM experiments are often integrated with manual, knowledge-driven or artificial intelligence-driven and physics-guided computational methods to build, fit, and refine molecular structures. Going beyond a single stationary-structure determination scheme, it is becoming more common to interpret the experimental data with an ensemble of models that contributes to an average observation. Hence, there is a need to decide on the quality of an ensemble of protein structures on-the-fly while refining them against the density maps. We introduce such an adaptive decision-making scheme during the molecular dynamics flexible fitting (MDFF) of biomolecules. Using RADICAL-Cybertools, the new RADICAL augmented MDFF implementation (R-MDFF) is examined in high-performance computing environments for refinement of two prototypical protein systems, adenylate kinase and carbon monoxide dehydrogenase. For these test cases, use of multiple replicas in flexible fitting with adaptive decision making in R-MDFF improves the overall correlation to the density by 40% relative to the refinements of the brute-force MDFF. The improvements are particularly significant at high, 2-3 Å map resolutions. More importantly, the ensemble model captures key features of biologically relevant molecular dynamics that are inaccessible to a single-model interpretation. Finally, the pipeline is applicable to systems of growing sizes, which is demonstrated using ensemble refinement of capsid proteins from the chimpanzee adenovirus. The overhead for decision making remains low and robust to computing environments. The software is publicly available on GitHub and includes a short user guide to install R-MDFF on different computing environments, from local Linux-based workstations to high-performance computing environments.

LongBondEliminator: A Molecular Simulation Tool to Remove Ring Penetrations in Biomolecular Simulation Systems

We develop a workflow, implemented as a plugin to the molecular visualization program VMD, that can fix ring penetrations with minimal user input. LongBondEliminator, detects ring piercing artifacts by the long, strained bonds that are the local minimum energy conformation during minimization for some assembled simulation system. The LongBondEliminator tool then automatically treats regions near these long bonds using multiple biases applied through NAMD. By combining biases implemented through the collective variables module, density-based forces, and alchemical techniques in NAMD, LongBondEliminator will iteratively alleviate long bonds found within molecular simulation systems. Through three concrete examples with increasing complexity, a lignin polymer, an viral capsid assembly, and a large, highly glycosylated protein aggrecan, we demonstrate the utility for this method in eliminating ring penetrations from classical MD simulation systems. The tool is available via gitlab as a VMD plugin, and has been developed to be generically useful across a variety of biomolecular simulations.

Progressive assembly of multi-domain protein structures from cryo-EM density maps

Progress in cryo-electron microscopy has provided the potential for large-size protein structure determination. However, the success rate for solving multi-domain proteins remains low because of the difficulty in modelling inter-domain orientations. Here we developed domain enhanced modeling using cryo-electron microscopy (DEMO-EM), an automatic method to assemble multi-domain structures from cryo-electron microscopy maps through a progressive structural refinement procedure combining rigid-body domain fitting and flexible assembly simulations with deep-neural-network inter-domain distance profiles. The method was tested on a large-scale benchmark set of proteins containing up to 12 continuous and discontinuous domains with medium- to low-resolution density maps, where DEMO-EM produced models with correct inter-domain orientations (template modeling score (TM-score) >0.5) for 97% of cases and outperformed state-of-the-art methods. DEMO-EM was applied to the severe acute respiratory syndrome coronavirus 2 genome and generated models with average TM-score and root-mean-square deviation of 0.97 and 1.3 Å, respectively, with respect to the deposited structures. These results demonstrate an efficient pipeline that enables automated and reliable large-scale multi-domain protein structure modelling from cryo-electron microscopy maps.

Energy landscape of the SARS-CoV-2 reveals extensive conformational heterogeneity

Cryo-electron microscopy (cryo-EM) has produced a number of structural models of the SARS-CoV-2 spike, already prompting biomedical outcomes. However, these reported models and their associated electrostatic potential maps represent an unknown admixture of conformations stemming from the underlying energy landscape of the spike protein. As with any protein, some of the spike's conformational motions are expected to be biophysically relevant, but cannot be interpreted only by static models. Using experimental cryo-EM images, we present the energy landscape of the glycosylated spike protein, and identify the diversity of low-energy conformations in the vicinity of its open (so called 1RBD-up) state. The resulting atomic refinement reveal global and local molecular rearrangements that cannot be inferred from an average 1RBD-up cryo-EM model. Here we report varied degrees of "openness" in global conformations of the 1RBD-up state, not revealed in the single-model interpretations of the density maps, together with conformations that overlap with the reported models. We discover how the glycan shield contributes to the stability of these low-energy conformations. Five out of six binding sites we analyzed, including those for engaging ACE2, therapeutic mini-proteins, linoleic acid, two different kinds of antibodies, switch conformations between their known apo- and holo-conformations, even when the global spike conformation is 1RBD-up. This apo-to-holo switching is reminiscent of a conformational preequilibrium. We found only one binding site, namely that of AB-C135 remains in apo state within all the sampled free energy-minimizing models, suggesting an induced fit mechanism for the docking of this antibody to the spike.

Exploring cryo-electron microscopy with molecular dynamics

Single particle analysis cryo-electron microscopy (EM) and molecular dynamics (MD) have been complimentary methods since cryo-EM was first applied to the field of structural biology. The relationship started by biasing structural models to fit low-resolution cryo-EM maps of large macromolecular complexes not amenable to crystallization. The connection between cryo-EM and MD evolved as cryo-EM maps improved in resolution, allowing advanced sampling algorithms to simultaneously refine backbone and sidechains. Moving beyond a single static snapshot, modern inferencing approaches integrate cryo-EM and MD to generate structural ensembles from cryo-EM map data or directly from the particle images themselves. We summarize the recent history of MD innovations in the area of cryo-EM modeling. The merits for the myriad of MD based cryo-EM modeling methods are discussed, as well as, the discoveries that were made possible by the integration of molecular modeling with cryo-EM. Lastly, current challenges and potential opportunities are reviewed.

Kinematic Reconstruction of Cyclic Peptides and Protein Backbones from Partial Data

We present an algorithm, QBKR (Quaternary Backbone Kinematic Reconstruction), a fast analytical method for an all-atom backbone reconstruction of proteins and linear or cyclic peptide chains from C_α coordinate traces. Unlike previous analytical methods for deriving all-atom representations from coarse-grained models that rely on canonical geometry with planar peptides in the trans conformation, our de novo kinematic model incorporates noncanonical, cis-trans, geometry naturally. Perturbations to this geometry can be effected with ease in our formulation, for example, to account for a continuous change from cis to trans geometry. A simple optimization of a spring-based objective function is employed for C_α-C_α distance variations that extend beyond the cis-trans limit. The kinematic construction produces a linked chain of peptide units, C_α-C-N-C_α, hinged at the C_α atoms spanning all possible planar and nonplanar peptide conformations. We have combined our method with a ring closure algorithm for the case of ring peptides and missing loops in a protein structure. Here, the reconstruction proceeding from both the N and C termini of the protein backbone (or in both directions from a starting position for rings) requires freedom in the position of one C_α atom (a capstone) to achieve a successful loop or ring closure. A salient feature of our reconstruction method is the ability to enrich conformational ensembles to produce alternative feasible conformations in which H-bond forming C-O or N-H pairs in the backbone can reverse orientations, thus addressing a well-known shortcoming in C_α-based RMSD structure comparison, wherein very close structures may lead to significantly different overall H-bond behavior. We apply the fixed C_α-based design to the reverse reconstruction from noisy Cryo-EM data, a posteriori to the optimization. Our method can be applied to speed up the process of an all-atom description from voluminous experimental data or subpar electron density maps.

CryoFold: determining protein structures and data-guided ensembles from cryo-EM density maps

Cryo-electron microscopy (EM) requires molecular modeling to refine structural details from data. Ensemble models arrive at low free-energy molecular structures, but are computationally expensive and limited to resolving only small proteins that cannot be resolved by cryo-EM. Here, we introduce CryoFold - a pipeline of molecular dynamics simulations that determines ensembles of protein structures directly from sequence by integrating density data of varying sparsity at 3-5 Å resolution with coarse-grained topological knowledge of the protein folds. We present six examples showing its broad applicability for folding proteins between 72 to 2000 residues, including large membrane and multi-domain systems, and results from two EMDB competitions. Driven by data from a single state, CryoFold discovers ensembles of common low-energy models together with rare low-probability structures that capture the equilibrium distribution of proteins constrained by the density maps. Many of these conformations, unseen by traditional methods, are experimentally validated and functionally relevant. We arrive at a set of best practices for data-guided protein folding that are controlled using a Python GUI.

A Bayesian approach to extracting free-energy profiles from cryo-electron microscopy experiments

Cryo-electron microscopy (cryo-EM) extracts single-particle density projections of individual biomolecules. Although cryo-EM is widely used for 3D reconstruction, due to its single-particle nature it has the potential to provide information about a biomolecule's conformational variability and underlying free-energy landscape. However, treating cryo-EM as a single-molecule technique is challenging because of the low signal-to-noise ratio (SNR) in individual particles. In this work, we propose the cryo-BIFE method (cryo-EM Bayesian Inference of Free-Energy profiles), which uses a path collective variable to extract free-energy profiles and their uncertainties from cryo-EM images. We test the framework on several synthetic systems where the imaging parameters and conditions were controlled. We found that for realistic cryo-EM environments and relevant biomolecular systems, it is possible to recover the underlying free energy, with the pose accuracy and SNR as crucial determinants. We then use the method to study the conformational transitions of a calcium-activated channel with real cryo-EM particles. Interestingly, we recover not only the most probable conformation (used to generate a high-resolution reconstruction of the calcium-bound state) but also a metastable state that corresponds to the calcium-unbound conformation. As expected for turnover transitions within the same sample, the activation barriers are on the order of [Formula: see text]. We expect our tool for extracting free-energy profiles from cryo-EM images to enable more complete characterization of the thermodynamic ensemble of biomolecules.

Energy Landscape of the SARS-CoV-2 Reveals Extensive Conformational Heterogeneity

Cryo-electron microscopy (cryo-EM) has produced a number of structural models of the SARS-CoV-2 spike, already prompting biomedical outcomes. However, these reported models and their associated electrostatic potential maps represent an unknown admixture of conformations stemming from the underlying energy landscape of the spike protein. As for any protein, some of the spike's conformational motions are expected to be biophysically relevant, but cannot be interpreted only by static models. Using experimental cryo-EM images, we present the energy landscape of the spike protein conformations, and identify molecular rearrangements along the most-likely conformational path in the vicinity of the open (so called 1RBD-up) state. The resulting global and local atomic refinements reveal larger movements than those expected by comparing the reported 1RBD-up and 1RBD-down cryo-EM models. Here we report greater degrees of "openness" in global conformations of the 1RBD-up state, not revealed in the single-model interpretations of the density maps, together with conformations that overlap with the reported models. We discover how the glycan shield contributes to the stability of these conformations along the minimum free-energy pathway. A local analysis of seven key binding pockets reveals that six out them, including those for engaging ACE2, therapeutic mini-proteins, linoleic acid, two different kinds of antibodies, and protein-glycan interaction sites, switch conformations between their known apo- and holo-conformations, even when the global spike conformation is 1RBD-up. This is reminiscent of a conformational pre-equilibrium. We found only one binding pocket, namely antibody AB-C135 to remain closed along the entire minimum free energy path, suggesting an induced fit mechanism for this enzyme.

Molecular Dynamics to Predict Cryo-EM: Capturing Transitions and Short-Lived Conformational States of Biomolecules

Single-particle cryogenic electron microscopy (cryo-EM) has revolutionized the field of the structural biology, providing an access to the atomic resolution structures of large biomolecular complexes in their near-native environment. Today's cryo-EM maps can frequently reach the atomic-level resolution, while often containing a range of resolutions, with conformationally variable regions obtained at 6 Å or worse. Low resolution density maps obtained for protein flexible domains, as well as the ensemble of coexisting conformational states arising from cryo-EM, poses new challenges and opportunities for Molecular Dynamics (MD) simulations. With the ability to describe the biomolecular dynamics at the atomic level, MD can extend the capabilities of cryo-EM, capturing the conformational variability and predicting biologically relevant short-lived conformational states. Here, we report about the state-of-the-art MD procedures that are currently used to refine, reconstruct and interpret cryo-EM maps. We show the capability of MD to predict short-lived conformational states, finding remarkable confirmation by cryo-EM structures subsequently solved. This has been the case of the CRISPR-Cas9 genome editing machinery, whose catalytically active structure has been predicted through both long-time scale MD and enhanced sampling techniques 2 years earlier than cryo-EM. In summary, this contribution remarks the ability of MD to complement cryo-EM, describing conformational landscapes and relating structural transitions to function, ultimately discerning relevant short-lived conformational states and providing mechanistic knowledge of biological function.

Protein Conformational States-A First Principles Bayesian Method

Automated identification of protein conformational states from simulation of an ensemble of structures is a hard problem because it requires teaching a computer to recognize shapes. We adapt the naïve Bayes classifier from the machine learning community for use on atom-to-atom pairwise contacts. The result is an unsupervised learning algorithm that samples a ‘distribution’ over potential classification schemes. We apply the classifier to a series of test structures and one real protein, showing that it identifies the conformational transition with >95% accuracy in most cases. A nontrivial feature of our adaptation is a new connection to information entropy that allows us to vary the level of structural detail without spoiling the categorization. This is confirmed by comparing results as the number of atoms and time-samples are varied over 1.5 orders of magnitude. Further, the method’s derivation from Bayesian analysis on the set of inter-atomic contacts makes it easy to understand and extend to more complex cases.