Final Report - Tensor Core Based Algorithms For Cryo Electron Microscopy
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Guo, Yirui↗
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The role of CenKR in the coordination of Rhodobacter sphaeroides cell elongation and division
ABSTRACT Cell elongation and division are essential aspects of the bacterial life cycle that must be coordinated for viability and replication. The impact of misregulation of these processes is not well understood as these systems are often not amenable to traditional genetic manipulation. Recently, we reported on the CenKR two-component system (TCS) in the Gram-negative bacterium Rhodobacter sphaeroides that is genetically tractable, widely conserved in α-proteobacteria, and directly regulates the expression of components crucial for cell elongation and division, including genes encoding subunit of the Tol-Pal complex. In this work, we show that overexpression of cenK results in cell filamentation and chaining. Using cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET), we generated high-resolution two-dimensional (2D) images and three-dimensional (3D) volumes of the cell envelope and division septum of wild-type cells and a cenK overexpression strain finding that these morphological changes stem from defects in outer membrane (OM) and peptidoglycan (PG) constriction. By monitoring the localization of Pal, PG biosynthesis, and the bacterial cytoskeletal proteins MreB and FtsZ, we developed a model for how increased CenKR activity leads to changes in cell elongation and division. This model predicts that increased CenKR activity decreases the mobility of Pal, delaying OM constriction, and ultimately disrupting the midcell positioning of MreB and FtsZ and interfering with the spatial regulation of PG synthesis and remodeling. IMPORTANCE By coordinating cell elongation and division, bacteria maintain their shape, support critical envelope functions, and orchestrate division. Regulatory and assembly systems have been implicated in these processes in some well-studied Gram-negative bacteria. However, we lack information on these processes and their conservation across the bacterial phylogeny. In R. sphaeroides and other α-proteobacteria, CenKR is an essential two-component system (TCS) that regulates the expression of genes known or predicted to function in cell envelope biosynthesis, elongation, and/or division. Here, we leverage unique features of CenKR to understand how increasing its activity impacts cell elongation/division and use antibiotics to identify how modulating the activity of this TCS leads to changes in cell morphology. Our results provide new insight into how CenKR activity controls the structure and function of the bacterial envelope, the localization of cell elongation and division machinery, and cellular processes in organisms with importance in health, host-microbe interactions, and biotechnology.
59 BASIC BIOLOGICAL SCIENCES↗
Structural basis of the American mink ACE2 binding by Y453F trimeric spike glycoproteins of SARS‐CoV‐2
Abstract Severe Acute Respiratory Syndrome Coronavirus 2 (SARS‐CoV‐2) enters the host cell by binding to angiotensin‐converting enzyme 2 (ACE2). While evolutionarily conserved, ACE2 receptors differ across various species and differential interactions with Spike (S) glycoproteins of SARS‐CoV‐2 viruses impact species specificity. Reverse zoonoses led to SARS‐CoV‐2 outbreaks on multiple American mink (Mustela vison) farms during the pandemic and gave rise to mink‐associated S substitutions known for transmissibility between mink and zoonotic transmission to humans. In this study, we used bio‐layer interferometry (BLI) to discern the differences in binding affinity between multiple human and mink‐derived S glycoproteins of SARS‐CoV‐2 and their respective ACE2 receptors. Further, we conducted a structural analysis of a mink variant S glycoprotein and American mink ACE2 (mvACE2) using cryo‐electron microscopy (cryo‐EM), revealing four distinct conformations. We discovered a novel intermediary conformation where the mvACE2 receptor is bound to the receptor‐binding domain (RBD) of the S glycoprotein in a “down” position, approximately 34° lower than previously reported “up” RBD. Finally, we compared residue interactions in the S‐ACE2 complex interface of S glycoprotein conformations with varying RBD orientations. These findings provide valuable insights into the molecular mechanisms of SARS‐CoV‐2 entry.
Virology↗
X‐ray scattering reveals disordered linkers and dynamic interfaces in complexes and mechanisms for DNA double‐strand break repair impacting cell and cancer biology
Abstract Evolutionary selection ensures specificity and efficiency in dynamic metastable macromolecular machines that repair DNA damage without releasing toxic and mutagenic intermediates. Here we examine non‐homologous end joining (NHEJ) as the primary conserved DNA double‐strand break (DSB) repair process in human cells. NHEJ has exemplary key roles in networks determining the development, outcome of cancer treatments by DSB‐inducing agents, generation of antibody and T‐cell receptor diversity, and innate immune response for RNA viruses. We determine mechanistic insights into NHEJ structural biochemistry focusing upon advanced small angle X‐ray scattering (SAXS) results combined with X‐ray crystallography (MX) and cryo‐electron microscopy (cryo‐EM). SAXS coupled to atomic structures enables integrated structural biology for objective quantitative assessment of conformational ensembles and assemblies in solution, intra‐molecular distances, structural similarity, functional disorder, conformational switching, and flexibility. Importantly, NHEJ complexes in solution undergo larger allosteric transitions than seen in their cryo‐EM or MX structures. In the long‐range synaptic complex, X‐ray repair cross‐complementing 4 (XRCC4) plus XRCC4‐like‐factor (XLF) form a flexible bridge and linchpin for DNA ends bound to KU heterodimer (Ku70/80) and DNA‐PKcs (DNA‐dependent protein kinase catalytic subunit). Upon binding two DNA ends, auto‐phosphorylation opens DNA‐PKcs dimer licensing NHEJ via concerted conformational transformations of XLF‐XRCC4, XLF–Ku80, and LigIV BRCT –Ku70 interfaces. Integrated structures reveal multifunctional roles for disordered linkers and modular dynamic interfaces promoting DSB end processing and alignment into the short‐range complex for ligation by LigIV. Integrated findings define dynamic assemblies fundamental to designing separation‐of‐function mutants and allosteric inhibitors targeting conformational transitions in multifunctional complexes.
59 BASIC BIOLOGICAL SCIENCES↗
Structural bases for stoichiometry‐selective calcium potentiation of a neuronal nicotinic receptor
Background and Purpose α4β2 nicotinic acetylcholine (nACh) receptors assemble in two stoichiometric forms, one of which is potentiated by calcium. The sites of calcium binding that underpin potentiation are not known. Experimental Approach To identify calcium binding sites, we applied cryo‐electron microscopy (cryo‐EM) and molecular dynamics (MD) simulations to each stoichiometric form of the α4β2 nACh receptor in the presence of calcium ions. To test whether the identified calcium sites are linked to potentiation, we generated mutants of anionic residues at the sites, expressed wild type and mutant receptors in clonal mammalian fibroblasts, and recorded ACh‐elicited single‐channel currents with or without calcium. Key Results Both cryo‐EM and MD simulations show calcium bound to a site between the extracellular and transmembrane domains of each α4 subunit (ECD‐TMD site). Substituting alanine for anionic residues at the ECD‐TMD site abolishes stoichiometry‐selective calcium potentiation, as monitored by single‐channel patch clamp electrophysiology. Additionally, MD simulation reveals calcium association at subunit interfaces within the extracellular domain. Substituting alanine for anionic residues at the ECD sites reduces or abolishes stoichiometry‐selective calcium potentiation. Conclusions and Implications Stoichiometry‐selective calcium potentiation of the α4β2 nACh receptor is achieved by calcium association with topographically distinct sites framed by anionic residues within the α4 subunit and between the α4 and β2 subunits. Stoichiometry‐selective calcium potentiation could result from the greater number of calcium sites in the stoichiometric form with three rather than two α4 subunits. The results are relevant to modulation of signalling via α4β2 nACh receptors in physiological and pathophysiological conditions.
Pharmacology & Pharmacy↗
Preparing Lamellae from Vitreous Biological Samples using a Dual-Beam Scanning Electron Microscope for Cryo-Electron Tomography
Presented here is a protocol for preparing cryo-lamellae from plunge-frozen grids of Plasmodium falciparum-infected human erythrocytes, which could easily be adapted for other biological samples. The basic principles for preparing samples, milling, and viewing lamellae are common to all instruments and the protocol can be followed as a general guide to on-grid cryo-lamella preparation for cryo-electron microscopy (cryoEM) and cryo-electron tomography (cryoET). Electron microscopy grids supporting the cells are plunge-frozen into liquid nitrogen-cooled liquid ethane using a manual or automated plunge freezer, then screened on a light microscope equipped with a cryo-stage. Frozen grids are transferred into a cryo-scanning electron microscope equipped with a focused ion beam (cryoFIB-SEM). Grids are routinely sputter coated prior to milling, which aids dispersal of charge build-up during milling. Alternatively, an e-beam rotary coater can be used to apply a layer of carbon-platinum to the grids, the exact thickness of which can be more precisely controlled. Once inside the cryoFIB-SEM an additional coating of an organoplatinum compound is applied to the surface of the grid via a gas injection system (GIS). This layer protects the front edge of the lamella as it is milled, the integrity of which is critical for achieving uniformly thin lamellae. Regions of interest are identified via SEM and milling is carried out in a step-wise fashion, reducing the current of the ion beam as the lamella reaches electron transparency, in order to avoid excessive heat generation. A grid with multiple lamellae is then transferred to a transmission electron microscope (TEM) under cryogenic conditions for tilt-series acquisition. A robust and contamination-free workflow for lamella preparation is an essential step for downstream techniques, including cellular cryoEM, cryoET, and sub-tomogram averaging. Development of these techniques, especially for lift-out and milling of high-pressure frozen samples, is of high-priority in the field.
59 BASIC BIOLOGICAL SCIENCES↗
Structures of the mycobacterial membrane protein MmpL3 reveal its mechanism of lipid transport
The mycobacterial membrane protein large 3 (MmpL3) transporter is essential and required for shuttling the lipid trehalose monomycolate (TMM), a precursor of mycolic acid (MA)-containing trehalose dimycolate (TDM) and mycolyl arabinogalactan peptidoglycan (mAGP), in Mycobacterium species, including Mycobacterium tuberculosis and Mycobacterium smegmatis. However, the mechanism that MmpL3 uses to facilitate the transport of fatty acids and lipidic elements to the mycobacterial cell wall remains elusive. Here, we report 7 structures of the M. smegmatis MmpL3 transporter in its unbound state and in complex with trehalose 6-decanoate (T6D) or TMM using single-particle cryo-electron microscopy (cryo-EM) and X-ray crystallography. Combined with calculated results from molecular dynamics (MD) and target MD simulations, we reveal a lipid transport mechanism that involves a coupled movement of the periplasmic domain and transmembrane helices of the MmpL3 transporter that facilitates the shuttling of lipids to the mycobacterial cell wall.
60 APPLIED LIFE SCIENCES↗
Structural analyses of the PKA RIIβ holoenzyme containing the oncogenic DnaJB1-PKAc fusion protein reveal protomer asymmetry and fusion-induced allosteric perturbations in fibrolamellar hepatocellular carcinoma
When the J-domain of the heat shock protein DnaJB1 is fused to the catalytic (C) subunit of cAMP-dependent protein kinase (PKA), replacing exon 1, this fusion protein, J-C subunit (J-C), becomes the driver of fibrolamellar hepatocellular carcinoma (FL-HCC). Here, we use cryo-electron microscopy (cryo-EM) to characterize J-C bound to RIIβ, the major PKA regulatory (R) subunit in liver, thus reporting the first cryo-EM structure of any PKA holoenzyme. We report several differences in both structure and dynamics that could not be captured by the conventional crystallography approaches used to obtain prior structures. Most striking is the asymmetry caused by the absence of the second cyclic nucleotide binding (CNB) domain and the J-domain in one of the RIIβ:J-C protomers. Using molecular dynamics (MD) simulations, we discovered that this asymmetry is already present in the wild-type (WT) RIIβ 2 C 2 but had been masked in the previous crystal structure. This asymmetry may link to the intrinsic allosteric regulation of all PKA holoenzymes and could also explain why most disease mutations in PKA regulatory subunits are dominant negative. The cryo-EM structure, combined with small-angle X-ray scattering (SAXS), also allowed us to predict the general position of the Dimerization/Docking (D/D) domain, which is essential for localization and interacting with membrane-anchored A-Kinase-Anchoring Proteins (AKAPs). This position provides a multivalent mechanism for interaction of the RIIβ holoenzyme with membranes and would be perturbed in the oncogenic fusion protein. The J-domain also alters several biochemical properties of the RIIβ holoenzyme: It is easier to activate with cAMP, and the cooperativity is reduced. These results provide new insights into how the finely tuned allosteric PKA signaling network is disrupted by the oncogenic J-C subunit, ultimately leading to the development of FL-HCC.
59 BASIC BIOLOGICAL SCIENCES↗
CryoDRGN-AI: neural ab initio reconstruction of challenging cryo-EM and cryo-ET datasets
Proteins and other biomolecules form dynamic macromolecular machines that are tightly orchestrated to move, bind, and perform chemistry. Cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET) can access the intrinsic heterogeneity of these complexes and are therefore key tools for understanding their function. However, 3D reconstruction of the collected imaging data presents a challenging computational problem, especially without any starting information, a setting termed ab initio reconstruction. Here, in this study, we introduce cryoDRGN-AI, a method leveraging an expressive neural representation and combining an exhaustive search strategy with gradient-based optimization to process challenging heterogeneous datasets. Using cryoDRGN-AI, we reveal new conformational states in large datasets, reconstruct previously unresolved motions from unfiltered datasets, and demonstrate ab initio reconstruction of biomolecular complexes from in situ data. With this expressive and scalable model for structure determination, we hope to unlock the full potential of cryo-EM and cryo-ET as a high-throughput tool for structural biology and discovery.
Levy, Axel [Stanford Univ., CA (United States); SL↗
STORM Super-Resolution Visualization of Self-Assembled γPFD Chaperone Ultrastructures in Methanocaldococcus jannaschii
Gamma-prefoldin (γPFD), a unique chaperone found in the extremely thermophilic methanogen Methanocaldococcus jannaschii, self-assembles into filaments in vitro, which so far have been observed using transmission electron microscopy and cryo-electron microscopy. Utilizing three-dimensional stochastic optical reconstruction microscopy (3D-STORM), here we achieve ~20 nm resolution by precisely locating individual fluorescent molecules, hence resolving γPFD ultrastructure both in vitro and in vivo. Through CF647 NHS ester labeling, we first demonstrate the accurate visualization of filaments and bundles with purified γPFD. Next, by implementing immunofluorescence labeling after creating a 3xFLAG-tagged γPFD strain, we successfully visualize γPFD in M. jannaschii cells. Through 3D-STORM and two-color STORM imaging with DNA, we show the widespread distribution of filamentous γPFD structures within the cell. These findings provide valuable insights into the structure and localization of γPFD, opening up possibilities for studying intriguing nanoscale components not only in archaea but also in other microorganisms.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Integrating AlphaFold and deep learning for atomistic interpretation of cryo-EM maps
Abstract Interpretation of cryo-electron microscopy (cryo-EM) maps requires building and fitting 3D atomic models of biological molecules. AlphaFold-predicted models generate initial 3D coordinates; however, model inaccuracy and conformational heterogeneity often necessitate labor-intensive manual model building and fitting into cryo-EM maps. In this work, we designed a protein model-building workflow, which combines a deep-learning cryo-EM map feature enhancement tool, CryoFEM (Cryo-EM Feature Enhancement Model) and AlphaFold. A benchmark test using 36 cryo-EM maps shows that CryoFEM achieves state-of-the-art performance in optimizing the Fourier Shell Correlations between the maps and the ground truth models. Furthermore, in a subset of 17 datasets where the initial AlphaFold predictions are less accurate, the workflow significantly improves their model accuracy. Our work demonstrates that the integration of modern deep learning image enhancement and AlphaFold may lead to automated model building and fitting for the atomistic interpretation of cryo-EM maps.
59 BASIC BIOLOGICAL SCIENCES↗
Cryo-EM structure of the Rhodospirillum rubrum RC–LH1 complex at 2.5 Å
The reaction centre light-harvesting 1 (RC–LH1) complex is the core functional component of bacterial photosynthesis. We determined the cryo-electron microscopy (cryo-EM) structure of the RC–LH1 complex from Rhodospirillum rubrum at 2.5 Å resolution, which reveals a unique monomeric bacteriochlorophyll with a phospholipid ligand in the gap between the RC and LH1 complexes. The LH1 complex comprises a circular array of 16 αβ-polypeptide subunits that completely surrounds the RC, with a preferential binding site for a quinone, designated Q P , on the inner face of the encircling LH1 complex. Quinols, initially generated at the RC Q B site, are proposed to transiently occupy the Q P site prior to traversing the LH1 barrier and diffusing to the cytochrome bc 1 complex. Thus, the Q P site, which is analogous to other such sites in recent cryo-EM structures of RC–LH1 complexes, likely reflects a general mechanism for exporting quinols from the RC–LH1 complex.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Quantitative Modeling of High-Energy Electron Scattering in Thick Samples Using Monte Carlo Techniques
Cryo-electron microscopy (cryo-EM) is a powerful tool for imaging biological samples but is typically limited by sample thickness, which is restricted to a few hundred nanometers depending on the electron energy. However, there is a growing need for imaging techniques capable of studying biological samples up to 10 µm in thickness while maintaining nanoscale resolution. This need motivates the use of mega-electron-volt scanning transmission electron microscopy (MeV-STEM), which leverages the high penetration power of MeV electrons to generate high-resolution images of thicker samples. In this study, we employ Monte Carlo simulations to model electron–sample interactions and explore the signal decay of imaging electrons through thick specimens. By incorporating material properties, interaction cross-sections for energy loss, and experimental parameters, we investigate the relationship between the incident and transmitted beam intensities. Key factors such as detector collection angle, convergence semi-angle, and the material properties of samples were analyzed. Our results demonstrate that the relationship between incident and transmitted beam intensities follows the Beer–Lambert law over thicknesses ranging from a few microns to several tens of microns, depending on material composition, electron energy, and collection angles. The linear depth of silicon dioxide reaches 3.9 µm at 3 MeV, about 6 times higher than that at 300 keV. Meanwhile, the linear depth of amorphous ice reaches 17.9 µm at 3 MeV, approximately 11.5 times higher than that at 300 keV. These findings are crucial for advancing the study of thick biological and semiconductor samples using MeV-STEM.
36 MATERIALS SCIENCE↗
A large expert-curated cryo-EM image dataset for machine learning protein particle picking
Cryo-electron microscopy (cryo-EM) is a powerful technique for determining the structures of biological macromolecular complexes. Picking single-protein particles from cryo-EM micrographs is a crucial step in reconstructing protein structures. However, the widely used template-based particle picking process is labor-intensive and time-consuming. Though machine learning and artificial intelligence (AI) based particle picking can potentially automate the process, its development is hindered by lack of large, high-quality labelled training data. To address this bottleneck, we present CryoPPP, a large, diverse, expert-curated cryo-EM image dataset for protein particle picking and analysis. It consists of labelled cryo-EM micrographs (images) of 34 representative protein datasets selected from the Electron Microscopy Public Image Archive (EMPIAR). The dataset is 2.6 terabytes and includes 9,893 high-resolution micrographs with labelled protein particle coordinates. The labelling process was rigorously validated through 2D particle class validation and 3D density map validation with the gold standard. The dataset is expected to greatly facilitate the development of both AI and classical methods for automated cryo-EM protein particle picking.
42 ENGINEERING↗
Selective inhibition of human translation termination by a drug-like compound
Methods to directly inhibit gene expression using small molecules hold promise for the development of new therapeutics targeting proteins that have evaded previous attempts at drug discovery. Among these, small molecules including the drug-like compound PF-06446846 (PF846) selectively inhibit the synthesis of specific proteins, by stalling translation elongation. These molecules also inhibit translation termination by an unknown mechanism. Using cryo-electron microscopy (cryo-EM) and biochemical approaches, we show that PF846 inhibits translation termination by arresting the nascent chain (NC) in the ribosome exit tunnel. The arrested NC adopts a compact α-helical conformation that induces 28 S rRNA nucleotide rearrangements that suppress the peptidyl transferase center (PTC) catalytic activity stimulated by eukaryotic release factor 1 (eRF1). These data support a mechanism of action for a small molecule targeting translation that suppresses peptidyl-tRNA hydrolysis promoted by eRF1, revealing principles of eukaryotic translation termination and laying the foundation for new therapeutic strategies.
59 BASIC BIOLOGICAL SCIENCES↗
Structural determination of a full-length plant cellulose synthase informed by experimental and in silico methods
Three-dimensional structure determination and prediction of proteins with intrinsically disordered regions, unstructured regions, conformational flexibility, and lacking homologous structures are challenging. We previously predicted and refined an in silico structure of a plant cellulose synthase from cotton (GhCESA1), and more recently, cryo-electron microscopy (cryo-EM) has resolved a majority of the lengths of two CESA structures from poplar (PttCESA8) and cotton (GhCESA7). However, 26–30% of these cryo-EM structures remain unresolved, including the N-terminal domain, half of the class-specific region, the gating loop region, and the C-terminal domain. Here, we describe the generation and evaluation of a full-length hybrid GhCESA1 model based on this cryo-EM PttCESA8 structure, with unresolved regions completed using this in silico refined GhCESA1 model. All-atom molecular dynamics simulations and subsequent energy minimizations were performed for the in silico and hybrid GhCESA1 models in a lipid bilayer-water-ion environment, and structural stability, dynamics, energetics, contacts, and quality were evaluated. The unresolved regions were found to be the most dynamic, in agreement with their poor electron density with cryo-EM. The hybrid model exhibited a higher total secondary structure content, more favorable intra-protein and protein-lipid interaction energies, and improved quality metrics. Moreover, hydrogen bonding was revealed to be a primary mechanism for intra-protein and protein-lipid contacts. These results demonstrate that in silico structure prediction and refinement may be useful to augment experimental structure determination, especially for disordered and unstructured regions. Furthermore, this hybrid model can serve as a steppingstone to derive full-length homology models of other CESAs found in more experimentally tractable organisms.
59 BASIC BIOLOGICAL SCIENCES↗
Structure of Geobacter OmcZ filaments suggests extracellular cytochrome polymers evolved independently multiple times
While early genetic and low-resolution structural observations suggested that extracellular conductive filaments on metal-reducing organisms such as Geobacter were composed of type IV pili, it has now been established that bacterial c -type cytochromes can polymerize to form extracellular filaments capable of long-range electron transport. Atomic structures exist for two such cytochrome filaments, formed from the hexaheme cytochrome OmcS and the tetraheme cytochrome OmcE. Due to the highly conserved heme packing within the central OmcS and OmcE cores, and shared pattern of heme coordination between subunits, it has been suggested that these polymers have a common origin. We have now used cryo-electron microscopy (cryo-EM) to determine the structure of a third extracellular filament, formed from the Geobacter sulfurreducens octaheme cytochrome, OmcZ. In contrast to the linear heme chains in OmcS and OmcE from the same organism, the packing of hemes, heme:heme angles, and between-subunit heme coordination is quite different in OmcZ. A branched heme arrangement within OmcZ leads to a highly surface exposed heme in every subunit, which may account for the formation of conductive biofilm networks, and explain the higher measured conductivity of OmcZ filaments. This new structural evidence suggests that conductive cytochrome polymers arose independently on more than one occasion from different ancestral multiheme proteins.
Cytochromes/metabolism↗
Cryo-electron tomography related radiation-damage parameters for individual-molecule 3D structure determination
To understand the dynamic structure–function relationship of soft- and biomolecules, the determination of the three-dimensional (3D) structure of each individual molecule (nonaveraged structure) in its native state is sought-after. Cryo-electron tomography (cryo-ET) is a unique tool for imaging an individual object from a series of tilted views. However, due to radiation damage from the incident electron beam, the tolerable electron dose limits image contrast and the signal-to-noise ratio (SNR) of the data, preventing the 3D structure determination of individual molecules, especially at high-resolution. Although recently developed technologies and techniques, such as the direct electron detector, phase plate, and computational algorithms, can partially improve image contrast/SNR at the same electron dose, the high-resolution structure, such as tertiary structure of individual molecules, has not yet been resolved. Here, we review the cryo-electron microscopy (cryo-EM) and cryo-ET experimental parameters to discuss how these parameters affect the extent of radiation damage. This discussion can guide us in optimizing the experimental strategy to increase the imaging dose or improve image SNR without increasing the radiation damage. With a higher dose, a higher image contrast/SNR can be achieved, which is crucial for individual-molecule 3D structure. With 3D structures determined from an ensemble of individual molecules in different conformations, the molecular mechanism through their biochemical reactions, such as self-folding or synthesis, can be elucidated in a straightforward manner.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗